Spatially Heterogeneous Prey Patterns may be Necessary for Predator Survival: a Model and a Review

of the Aquatic Literature

by

Fabio Giuseppe Cinquemani

A thesis submitted in conformity with the requirements for the degree of Master of Science Ecology and Evolutionary Biology

University of Toronto

© Copyright by Fabio Giuseppe Cinquemani 2012

ii

Spatially Heterogeneous Prey Patterns may be Necessary for Predator Survival: a Model and a Review of the Aquatic Literature

Fabio Giuseppe Cinquemani

Master of Science

Ecology and Evolutionary Biology

University of Toronto

2012

ABSTRACT

The Allen Paradox is the observation that, in aquatic communities, there is

insufficient prey production to support predator growth. An assessment of the

literature reveals that this paradox remains apparent in at least one of every four

studies. Here, a novel explanation for this paradox is proposed: predators feeding in

a spatially-heterogeneous-prey environment (SHPE) may experience a greater net

energy gain than in a corresponding uniform-prey environment (UPE), meaning that

predators may require less food than has been traditionally perceived. A model was

developed to simulate a predator’s energy gain while feeding in a SHPE rather than

a UPE. According to the simulation, a greater net energy gain in a SHPE than a UPE

is possible, but only under certain conditions. Since prey can be utilized more

efficiently in a SHPE, a given amount of prey production can supply more predator

growth, which can have positive implications in fish stocking.

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ACKNOWLEDGEMENTS

This thesis would not have been possible without the outstanding help that

I’ve received throughout. Most of all, I would like to thank my outstanding supervisor,

Gary Sprules for his continued support throughout my graduate experience. He has

been extremely patient and understanding with me. I have benefitted substantially

from his comments, advice and unfailing guidance throughout the project and I have

learned a ton from him. I am extremely grateful to have worked with Gary, and to

have had access to his vast bank of knowledge.

I thank my committee members, Marie-Josée Fortin and Hélène Cyr, for

taking the time to read my thesis proposals and for making key suggestions to help

guide the project in the right direction. I would also like to thank my examining

committee for devoting their precious time to read my thesis.

I would also like to thank Audrey for being such an awesome lab-mate, Renée

for always providing much-needed distractions and for being a fellow Québécoise,

and Lauren for livening up the lab. Stefan, thanks for kicking my butt in ping-pong

and “gyming it up”. I would also like to thank Pedro and Santiago for always being

there when I needed a furry friend.

Finally, I’d like to thank my family for the constant support and motivation.

Branden, thanks for coming to visiting me as often as you did. Sam, thanks for your

nonstop encouragement; you dealt with this like a champ.

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TABLE OF CONTENTS

ABSTRACT ................................................................................................................ ii

ACKNOWLEDGEMENTS ......................................................................................... iii

LIST OF TABLES ...................................................................................................... vi

LIST OF FIGURES ................................................................................................... vii

LIST OF APPENDICES ............................................................................................. ix

INTRODUCTION ........................................................................................................ 1

METHODS .................................................................................................................. 7 1. Mechanism by which predators gain an advantage by feeding in a prey patch ..................................................................................................................... 11 2. Ratio of prey production to predator consumption (PP:PC) ....................... 13 3. Patch energetics simulation .......................................................................... 16

RESULTS ................................................................................................................. 20 1. Mechanism by which predators gain an advantage by feeding in a prey patch ..................................................................................................................... 20

Encountering a prey patch ................................................................................. 20 Change in swimming behaviour ......................................................................... 24 Ingestion ............................................................................................................ 27 Digestion and the specific dynamic action (SDA) .............................................. 34 Assimilation ........................................................................................................ 37 Growth and reproduction ................................................................................... 40 Energy expenditure, oxygen consumption and respiration costs ...................... 42 Energetic efficiencies ......................................................................................... 54 Exploitation efficiency ........................................................................................ 54 Assimilation efficiency ........................................................................................ 55 Net production efficiency ................................................................................... 56

2. Ratio of prey production to predator consumption (PP:PC) ....................... 60 3. Patch energetics simulation .......................................................................... 61

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DISCUSSION ............................................................................................................ 66 REFERENCES……………………………………………………………………………. 76

Appendix A: Collection of PP:PC ratios from the literature ............................... 87

vi

LIST OF TABLES

Table 1 Conversion factors and equivalencies ......................................................... 21!

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LIST OF FIGURES

Figure 1 Flow of energy among and within trophic levels .............................................. 9

Figure 2 Flowchart exploring how the energy-requiring processes change as a result of

predators encountering a prey patch.......................................................................... 12

Figure 3 Speed as a function of food concentration developed with SEARCH model...... 28

Figure 4 Turning angle (STDEV) as a function of food concentration developed with

SEARCH model ....................................................................................................... 29

Figure 5 Theoretical functional response curves based on mathematical equations........ 31

Figure 6 Plot of energy ingestion rates of various Daphnia species as a function of food

concentration........................................................................................................... 33

Figure 7 Energy expended on specific dynamic action (SDA) and duration of SDA-

associated physiological processes........................................................................... 36

Figure 8 Linear regression showing assimilation varying with algal concentration...…… 39

Figure 9 Daphnia assimilation versus ingestion on nine algal species........................... 41

Figure 10 Daphnia individual juvenile growth rate varying with algal concentration….… 43

Figure 11 Relationship between spontaneous swimming costs and forced swimming

costs....................................................................................................................... 46

Figure 12 Respiration rate versus swim speed in the copepod Dioithona oculata........... 48

Figure 13 Theoretical scenario of the total energy cost and gain as a function of ingestion

rate.......................................................................................................................... 51

Figure 14 Plot of rate of energy expended on respiration of Daphnia magna as a function

of food concentration................................................................................................. 53

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Figure 15 Net assimilation efficiency plotted against algal concentration for Daphnia magna

feeding on different concentrations of Chlamydomonas............................................... 57

Figure 16 Net production efficiency at different algal concentrations for a copepod........ 59

Figure 17 PP:PC ratios calculated from 34 ecosystems............................................... 62

Figure 18 Modeled ratios of net energy gain while Daphnia feed in a patchy environment

versus a uniform environment in a mesotrophic lake.................................................... 64

Figure 19 Modeled ratios of net energy gain while Daphnia feed in a patchy environment

versus a uniform environment in a eutrophic lake........................................................ 65

ix

LIST OF APPENDICES

Appendix A: Collection of PP:PC ratios from the literature…….........……........….. 87

1

INTRODUCTION

In a classic study on the Horokiwi Stream in New Zealand, Allen (1951)

discovered that brown trout production might exceed that of its benthic invertebrate

prey. Since then, many studies have shown that benthic invertebrate production in

streams is often insufficient to meet the food demands by trout populations (Waters

1988, Waters 1993, Huryn 1996). This discrepancy in production measurements

later became known as Allen's paradox (Hynes 1970). It is paradoxical because a

predator population that is not in decline must somehow acquire sufficient energy to

satisfy its demands. This indicates that the paradox lies within the researchers’

inappropriate or biased methods.

Many researchers have failed to fully explain why the discrepancy between

prey and predator production (Allen paradox) is seen in nature. Early explanations

for this discrepancy included systematic underestimates of benthic invertebrate

turnover rates compared to the turnover rate by trout (Allen 1951, Benke 1993). Both

Waters (1988, 1993) and Huryn (1996) proposed that other significant sources of

prey were not being considered in production budgets (e.g. other fishes). Other, less

common prey types such as winged insects (Garman 1991), unknown prey, or

occurrences of cannibalism (Huryn 1996) were also proposed to influence

production budgets. Another possible explanation is the out-of-phase sampling of

cyclic populations (i.e. sampling when predator abundance is high while prey

abundance is low or vice versa).

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Huryn (1996) explored Allen’s Paradox by analyzing a comprehensive

production budget in a New Zealand trout stream. Rather than including a single,

common prey type as was previously done in trout streams (e.g. Allen 1951), Huryn

composed a budget that comprised of multiple prey types (e.g. surficial, hyporheic

and terrestrial macroinvertebrates) and cannibalism. He found that the predator and

prey production discrepancy did decrease after the inclusion of additional prey types,

but did not account for the discrepancy entirely. Waters (1988) performed an

elaborate literature review comparing trout and benthos production to assess the

prevalence of the Allen Paradox. He found that 10 out of 12 reports on trout streams

were deemed to have insufficient prey production to satisfactorily supply the

observed predator production, and consequently, their consumption. Waters

suggested that the exclusion of other, significant food sources in production budgets

is partially responsible for the Allen Paradox. Both Waters (1988) and Huryn (1996)

seem to agree that inclusion of additional prey explains the paradox, but only

partially.

Generally, measurements of production and consumption do not include the

spatially complex patterns of prey and are thus calculated under the assumption that

organisms are uniformly distributed in space either because it is easier to do so,

because researchers do not see it as of importance, or simply because they do not

think to consider it. Hence, the amount of prey required by a predator is always

calculated on the implicit presumption that prey are homogeneously distributed, with

no regard to how this may influence a predator’s processes (includes ingestion,

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digestion, assimilation and growth (somatic and gonadal)) or energetic efficiencies

(includes exploitation, assimilation and net production efficiencies) and may thus be

overestimating the amount of prey production needed for predator populations to

survive since in reality less prey is required because of these efficiency changes.

Ideally, one would compare studies that have included spatial heterogeneity of prey

as a parameter in their calculations, to those that have not, in order to test for the

effect of prey being heterogeneously distributed. Unfortunately, no study of which I

am aware has yet to integrate spatial heterogeneity of prey into production budget

calculations, thus comparing studies that have and have not included the spatial

heterogeneity of prey is impossible at this point.

It has been very well documented that aquatic and marine organisms are

distributed in a spatially complex manner or a ‘patch’ (e.g. Mackas et al. 1985, Davis

et al. 1991, Folt and Burns 1999). A patch of prey is typically defined as an area of

the water column that contains a high-density aggregation of one or more similar

species in comparison to the surrounding environment. Concrete evidence for

patches of phytoplankton and zooplankton have been observed in Lake Opeongo,

Ontario using data from an optical plankton counter (OPC) and a fluorometer

(Blukacz et al. 2010). Despite ongoing advancement in both spatial ecology and

bioenergetics, the idea of an organism gaining some sort of energetic advantage

while feeding in a patch of prey has never been thoroughly considered as a potential

solution to Allen’s paradox. Using computer simulations together with empirical data

on the concentrations and spatial distributions of zooplankton and phytoplankton,

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Blukacz et al. (2010) found that both cladocerans and copepods could increase their

energy gain by feeding on spatially heterogeneous prey rather than uniform prey at

the same mean concentration. In all the different simulation scenarios explored,

zooplankton feeding in a spatially heterogeneous distribution of prey could gain an

energy advantage in up to 82% of the transects that were sampled, when compared

to a uniform prey distribution. Menden-Deuer and Grünbaum (2006) reported similar

findings. They found that dinoflagellate predators are likely to aggregate within a thin

microalgae layer (heterogeneous prey environment) and that population growth rates

and individual ingestion rates (ingestion rate interchangeable with both feeding rate

and consumption rate herein) for populations with these aggregating behaviours

increased by an order of magnitude compared to those typical of a uniform

distribution of prey at the same mean concentration.

It is well known that the transfer of energy from one trophic level to the next

(ecological efficiency) is rather inefficient; roughly 10% of the energy produced by

lower trophic levels is transferred to the next trophic level (Lindeman 1942, Begon et

al. 2006). Of the energy transferred, most is lost as waste (through egestion and

excretion) and respiration (costs associated with maintenance) leaving only a small

fraction for the generation of new biomass or production. Thus the consumption of

the predator, rather than its production, is a more fitting metric to consider when

addressing the discrepancy in what is available to the predator versus what is

needed since knowing the total energy that enters a predator rather than the energy

that is being used for growth and reproduction is what is of interest. Waters (1988)

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seemed to agree that this can indeed be seen from two perspectives, “One of the

major problems in resolving the Allen paradox lies in the definition of objectives: from

the predator’s (or fisheries biologist’s) point of view, the objective is fish food

consumption; from the prey’s (or benthologist’s) [it’s benthic production]”.

The objectives of this thesis are twofold. The first is to determine the

magnitude of the discrepancy between measures of predator consumption and their

prey’s production by compiling and comparing these numbers from the available

literature. This will provide insight on the number of studies that report insufficient

prey production to support a predator’s consumption. Second is to explore the

hypothesis that predators can gain an energetic advantage by feeding in patches of

prey by scouring the relevant literature and piecing together the different behavioural

and physiological changes that occur in consumers once they encounter a prey

patch. To accompany this, a simple model will be constructed that will simulate the

potential energy gain an organism can experience while feeding in spatially

heterogeneous environment rather than a uniform one.

This study differs from existing compilations (e.g. Allen 1951, Waters 1988,

Huryn 1996) in that they compare prey production to predator production whereas

this study compares prey production to predator consumption. Furthermore, existing

compilations do not consider the potential energy gain that predators may

experience by feeding in prey patches as a solution to Allen’s paradox. This thesis is

to serve as a preliminary exploration for future investigators who wish to calculate

production budgets for lake or ocean systems. It is my conjecture that this project will

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inform those interested in spatial ecology and bioenergetics, that incorporating prey

heterogeneity into bioenergetic models and empirical production budgets is essential.

Failure to do so may result in overestimation of the amount of prey required to

achieve observed predator production since in reality, predators may need to

consume less food to satisfy their demands (this remains an assumption at this point,

but will be tested). This is because of potential increases in energetic efficiencies

that predators may experience as result of feeding in spatially heterogeneous

distributions of prey.

After exploring the mechanism that explains how predators may gain an

energetic advantage by feeding in a spatially explicit environment rather than a

uniform environment and modelling the potential energy gain in the former, it will

become clear whether or not the current methods of calculating production budgets

include all relevant and necessary parameters in order to provide a thorough

estimate. If not, then it is proposed that spatial heterogeneity of prey can explain or

at least partially explain why the Allen Paradox is seen in natural communities.

7

METHODS

Three separate explorations have been done in order to answer my major

questions. First, evidence from the literature is presented to show how physiological

and behavioral processes change with varying prey concentrations. Second is to

explore how prevalent the mismatch between corresponding prey production and

predator consumption is in the literature. Lastly, an attempt to summarize the

evidence collected from the literature by constructing a simple patch energetics

simulation that demonstrates the difference in energy gain among spatially

heterogeneous and homogeneous environments. Before going into detail about the

three major explorations mentioned above, some basic principles of energy flow and

methods of calculating predator consumption and prey production are reviewed.

Almost all life on Earth is dependent on primary production by autotrophs.

Autotrophs harvest light energy from the sun and convert this into chemical energy

that is made available to higher trophic levels (herbivores), which in turn provide

energy to even higher trophic levels (consumers). Of the energy ingested by

herbivores (trophic level 2) from primary production, some passes through the

digestive tract and is egested as waste and the remainder is digested. Of the

digested energy, some is further lost as urinary waste and is excreted; and the

remaining energy is assimilated into the organism. This assimilated energy

contributes to the growth and reproduction of an individual, which, when summed for

the entire population or trophic level, leads to the production. Each of the

abovementioned processes has an associated cost; this is the energy lost through

8

respiration. A portion of a trophic level’s production is lost through non-predatory

mortality and the remainder is available to the next trophic level, and this process

reoccurs until the energy reaches the highest trophic level (Figure 1). The net

production of a trophic level is the difference between total production and costs

associated with this production (respiration). The proportion of the net production

(NP1) that is ingested (I) by the next trophic level is the exploitation efficiency (EE =

I/NP1); the proportion of this ingested energy that is assimilated (A) has been termed

the assimilation efficiency (AE = A/I); and the proportion of the assimilated energy

that contributes to the net production of that trophic level (NP2) is the net production

efficiency (NPE = NP2/A; Figure 1).

All organisms incur general costs associated with living. A major cost is that

associated with foraging. Of course these costs vary from organism to organism, as

they differ in how they acquire their food. For instance, a cheetah must chase down

and kill its prey whereas a giraffe must simply locate leaves of tall trees. Aquatic

invertebrate herbivores such as cladocerans or copepods feed by filtering the water

around them and ingesting algal cells found in the water (Horton et al. 1979, Koehl

and Strickler 1981, Peters and Downing 1984).

Exploring the methods traditionally used for estimating production and

consumption will lead to an understanding of how these estimates can be improved

by including the additional prey heterogeneity as a parameter. The process of

measuring production in the field is rather simple in theory. Consider a population of

fish at age zero, i.e. one that is just born and that is being tracked through time.

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Non-predatory mortality

TROPHIC LEVEL 2 Ingestion (I)

Egestion (W)

Excretion (U)Assimilation (A)

Digestion (D)

Respiration (R)

Growth + Reproduction (G)

Non-predatory mortality

TROPHIC LEVEL 1

TROPHIC LEVEL 3

Net (tertiary) production

...

Net production (NP1)

Net production (NP2)

Net production (NP3)

Exploitation efficiency (EE)

Assimilation efficiency (AE)

Net production efficiency (NPE)

Figure 1 Flow of energy among and within trophic levels showing processes that transform energy. Arrows pointing to the right denote energy lost to the environment or as respiration. The two processes involved in each of the energetic efficiencies indicated on the left are connected by a dotted line (EE = I/NP1; AE = A/I; NPE = NP2/A).

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From birth, only growth (individual and reproduction) and mortality can occur in an

age class of the population. The number of individuals (Y) and individual mass (W)

of the organisms in the age class are measured at regular intervals. From this,

production (P) between each interval can be calculated by multiplying the change in

weight, by the mean number of individuals among sample dates (P = ΔW • Ȳ).

Production measures from each time interval can be summed for any time period,

e.g. growing seasons or annually.

To calculate consumption, fisheries researchers almost always use

bioenergetic models rather than collecting empirical data because it is more time and

cost effective even though these numbers may be less accurate (Chipps &

Bennett2002, Chipps & Wahl 2008). Bioenergetics is the study of energy flow and

energy transformation in living organisms. In its simplest form, energy ingested as

food must equal the energy lost as waste and the energy retained as growth

(somatic and gonadal). A bioenergetic model is a mathematical representation of

this; a population’s consumption must equal the sum of its metabolism (including

basal metabolism or respiration, active metabolism, and specific dynamic action),

production (somatic and gonadal growth) and waste (egestion and excretion)

(Hansen et al. 1993, Rudstam et al. 1994). All components of the model are

estimated using a variety of calorimetric and respirometric laboratory methods (e.g.

see previous paragraph on how production is measured). All of these parameters

depend on the surrounding temperature, the size of the organism, and a variety of

species-specific physiological parameters estimated in laboratory experiments. No

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study has yet included a prey heterogeneity parameter as part of their production or

consumption calculations, a parameter herein hypothesized to be crucial in these

types of estimates.

1. Mechanism by which predators gain an advantage by feeding in a prey patch

Given the objectives of this study, it is appropriate to explore how predators can

gain an energetic advantage by encountering and feeding in prey patches. By using

a typical bioenergetic model (consumption as a sum of metabolism, growth and

waste) as a backbone, a proposed mechanism was developed that explored how

predators change their behaviour of feeding, ingestion, digestion and assimilation

after encountering a prey patch (Figure 2). Each stage in the process was then

developed in detail using supporting data from the literature. For example it is

hypothesized that, consumers experience increased ingestion rates and alter their

swimming behaviour after encountering a prey patch. The literature was searched

for studies bringing evidence to bear on this conjecture from field data, laboratory

experiments, or modelling approaches that show how predator ingestion rates or

swimming behaviour change as a function of prey concentration. This approach was

repeated for all steps in the ecological and physiological processes by which

predators may gain an advantage by feeding in spatially heterogeneous rather than

uniform distributions of their prey. When the data were available, up to three

separate studies were explored and used as evidence to support each step.

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Consumers encounter a prey patch and alter

swimming behaviour by decreasing swim speed and increasing turning motions

(area-restricted search)

Consumers experience an increase in digestion and

digestion rates

Consumers experience an increase in assimilation and

assimilation rates

Consumers experience increased ingestion rates

Consumers experience an increase in growth and

reproduction

Consumers experience a change in assimilation efficiency (assimilation/

ingestion)

Consumers experience an increase in net production

efficiency (consumer production/assimilation)

Consumers experience an increase in exploitation efficiency (consumer

ingestion/prey production)

Net primary production

Net secondary production

Figure 2 Flowchart exploring how the energy-requiring processes change as a result of predators encountering a prey patch. Arrows pointing to the right denote energy lost due to respiration as specific dynamic action (total energy expended on all the processes associated with the ingestion, digestion, and assimilation of a meal).

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2. Ratio of prey production to predator consumption (PP:PC)

Given the interest in exploring the role of spatial patchiness in accounting for

apparent mismatches between prey production and predator consumption, it is first

important to determine how often and to what degree such mismatches are reported

in the literature. The scientific literature was thoroughly searched for studies that

have discussed the consumption and production of natural populations using online

academic citation index databases (Google Scholar, SciVerse Scopus, Web of

Science) and other printed materials such as conference proceedings. Among these

studies, only a few provide measurements for both the consumption of a predator

population and the production of its prey population(s). Only studies in which data

were collected from aquatic or marine systems for at least an entire growing season

(typically May to September) were included since these studies average the daily or

monthly variability in production and consumption estimates. For instance, primary

production in temperate, sub-polar and coastal waters in early summer is very high

compared to the remainder of the growing compared to the remainder of the growing

season. No trophic levels were targeted specifically, but information on phyto-

plankton and zooplankton make up the majority of the dataset because those data

were more available. At first, only empirical measures of production and

consumption were to be included in the compiled dataset, but since so few such

studies could be found, papers using modeled estimates were also included (applies

mostly to consumption data).

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The resultant dataset was then used to calculate the ratio of prey production

(PP) to predator consumption (PC) within each system. PP:PC ratios were

differentiated by aquatic system (e.g. lake, stream, estuary, river, etc.) and by trophic

interaction where primary trophic interaction is defined by trophic level 2 feeding on

trophic level 1 (e.g. zooplankton feeding on algae), secondary trophic interaction is

defined by trophic level 3 feeding on trophic level 2 (e.g. planktivorous fish feeding

on zooplankton) and tertiary trophic interaction is defined by trophic level 4 feeding

on trophic level 3 (e.g. piscivorous fish feeding on other fish).

The PP:PC ratio is used as a quantitative measure to determine whether the

prey production of an ecosystem is sufficient to support the predator’s consumption

needs. For illustrative purposes, if it is assumed that a predator can consume the

entire prey population’s production, PP would equal PC and the PP:PC ratio would

be 1.00. If this ratio is above 1.00, then there is enough prey production to supply the

energy demands of the predator. If the ratio is below 1.00, then it appears that there

is insufficient prey production to support the predator population. Of course, no

consumer population is capable of consuming 100% of its prey population on a

sustained basis, and in regards to herbivorous zooplankton grazing on algae, not all

of the algal production can be utilized by herbivores because some species may be

too large or distasteful (but for the purposes of this study, it is conservatively being

assumed that all are available). Therefore the maximum proportion of the prey

population that the consumer can remove or consume, coined the ecotrophic

coefficient by Ricker (1946), before driving its prey out of existence, must be

15

considered here. These proportions (as reported by Waters (1988)) have been

reported to be quite low; Boruckij (1939) on lake benthos: 0.25; Wright (1965) on

zooplankton in a reservoir: 0.33; Westlake et al. (1972) on trout stream benthos:

0.31. After reviewing these, and other studies, Waters (1988) suggested an

approximate range of 30–50% for ecotrophic coefficients. Another way of dealing

with this issue is by using the maximum sustainable yield (MSY) of fish populations.

In the fisheries literature, the MSY of a fish population is the largest theoretical yield

(or catch) that can be collected without causing the extinction of a population.

Although variable among species, Fox (1970) modeled the MSY for fisheries to

occur at approximately 37% of unfished biomass, which falls well within the range at

which MSY occurs (about 25-45%), described for fish in many other studies (e.g.

Wright 1965, Westlake et al. 1972, Mace 2001, Mueter and Megrey 2006, Worm et

al. 2009). Recall that Waters’ (1988) review approximates an ecotrophic coefficient

range of 30-50%, which is very much in line with others for MSY. Applying both the

ecotrophic coefficient range and the MSY theory to this study, using the range of 25–

50% (this encompasses both the ecotrophic coefficient and MSY theories) of original

population as the maximum possible proportion of prey that a predator can consume,

the following cutoff ratios have been estimated: if PP:PC ratios are above 4.00

(0.25-1, for the lower limit), then it seems there is enough prey production to support

predator consumption; if PP:PC ratios are below 2.00 (0.50-1), then it seems there is

insufficient prey production to support energy demands of the predator in the

system; if the PP:PC ratios are found to be between 2.00 and 4.00, it indicates that

16

systems are near maximum sustainable mortality, given the variability in this metric.

Recall that the MSY ranges use maximum yield, thus these ratios are conservative

in that they assume that predators always consume the maximum ‘allowable’

amount of prey. A ratio below 2.00 cannot sustain a predator population in the long

term, thus if the predator population is not in decline, then authors have failed to

account for all involved processes.

3. Patch energetics simulation

To integrate all the evidence from the literature, a novel series of simple

simulations were modeled, using Microsoft Excel, in order to determine how much

more energy a predator could potentially gain while feeding in a spatially

heterogeneous prey distribution rather than a uniform one and to discover whether

this can have an effect on the PP:PC ratio. Consider a daphnid that swims in its

environment. For simplicity, when their algal prey are patchily distributed, it is

assumed that the daphnid can only encounter two prey concentrations– the lower

prey concentration representing conditions in between patches and the higher prey

concentration representing conditions within a patch. For the purpose of this study, it

will be assumed that the concentration of the uniform distribution of algae is the

mean of the lowest and the highest concentrations of the patchy environment (this is

what researchers typically do– take a mean algal concentration for entire systems

and thereby assume a uniform distribution of prey in the system).

17

Chow-Fraser and Sprules’ (1992) study was used for obtaining ingestion rate

as a function of algal concentration since it incorporated data from other studies (e.g.

Burns and Rigler 1967, Porter et al. 1982) that were run at similar conditions and

covered a similar range of food concentration. This, together with per-cell energy

content was used to find the amount of energy ingested at different algal

concentrations (see Results section). Data from Lampert’s (1986) publication were

used to determine how energy respired varied with algal concentration (see Results

section). The difference between energy ingested and energy respired results in the

net energy gain for a daphnid feeding at any given food concentration. This was later

used to compare the energy differentials among different spatial environments.

For a patchy environment, adding the net energy gain for a daphnid in the

highest food concentration (within patch; NetEH) and the net energy gain in the lowest

food concentration (in between patches; NetEL) will result in the total net energy gain

in the patchy environment (NetEP). This is true only if the daphnid spends equal time

within and between patches. If it does not, this can be adjusted by weighting the net

energy gains accordingly. For example, if a daphnid spends 70% of its time within a

patch (pH) and 30% in between patches (pL), then the NetEH would be multiplied by

70%, and the NetEL by 30%; the total net energy gain in a patchy environment would

be represented as follows:

NetEP = NetEHpH + NetELpL.

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In a uniform distribution of algae, the net energy gain (NetEU) is simply the difference

between energy ingested and energy respired at that algal concentration (set to the

mean of high and low concentrations of the patchy environment).

The simulation described was run for two separate lake trophies: mesotrophy

and eutrophy (defining concentration ranges below) to discover how the energetic

efficiencies differ among them (oligotrophy simulation was impossible because

functions used are undefined for such low concentrations). Each trophy level was

simulated for nine separate daphnid allocations of time, ranging from 10% between

patches and 90% within patches to 90% between and 10% within, in steps of 10%.

The lower (in-between patches) algal concentration in the patchy environment of the

mesotrophic lake was 6,000 cells mL-1 for each iteration of the simulation, with the

higher (within patches) concentration beginning at 6,100 cells mL-1 for the first

iteration and increasing by 100 cells mL-1 for each iteration thereafter, up to a

maximum of 17,800 cells mL-1. The lower (in-between patches) algal concentration

in the patchy environment of the eutrophic lake was fixed to 10,000 cells mL-1 for

each iteration of the simulation, whereas the higher (within patches) began at 11,000

cells mL-1 for the first iteration and increased by 1,000 cells mL-1 for each iteration

thereafter, up to a maximum of 128,000 cells mL-1. These concentrations were

chosen using Carlson’s (1996) trophy level separations for a temperate lake. From

these concentrations, the degree of patchiness, defined as the ratio of concentration

within patch to concentration in between patches, for each iteration of the simulation

19

can be determined. For each iteration, the corresponding concentration for the

uniform environment was set to the mean of within and in-between patch

concentrations. For each iteration of the simulation the total energy ingested and

respired, the net energy gain for both patchy and uniform environments, and the

ratio of net energy gain in the patchy environment to that of the uniform environment

(NetEP : NetEU) were computed across the concentration gradient and for different

time proportions. This is meant to serve as an overall summary model of energetic

gains and losses occurring in a daphnid at given algal concentrations that includes

all processes and efficiencies that occur within the organism.

20

RESULTS

1. Mechanism by which predators gain an advantage by feeding in a prey patch

There are a number of different behavioural and physiological processes that

occur when a consumer first encounters its prey until the energy contained in the

prey is used for growth and reproduction. Prey being heterogeneously distributed in

the environment may affect each of these processes in different ways. Here,

evidence from the literature is provided to address how and when these changes

take place and how they may affect an organism’s energy budget, starting from

when an organism first encounters a prey patch.

Encountering a prey patch

It is well known that aquatic and marine organisms are not uniformly

distributed in their environment; rather, they are distributed in a spatially

heterogeneous or patchy manner (e.g. Mackas et al. 1985, Davis et al. 1991,

Abraham 1999, Folt and Burns 1999). Patches of phytoplankton, for example, can

be described at small spatial scales 0.1m to about 10m and at larger spatial scales

up to tens of hundreds of kilometers (Mackas et al. 1985). Zooplankton patches can

reach concentrations of up to 1000 times the median concentration of the water

column (Megard et al. 1997).

Algal concentrations can vary considerably from lake to lake, depending on

trophy, size, temperature, climate, etc. Blukacz et al. (2010) reported typical algal

concentrations that range from 3,000 to 10,000 cells mL-1 (converted from µg chl. a

L-1; see Table 1) for Lake Opeongo, an oligotrophic lake in Algonquin Park, Ontario.

21

Table 1 Conversion factors and equivalencies used throughout this document. The per cell chlorophyll contents, energy contents and digestibility do vary among species, but the following are used as typical representative values.

1 µg chl. a L-1 = 2000 cells mL-1 Pfeiffer-Hoyt and McManus (2005)

1 ppm = 5000 cells mL-1 Hansen et al. (1997)

1 ppm = 2.5 µg chl. a L-1 Hansen et al. (1997) and Pfeiffer- Hoyt and McManus (2005)

1 mL O2 = 20.1 J Peters (1983)

1 cal = 4.184 J Peters (1983)

1 mg O2 = 0.7 mL O2 Downing and Rigler (1984)

1 mg O2 = 31.25 µmol O2 Downing and Rigler (1984)

1 mg O2 = 0.3753 mg C* Downing and Rigler (1984)

1 cell = 5.4 × 10-5 µg dry wt.** Porter et al. (1982)

1 µg fresh wt. = 2.79 µg dry wt.† Nalewajko (1966)

1 cell = 11.09 µm3‡ Rocha and Duncan (1985)

1 cell contains 3.0 pg C‡ Rocha and Duncan (1985)

1 cell contains 1.308 × 10-6 cal** Richman (1958)

* to be multiplied by the respiration quotient (RQ)

† for Chlamydomonas angulosa

‡ for Chlorella vulgaris

** for Chlamydomonas reinhardi

22

Data were collected using a fluorometer attached to a boat which ran linear transects

along the greatest open fetch of the lake. It is presumed that the upper end of the

concentration range was collected while in a patch of algae, and the lower end, in

between patches (non-patches). Extending this to similar oligotrophic lakes, it can be

said that patchy areas are roughly 3.5 times more concentrated than non-patchy

areas. Cyr and Pace (1992) report algal concentrations in eutrophic lakes ranging

from 8,200 to 36,200 cells mL-1 (converted from µg chl. a L-1) in Lake Tyrrel, located

in Dutchess, New York and ranging from 22,600 to 141,000 cells mL-1 (converted

from µg chl. a L-1) in Lake Myosotis located in Albany, New York. Again, if the lower

end of the range is assumed to be a typical non-patch concentration and the upper

end to be a typical patch concentration, this would mean that similar eutrophic lakes

could have patches that are up to six times more concentrated than non-patches.

Organisms behave differently prior to encountering a patch of food than they

do once in a patch of food. Bundy et al. (1993) investigated female calanoid copepod

behaviour using a three-dimensional video-recording system to track movement in

high (1.4 × 104 cells L-1) and low (6.0 × 103 cells L-1) food concentrations. They found

that in lower food concentrations, copepods swam at greater velocities and

swimming paths were more linear (i.e. less change in vertical position), compared to

higher food concentrations. Thus, prior to encountering a patch of greater food

concentration, consumers are in a so-called search or hunting mode; by swimming

at greater speeds and turning less frequently, they are able to locate food more

efficiently (Bundy et al. 1993).

23

By experimentally pumping either yeast, clay or water (control) into the littoral

zone of a lake, Jensen et al. (2001) were able to determine that Daphnia best locate

food by mechanical and/or chemical perception, since Daphnia were found to

aggregate to yeast patches significantly more than to clay patches. Copepods can

discover algal food by chemical detection simply by means of molecular diffusion;

algal exudates activate antennal sensors that alert the individual copepod to the

location of a food particle (Okubo et al. 2001). Jonsson and Tiselius (1990) reported

that the copepod Acartia tonsa can detect individual prey ciliates up to 0.7mm away

from its first antenna; this can vary with different prey sizes.

The plankton (microbes, phytoplankton, zooplankton) are what typically make

up the characteristic patchy environment of oceans and lakes. For phytoplankton,

this spatial heterogeneity is likely driven almost exclusively by physical factors such

as wind, but buoyancy-regulated mechanisms of some phytoplankton (blue-green

algae, dinoflagellates, etc.) can also be a factor as this can move them vertically in

and out of particular current zones (Borics et al. 2011). For zooplankton, patchiness

is likely driven by wind at larger scales (Blukacz et al. 2010, Folt and Burns 1999)

and biological factors, such as diel vertical migration, predator avoidance, food

searching, and mating at smaller scales (Folt and Burns 1999). But larger organisms,

such as fish, also aggregate to form patches (i.e. schools), although instead of doing

so because they are being moved by water currents, as do planktonic organisms,

fish school as a result of evolutionary responses to predators and other physical

stimuli. There are many advantages to aggregate and form schools or shoals (a

24

“patch”): locating resources more quickly (Pitcher 1982), anti-predator benefits such

as the encounter dilution effect– the larger the school of prey fish, the lesser the

probability that any particular individual within the school will be eaten (Turner and

Pitcher 1986); predator confusion effect– the decreased ability to single out and

attack an individual prey from a large school as a result of cognitive or sensory

limitations of some predators (Milinski and Heller 1978); and the many eyes

hypothesis– the larger the school, the less time any given individual must spend

looking out for potential predators since the this task is being shared by other ‘eyes’

in the group (Lima 1995).

Change in swimming behaviour

Spatial aggregations of prey are more concentrated than the surrounding

environment. This may have an effect on consumers that encounter such patches

and can result in a change in their swimming behaviour such as decreased

swimming speed (Leising and Franks 2000, Davis et al. 1991) and increased turning

and rotating behaviours (Leising and Franks 2000, Menden-Deuer and Grünbaum

2006, Colton and Hurst 2010). This behaviour has been termed the area-restricted

search (ARS) foraging strategy (Tinbergen et al. 1967) and is a means by which

consumers locate and remain within prey patches (Leising and Franks 2000, 2002).

Menden-Deuer and Grünbaum (2006) found that the protist predator Oxyrrhis

marina’s behaviour changes significantly when presented with a thin phytoplankton

layer in small octagonal tanks in the laboratory. Before the addition of prey cells, the

swimming trajectories of O. marina were much less complex; their motion was

25

generally more vertical than horizontal. After the introduction of a thin prey patch,

movement became more horizontal and the turning rate of the predatory protist

increased by 25%. O. marina were also found to be up to 20 times more abundant

within the layer of prey cells after four hours than in the rest of the container, further

confirming a behavioural response of the protist to the patch and attempt to remain

within it.

Leising and Franks (2002) observed behaviours consistent with ARS in

calanoid copepods that fed in prey patches. Herbivorous copepods feed by filtering

the water that surrounds them (termed filter-feeding); this creates currents that move

algae towards their mandibles and into their gut. They found a significant difference

in behaviour between feeding copepods and non-feeding copepods. Feeding

copepods altered their swimming direction more often and swam shorter distances

at slower speeds when compared to unfed controls, a foraging behaviour that allows

organisms to remain within the patch of prey.

In an earlier study, Leising and Franks (2000) developed a foraging model for

copepods feeding in prey patches using ARS behaviour, where copepods were

represented as single points capable of traveling strictly in the vertical direction. ARS

behaviour was simulated by allowing each copepod to move either upward or

downward at each time step (one-second resolution), with a velocity varying as a

function of algal concentration at the copepod’s location. In the constant-speed

control, copepod step length (a measure of travelled distance per time step in the

simulation) was kept constant regardless of food concentration. In the random-speed

26

control, copepod step-length at each time step was randomly chosen to be between

zero and twice the speed of the constant-speed control. They discovered that the

ARS behaviour led copepods to consume more cells while reducing their distance

traveled compared to constant-speed and random-speed controls.

Tiselius (1992) observed the feeding behaviour of copepods when presented

with a heterogeneous distribution of the diatom Thalassiosira weissflogii as prey.

Experiments were conducted in the laboratory where short-lived patches were

established using haloclines. He found that copepods spent most of their time within

the food layer, that feeding bouts increased, and that the frequency of jumps was

reduced within the food layer. By reducing their motility and employing more

horizontal swimming, copepods were able to remain within food layers. When the

organisms approached the edge of a food patch, they were observed to direct their

movement back toward the food patch, a behaviour that has also been observed in

euphausiids (Price 1989).

In Neary et al.’s (1994) laboratory study, Daphnia pulex individuals were

found to modify their spatial distribution in response to a food concentration gradient.

They aggregated towards higher food concentrations within a food concentration

gradient and followed the preferred concentration in a dynamic gradient (i.e. a

gradient in which high and low concentrations were continually reversed). A similar

study by Shatz and McCauley (2007) found that Daphnia were quickly (less than 10

minutes) able to detect higher quality algae within a spatial gradient differing in their

carbon to phosphorus ratios. Extending the behavioural response to prey patches to

27

larger organisms, Colton and Hurst (2010) observed a reduction in swimming bouts

in Pacific cod and walleye Pollock while fish fed in a prey patch.

The general trend from these studies is that organisms reduce swimming

speeds (Figure 3) and increase their turning behaviours (Figure 4; ARS foraging

strategy) when feeding in high-concentration prey patches. This ability of consumers

to respond to food patches by modifying their behaviour may be essential to exploit

patch resources efficiently and may lead to higher overall fitness of an individual or a

population of consumers.

Ingestion

Stemming from the fact that patches of prey have a relatively higher

concentration of food than the surrounding environment, consumers that feed in

such patches should have increased ingestion (or feeding) rates (e.g. Holling 1959,

Frost 1972, Peters and Downing 1984). As the prey concentration in a predator’s

environment increases, so does the probability of a predator coming into contact,

and thus ingesting its prey. This is analogous to collision theory in chemical reaction

kinetics, which states that reactants must collide in order to react– the more reacting

molecules present, the greater the frequency of collisions and the greater the rate of

reaction.

Since Holling’s (1959) seminal study describing the functional response

(ingestion rate plotted as a function of food concentration) of small mammals on pine

sawflies, much work has been done to develop the functional response of other

28

1,0000 200 400 600 800

1

0

0.2

0.4

0.6

0.8

Food concentration (cells/mL)

Spee

d (g

rid u

nits

/s)

S = Smax (1 – C / (ksv + C))

Figure 3 Adapted from Figure 3 in Leising (2000). Speed as a function of food concentration developed with SEARCH (Simulator for Exploring Area-Restricted search in Complex Habitats) model and mathematical equations detailed in Leising (2000). At each time-step, the copepod moves a particular step length (S; distance travelled in a straight line), which varies with food concentration (C). Smax is the maximum step length allowed and is set to 1 grid unit s-1; ksv is the ‘half-saturation constant’ of step-length response and is set to 250 cells mL-1. Speed unit refers to the grid in which copepod swimming was simulated.

29

1,0000 200 400 600 800

120

0

20

40

60

80

100

Food concentration (cells/mL)

Turn

ing

angl

e ST

DEV

(deg

rees

)

Astd = AmaxC / (kag + C)

Figure 4 Adapted from Figure 3 in Leising (2000). Turning angle (STDEV) as a function of food concentration developed with SEARCH (Simulator for Exploring Area-Restricted search in Complex Habitats) model and mathematical equations detailed in Leising (2000). Before moving to the next location at each time-step, the copepod turns at a given angle. The probability of each turn angle is given by a Gaussian distribution of a particular mean and standard deviation (Astd). The standard deviation of this turn angle varies with food concentration (C). Amax is the maximum allowed standard deviation of the probability density function for turning angle and is set to 1 grid unit s-1; kag is the ‘half-saturation constant’ for turning angle and is set to 625 cells mL-1.

30

organisms (e.g. Frost 1972, Chow-Fraser and Sprules 1992). Three different

functional responses have been observed in nature. A type I functional response is

described by a constant, linear increase in feeding rate with an increase in prey

concentration where predator search rate is constant and handling of prey is

negligible. A type II response is also characterized by a constant search rate but the

consumer’s food intake rate decelerates until it reaches the maximum intake rate

(MIR) of the consumer possibly because it is limited by the time required to handle

its prey (Dale 1994) or because it is becoming satiated. In a type III response, both

the search rate and the handling time vary with changes in prey concentration; at low

prey concentrations, search rate declines, so feeding rate initially accelerates, but

then decelerates as prey concentration increases until MIR is reached (Figure 7).

Ingestion rate (IR, cells hr-1) as a function of phytoplankton concentration, as

recorded in the laboratory at 20ºC, was combined from four studies on various

Daphnia species (D. magna, D. rosea, D. pulex, D. longispina) in Chow-Fraser and

Sprules (1992). In order to determine the weight-specific amount of energy each

daphnid ingests at any given concentration (EI), the amount of energy per algal cell,

hourly rates of ingestion, and daphnid mass were required. Although the amount of

energy per algal cell (EA) varies from species to species, it was assumed to be

5.47×10-9 KJ cell-1 (for Chlamydomonas reinhardi from Richman (1958); converted

from cal/cell to KJ cell-1 using 1 cal = 0.004184 KJ, see Table 1) and used as a

typical value. The product of ingestion rate and energy content per cell scaled to

daphnid mass results in the amount of energy ingested in KJ mg of animal-1 hour-1;

31

0 2 4 6 8 10 12 14 16 18 20Algal concentration (× 10,000 cells/mL)

0

20

40

60

80

100

120

Inge

stio

n ra

te (×

10,0

00 c

ells

/ani

mal

/day

)

Type IType IIType III

I = 100C / 1 + C

I = 20.4C

I = 100C3 / 5 + C3

Figure 5 Modified from Figure 1a in Chow-Fraser and Sprules (1992). Theoretical functional response curves based on mathematical equations, where I is ingestion rate and C is algal concentration. Type II (Holling, 1959), type III (Real, 1977).

32

EI = (IR × EA)/M, where M is daphnid mass in mg, results in the following equation

for the function:

EI = 0.000265lnF – 0.001738

where EI is energy ingested in KJ mg of animal-1 hour-1 and F is algal concentration

in cells mL-1 (Figure 6).

In a classic study by Frost (1972) ingestion rates of female copepods on four

different-sized diatoms, each at various concentrations, was investigated. He found

the same pattern of ingestion rates for all prey sizes: a positive, linear increase up to

a MIR (i.e. Holling type I functional response), and that this MIR decreased as prey

size increased. Similar results were found by Peters and Downing (1984); they

reviewed published data on the filtering and feeding rates of calanoid copepods and

cladocerans on algal prey and found a positive, linear functional response (Holling

type I) at low prey concentrations. No feeding saturation was seen presumably

because prey were only available at 0.1 – 1000 ppm vol./vol., concentrations well

below which MIR is known to occur. Demott (1982) discovered a type II feeding

response in his feeding experiments with Bosmina and Daphnia on Chlamydomonas,

i.e. increase in ingestion rate with an increase in food concentration, up until a

threshold is reached presumably because it is limited by its capability to process

additional prey. Chow-Fraser and Sprules (1992) plotted a curve, based on data

from the literature, of diaptomid copepod ingestion rates versus phytoplankton

concentration and found that copepod ingestion rates followed a type III functional

response.

33

EI = 0.000265ln(F) – 0.001738#r² = 0.7220#

0.0000#

0.0005#

0.0010#

0.0015#

0.0020#

0.0025#

0.0030#

100 # 1,000 # 10,000 # 100,000 # 1,000,000 # 10,000,000 #

Ener

gy in

gest

ed (K

J/m

g of

ani

mal

/hr)#

Food concentration (cells/mL)#

Figure 6 Modified from Figure 6b in Chow Fraser and Sprules (1992). Semi-log plot of energy ingestion rates of various Daphnia species as a function of food concentration. Straight line fitted using Microsoft Excel logarithmic function. Explained variance (r2) is shown. EI = energy ingested and F = algal concentration. See text for details.

34

Although there are different feeding responses (types I, II and III) to changes

in food concentration, the overall trend is that predator ingestion rate increases with

food concentration as has been shown by Holling (1959), Frost (1972), Demott

(1982), Peters and Downing (1984) and Chow-Fraser and Sprules (1992), but it is

clear that this does not occur indefinitely. Ingestion rate plateaus mostly because the

predator is limited by its ability to handle and process prey (Dale 1994), including gut

fullness and satiation.

Digestion and the specific dynamic action (SDA)

Since consumers experience increased feeding rates, they should also

experience an increase in specific dynamic action (SDA), which is the increased

metabolic expenditure due to the processing of food material. Traditionally,

ecologists have defined the SDA to include the total energy expended on all the

processes broadly associated with the ingestion, digestion, and assimilation of a

meal (Jobling 1981, Secor and Faulkner 2002). McCue (2006) comprehensively

reviewed the detailed physiological processes that have been deemed to contribute

to the SDA in the past hundred years. Specific examples include: gut peristalsis, acid

secretion, nutrient transport across membranes, ketogenesis, urea production, and

many others. It seems that a consensus on an operational definition of what

comprises SDA in ecology is lacking, and accounting for all the physiological

processes associated with SDA would be impossible considering the multitude of

specific processes that apparently contribute to it (McCue 2006).

35

It can be assumed that the bulk of the SDA consists of energetic costs that

are attributable to digestion and assimilation (i.e. ingestion costs negligible). Since

researches rarely separate costs of the two, SDA will be used as a proxy for

changes in the costs of digestion activity (assuming that increased digestion/

digestion rates leads to increase energetic costs). Although the magnitude of SDA

will not strictly equal that of digestion, the trend (either increase or decrease) is what

is of interest. Among other things, the amount of food consumed has a large effect

on the SDA of any given organism (Secor and Faulkner 2002, Fu et al. 2005).

Fu et al. (2005) investigated the effect of feeding level (ranging from 0.5 to 4%

dry weight (DW) per wet fish body weight (WW)– DW/WW) on SDA in the southern

catfish (Silurus meridionalis) that were fed a diet mostly of fishmeal, cornstarch and

micro-crystal cellulose. The oxygen consumption was recorded using a continuous

flow respirometer to measure metabolic rate beginning from six hours prior to

feeding (in order to obtain basal metabolic rate) until 48 hours after feeding. The

energy expended on SDA was calculated by subtracting the standard metabolic rate

from the total metabolic rate recorded during the feeding experiment. They found

that energy expended on SDA increased significantly as a linear function of feeding

level; SDA energy expenditure for the 4% DW/WW meal was 75.3 KJ kg-1, compared

to 10.3 KJ kg-1 for the 0.5% DW/WW meal, a seven-fold increase (Figure 7). They

also found that feeding level had an effect on the duration of SDA-associated

physiological processes; a 54% increase in duration from the 0.5% to the 4% (Figure

7).

36

Figure 7 Composed using data from Table 2 in Fu et al. (2005). Energy expended on specific dynamic action (SDA) and duration of SDA-associated physiological processes as a function of feeding level. Plotted data are means ± standard error (n = 8).

37

Jobling and Davies (1980) also compared SDA to meal size in lab-reared

plaice (Pleuronectes platessa). They used a continuous flow respirometer to

measure oxygen consumption and thus SDA. Similar to Fu et al. (2005), both the

magnitude and duration of SDA increased with food intake. A six-fold increase in

meal size (0.2 mL to 1.2 mL) resulted in about a ten-fold increase in total post-

prandial oxygen consumption above resting level and doubled SDA duration.

It is no surprise that when an animal has more food in its gut, it will require

more time and energy to digest it, as has been shown by Fu et al. (2005) and Jobling

and Davies (1980), along with many others that found digestion to increase (as

measured by SDA; e.g. Beamish, 1974, Guinea and Fernandez 1997, Secor and

Faulkner 2002). Both Secor and Faulkner (2002) and Fu et al. (2005) calculate the

energy expended on SDA as a percentage of energy ingested from a meal, termed

the SDA coefficient. Fu et al. (2005) found similar SDA coefficients for the five

different feeding levels they tested, ranging from 12.15 to 13.44%. Thus with

increases in food concentration, the energy expended on SDA increases

substantially, up to ten-fold for a six-fold increase in food concentration, and SDA

duration is doubled for this same increase in food concentration.

Assimilation

Assimilation is the process by which food material that is broken down into its

components (i.e. minerals, vitamins and nutrients), is incorporated into a consumer’s

own tissue for growth and reproduction. While consumers feed at higher prey

38

concentration (prey patches), their ingestion rate increases, which will lead to a

change in their assimilation rate and total assimilated energy.

Schindler (1968) investigated the feeding and assimilation rate of Daphnia

magna under different phytoplankton concentrations (54,000 – 540,000 cells mL-1;

converted from 1 – 10 mg L-1 using equivalencies in Table 1 and assuming

Chlamydomonas reinhardi weight) and qualities (energy content; 2–5 cal mg-1). D.

magna were allowed to graze on carbon-14 radioactive algae in order to determine

the calories of food assimilated (A cal mg of animal-1), which was calculated as the

product of calories per unit radioactivity of food (C) and radioactivity per animal after

feeding (R; A = C × R). A multiple linear regression model of assimilation (A) was

derived to be:

A = 0.0286E + 0.0038T + 0.0031C – 0.1444W – 0.1405

where T is temperature (ºC), E is food energy content (cal mg-1), W is animal weight

(mg animal-1) and C is algal concentration (mg L-1). The model revealed a significant

effect of both food concentration and food quality on assimilation rate; as algal

concentration and food quality increased, so too did the rate of assimilation (Figure

8).

Arnold (1971) examined various growth processes in Daphnia pulex, including

ingestion and assimilation. Five D. pulex individuals per 0.2 L container were allowed

to feed on radiolabeled algae for one hour. Daphnia were rinsed and then

transferred to a container where they were allowed to feed on non-labeled algae for

39

Figure 8 Adapted from Figure 7 in Schindler (1968). Plotted line is the solution to a linear regression equation showing how assimilation, A = 0.0286E + 0.0038T + 0.0031C – 0.1444W – 0.1405 varies with algal concentration (C), temperature (T) = 15ºC, food energy content (E) = 5.0 cal mg-1 and animal weight (W) = 0.030 mg animal-1.

40

two hours in order to remove the radiolabeled food from the animal’s gut; the

residual radioactivity in the animals was due to food that had been assimilated.

Plotting Arnold’s (1971) data reveals that food assimilation generally increases with

food ingested (Figure 9). The outlier in the data represents the algal species

Anacystis nidulans. This species was rarely ingested by the Daphnia, and when it

was, only 15.8% of material was assimilated. Daphnia that fed on A. nidulans were

found to have a poor survival rate (Arnold 1971), suggesting that this algal species

may have a lethal effect on Daphnia. Although not presented (due to data paucity of

relevant studies), presumably once the animal’s ingestion rate saturates the amount

of material assimilated will saturate as well. Thus assimilation is found to increase

indirectly with ambient food concentration, but directly with ingestion rate.

Growth and reproduction

The energy assimilated by an organism eventually contributes to its individual

growth and reproduction, which ultimately leads to the growth of a population.

Individual growth (also somatic growth) refers to the increase in an organism’s mass

per unit time, whereas reproduction (gonadal growth) refers to the energy used to

produce offspring (differs among males and females). While consumers feed in

higher food concentrations, their assimilation rate increases, which may lead to an

increase in growth and reproduction.

Lampert and Trubetskova (1996) were interested in whether an increase in

food concentration would lead to a greater individual fitness (as measured by

individual growth rate). Juvenile Daphnia magna growth rate was measured by

41

Figure 9 Composed using data from Table 1 in Arnold (1971). Plotted data show Daphnia pulex assimilation versus ingestion on nine different radiolabeled algal species (each dot represents a different algal species). Data shown represents means of 5 groups with 5 individuals each ± standard deviation.

42

weighing Daphnia before and after they were placed in a flow-through system

(means of exposing organisms to a constant algal concentration) where they fed

exclusively on different concentrations of Scenedesmus acutus at 20ºC. Experiments

were developed using three separate chambers (replicates) for each algal

concentration treatment. Juvenile D. magna individual growth rates were found to

increase rapidly at lower concentrations (< 0.5mgC L-1), and steadily increase at

higher concentrations until they begin to level off (> 0.5mgC mL-1; Figure 10). Thus

growth rate increases as ambient food concentration increases.

Energy expenditure, oxygen consumption and respiration costs

Cellular respiration comprises a complex series of chemical reactions (major

steps include glycolysis, citric acid cycle, oxidative phosphorylation) that take place

in all multicellular organisms in order to convert the biochemical energy stored in

molecules (e.g. glucose, amino acids) into energy the organism can use.

Multicellular organisms require oxygen to achieve these energy conversions. In

these organisms, oxygen, being highly electro-negative, acts as the final electron

acceptor in a series of reactions in which high energy electrons are transported. The

process of using up oxygen generates an electrochemical gradient across a

membrane and energy is ultimately produced. In multicellular organisms, the

process of cellular respiration requires organic energy (glucose) and oxygen and

produces energy, carbon dioxide, and water.

In order to measure respiration rates in the laboratory, one must either

measure the rate of the reactants (oxygen) consumed or the rate of the products

43

Figure 10 Modified from Figure 2 in Lampert and Trubetskova (1996). Shows how Daphnia magna individual juvenile growth rate varies with algal (Scenedesmus acutus) concentration. Standard deviation bars too small to be shown (n = 3 per algal concentration).

44

produced (carbon dioxide and water); but most measure the former (e.g. Brett and

Sutherland 1965, Jobling and Davies 1980, Fu et al. 2005). This is done by placing

an animal inside a sealed chamber and measuring the oxygen concentration at the

start and end of the experiment, and noting the change.

There is no debating that oxygen consumption by an organism increases with

energy expenditure. The energy cost and thus presumably the respiration of

organisms that feed at increased rates also increases, although this was not

explicitly shown (Rapport and Turner, 1975). Respiration was also found to increase

with specific dynamic action in catfish (Fu et al. 2005) and plaice (Jobling and Davies,

1980) as a result of ingesting more food. Finally, contrary to all other changes that

were found to occur within a patch, respiration decreased as pumpkinseed

decreased their swimming speeds (Brett and Sutherland, 1965). All aforementioned

studies found that oxygen consumption increased with behaviours that require

greater energy expenditures. Thus it can be said that respiration rate or

oxygen consumption is a means to measure the amount of energy expended by an

animal.

A question one may ask in regard to the energetic costs related to activity is

whether it increases or decreases while consumers are in an area of high food

concentration (patch). It is known, from the literature, that two relevant behavioural

changes occur in a consumer once it encounters a prey patch: increased turning

behaviour, and decreased swimming speed. How each of these behavioural

changes affects the associated respiration costs must now be explored.

45

The literature describing how an animal’s energy expenditure varies with

increased turning rates (a behaviour that is observed in consumers feeding in high

food concentrations) is quite weak; the only study to address this question is Krohn

and Boisclair (1994). They used a stereo-video system to measure and compare the

energy expenditure of free-swimming (non-constant speed and multidirectional

motion) and forced-swimming (constant speed and unidirectional motion) in brook

trout (Salvelinus fontinalis). The energetic costs associated with free-swimming fish

behaviour, as measured by oxygen respiration, were found to be six times greater

than forced-swimming fish for the same average speed, indicating that acceleration,

deceleration and turning may be energetically expensive (Figure 11).

Many investigators have studied how the energetic costs associated with

swimming vary with velocity (e.g. Brett and Sutherland 1965, Torres 1984, Morris et

al. 1985). Using a tunnel respirometer in which known current velocities were used,

Brett and Sutherland (1965) measured oxygen consumption (used as a proxy for

energy expenditure) as a function of velocity in pumpkinseed (Lepomis gibbosus).

The results indicate a positive linear relationship between oxygen consumption and

velocity, indicating that it is less costly for pumpkinseed to swim at a low speed, a

behaviour that is common in organisms that feed in prey patches. For a 45-gram fish,

oxygen consumption increased by 445% from minimum oxygen consumption (at a

velocity of about 0.6 body lengths per second) to maximum oxygen consumption (at

a velocity of about 3.0 body lengths per second).

46

Cs = 6.2Cf + 0.0077#R² = 0.81#

0#

0.05#

0.1#

0.15#

0.2#

0.25#

0.3#

0# 0.01# 0.02# 0.03# 0.04# 0.05#

Spon

tane

ous

swim

min

g co

st (m

g O

2/g/h

)#

Forced swimming cost (mg O2/g/h)!#

Figure 11 Modified from Figure 2 in Krohn and Boisclair (1994). Relationship between spontaneous swimming costs (Cs) and forced swimming costs (Cf) at same average speed with 95% confidence intervals. Dotted line represents the 1:1 relationship. Slope of the line reveals that spontaneous swimming is 6.2 times as costly as forced swimming.

47

Buskey (1998a) obtained direct measurements of oxygen consumption as a

function of swimming speed in a cyclopoid copepod (Dioithona oculata) using a

variable-speed flow-through chamber. Copepods were induced to swim at different

speeds inside the chamber by varying the current speeds (< 1mm s-1, 7.7mm s-1,

17.2mm s-1). This resulted in estimated copepod swim speeds of about 3.5 mm s-1

(typical speed of routine metabolism), 8.6 mm s-1, and 18.1 mm s-1 (typical speed of

active metabolism), respectively. Respiration rate was found to increase linearly with

swimming speed (r2 = 0.92, Figure 12). Using a similar setup in a separate study,

Buskey (1998b) also found respiration in planktonic mysids to increase linearly with

mean swimming speed (r2 = 0.67).

Energetic consumption data for small aquatic organisms such as cladocerans

and copepods, has also been provided through modeled data. To determine the cost

of transport in smaller crustaceans, Morris et al. (1985) used the costs of locomotion

derived from fluid dynamic theory and their own complex hydromechanical

swimming model. According to their model, the net cost of transport increases

linearly with average swim speed so that the net cost at a velocity of 5.3 body

lengths s-1 is almost five times greater than the net cost at 3.0 body lengths s-1.

Torres (1984) explored the swimming efficiency (which he defines as “the

ratio of thrust power required to overcome hydrodynamic drag to net metabolic

energy expenditure”) of krill and compared that efficiency to other, larger organisms.

He compiled the net cost of transportation of 12 different swimming species (ranging

48

Figure 12 Adapted from Figure 2 in Buskey (1998a). Respiration rate (RR) versus swim speed (S) in the copepod Dioithona oculata. See text for details

49

in size from krill to salmonids) and found that the net cost of transport was higher

among smaller organisms by an entire order of magnitude. This is not surprising

considering that smaller organisms are much less efficient swimmers than larger

organisms (Torres 1984), because at their size scale the environment is relatively

more viscous for small organisms than for larger organisms (Purcell 1976).

Consider an object with dimension (d) moving with a given velocity (v) through

a fluid with a given viscosity (η) and density (ρ). The Reynolds number (term

popularized by Reynolds (1883)), is the ratio of the inertial forces (drag) to the

viscous forces or, roughly put: dvρ / η. When this number is small (i.e. when inertial

forces or drag is low), the viscosity or viscous forces of the medium in which an

organism swims becomes the dominant factor determining ease of mobility in a

medium; this is the case with smaller organisms. The smaller the organism, the less

it can rely on inertia to propel it forward, since these forces are so tiny compared to

the viscosity of the medium in which they inhabit. These organisms must constantly

expend energy to swim if they want to remain in motion, and this is energetically

costly. Larger animals with larger Reynolds numbers (increased d and v) rely less on

the viscosity of the medium and more on the inertial forces to determine their

efficiency of mobility. Unfortunately, empirical data showing whether animals with

low Reynolds numbers, such as aquatic invertebrates, expend a lot of energy no

matter how they move (i.e. linear swimming versus ARS swimming) is currently

lacking. Both changes in activity come as a direct result of being located inside a

prey patch. With changes in activity, come changes in the energetic costs associated

50

with them (respiration). According to the literature, energy costs increase with

turning/rotating behaviours, but decrease as swimming speed decreases.

Rapport and Turner (1975) developed a simple graphical model to determine

how a consumer’s total energy gain and energy cost varies with feeding rate, where

energy gain is defined as the total of assimilated energy per unit prey and total

energy cost includes the costs of foraging, basal metabolism and reproduction.

Assuming that predator and prey population sizes remains constant, the total energy

gained as a function of feeding rate is represented by an increasing function with

decreasing slope and the total energy cost increases exponentially with the quantity

of food consumed per unit time (Figure 13). According to the authors, the energy

gain function has a decreasing slope since assimilated energy per unit prey may

decrease with increased consumption rates and the cost function has an increasing

slope because the predator is less efficient in capturing and digesting its prey as it

increases its feeding rate. According to Figure 13, at both high and low feeding rates,

the cost of feeding is greater than the energy gain and can obviously not maintain a

predator in the long term; only at intermediate feeding rates does the consumer

obtain an energy surplus due to feeding. Since this is a purely qualitative, theoretical

study, no numerical data are provided as threshold feeding rates for consumers to

have an energy surplus where energy gains exceed energy costs. Although a

consumer may feed at low rates (below the point where gains exceed the costs)

when food is scarce, it is unlikely that a consumer ever experiences feeding rates at

elevated levels such that the cost of feeding is greater than the gain because at this

51

Figure 13 Modified from Figure 1 in Rapport and Turner (1975). Theoretical scenario of the total energy cost and gain as a function of ingestion rate. Reasoning behind the shapes of both cost and gain function explored in detail in the text. The total energy gain per unit time is defined as the assimilated energy per unit prey multiplied by the feeding rate. The total energy cost per unit time is defined as the energetic cost per unit prey multiplied by the feeding rate. Energy surplus is only positive in the space between the cost and gain functions.

52

point, the organism would simply cease feeding due to satiation; also provided that

the cost of rejecting particles while feeding at high concentrations remains relatively

low, which Taghon et al. (1978) suggests is the case.

Lampert (1986) recorded respiration rates as a function of Scenedesmus

concentration, in the laboratory at 20ºC. The amount of energy respired (converted

from µgO2 to KJ; see Table 1) by a daphnid at any given algal concentration can be

represented by the following equation:

ER = 0.00000236F0.3247

where ER is energy respired in KJ mg of animal-1 hour-1 and F is algal concentration

in cells mL-1 (Figure 14). These rates were similar to those found in other Daphnia

respiration studies (e.g. Lampert and Bohrer 1984, Kersting and Leeuw-Leegwater

1976) but covered a much wider range of food concentrations which is the principle

reason for its use.

To summarize, when a consumer feeds in a prey patch, it experiences an

increase in energetic costs due to increased turning behaviours, increased feeding

rates, increased SDA-related processes (ingestion, digestion and assimilation), but a

decrease in energetic costs due to the decrease in swimming speed. The sum of the

overall energetic cost/gain (net) was not explicitly explored from individual studies,

but a theoretical scenario from Rapport and Turner (1975) provides an account of

this, where intermediate feeding rates result in a net energy gain. A modeled

simulation is later explored to summarize the net energy gain in the different

environments (uniform vs. non-uniform).

53

ER = 0.00000236F0.3247#r² = 0.9103#

0.00001#

0.0001#

0.001#

1,000 # 10,000 # 100,000 # 1,000,000 #

Ener

gy e

xpen

ded

on re

spira

tion

(KJ/

mg

of a

nim

al/h

r)#

Food concentration (cells/mL)#

Figure 13 Modified from Figure 7 in Lampert (1986). Log-log plot of rate of energy expended on respiration of Daphnia magna as a function of Scenedesmus (food) concentration. Straight line fitted using Microsoft Excel power function. Explained variance (r2) is shown. ER= energy respired and F = algal concentration. See text for details.

54

Energetic efficiencies

There are many behavioural and physiological changes that occur in an

organism after encountering a prey patch. But these processes themselves do not

inform us of how an organism’s energetic efficiencies change as a result of

encountering these prey patches. These efficiencies include: assimilation efficiency,

the amount of assimilated material per amount of food material ingested for a given

animal; exploitation efficiency, the ratio of consumer ingestion to its prey’s

production; and the net production efficiency, the ratio of consumer production to

assimilation. Getting a measure of how these efficiencies change from an organism

that feeds in a uniform environment versus an organism that feeds in a patchy

environment is crucial to understanding the true benefit of feeding in patches. Below,

we explore each of these efficiencies in detail.

Exploitation efficiency

An animal’s exploitation efficiency is defined as the ratio of consumer

ingestion to its prey’s production. Exploitation efficiency may change as a direct

result of increased ingestion rates, which is in turn a result of an area of the

environment having a greater prey concentration. As far as I am aware, no study has

yet explicitly compared an animal’s exploitation efficiency with its ingestion rate or

surrounding prey concentration.

Since exploitation efficiency is the ratio of consumer ingestion per unit prey

production, it will change as a function of relative changes in ingestion and prey

production. Consumer ingestion was already shown to increase in prey patches as a

55

result of increased prey concentration (see section ‘Ingestion’; Holling 1959, Frost

1972, Demott 1982, Peters and Downing 1984, Chow-Fraser and Sprules 1992). In

regards to prey production in oceans and lakes, prey production may be affected by

(1) consumers ingesting at such increased rates on a sustained basis that prey

numbers (and hence prey production) begin to decrease significantly and eventually

cause prey extinction and (2) prey having access to fewer resources per individual in

higher prey concentration simply because these resources are being shared among

a greater number of individuals. But prey production increases if they are more

numerous in the environment or in a section of the environment (higher

concentration). If it is assumed that prey production either decreases or remains the

same, and it is known that ingestion certainly increases, it suggests that exploitation

efficiency increases in a prey patch as a result of increased feeding rates.

Assimilation efficiency

The assimilation efficiency (AE) is the total amount of assimilated material (A)

per amount of food material ingested (I) for a given animal (AE = A/I). With an

increase in food concentration, consumers have been found to increase both their

ingestion (Holling 1959, Frost 1972, Peters and Downing 1984) and the amount of

assimilated material (Schindler 1968, Arnold 1971, Mundahl et al. 2005). Both

elements that make up the assimilation efficiency increase with the characteristic

increase in prey concentration within a patch. But ingestion and assimilation do not

necessarily increase at the same rate and either may plateau at different points

meaning that assimilation efficiency may either increase, if assimilation increases at

56

a greater rate than ingestion, or decrease if ingestion increases at a greater rate

than assimilation.

Porter et al. (1982) were interested in seeing how food concentration, among

other things, affected the assimilation efficiency in Daphnia magna. Daphnia fed on

different Chlamydomonas reinhardi concentrations ranging from 103 to 106 cells mL-1.

This was used to determine assimilation and ingestion rates in order to calculate

assimilation efficiency. Plotting the net assimilation efficiency data versus the algal

concentration the Daphnia fed on, results in a weak negative relationship. Strangely,

the highest algal concentration resulted in the lowest net assimilation efficiency,

which may be an indication that further assimilation beyond a certain ingestion

threshold may be impossible or even disadvantageous. The algal concentration used

for the aforementioned data point is atypical of that found in nature, even in high-

density patches of eutrophic lakes (e.g. the highest phytoplankton concentration

found by Cyr and Pace (1992), who sampled 16 different lakes in northeastern USA,

was 141,000 cells mL-1) and was thus excluded from the relationship. Upon removal

of this data point, the relationship becomes weakly positive such that net assimilation

efficiency increases slightly with algal concentration, at least for concentrations less

than 500,000 cells mL-1 (Figure 15).

Net production efficiency

The net production efficiency (NPE) of a consumer population is the ratio of a

consumer’s production to its assimilation. The NPE is the efficiency with which a

57

0#

20#

40#

60#

80#

100#

120#

140#

1,000 # 10,000 # 100,000 # 1,000,000 # 10,000,000 #

Net a

ssim

ilatio

n ef

ficie

ncy

(%)#

Algal concentration (cells/mL)!#

Figure 15 Composed using data from Table 3 in Porter et al. (1982). Semi-log plot of net assimilation efficiency (%; calculated by dividing net assimilation rate by ingestion rate) plotted against algal concentration for Daphnia magna feeding on different concentrations of Chlamydomonas algae (total n = 70). Point designated by ▲ was not included in the line function; see text for details.

58

consumer converts assimilated energy into energy for tissue growth and

reproduction, which essentially contributes to the production of the trophic level. The

NPE will vary among different groups of organisms principally because they may

differ in metabolic requirements (i.e. homeotherms versus poikilotherms); the size of

the organism has a negligible effect on NPE and all other energetic efficiencies

(Peters 1983). The difference in the NPE lies in the fact that homeotherms must

expend additional energy on maintaining body temperature, whereas poikilotherms

do not.

Vidal’s (1980) study focused on how different factors (algal concentration,

temperature and body size) affect the NPE of the marine copepod Calanus pacificus

as a consumer of algae. Weight-specific production rates were defined as the daily

increase in particulate body carbon, including growth, molting and reproduction.

Assimilation rates, defined as the difference between ingestion and egestion rates.

These rates were not directly measured thus assimilation rates were estimated as

the sum of weight-specific rates of growth, molting, respiration and excretion. Vidal

found the NPE for each combination of algal concentration, animal weight and

temperature. For a 65µg animal (intermediate animal weight), NPE increases rapidly

at low algal concentrations (< 4ppm, or < 20,000 cells mL-1; see Table 1) but

increases only slightly at higher concentrations (> 4ppm, or > 20,000 cells mL-1)

(Figure 16).

59

0#

10#

20#

30#

40#

50#

60#

0# 2# 4# 6# 8# 10# 12# 14# 16# 18#

Net p

rodu

ctio

n ef

ficie

ncy

(%)#

Algal concentration (ppm)!#

8.0ºC, 65µg#12.0ºC, 65µg#15.5ºC, 65µg#

Figure 16 Composed using data from Table 2 in Vidal (1980). Net production efficiency shown for three temperatures at different algal concentrations for a 65µg copepod.

60

From Vidal’s (1980) work on NPE, taking the lowest algal concentrations

tested (1.3ppm, or 6,500 cells mL-1) as typical of between prey patches (mean NPE

across all temperatures = 34.83%) and the highest ones (15.8ppm, or 79,000 cells

mL-1) as typical of within patch prey concentrations (mean NPE across all

temperatures = 53.83%) typical of patches indicates that the typical increase in NPE

from between to within algal patches is 54.55% [(53.83%–34.83%)/34.83%]. From

6,500 cells mL-1 to 19,000 cells mL-1 there is an NPE increase of 45.94%; from 6,500

cells mL-1 to 39,000 cells mL-1 there is an NPE increase of 53.12%.

Urabe and Watanabe (1991) have also explored how net production efficiency

varies with food concentration in their study on Daphnia galeata and obtained similar

results to Vidal (1980). Using existing equations from the literature (e.g. efficiencies:

Richman 1958; body weights after molting: Urabe 1988; oxygen consumption: Urabe

1990), they found that for adult instars, NPE was about 1.5 times higher under food

that was 5 times as concentrated (calculated from range midpoints). This implies that

at higher ingestion rates, a higher percentage of assimilated food is used for growth

and reproduction rather than maintenance metabolism.

2. Ratio of prey production to predator consumption (PP:PC)

Fifty-six PP:PC ratios were calculated using data from 34 independent aquatic

systems from 28 different studies. Of the 21 PP:PC ratios that were calculated from

primary trophic interactions, 4 were found to be below the lower end (y = ln(2.00)) at

which the maximum sustainable yield (MSY) occurs / ecotrophic coefficient range,

61

11 were within the MSY variation range and 6 were above it. As for the 28 PP:PC

ratios that were calculated from secondary trophic interactions, 10 were found to be

below the lower end of the MSY range chosen, 5 were within the range, and 13 were

above it. Finally, the remaining 7 PP:PC ratios from tertiary trophic interactions, none

were found below the range, 1 within it, and 6 above it.

Overall, 23 of 56 or 41.1% of the aquatic systems were above the upper MSY

boundary and thus provided sufficient prey production to sustain predator

populations, 19 out of 56 or 33.9% were between the boundaries indicating that

predators required almost all prey production, and 14 out of 56 or 25.0% were below

the lower MSY boundary indicating apparently insufficient prey production to a

sustain predator population (Figure 17).

3. Patch energetics simulation

All iterations of NetEP : NetEU (net energy gain in patchy environment : net

energy gain in uniform environment) were plotted as a function of the degree of

patchiness (DP) for each trophy level and each of nine different proportions of time

spent within or in between patches. In the mesotrophic simulation (concentration

range of 6,000 – 17,800 cells mL-1), organisms that spend 90, 80 and 70% of the

time within a patch have a NetEP : NetEU consistently above 1.00 for a degree of

patchiness up to 3.0. Those that spend 60% of the time within a patch have a NetEP :

NetEU above 1.00 for DP up to 2.3, and below 1.00 for DP above 2.3. The remaining

62

Figure 17 Fifty-six PP:PC ratios calculated from 34 ecosystems, differentiated by trophic interaction and environmental system. Primary trophic interaction (–) is defined by trophic level 2 feeding on trophic level 1, secondary trophic interaction (●) is defined by trophic level 3 feeding on trophic level 2 and tertiary trophic interaction (■) is defined by trophic level 4 feeding on trophic level 3. Horizontal lines (a) y = ln(4.00) and (b) y = ln(2.00) bracket the variation in which the maximum sustainable yield (MSY) occurs, derived from the literature. Ecosystems above line (a) appear to have sufficient prey production to support predator consumption; ecosystems below line (b) do not. Ecosystems found between lines are those in which predators consume prey at the maximally sustainable rates.

y = ln(2.00)!

y = ln(4.00)!

-3!

-2!

-1!

0!

1!

2!

3!

4!

5!

0! 1! 2! 3! 4! 5! 6! 7!

LN p

rey

prod

uctio

n : p

reda

tor c

onsu

mpt

ion

(PP:

PC)!

Environmental system!

– 1º trophic interaction! • 2º trophic interaction! � 3º trophic interaction!

63

time proportions (< 50% within patch) have a NetEP : NetEU equal to or below 1.00

(Figure 18).

In the eutrophic simulation (concentration range of 10,000 – 128,000 cells

mL-1), organisms that spend 90 and 80% of the time within a patch have a NetEP :

NetEU consistently above 1.00 for a degree of patchiness up to 13.0. Those that

spend 70% or 60% of the time within a patch have a NetEP : NetEU above 1.00 for

certain DP and below for others. The remaining time proportions (< 50% within

patch) have a NetEP : NetEU equal to or below 1.00 (Figure 19).

64

0.75!

0.80!

0.85!

0.90!

0.95!

1.00!

1.05!

1.10!

1.15!

1.0! 1.5! 2.0! 2.5! 3.0!

Net e

nerg

y ga

in in

pat

ch :

net e

nerg

y ga

in in

uni

form!

Degree of patchiness!

90:10!80:20!70:30!60:40!50:50!40:60!30:70!20:80!10:90!

Figure 18 Modeled ratios of net energy gain while Daphnia feed in a patchy environment to a uniform environment for different degrees of patchiness (ratio of highest to lowest concentration) in a mesotrophic lake. Different models generated for different amounts of time spent in patch versus in between patches, e.g. 70:30 line models a daphnid that spends 70% of the time feeding within a patch, and 30% feeding in between patches. Dotted line represents the line at which net energy gain in patchy environments is equal to that in uniform environments. See text for details on model.

65

0.60!

0.70!

0.80!

0.90!

1.00!

1.10!

1.20!

1.0! 3.0! 5.0! 7.0! 9.0! 11.0! 13.0!

Net e

nerg

y ga

in in

pat

ch :

net e

nerg

y ga

in in

uni

form!

Degree of patchiness!

90:10!80:20!70:30!60:40!50:50!40:60!30:70!20:80!10:90!

Figure 19 Modeled ratios of net energy gain while Daphnia feed in a patchy environment to a uniform environment for different degrees of patchiness (ratio of highest to lowest concentration) in a eutrophic lake. Different models generated for different amounts of time spent in patch versus in between patches, e.g. 70:30 line models a daphnid that spends 70% of the time feeding within a patch, and 30% feeding in between patches. Dotted line represents the line at which net energy gain in patchy environments is equal to that in uniform environments. See text for details on model.

66

DISCUSSION

Existing data from the literature, along with a simple literature-based

simulation, were used to explore how the heterogeneous spatial distribution of prey

animals could account for the prevalence of Allen’s paradox in the literature. From

the 56 PP:PC ratios calculated from the 34 different aquatic systems from 28

different studies, where prey production and predator consumption were compared,

14 out of the 56, or 25.0%, showed evidence of insufficient prey production to

support predator consumption. Thus on average, one out of every four published

production budget analysis is reported as unbalanced. This seems to be most

prominent in primary and secondary trophic interactions where all instances of

insufficient prey production for predator consumption arise (i.e. all tertiary trophic

interactions show sufficient prey production). Waters (1988) and Huryn (1996) both

agreed that this production budget mismatch or Allen paradox may be partially

caused by the exclusion of prey types that may contribute considerably to satisfying

a predator’s consumption demands. While this may indeed play a role in the studies

mentioned here, it does not account for it entirely, according to both Huryn and

Waters. However, these authors were focused on streams where the mismatch

between predator consumption and prey production seems to be more prominent

likely because there is more input from other sources (e.g. terrestrial sources) when

compared to a more pelagic system where there is less input from external sources.

Here, an additional explanation was proposed: organisms can gain an energetic

advantage while feeding in a spatially heterogeneous prey environment and may

67

thus require less prey than has been traditionally believed since environments are

traditionally assumed to be uniformly distributed with prey animals.

Animals can have increased energetic efficiencies while feeding in higher

concentrations of prey. The exploitation efficiency of an organism was shown to

increase with food concentration, because an organism ingests more prey per unit

time in such conditions, while its prey’s production presumably does not change

considerably. Organisms that feed in patchy environments are given the “choice” to

feed in either high or low food concentrations rather than an artificial uniform

average that investigators assign to lake systems. Thus they have the potential (if

they chose to feed in the higher prey concentration, which they often do (Tiselius

1992)) to ingest more food per unit of energy expended. This greater ingestion,

leads to a higher exploitation efficiency, which essentially means they are using (or

ingesting) their resource more efficiently. It has been shown that organisms acquire

energy (ingest) at a faster rate than they use it (respiration) by comparing slopes of

these relationships (slope of ingestion vs. food concentration is greater than slope of

respiration vs. food concentration). However, it has been argued above that a

solution to Allen’s paradox is that predators may require less prey production in

patchy environments. This can be possible if predators feed in bursts; high ingestion

rate while in patches, along with very little ingestion while in between patches; as

opposed to constant intermediate feeding in a uniform environment. Thus

exploitation efficiency can be higher while total ingestion may be lower while feeding

in a patchy environment rather than a uniform environment.

68

The assimilation efficiency was explored using Porter et al.’s (1992) study; it

has been concluded that assimilation efficiency increases with algal concentration, at

least for concentrations up to a 500,000 cells mL-1. This means that for increases in

food concentrations of this magnitude (1,000 – 500,000 cells mL-1), a greater portion

of the food material that is ingested is being assimilated. This may suggest that after

a certain ingestion threshold, assimilation efficiency decreases. Presumably this may

be caused by an over saturation of prey in the environment, which can cause an

organism to unwillingly ingest and material to be egested without ever being

assimilated. This results in higher ingested food and lower assimilated food, which

results in a lower assimilation efficiency at very high concentrations (around 106 cells

mL-1).

The net production efficiency (NPE), as explored by Vidal (1980), was shown

to increase with increased algal concentrations, regardless of temperature, but only

until a threshold NPE of about 50% was reached at about 20,000 cells mL-1. Thus

organisms feeding in areas that have concentrations above 20,000 cells mL-1, have

a greater proportion of assimilated energy that contributes to production of that

population or trophic level, meaning that there is less energy being lost as respiration

once organisms feed in higher prey concentration.

Investigators rarely, if ever, consider all of these potential increases in

energetic efficiencies described above when publishing production and consumption

estimates. They implicitly assume that these efficiencies are fixed since they assume

a uniform prey distribution throughout the lake they are sampling. All changes in

69

efficiencies explored do not truly simulate what happens in a heterogeneous

environment, but only what happens at different prey concentrations. Only how they

differ among lower and higher concentrations is being explored (assuming that the

mean of these high and low concentrations are what researchers use as uniform

concentrations and that the higher concentrations are characteristic of within patch

concentration). This is the best we can do because studies that explore energetic

efficiencies (or other process for that matter) rarely ever consider spatial

heterogeneity of prey in their analysis. Few studies explicitly investigate the potential

energy gain in a heterogeneous prey environment. Blukacz et al. (2010) and

Menden-Deuer and Grünbaum (2005) found that both cladocerans and copepods

and a predatory protist, respectively, could increase their energy gain by feeding in a

spatially explicit prey environment rather than a uniform environment.

Once a prey patch is encountered, the general trend is an increase in both

activity and physiological processes with swim speed being an exception.

Organisms were found to exhibit ARS behaviour once in a patch, which is a

behaviour that enables the predators to remain within it (Leising and Franks 2000,

2002). Prior to encountering the prey patch, however, predators were shown to

exhibit the reverse of ARS behaviour; they swim at greater speeds and turn less

frequently, a behaviour that allows them to locate a prey patch more quickly (Bundy

et al. 1993). Swim speed has been shown to decrease while organisms are in a

patch, implying that less energy is being expended at these lower speeds. However,

there is indirect empirical evidence that ARS swimming shows substantially higher

70

costs than linear swimming (Krohn and Boisclair 1994). Although the “sticky”

environment smaller organisms, such as zooplankton, experience may affect this,

there are no zooplankton data available on this, but Morris et al. (1985) shows that

for the same body size small organisms have higher motion costs than larger ones.

So it seems that activity costs may be higher in patches but these could potentially

be offset by the higher energy acquisition at high prey concentrations as a result of

both increased ingestion and assimilation.

Ingestion, digestion and assimilation were all found to increase as a result of

predators encountering a higher concentration of food (prey patch). Ingestion rates

increased, since there was more food available, but only until a threshold ingestion

rate was reached where the time required to handle the food exceeded the rate at

which it could be ingested. The duration and the energy expended on digestion as

measured by SDA increased, not surprisingly, since more food was ingested and

thus more time and energy are required to digest it. Similarly, more food ingested

results in an increase in assimilation. Given that ingestion rate plateaus at higher

food concentrations, assimilation will also plateau at higher food concentrations. The

increases in both physical activity and energetic processes result in increased

respiration costs. For example, spontaneous swimming (multidirectional and non-

constant) characteristic of ARS swimming behaviour is more costly than constant,

unidirectional swimming of the ‘hunting mode’ swimming (Krohn and Boisclair, 1994).

The simple patch energetic model was meant to simulate the total energy

gain and lost in both patchy and uniform environments. By using both the energy

71

ingested from food and the energy expended as respiration as a function of ambient

food concentration, it was presumed that all changes in physiologic processes,

efficiencies and behaviours were inherently taken into account when these data

were collected. Thus the simulations sum all the respective changes in their

environments and produce a summarized net energy gain function for both patchy

and uniform environments for different lake trophies and for different time

proportions.

The simulation used is quite simplistic. The concentrations used for

mesotrophic and eutrophic lakes reflect typical field concentration ranges, though it

does not consider the dynamic nature of patches. Patch concentrations can change

frequently as a result of either wind-driven currents (Blukacz et al. 2010), or by being

grazed down by consumers. These systems are not closed, thus algal and

zooplankton patches can also be repopulated through immigration from other parts

of the lakes. Hence patches can last varying lengths of time and concentrations

within patches can change frequently as a result of these physical and biological

factors. As a result of this, consumers likely return to their more linear “hunting mode”

swimming once the surrounding concentration falls below a certain threshold, and

return to ARS when the concentration is above this threshold; thus swimming

behaviours are also dynamic, depending on patch dynamics.

In all lake trophy simulations, an organism that spends at least 80% of the

time within a patch, as opposed to in between patches, has a greater net energy

gain in the patchy environment than the uniform environment for equal prey

72

availability (i.e. NetEP : NetEU > 1.00). This is because at high prey concentrations

characteristic of within prey patches, the net energy gain (EI – ER) is higher

compared to lower concentrations because energy ingested increased at a faster

rate than energy respired; i.e. the slope of energy ingested versus food

concentration is greater than that for energy expended on respiration. This means

that organisms acquire energy at a faster rate than they use it.

For all lake trophy simulations, all instances in which predators spend 50% or

less of the time within a patch resulted in a negative energy gain when compared to

the corresponding uniform environment (i.e. NetEP : NetEU < 1.00). This shows the

importance for organisms to come across high concentration patches and to remain

within them. Indeed, it has been shown that organisms perform behaviours that allow

them to find a patch when not it one (‘hunting mode’) and remain within one (ARS

behaviour).

As for organisms that spend 60–70% of the time within patches, they have a

greater energy gain in a patchy environment for lower degrees of patchiness (DP),

but vice versa for higher degrees of patchiness. This may be because the higher

degrees of patchiness, and hence patch concentrations, fall on the plateaus of

ingestion rate where after the ingestion threshold is reached, energy ingested

remains constant regardless of ambient food concentration. So when the energy

gain in a uniform environment (recall that this is taken as the mean concentration of

low, in between and high, within patches) is compared to the high DP patchy

environment, the mean, uniform energy gain is almost equivalent to the high, within

73

patch energy gain. This indicates that the net energy gain at the mean food

concentration will be greater than the net energy gain of the combination of within

and in between patches because the net energy gain at very low concentrations

weighs down the net energy gain in the patchy environment.

High degrees of patchiness may not be typical of field measurements, for

example the chlorophyll a concentrations from the oligotrophic Lake Opeongo 3.5km

transect, range from about 2.0µg L-1 to less than 6.0µg L-1, a degree of patchiness of

only 3.0. Cyr and Pace (1992) also present chlorophyll a data from different stations

in different eutrophic lakes; the highest degree of patchiness (ratio of highest

concentration to lowest) is about 6.0. Thus, lakes with lower degrees of patchiness

may be more typical of lakes than higher degrees of patchiness, thus high DP

simulations should be interpreted with caution, as they may be unrealistic.

Chlorophyll a concentrations of Lake Opeongo (an oligotrophic lake) suggest that the

majority of the time, consumers are exposed to relatively low prey concentrations

with only occasional high prey concentration patches. But consumers have been

shown to modify their behaviour to find and actively remain within high concentration

patches so it may be possible that they are in fact spending more time in the more

scarce, high concentration patches by engaging in these behaviours.

The component functions for the three different trophy simulations, all seem to

have the greatest NetEP : NetEU ratio for relatively low DP (< 3.00). The shape of the

simulation functions has everything to do with the way the functions relate to algal

concentration and the degree of patchiness since the available food concentrations

74

is the only variable being varied. According to these models the NetEP : NetEU is not

only sensitive to surrounding prey concentration, but to the ratio of high and low

concentration (degree of patchiness). In all simulations, the greatest net energy gain

differential (in a patchy environment versus a uniform environment) is approximately

10%. This accords well with Blukacz et al. (2010), who found a maximum energy

gain ranging from 9 to 20% in organisms feeding in a spatially explicit environment

versus a uniform one.

In many ways, both Lampert and Trubetskova’s (1996) study on individual

growth rate in D. magna and Vidal’s (1980) study on the net production efficiency

(NPE) in C. pacificus, answer the question of whether organisms can experience a

net energy gain while feeding in a patchy environment. Growth rate can be seen as

a means to measure an organism’s fitness (i.e. an organism’s ability to survive and

reproduce), and was seen to increase with increased algal concentration, a main

characteristic of within a patch in a spatially heterogeneous environment. Net

production efficiency is the efficiency with which assimilated energy is used for

growth and reproduction, thus a higher NPE in higher prey concentrations,

characteristic of prey patches, implies that an organism is using energy more

efficiently since less is being lost to respiration.

Despite the tools and knowledge of today, there remain studies that present

unbalanced production and consumption estimates. The simulated explorations

herein reveal that under certain circumstances, spatially heterogeneous prey

distributions can have an effect on the net energy gain of a feeding organism. Naïve

75

homogeneous spatial assumption leads to overestimates of prey production required

to satisfy predators’ growth demands. For instance, this can become an issue for

fish stocking in lakes. Because predators can feed more efficiently in a patchy

environment, i.e. growth can be achieved with less prey production than has been

traditionally calculated using lake-wide mean prey averages, there is potential to

stock more fish. Since prey are being utilized more efficiently in spatially

heterogeneous environments, a given amount of prey production can in reality

supply more predator consumption. This can lead to an acceleration of the desired

effects of stocking fish on a given system. Thus, it is important that future estimates

of production and consumption of aquatic and marine systems take the spatial

heterogeneity of prey into account. This document is meant to provide a starting

point for further, empirical development on the effects of spatial heterogeneity and

how this may influence the flow of energy among trophic levels.

76

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Waters, T.F. 1993. Dynamics in stream ecology. Canadian Special Publications of Fisheries and Aquatic Sciences. 118: 1-8. Westlake D., Casey H., Dawson H., Ladle M., Mann R.H., Marker A.F.H. 1972. The Chalk Stream ecosystem. Pages 615-635 in Kajak Z., Hillbricht-Illkowska A., eds. Productivity problems in freshwaters. International Biological Programme, UNESCO. Warsaw, Poland: Polish Scientific Publishers. Winberg G. G. 1972. Some interim results of Soviet IBP investigations on lakes. Pages 363-381 in Kajak Z., Hillbricht-Illkowska A., eds. Productivity problems in freshwaters. International Biological Programme, UNESCO. Warsaw, Poland: Polish Scientific Publishers. Winberg G. G., Babitsky V. A., Gavrilov S. I., Gladky G.V., Zakharenkov I.S., Kovelevskaya R.Z., Mikheyeva T.M., Nevyadomskaya P.S., Ostapenya A.P., Petrovich P.G., Potaenko J.S., Yakushko O.F. 1972. Biological productivity of different types of lakes. Pages 383-404 in Kajak Z., Hillbricht-Illkowska A., eds. Productivity problems in freshwaters. International Biological Programme, UNESCO. Warsaw, Poland: Polish Scientific Publishers. Woodson C. B., Webster D. R., Weissburg M. J., Yen J. 2007. The prevalence and implications of copepod behavioural responses to oceanographic gradients and biological patchiness. Integrative and Comparative Biology 47: 831-846. Worm B., Hilborn R., Baum J. K., Branch T. A., Collie J. S., Costello C., Fogarty M. J., Fulton E. A., Hutchings J. A., Jennings S., Jensen O. P., Lotze H. K., Mace P. M., McClanahan T. R., Minto C., Palumbi S. R., Parma A. M., Ricard D., Rosenberg A. A., Watson R., Zeller D. 2009. Rebuilding global fisheries. Science 325: 578-585. Wright J. C. 1965. The population dynamics and production of Daphnia in Canyon Ferry Reservoir, Montana. Limnology and Oceanography 10: 583-59

87

Appendix A: Collection of PP:PC ratios from the literature

#" Study"#" Authors" Year"of"

publication" Predator"spp." Prey"spp."Predator"

consumption"(PC)"

Prey"production"

(PP)"PP:PC" Environmental"

system" Data"collection"

1" 1" Sprules,"W.G." 1980" planktivorous"fish" herbivorous"zooplankton" n/a" n/a" 1.515" unclear" empirical"

2" "" Sprules,"W.G." 1980" herbivorous"zooplankton" primary"producer" n/a" n/a" 1.613" unclear" empirical"

3" 2" HillbrichtDIlkowska,"A."et#al." 1972" zooplankton" whole"phytoplankton"

community" 212.75" 553.5" 2.602" Mikolasjkie"Lake,"Poland" empirical"

4" 3" Greenstreet"et#al." 1997" Demersal"piscivores" zooplankton,"benthos,"other"fish"

126601.6" 4823878" 38.103" North"Sea" review/modelled"

5" "" Greenstreet"et#al." 1997" demersal"benthivores"

benthos"and"demersal"benthivores"

165596.8" 560565" 3.385" North"Sea" review/modelled"

6" "" Greenstreet"et#al." 1997" pelagic"piscivores" zooplankton,"benthos,"other"fish"

55718.1" 4759178" 85.415" North"Sea" review/modelled"

7" "" Greenstreet"et#al." 1997" pelagic"planktivores" zooplankton,"benthos" 259392.7" 4759178" 18.347" North"Sea" review/modelled"

88

8" 4" Sprules,"W.G." 2000" Mysis" zooplanktous"prey" 285.075" 5605.8" 19.664" Lake"Ontario" empirical"

9" 5" Alimov,"A.F."et"al." 1972"nonDpredatory"zooplankton"+"

benthos"phytoplankton" 18.85" 135" 7.162" Lake"Krivoe" empirical"

10" "" Alimov,"A.F."et"al." 1972"nonDpredatory"zooplankton"+"

benthos"phytoplankton" 15.47" 36" 2.327" Lake"Krugloe" empirical"

11" 6" Andronikova,"I.N."et#al." 1972"

nonDpredatory"zooplankton"+"

benthos"phytoplankton" 355.6" 1093" 3.074" Red"Lake" empirical"

12" 7" Krogius,"F.V."et"al." 1972" nonDpredatory"fish" zooplankton" 216" 417" 1.931" Lake"Dalnee" empirical"

13" 8" Moskalenko,"B.K."and"Votisnsev,"K.K." 1972" nonDpredatory"

zooplankton"primary"production"+"

bacteria" 407" 1175.7" 2.889" Lake"Baikal" empirical"

14" "" Moskalenko,"B.K."and"Votisnsev,"K.K."

1972" total"fish"reported" pred"and"nonDpred"zooplankton"

12.44" 88.6" 7.122" Lake"Baikal" empirical"

15" 9" Winberg,"G.G."et"al." 1972"nonDpredatory"zooplankton"+"

benthos"

phytoplankton"+"bacterioplankton"

298.2" 655.6" 2.199" Naroch"Lake" empirical"

16" "" Winberg,"G.G."et"al." 1972" planktivorous"fish" pred"and"nonDpred"zooplankton"

9.1" 290.8" 31.956" Naroch"Lake" empirical"

89

17" "" Winberg,"G.G."et"al." 1972" benthivorous"fish" benthos" 5.4" 71.2" 13.185" Naroch"Lake" empirical"

18" "" Winberg,"G.G."et"al." 1972"nonDpredatory"zooplankton"+"

benthos"

phytoplankton"+"bacterioplankton" 504.4" 1574" 3.121" Myastro"Lake" empirical"

19" "" Winberg,"G.G."et"al." 1972" planktivorous"fish"pred"and"nonDpred"

zooplankton" 10" 161.3" 16.130" Myastro"Lake" empirical"

20" "" Winberg,"G.G."et"al." 1972" benthivorous"fish" benthos" 10.9" 4" 0.367" Myastro"Lake" empirical"

21" "" Winberg,"G.G."et"al." 1972"nonDpredatory"zooplankton"+"

benthos"

phytoplankton"+"bacterioplankton" 622.7" 1758" 2.823" Batorin"Lake" empirical"

22" "" Winberg,"G.G."et"al." 1972" planktivorous"fish" pred"and"nonDpred"zooplankton" 3.8" 191.8" 50.474" Batorin"Lake" empirical"

23" "" Winberg,"G.G."et"al." 1972" benthivorous"fish" benthos" 25" 12.9" 0.516" Batorin"Lake" empirical"

24" 10" Gak,"D.Z."et"al." 1972" nonDpredatory"zooplankton"

phytoplankton"+"bacterioplankton"

199" 1937" 9.734" Kiev"Reservoir" empirical"

25" "" Gak,"D.Z."et"al." 1972" macrofauna"feeding"on"macrophytes"

macrophytes" 44.2" 176" 3.982" Kiev"Reservoir" empirical"

90

26" 11" Pidgaiko,"M.L."et"al." 1972" 2nd"trophic"level" 1st"trophic"level" 150.5" 8813.7" 58.563" Kurakhov's"Reservoir" estimates/empirical"

27" "" Pidgaiko,"M.L."et"al." 1972" 3rd"trophic"level" 2nd"trophic"level" 72.9" 41.32" 0.567" Kurakhov's"Reservoir" estimates/empirical"

28" 12" Sorokin,"Y.I." 1972" predatory"fish"(TL"5)" fish"(TL"4)" 2.5" 6.3" 2.520" Rybinsk"reservoir" modelled/empirical"

29" "" Sorokin,"Y.I." 1972" fish"(TL"4)" zooplankton"(TL"3)" 7" 6.45" 0.921" Rybinsk"reservoir" modelled/empirical"

30" "" Sorokin,"Y.I." 1972" predatory"zooplankton"(TL"3)" zooplankton"(TL"2)" 18.5" 78" 4.216" Rybinsk"

reservoir" modelled/empirical"

31" "" Sorokin,"Y.I." 1972" zooplankton"and"others"

phytoplankton"+"bacterioplankton" 329.6" 850" 2.579" Rybinsk"

reservoir" modelled/empirical"

32" 13" Gaichas"et"al." 2009" herbivorous"zooplankton"

phytoplankton" 3822.205" 3609.674" 0.944" Gulf"of"Maine" modelled"

33" "" Gaichas"et"al." 2009" total"mid"TL" total"low"TL" 945.313" 5316.198" 5.624" Gulf"of"Maine" modelled"

34" "" Gaichas"et"al." 2009" total"high"TL" total"mid"TL" 2.01" 154.617" 76.924" Gulf"of"Maine" modelled"

91

35" 14" Nienhuis,"P." 1993"

primary"consumer"(macrozoobenthos"

and"other"herbivores)"

primary"producer"(phytoplanton"and"

micro"and"macrophytobenthos)"

33" 155" 4.697" Dollard"estuary" modelled/empirical"

36" "" Nienhuis,"P." 1993"

secondary"consumer"(fish"and"

invertebrates"and"birds)"

primary"consumer"(macrozoobenthos"and"

other"herbivores)"5.7" 33" 5.789" Dollard"estuary" modelled/empirical"

37" "" Nienhuis,"P." 1993"

primary"consumer"(macrozoobenthos"

and"other"herbivores)"

primary"producer"(phytoplanton"and"

micro"and"macrophytobenthos)"

220" 305" 1.386" Wadden"Sea" modelled/empirical"

38" "" Nienhuis,"P." 1993"

secondary"consumer"(fish"and"

invertebrates"and"birds)"

primary"consumer"(macrozoobenthos"and"

other"herbivores)"7" 220" 31.429" Wadden"Sea" modelled/empirical"

39" "" Nienhuis,"P." 1993"

primary"consumer"(macrozoobenthos"

and"other"herbivores)"

primary"producer"(phytoplanton"and"

micro"and"macrophytobenthos)"

134" 315" 2.351" Grevelingen"estuary" modelled/empirical"

40" "" Nienhuis,"P." 1993"

secondary"consumer"(fish"and"

invertebrates"and"birds)"

primary"consumer"(macrozoobenthos"and"

other"herbivores)"4" 134" 33.500" Grevelingen"

estuary" modelled/empirical"

41" "" Nienhuis,"P." 1993"

primary"consumer"(macrozoobenthos"

and"other"herbivores)"

primary"producer"(phytoplanton"and"

micro"and"macrophytobenthos)"

137" 440" 3.212" Lake"Veere" modelled/empirical"

42" "" Nienhuis,"P." 1993"

secondary"consumer"(fish"and"

invertebrates"and"birds)"

primary"consumer"(macrozoobenthos"and"

other"herbivores)"5" 137" 27.400" Lake"Veere" modelled/empirical"

43" 15" HillbrichtDIlkowska,"A."

1974" nonDpredatory"zooplankton"

phytoplankton" 70" 200" 2.857" many"lakes" estimates/empirical"

92

44" 16" Westlake,"D."et"al." 1972" herbivorous"benthos" trout"and"other"fishes" 2400" 7800" 3.250" Bere"Stream,"England" D"

45" 17" Hopkins,"C.L." 1970,"71,"76"herbivorous"and"

carnivorous"benthos" trout"and"other"fishes" 3455" 2550" 0.738" Hinau"Stream,"New"Zealand" D"

46" 18" Tsuda,"M."et#al." 1975"herbivorous"and"

carnivorous"benthos" trout"and"other"fishes" 490" 400" 0.816" Takami"River,"Japan" D"

47" 19" Mortensen,"E." 1984" herbivorous"and"carnivorous"benthos" trout"and"other"fishes" 917" 922" 1.005"

Bisballe"baek,"Denmark"(stream)"

D"

48" 20" Staples,"J.A." 1992" all"fish"(e.g."roach,"gudgeon,"perch)"

macrophytes,"zooplankton,"benthos" 16297.7" 913.992" 0.056" Shropshire"

Union"(canal)" D"

49" 21" Gieskes,"W.W."and"Kraay,"G.W." 1977" heterotrophs" primary"production" 80" 105" 1.313" Southern"North"

Sea" estimates"

50" 22" Dumitru,"C."et#al." 2001" Bythotrphes" zooplankton" 199" 783" 3.935" Harp"Lake,"Canada"

estimates"from"models"

51" 23" Currin,"B.M."et"al." 1984" spot"and"croaker"

benthic"macroinvertebrates"available"to"juvenile"

fish"

6.48" 42" 6.481" Rose"Bay" various"sources"

52" 24" Bennett,"B.A."and"Branch,"G.M."

1990" resident"fish"many"prey"(e.g."

isopods,"copepods,"ostracods,"mollusks)"

5766" 34608" 6.002" the"Bot,"South"African"Estuary"

estimates"

93

53" 25" Collie,"J.S." 1987" yellowtail"flounder"amphipods,"

polychaetes"e.g." 2.86" 12.15" 4.248"3"sites"New"England"coast"

(ocean)"modelled/"literature"

54" 26"Clarke,L.R."and"Bennett,"D.H." 2007" kokanee"

crustacean"zooplankton" 4.6" 118.15" 25.685" Lake"Pend"

Oreille" modelled"

55" 27"Semenova,"A.S."and"Aleksandrov,"S.V." 2009"

herbivorous"zooplankton" phytoplankton" 0.585" 3.1" 5.299"

Curonian"Lagoon"of"the"Baltic"Sea""

empirical"and"estimates"

56" 28" Geller,"W" 1985" Daphnia" primary"production" 227" 600" 2.643" Lake"Constance" literature"empirical"and"estimates"