MacArthur Green Seabird PBA Report August 2015... · This report provides details of population...

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MacArthur Green Seabird PBA Report – August 2015

Appendix M to the Response submitted for Deadline IIA

Application Reference: EN010053

25 August 2015

Flamborough and Filey Coast pSPA

Seabird PVA Report

Prepared by: Dr. Mark Trinder Reviewed by: Prof. Bob Furness Date: 24

th August 2015

Tel: 0141 342 5404 Email: [email protected] Web: www.macarthurgreen.com Address: 95 South Woodside Road | Glasgow | G20 6NT

http://www.macarthurgreen.com/

Flamborough and Filey Coast pSPA PVA

MGL/MT/24-08-2015/1.2

Document Quality Record.

Version Status Authorised by Date

1.0 Draft Mark Trinder 14/07/2015

1.1 Minor Revisions Mark Trinder 5/08/2015

1.2 Revised content Mark Trinder 24/08/2015


CONTENTS

1. Introduction .................................................................................................................................... 4

2. Methods .......................................................................................................................................... 4

3. Results ................................................................................................................................................. 8

Gannet............................................................................................................................................... 10

Kittiwake ........................................................................................................................................... 10

Guillemot .......................................................................................................................................... 10

Razorbill ............................................................................................................................................ 11

Puffin ................................................................................................................................................. 11

4. Discussion ...................................................................................................................................... 11

Guidance on Interpretation .............................................................................................................. 11

Choice of demographic rate set .................................................................................................... 11

Density dependent or density independent ................................................................................. 12

References ............................................................................................................................................ 14

APPENDIX 1 – Figures ............................................................................................................................ 15

APPENDIX 2 - Tables .............................................................................................................................. 56


1. Introduction

This report provides details of population viability analysis (PVA) for five populations of seabirds

(gannet, kittiwake, guillemot, razorbill and puffin) which breed at the colonies which comprise the

Flamborough and Filey Coast (FFC) pSPA. The population models were developed using two

alternative sets of demographic rates; the first were obtained from a review of the literature for

these species (and used previously for modelling these populations; MacArthur Green 2014) and the

second were taken from a review conducted by the British Trust for Ornithology (BTO; Horswill and

Robinson 2015), combined with productivity data collected by the RSPB (Aitken et al. 2014). Full

details of the methods are provided below. The predicted change in population growth rate and the

ratio of the impacted to unimpacted population sizes are presented across a range of impact levels.

The discussion reviews the results and provides a guide for their interpretation.

2. Methods

The population models included the following aspects:

Environmental stochasticity;

Demographic stochasticity; and,

Density independent and density dependent formulations.

The models used a matrix formulation and simulated an annual post-breeding census over a period

of 25 annual time steps with the population made up of single year age classes up to adults, which is

a multi-age class for all individuals from age of first breeding and older. The initial population size

used for each species was the most recent count (as advised by Natural England; Table 1).

Table 1. Initial population sizes used in the modelling. The figures and sources were provided by Natural

England. Note that the guillemot and razorbill populations have been adjusted as per Harris (1989) to convert

from individuals on land to breeding pairs.

Species Initial population size

(breeding individuals) Year Source

Gannet 22122 2012 Census of breeding adults, Seabird Monitoring Programme

(SMP)

Kittiwake 89041 2008 Breeding adults for original SPA (SMP) plus RSPB counts for

terrestrial extension of SPA (2009-2011), unpublished.

Guillemot 83214 2008 Breeding adults for original SPA (SMP) plus RSPB counts for


Razorbill 21140 2008 Breeding adults for original SPA (SMP) plus RSPB counts for


Puffin 1960 2008 Breeding adults for original SPA (SMP) plus RSPB counts for


Two alternative sets of demographic rates were used. The first was obtained from an independent

review of published studies (see Table 3 for sources), while the second was taken from a recent

review conducted for the JNCC (Horswill and Robinson 2015; Table 2).


Table 2. Demographic rates used in the population models.

Model

Survival Reproduction

0-1 1-2 2-3 3-4 4-5 Adult Fledged young

per pair Age first breeding

GX1 Mean 0.42 0.829 0.891 0.895 - 0.919 0.77

5 SD 0.078 0.031 0.031 0.031 - 0.012 0.035

GX2 Mean 0.42 0.829 0.891 0.895 - 0.919 0.828*

5 SD 0.078 0.031 0.031 0.031 - 0.012 0.028

KI1 Mean 0.79 0.85 0.87 - - 0.882 0.672

4 SD 0.035 0.035 0.035 - - 0.035 0.3

KI2 Mean 0.790 0.854 0.854 - - 0.854 0.847*

4 SD 0.051 0.051 0.051 - - 0.051 0.219

GU1 Mean 0.56 0.792 0.917 0.938 - 0.965 0.68

5 SD 0.014 0.030 0.017 0.017 - 0.010 0.113

GU2 Mean 0.56 0.792 0.917 0.939 0.939 0.939 0.775*

6 SD 0.014 0.030 0.017 0.015 0.015 0.015 0.026

RA1 Mean 0.9 0.9 0.9 - - 0.9 0.63

4 SD 0.028 0.028 0.028 - - 0.028 0.085

RA2 Mean 0.63 0.63 0.895 0.895 - 0.895 0.683*

5 SD 0.209 0.209 0.067 0.067 - 0.067 0.056

PU1 Mean 0.924 0.924 0.924 0.924 - 0.924 0.67

5 SD 0.010 0.010 0.010 0.010 - 0.010 0.156

PU2 Mean 0.709 0.709 0.760 0.805 - 0.906 0.617

5 SD 0.083 0.083 0.083 0.083 - 0.083 0.151

* Reproduction data taken from Aitken et al. (2014) for the period 2009-2014. Table 3. Seabird demographic rate source literature for models with suffix ‘1’; models with suffix ‘2’ data from Horswill & Robinson (2015) and RSPB (Aitken et al. 2014).

Species Rate Source

Gannet

All survival rates Wanless et al. 2006

Age first breeding Nelson 2002

Reproduction WWT 2012 (Bempton specific value)

Population size SMP Database (2008)

Kittiwake

Juvenile survival Robinson 2005

Immature survival

Frederiksen et al. 2004. Age based survival rates from this study (see Fig 3

of source paper) were used to calibrate rates to match the juvenile and

adult rates.

Adult survival Robinson 2005

Age first breeding Robinson 2005

Reproduction JNCC database (this was cited as Mavor 2008).


Guillemot

All survival rates Harris et al. 2007

Age first breeding Birkhead and Hudson 1977



Razorbill

Adult survival Chapdelaine 1997 and Birkhead and Hudson 1977

Juvenile and

immature survival

Lloyd and Perrins 1977 (survival to breeding age estimated at 0.82, which

gives annual survival as 0.936 (0.82(1/3)

). Note that on the basis of the

literature annual sub-adult survival (0.936) is reported to be higher than

adult survival (0.9). This was considered unlikely and therefore a constant

rate of 0.9 for all age classes was assumed.


Species Rate Source

Age first breeding Robinson 2005



Puffin

All survival rates Harris et al. 1997

Age first breeding Birkhead and Hudson 1977



During population simulations, survival rates were drawn from beta distributions and the number of

fledged young from stretched beta distributions (Morris and Doak 2002). Use of these probability

distributions ensures that randomly selected values for each demographic rate are constrained to lie

within biologically reasonable bounds. Demographic stochasticity on survival was modelled using a

binomial process, whereby the number of individuals which survive from one year to the next is

obtained using a binomial function (Akçakaya 1991). Combining environmental and demographic

stochasticity in this manner permits both large scale effects (environmental) and chance population

effects (demographic) to be simulated.

Both density independent (DI) and density dependent (DD) versions of the models were developed.

The density independent versions simulate the populations with no feedback between population

size and demographic rates. Population projections produced by such models will either increase to

infinity or decrease to extinction.

Horswill and Robinson (2015) reviewed the evidence for density dependent regulation in seabird

populations and found that regulation can operate via a range of mechanisms. At the scale of the

populations being modelled for this report it is therefore likely that regulation may be operating on

different components of the populations by different means. Ecological theory suggests that long

lived slow breeding species, such as seabirds, buffer themselves against variations in their

environment through varying reproductive success rather than survival. Thus the demographic rate

most likely to reflect density dependent effects will be reproduction, with breeding success declining

as population approaches the ceiling set by food resources. Thus, it was considered more

appropriate to model regulation through reproduction rather than across multiple rates. This is also

more precautionary for assessing mortality impacts, since seabird population growth is more

sensitive to variation in survival (particularly of adults). Thus, the modelled population’s ability to

recover is lower when density dependence operates through reproduction than through survival.

Relating the reproductive rate to the population size also corresponds with studies which indicate

that foraging ranges are negatively related to food availability which in turn affects variations in

reproductive success between colonies. A wide range of values of density dependence could be

explored, but the aim of the work was to indicate the possible difference in output between a

biologically unrealistic density independent (worst case) scenario, and a plausible density dependent

model (more realistic but with a precautionary density dependent formulation in the absence of

empirical evidence on density dependent mechanisms in this population).

A Weibull function was used for the density dependent modelling. This function relates reproduction

(F) to population size (N) using the following equation:


F = maxF * exp(-a * (Nb))

Where maxF = the estimated biological maximum reproductive rate for the species being modelled

and a and b are scale and shape parameters (respectively) for the Weibull function.

Previous population modelling of these species (MacArthur Green 2014) reviewed available

evidence and determined that a precautionary, but realistic value for b was 1.2 as this generates

population trends similar to those observed for a range of seabird species and populations (Cury et

al. 2011). Following this, the value for a was calculated using the equation above with b = 1.2, F = to

the mean reproductive rate (Table 1), maxF = to each species’ estimated biological maximum (0.85

for gannet and auks, 1.25 for kittiwake) and N = to the initial population estimate (Table 1).

Estimating the value for a in this manner makes the assumption that the populations are currently at

their carrying capacity, and ensured that baseline simulations (i.e. with no additional mortality) were

tuned to remain around this size (although with variations due to stochastic variation in the

parameters). In practice, at the beginning of each simulation the model was run with incremental

adjustment to parameter a until the end population size (after 25 years) under baseline conditions

was close (within 0.5%) of the initial size. The value of a thus obtained was then used for predictive

simulations with increasing levels of additional mortality.

The density independent models were not tuned in this manner, with population predictions

generated on the basis of the rates in Table 2 with no adjustment.

For all species closed populations were assumed. This was a necessary simplification since rates of

exchange between colonies are unknown. While this is unrealistic, it was considered to be a

pragmatic and precautionary approach, since immigration from other colonies will tend to buffer

any additional mortality impact on the focal population. However, it should be noted that the gannet

population appears to have grown at a rate much higher than the density independent model

predicted. MacArthur Green (2014) conducted simulations to explore the potential role of

immigration in this growth. Starting from the 2000 population count, the number of sub-adults (the

final pre-breeding age class) present was multiplied by a constant inflation value to replicate

recruitment of birds into the breeding population. A range of immigration rates was trialled with the

aim of achieving a median population trend which matched recent AON counts (between 2004 and

2012). Summary results were presented from these validation simulations. Model predictions

assuming continued immigration at this level were included in the main results section (MacArthur

Green 2014), but are not reproduced here.

A range of additional mortality values was modelled, from zero to an upper value in excess of the

highest in-combination value under consideration for each species, at increments appropriate to the

species (e.g. 20-25). The additional mortality was modelled as a per capita rate. The rate was

calculated at the beginning of each simulation as the absolute mortality for that simulation divided

by the initial total population size. In this manner the estimated mortality in the starting year (e.g.

100 individual per year) remains in proportion with changes in the population size, such that if the

population doubles in size then the mortality rate also doubles (and vice versa). Furthermore, the

additional mortality was applied to all age classes in proportion to their presence (i.e. wind farm

mortality was not considered to target specific cage classes).


Although additional mortality was applied to all age classes, the outputs are presented in relation to

the adult component of the total. This keeps the outputs consistent with the units which breeding

colonies are counted in (e.g. breeding pairs). Thus, if a figure or table presents a mortality rate of

100 adults this actually represents a total mortality (for all age classes) which will be approximately

double this, since adults typically represent 50-60% of the population (as estimated from the stable

age distributions, Tables 4 and 5).

At each level of mortality, 5,000 simulations were conducted and summary outputs calculated. Most

outputs used data from all years of each simulation, however the population growth rate was

calculated as the average rate between the fifth and the final (25th) year to avoid initial conditions

exerting a bias on the value obtained. Note that since all the predictions use past data on

demographic parameters they therefore take no account of impacts of continuing climate change on

seabird demography.

Graphical and tabulated outputs for each simulated scenario are provided in Appendices 1 and 2:

Change in population growth rate, presented across the full mortality range for each species,

calculated at the following percentiles: 2.5%, 33% 50% (median), 67%, 97.5% (note that the

confidence intervals are two-sided, with 95% of simulated outputs lying between the 2.5%

and 97.5% lines); and,

Ratio of impacted population size to un-impacted size (Counterfactual of Population Size;

CPS) across the full mortality range for each species, calculated at 5 year intervals up to 25

years.

3. Results

The stable age distribution for each population and parameter set are provided in Tables 4 and 5 for

density independent and density dependent model runs respectively. Note that these represent the

average age distributions for each model as they were calculated using the average demographic

rates. During stochastic simulations the ratios will vary around these mean values. As density

dependence operates in the models through reproduction, differences in the age ratios between the

density independent and density dependent versions reflects modification to the rate of

reproduction (e.g. reduced reproduction will reduce the proportion of all sub-adult age classes and

increase the proportion of adults).

Table 4. Density independent stable age distributions for each population and parameter set.

Age

class

Population and parameter set

GX1 GX2 KI1 KI2 GU1 GU2 RA1 RA2 PU1 PU2

0-1 0.203 0.211 0.170 0.190 0.182 0.182 0.158 0.178 0.149 0.162

1-2 0.085 0.088 0.129 0.145 0.096 0.098 0.133 0.112 0.127 0.115

2-3 0.069 0.072 0.106 0.119 0.071 0.074 0.112 0.071 0.108 0.082

3-4 0.061 0.063 - - 0.062 0.065 - 0.064 0.092 0.063

4-5 - - - - - 0.058 - - - -

Adult 0.581 0.566 0.595 0.547 0.589 0.523 0.597 0.576 0.524 0.577


Table 5. Density dependent stable age distributions for each population and parameter set.

Age

class

Population and parameter set

GX1 GX2 KI1 KI2 GU1 GU2 RA1 RA2 PU1 PU2

0-1 0.185 0.186 0.136 0.157 0.079 0.119 0.101 0.187 0.077 0.171

1-2 0.078 0.079 0.107 0.124 0.044 0.066 0.091 0.118 0.071 0.121

2-3 0.065 0.065 0.091 0.106 0.035 0.053 0.082 0.074 0.066 0.086

3-4 0.058 0.058 - - 0.032 0.048 - 0.066 0.061 0.065

4-5 - - - - - 0.045 - - - -

Adult 0.614 0.613 0.666 0.612 0.810 0.669 0.727 0.556 0.726 0.557

A summary of the baseline and maximum impact results for each species using each set of

demographic rates, with and without density dependence operating is provided in Table 6. In each

case the second set of demographic rates generated lower growth rates in the density independent

cases, with the greatest differences for razorbill and puffin (change from positive to negative growth

under baseline conditions). The differences between the two demographic rate sets were much less

for the density dependent simulations due to the regulation on higher rates this imposed.

Table 6. Summary outputs from the population models for baseline simulations (0 additional mortality) and with the maximum simulated annual additional adult mortality.

Species

Maximum

additional

adult

mortality

Demographic

rate set

Density

dependence

Reduction in growth rate

at max. annual additional

mortality (%)

CPS 25 at max.

additional

mortality (%)

Gannet 500

1 Off 2.28 57.96

On 1.64 66.04

2 Off 2.29 57.78

On 1.65 65.96

Kittiwake 1600

1 Off 1.87 64.84

On 0.50 85.57

2 Off 1.88 64.78

On 0.54 84.49

Guillemot 1600

1 Off 2.04 62.89

On 0.96 77.16

2 Off 2.02 62.60

On 1.07 75.34

Razorbill 1600

1 Off 5.05 31.26

On 1.82 58.99

2 Off 4.73 31.24

On 4.18 35.12

Puffin 50

1 Off 2.77 53.80

On 0.89 76.67

2 Off 2.47 54.29

On 2.00 60.34


Gannet

Demographic rate sets 1 and 2 for gannet were very similar, and therefore the model results were

closely matched too. The density independent growth rates were predicted to decrease by 2.3% for

both rate sets at an annual adult mortality of 500. The equivalent reduction in growth for the density

dependent models was 1.6%.

The observed rate of increase in the number of gannet AON at Bempton has averaged 10% between

1985 and 2008 and 13% between 2000 and 2008. The maximum predicted growth rate for this

species is 9.9%, calculated using the method proposed by Niel & Lebreton (2005). Therefore, the

population appears to have grown at a rate similar to or above the predicted maximum. Previous

modelling has suggested that the population has undergone considerable net immigration which has

permitted the observed rate of growth (MacArthur Green 2014). This work indicated that

multiplying the number of sub-adults at each time step by 3.5 generated median predictions which

matched the number of AON since 2000 (i.e. immigration into this age class of 250%, which equates

to a rate of 15% when considered across all age classes).

Kittiwake

The density independent growth rates were predicted to decrease by 1.9% for both rate set 1 and 2

at an annual adult mortality of 1,600. The equivalent reduction in growth for the density dependent

models was 0.5%. Although there is some uncertainty about how the kittiwake population at

Bempton has changed since the 1970s (http://jncc.defra.gov.uk/page-2889), it seems likely that the

population has remained around 40,000 pairs for much of that time. This is close to the maximum

size for colonies of this species, suggesting strong competition for resources and colony size

limitation by density-dependence (Jovani et al. 2012). This would suggest that the population has

been regulated at this size (i.e. the population has been at the carrying capacity of the environment

for all of this time). This being the case the density dependent model would be expected to be the

more reliable model on which to base predictions. The reduction in growth rate predicted by the

density dependent model is very small when compared with the potential rate at which kittiwake

populations can grow; a maximum growth rate of 13.3% has been calculated for kittiwake (following

Niel and Lebreton 2005). This indicates that any reductions in population size which might be

predicted due to additional mortality can be expected to be balanced by reduced competition

allowing increases in other demographic rates such that the annual growth rate increases towards

the estimated maximum. In other words, populations subject to density dependent regulation are

effectively buffered against potentially negative effects which do not impinge on the limiting

resource.

Guillemot

The baseline density independent reduction in population growth rate predicted by the models was

just over 2%, with the density dependent equivalent around 1%. These compare with a rate of

increase of estimated pairs at FFC which has averaged 3% since 2000 and a maximum predicted

growth rate for this species of 7.1%, calculated using the method proposed by Niel & Lebreton

(2005). The less realistic density independent predictions for reduced growth would therefore

approximately offset the observed rate at which this population has grown (3%), and compares to

the estimated potential rate at which this species could recover from losses (7.1%). The predictions


from the more realistic density dependent model indicate much smaller maximum reductions are

likely (approx. 1%) which is much less than the potential recovery rate for this species.

Razorbill


around 5% for both rate sets, with the density dependent reductions between 1.8% (rate set 1 and

4% (rate set 2). This compares with a rate of increase of estimated pairs which has averaged 7.2%

since 2000 and a maximum predicted growth rate for this species of 9.7%, calculated using the

method proposed by Niel & Lebreton (2005). The less realistic density independent predictions for

reduced growth would therefore partially offset the observed rate at which this population has

grown (7.2%), and compares to the estimated potential rate at which this species could recover from

losses (9.7%). The predictions from the more realistic density dependent model indicate the

reductions are likely to be less than the potential recovery rate for this species.

Puffin


around 2.5% for both rate sets, while the density dependent reductions were 1% (rate set 1) and 2%

(rate set 2). The population is estimated to have declined from 2615 individuals to 1960 between

2000 and 2008, representing an average annual decline of 3.4%. However, puffin colonies are very

difficult to survey reliably, therefore this decline should be treated with caution. Furthermore, it is

not necessarily the case that this decline will continue. The maximum predicted growth rate for this

species is 9.7%, calculated using the method proposed by Niel & Lebreton (2005). Therefore, these

reductions are less than the potential rate at which this species could recover from losses.

4. Discussion

Guidance on Interpretation

Choice of demographic rate set

In the absence of density dependent regulation, for all species, there is little difference between the

two demographic rate sets in terms of the reduction in population growth rate obtained and the

ratio of impacted to unimpacted population sizes (CPS). For gannet, kittiwake and guillemot the

same is true for the comparison in density dependent outputs: there is little difference between rate

sets 1 and 2. This suggests that the results are relatively insensitive to the choice of rates used and

therefore either can be considered suitable for impact predictions. However, for razorbill and puffin

the density dependent results using rate set 2 predicted greater reductions in growth rate (approx

twice the reduction) than with rate set 1. Similarly the CPS is smaller for rate set 2 than for 1.

The razorbill population has also grown, at a rate similar to that obtained from the density

independent rate set 1 outputs, which suggests that rate set 1 may be more suitable for predictions.

However, the density dependent results from rate set 1 appear to be outliers when compared with

those obtained for both rate sets and either with or without density dependence, giving the smallest

magnitude of impact. Furthermore, rate set 1 for razorbill makes more assumptions about age

related survival than those in rate set 2. Overall, therefore, rate set 2 is considered more likely to be

reliable, although consideration should also be given rate set 1.


A similar pattern is apparent for puffin, with the density dependent rate set 1 results sitting outside

the range of the others. Thus, the same conclusion, that rate set 2 is more suitable but rate set 1

should also be considered, is proposed for this species.

Density dependent or density independent

Several of the populations included here (gannet, guillemot, razorbill) have increased in size

between recent censuses. Given these increases and on the assumption that they will continue, it

could be considered sensible to develop models which generate further increases in line with the

recent trends. In addition, since the density dependent model has been tuned to maintain the

current size, this could lead to a conclusion that the density independent models (which generate

continued increases) provide more realistic predictions. However, this conclusion is based on the

premise that the models should generate accurate predictions of future growth. Over the period of

projections (25 years) this is almost certainly an impossible aim, and indeed is not the intention. The

primary purpose of the modelling is to compare predictions with and without additional impacts.

We have confidence in the counterfactual (the difference between predicted numbers in the

absence of an impact and in the presence of an impact). However, a model aiming to predict actual

population size in the future would need to include estimates of how demographic parameters will

change in future. The present models do not do that, but are rather based on historic demographic

parameter values. Predicting future numbers would require estimates of how survival and

productivity will be influenced by anticipated climate change and by the dynamics of fish

populations, with stocks of large predatory fish recovering (as a consequence of conservation

measures) but continued harvest of forage fish such as sandeels and sprats. Predictive modelling of

population sizes in the absence of offshore wind farm impacts is not within the scope of the work

presented here.

Assessing the counterfactual leads to a more important requirement that the models provide robust

simulations of the population dynamics (i.e. how they change) but not of the actual population sizes

themselves. In this context, the key consideration is that underlying factors which regulate

populations are incorporated. These are included in the density dependent models, where

reproduction in any given year of a simulation reflects the population size on the basis that breeding

individuals compete (e.g. for breeding space, food, mates, etc.). Since the density independent

models lack this regulatory mechanism they are considered to be less suitable tools for the current

exercise since they lack any form of inherent regulation which will nearly always be present in

natural populations.

It must be stated that the density dependent models also have limitations. The density dependent

mechanism used has been assumed to apply to reproduction rather than survival and, as the

environment’s carrying capacity is unknown, it has been assumed that the carrying capacity is the

current population size. Neither of these assumptions is expected to be accurate, however they are

both more reasonable than assuming there is no limit to the population size as the density

independent models do. A density independent model will either predict continuous increase in a

population or continuous decline to extinction. Neither is realistic. It should also be noted that

modelling regulation of seabird populations through reproduction rather than survival represents a

precautionary mechanism. This is because losses to mortality can only be replaced through


increased numbers of fledglings which can only contribute to elevated population growth once they

reach maturity. Thus, there is both a time lag (to reach maturity) and also natural losses (younger

age classes suffer higher natural mortality) which reduce the degree of compensation. If density

dependence operates through survival, mortality losses are effectively immediately offset by

enhanced survival of the remaining population, and recovery is therefore much more closely linked

to losses.

Therefore, from the perspective of generating reasonable comparative predictions of novel impacts

the density dependent models are considered to be more reliable, whilst also retaining precaution.

Additional discussion on aspects of population modelling is provided in MacArthur Green (2014)

along with modelling outputs which explore variations in the strength of density dependence and

the potential role of immigration in the gannet population trend.


References

Aitken, D., Babcock, M., Clarkson, K. & Jeavons, R. (2014) Flamborough Head and Bempton Cliffs SPA

Seabird Monitoring Programme 2014 Report. Unpublished report.

Akçakaya, H. R. (1991). A method for simulating demographic stochasticity. Ecological Modelling 54:

133-136.

Cury P. M., Boyd I., Bonhommeau S., Anker-Nilssen T., Crawford R. J. M., Furness R. W., Mills J. A., et

al. (2011). Global seabird response to forage fish depletion: one-third for the birds. Science 334:

1703–1706.

Frederiksen, M., Wanless, S. & Harris, M. P., (2004). Estimating true age–dependence in survival

when only adults can be observed: an example with Black–legged Kittiwakes. Animal Biodiversity

and Conservation, 27.1: 541–548.

Horswill, C. & Robinson R. A. (2015). Review of seabird demographic rates and density dependence. JNCC Report No. 552. Joint Nature Conservation Committee, Peterborough Harris, M.P. (1989). Variation in the correction factor used for converting counts of individual guillemots Uria aalge into breeding pairs. Ibis 131: 85-93. Jovani, R., Schielzeth, H., Mavor, R. and Oro, D. (2012). Specificity of grouping behaviour: comparing

colony sizes for the same seabird species in distant populations. J. Avian Biol.43: 397–402. MacArthur Green (2014). Hornsea Offshore Wind Farm Project One Updated PVA Note. Appendix N to the Response submitted for DeadlineIV Application Reference: EN010033 14 May 2014: Flamborough and Filey Coast pSPA Seabird PVA Final Report (http://infrastructure.planninginspectorate.gov.uk/wp-content/ipc/uploads/projects/EN010033/2.%20Post-Submission/Representations/Additional%20Representations/14-05-2014%20-%20Deadline%20V/Appendix%20N.%20Updated%20PVA%20Note.pdf) – accessed 14/07/2015

Mavor, R.A., Heubeck, M., Schmitt, S. and Parsons, M. (2008). Seabird numbers and breeding success in Britain and Ireland, (2006). JNCC. Peterborough. (UK Nature Conservation, No. 31).

Morris, W.F. and Doak, D.F. (2002). Quantitative conservation biology: theory and practice of population viability analysis. Sinauer, MA.

Robinson, R.A. (2005) BirdFacts: profiles of birds occurring in Britain & Ireland (BTO Research Report 407). BTO, Thetford

http://infrastructure.planninginspectorate.gov.uk/wp-content/ipc/uploads/projects/EN010033/2.%20Post-Submission/Representations/Additional%20Representations/14-05-2014%20-%20Deadline%20V/Appendix%20N.%20Updated%20PVA%20Note.pdf





APPENDIX 1 – Figures

Key to figure numbers. Species Demographic

rate set Density dependence Figure

numbers

Gannet 1 Density independent 1 to 2

Density dependent 3 to 4

2 Density independent 5 to 6


Kittiwake 1 Density independent 9 to 10




Guillemot 1 Density independent 17 to 18




Razorbill 1 Density independent 25 to 26




Puffin 1 Density independent 33 to 34





Figure A1.1 Gannet: Density independent model. Change in population growth rate.

0 100 200 300 400 500

-0.03

-0.02

-0.01

0.00

Median

2.5%

97.5%

33%

66%

Additional adult mortality

Ch

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ate

GX1, breeding, Density Independent.

Change in population growth rate.


Figure A1.2 Gannet - breeding: Density independent model. Median population size at 5 year

intervals as a proportion of un-impacted median population size.

0 100 200 300 400 500

0.0

0.2

0.4

0.6

0.8

1.0


Pre

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me

dia

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as p

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ort

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of u

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mp

acte

d p

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ula

tio

n

5 yrs

10 yrs

15 yrs

20 yrs

25 yrs


Population size at 5 yr intervals as proportion of un-impacted population

breeding.


Figure A1.3 Gannet: Density dependent model. Change in population growth rate.

0 100 200 300 400 500

-0.020

-0.015

-0.010

-0.005

0.000

0.005

Median

2.5%

97.5%

33%

66%


Ch

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in

po

pu

latio

n g

row

th r

ate

GX1, breeding, Density Dependent: Weibull b=1.2 .



Figure A1.4 Gannet - breeding: Density dependent model. Median population size at 5 year intervals

as a proportion of un-impacted median population size.

0 100 200 300 400 500

0.0

0.2

0.4

0.6

0.8

1.0


Pre

dic

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me

dia

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of u

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5 yrs

10 yrs

15 yrs

20 yrs

25 yrs



breeding.


Figure A1.5 Gannet: Density independent model. Change in population growth rate.

0 100 200 300 400 500

-0.03

-0.02

-0.01

0.00

Median

2.5%

97.5%

33%

66%


Ch

an

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in

po

pu

latio

n g

row

th r

ate




Figure A1.6 Gannet - breeding: Density independent model. Median population size at 5 year


0 100 200 300 400 500

0.0

0.2

0.4

0.6

0.8

1.0


Pre

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me

dia

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as p

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of u

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5 yrs

10 yrs

15 yrs

20 yrs

25 yrs



breeding.


Figure A1.7 Gannet: Density dependent model. Change in population growth rate.

0 100 200 300 400 500

-0.020

-0.015

-0.010

-0.005

0.000

0.005

Median

2.5%

97.5%

33%

66%


Ch

an

ge

in

po

pu

latio

n g

row

th r

ate




Figure A1.8 Gannet - breeding: Density dependent model. Median population size at 5 year intervals


0 100 200 300 400 500

0.0

0.2

0.4

0.6

0.8

1.0


Pre

dic

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me

dia

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of u

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5 yrs

10 yrs

15 yrs

20 yrs

25 yrs



breeding.


Figure A1.9 Kittiwake: Density independent model. Change in population growth rate.

0 500 1000 1500

-0.03

-0.02

-0.01

0.00

0.01

Median

2.5%

97.5%

33%

66%


Ch

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in

po

pu

latio

n g

row

th r

ate

KI1, breeding, Density Independent.



Figure A1.10 Kittiwake - breeding: Density independent model. Median population size at 5 year


0 500 1000 1500

0.0

0.2

0.4

0.6

0.8

1.0


Pre

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me

dia

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as p

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of u

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d p

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tio

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5 yrs

10 yrs

15 yrs

20 yrs

25 yrs



breeding.


Figure A1.11 Kittiwake: Density dependent model. Change in population growth rate.

0 500 1000 1500

-0.010

-0.005

0.000

0.005

Median

2.5%

97.5%

33%

66%


Ch

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ge

in

po

pu

latio

n g

row

th r

ate

KI1, breeding, Density Dependent: Weibull b=1.2 .



Figure A1.12 Kittiwake - breeding: Density dependent model. Median population size at 5 year


0 500 1000 1500

0.0

0.2

0.4

0.6

0.8

1.0


Pre

dic

ted

me

dia

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ort

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of u

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tio

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5 yrs

10 yrs15 yrs20 yrs25 yrs



breeding.


Figure A1.13 Kittiwake: Density independent model. Change in population growth rate.

0 500 1000 1500

-0.03

-0.02

-0.01

0.00

0.01

0.02

Median

2.5%

97.5%

33%

66%


Ch

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in

po

pu

latio

n g

row

th r

ate




Figure A1.14 Kittiwake - breeding: Density independent model. Median population size at 5 year


0 500 1000 1500

0.0

0.2

0.4

0.6

0.8

1.0


Pre

dic

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me

dia

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as p

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ort

ion

of u

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mp

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d p

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ula

tio

n

5 yrs

10 yrs

15 yrs

20 yrs

25 yrs



breeding.


Figure A1.15 Kittiwake: Density dependent model. Change in population growth rate.

0 500 1000 1500

-0.015

-0.010

-0.005

0.000

0.005

0.010

Median

2.5%

97.5%

33%

66%


Ch

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in

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latio

n g

row

th r

ate




Figure A1.16 Kittiwake - breeding: Density dependent model. Median population size at 5 year


0 500 1000 1500

0.0

0.2

0.4

0.6

0.8

1.0


Pre

dic

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me

dia

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as p

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ort

ion

of u

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mp

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d p

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tio

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5 yrs

10 yrs15 yrs20 yrs25 yrs



breeding.


Figure A1.17 Guillemot: Density independent model. Change in population growth rate.

0 500 1000 1500

-0.025

-0.020

-0.015

-0.010

-0.005

0.000

Median

2.5%

97.5%

33%

66%


Ch

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in

po

pu

latio

n g

row

th r

ate

GU1, breeding, Density Independent.



Figure A1.18 Guillemot - breeding: Density independent model. Median population size at 5 year


0 500 1000 1500

0.0

0.2

0.4

0.6

0.8

1.0


Pre

dic

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me

dia

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as p

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ort

ion

of u

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d p

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tio

n

5 yrs

10 yrs

15 yrs

20 yrs

25 yrs



breeding.


Figure A1.19 Guillemot: Density dependent model. Change in population growth rate.

0 500 1000 1500

-0.010

-0.005

0.000

Median

2.5%

97.5%

33%

66%


Ch

an

ge

in

po

pu

latio

n g

row

th r

ate

GU1, breeding, Density Dependent: Weibull b=1.2 .



Figure A1.20 Guillemot - breeding: Density dependent model. Median population size at 5 year


0 500 1000 1500

0.0

0.2

0.4

0.6

0.8

1.0


Pre

dic

ted

me

dia

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as p

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ort

ion

of u

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tio

n

5 yrs

10 yrs

15 yrs20 yrs25 yrs



breeding.


Figure A1.21 Guillemot: Density independent model. Change in population growth rate.

0 500 1000 1500

-0.025

-0.020

-0.015

-0.010

-0.005

0.000

0.005

Median

2.5%

97.5%

33%

66%


Ch

an

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in

po

pu

latio

n g

row

th r

ate




Figure A1.22 Guillemot - breeding: Density independent model. Median population size at 5 year


0 500 1000 1500

0.0

0.2

0.4

0.6

0.8

1.0


Pre

dic

ted

me

dia

n p

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as p

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ort

ion

of u

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5 yrs

10 yrs

15 yrs

20 yrs

25 yrs



breeding.


Figure A1.23 Guillemot: Density dependent model. Change in population growth rate.

0 500 1000 1500

-0.010

-0.005

0.000

Median

2.5%

97.5%

33%

66%


Ch

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in

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latio

n g

row

th r

ate




Figure A1.24 Guillemot - breeding: Density dependent model. Median population size at 5 year


0 500 1000 1500

0.0

0.2

0.4

0.6

0.8

1.0


Pre

dic

ted

me

dia

n p

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ize

as p

rop

ort

ion

of u

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acte

d p

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ula

tio

n

5 yrs

10 yrs

15 yrs

20 yrs25 yrs



breeding.


Figure A1.25 Razorbill: Density independent model. Change in population growth rate.

0 200 400 600 800 1000

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0.00

0.01

Median

2.5%

97.5%

33%

66%


Ch

an

ge

in

po

pu

latio

n g

row

th r

ate

RA1, breeding, Density Independent.



Figure A1.26 Razorbill - breeding: Density independent model. Median population size at 5 year


0 200 400 600 800 1000

0.0

0.2

0.4

0.6

0.8

1.0


Pre

dic

ted

me

dia

n p

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as p

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ort

ion

of u

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mp

acte

d p

op

ula

tio

n

5 yrs

10 yrs

15 yrs

20 yrs

25 yrs



breeding.


Figure A1.27 Razorbill: Density dependent model. Change in population growth rate.

0 200 400 600 800 1000

-0.025

-0.020

-0.015

-0.010

-0.005

0.000

0.005

Median

2.5%

97.5%

33%

66%


Ch

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ge

in

po

pu

latio

n g

row

th r

ate

RA1, breeding, Density Dependent: Weibull b=1.2 .



Figure A1.28 Razorbill - breeding: Density dependent model. Median population size at 5 year


0 200 400 600 800 1000

0.0

0.2

0.4

0.6

0.8

1.0


Pre

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me

dia

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as p

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ort

ion

of u

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5 yrs

10 yrs

15 yrs

20 yrs25 yrs



breeding.


Figure A1.29 Razorbill: Density independent model. Change in population growth rate.

0 200 400 600 800 1000

-0.06

-0.04

-0.02

0.00

0.02

Median

2.5%

97.5%

33%

66%


Ch

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latio

n g

row

th r

ate




Figure A1.30 Razorbill - breeding: Density independent model. Median population size at 5 year


0 200 400 600 800 1000

0.0

0.2

0.4

0.6

0.8

1.0


Pre

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me

dia

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as p

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of u

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5 yrs

10 yrs

15 yrs

20 yrs

25 yrs



breeding.


Figure A1.31 Razorbill: Density dependent model. Change in population growth rate.

0 200 400 600 800 1000

-0.06

-0.04

-0.02

0.00

0.02

Median

2.5%

97.5%

33%

66%


Ch

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Figure A1.32 Razorbill - breeding: Density dependent model. Median population size at 5 year


0 200 400 600 800 1000

0.0

0.2

0.4

0.6

0.8

1.0


Pre

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me

dia

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of u

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5 yrs

10 yrs

15 yrs

20 yrs

25 yrs



breeding.


Figure A1.33 Puffin: Density independent model. Change in population growth rate.

0 10 20 30 40 50

-0.030

-0.025

-0.020

-0.015

-0.010

-0.005

0.000

0.005

Median

2.5%

97.5%

33%

66%


Ch

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in

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pu

latio

n g

row

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PU1, breeding, Density Independent.



Figure A1.34 Puffin - breeding: Density independent model. Median population size at 5 year


0 10 20 30 40 50

0.0

0.2

0.4

0.6

0.8

1.0


Pre

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me

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ort

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of u

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tio

n

5 yrs

10 yrs

15 yrs

20 yrs

25 yrs



breeding.


Figure A1.35 Puffin: Density dependent model. Change in population growth rate.

0 10 20 30 40 50

-0.010

-0.005

0.000

Median

2.5%

97.5%

33%

66%


Ch

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in

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pu

latio

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row

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PU1, breeding, Density Dependent: Weibull b=1.2 .



Figure A1.36 Puffin - breeding: Density dependent model. Median population size at 5 year intervals


0 10 20 30 40 50

0.0

0.2

0.4

0.6

0.8

1.0


Pre

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me

dia

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ort

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of u

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5 yrs

10 yrs

15 yrs20 yrs25 yrs



breeding.


Figure A1.37 Puffin: Density independent model. Change in population growth rate.

0 10 20 30 40 50

-0.06

-0.04

-0.02

0.00

0.02

Median

2.5%

97.5%

33%

66%


Ch

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row

th r

ate




Figure A1.38 Puffin - breeding: Density independent model. Median population size at 5 year


0 10 20 30 40 50

0.0

0.2

0.4

0.6

0.8

1.0


Pre

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me

dia

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of u

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5 yrs

10 yrs

15 yrs

20 yrs

25 yrs



breeding.


Figure A1.39 Puffin: Density dependent model. Change in population growth rate.

0 10 20 30 40 50

-0.04

-0.03

-0.02

-0.01

0.00

0.01

0.02

Median

2.5%

97.5%

33%

66%


Ch

an

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in

po

pu

latio

n g

row

th r

ate




Figure A1.40 Puffin - breeding: Density dependent model. Median population size at 5 year intervals


0 10 20 30 40 50

0.0

0.2

0.4

0.6

0.8

1.0


Pre

dic

ted

me

dia

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ize

as p

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ort

ion

of u

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5 yrs

10 yrs

15 yrs

20 yrs

25 yrs



breeding.


APPENDIX 2 - Tables

Key to table numbers. Species Demographic

rate set Density dependence Table

numbers

Gannet 1 Density independent 1 to 2




Kittiwake 1 Density independent 9 to 10




Guillemot 1 Density independent 17 to 18




Razorbill 1 Density independent 25 to 26




Puffin 1 Density independent 33 to 34





Table A2.1 GX1, breeding, Density Independent. Change in population growth rate.

Additional adult mortality Change in median growth rate Lower 95% c.i. Upper 95% c.i.

0 0.00000 -0.00729 0.007383

25 -0.00106 -0.00849 0.006188

50 -0.00229 -0.00974 0.005083

75 -0.00331 -0.01067 0.003791

100 -0.00450 -0.01189 0.002768

125 -0.00565 -0.01301 0.001281

150 -0.00678 -0.01420 0.000457

175 -0.00795 -0.01508 -0.000969

200 -0.00912 -0.01657 -0.002130

225 -0.01029 -0.01759 -0.003217

250 -0.01138 -0.01845 -0.004218

275 -0.01262 -0.01970 -0.005348

300 -0.01370 -0.02080 -0.006782

325 -0.01484 -0.02170 -0.007672

350 -0.01596 -0.02341 -0.008970

375 -0.01715 -0.02393 -0.010171

400 -0.01829 -0.02551 -0.011405

425 -0.01940 -0.02656 -0.012442

450 -0.02049 -0.02762 -0.013702

475 -0.02183 -0.02880 -0.014889

500 -0.02281 -0.02974 -0.016171


Table A2.2 GX1, breeding, Density Independent. Ratio of median population sizes at 5 year intervals.

Additional adult mortality 5th. yr. 10th. yr. 15th. yr. 20th. yr. 25th. yr.

0 1.000 1.000 1.000 1.000 1.000

25 0.998 0.991 0.985 0.982 0.975

50 0.992 0.980 0.970 0.959 0.947

75 0.987 0.970 0.954 0.938 0.923

100 0.983 0.959 0.940 0.920 0.898

125 0.979 0.951 0.925 0.899 0.874

150 0.975 0.941 0.909 0.881 0.851

175 0.970 0.932 0.896 0.861 0.828

200 0.966 0.922 0.882 0.844 0.806

225 0.961 0.910 0.868 0.826 0.783

250 0.957 0.903 0.855 0.809 0.763

275 0.953 0.894 0.842 0.790 0.741

300 0.948 0.884 0.827 0.773 0.721

325 0.943 0.875 0.814 0.758 0.703

350 0.940 0.868 0.800 0.740 0.684

375 0.935 0.857 0.788 0.724 0.664

400 0.931 0.849 0.776 0.710 0.648

425 0.928 0.842 0.765 0.695 0.631

450 0.922 0.831 0.752 0.678 0.612

475 0.918 0.822 0.739 0.662 0.594

500 0.914 0.814 0.727 0.649 0.580


Table A2.3 GX1, breeding, Density Dependent: Weibull b=1.2 . Change in population growth rate.


0 0.000000 -0.00515 0.005113

25 -0.000655 -0.00598 0.004397

50 -0.001467 -0.00674 0.003696

75 -0.002170 -0.00743 0.003017

100 -0.002990 -0.00806 0.002208

125 -0.003699 -0.00916 0.001109

150 -0.004543 -0.00987 0.000398

175 -0.005328 -0.01059 -0.000288

200 -0.006118 -0.01131 -0.001037

225 -0.006977 -0.01226 -0.001952

250 -0.007666 -0.01296 -0.002544

275 -0.008604 -0.01415 -0.003440

300 -0.009449 -0.01483 -0.004278

325 -0.010232 -0.01567 -0.005070

350 -0.011096 -0.01656 -0.005900

375 -0.011979 -0.01734 -0.006748

400 -0.012851 -0.01851 -0.007702

425 -0.013737 -0.01929 -0.008457

450 -0.014593 -0.02016 -0.009359

475 -0.015487 -0.02101 -0.010168

500 -0.016421 -0.02204 -0.011143


Table A2.4 GX1, breeding, Density Dependent: Weibull b=1.2 . Ratio of median population sizes at 5

year intervals.


0 1.000 1.000 1.000 1.000 1.000

25 0.996 0.992 0.988 0.987 0.984

50 0.992 0.982 0.975 0.968 0.963

75 0.988 0.975 0.963 0.954 0.946

100 0.984 0.966 0.950 0.938 0.926

125 0.979 0.957 0.937 0.922 0.910

150 0.976 0.949 0.925 0.907 0.890

175 0.971 0.940 0.913 0.891 0.871

200 0.967 0.932 0.901 0.876 0.855

225 0.964 0.923 0.890 0.862 0.837

250 0.959 0.915 0.878 0.848 0.822

275 0.955 0.908 0.868 0.833 0.804

300 0.952 0.899 0.854 0.818 0.787

325 0.947 0.892 0.845 0.805 0.771

350 0.943 0.883 0.832 0.791 0.754

375 0.940 0.875 0.821 0.777 0.738

400 0.935 0.867 0.810 0.763 0.721

425 0.931 0.860 0.799 0.749 0.706

450 0.928 0.852 0.788 0.736 0.692

475 0.923 0.843 0.777 0.722 0.675

500 0.920 0.837 0.767 0.710 0.660


Table A2.5 GX2, breeding, Density Independent. Change in population growth rate.


0 0.000000 -0.00728 0.007601

25 -0.000956 -0.00874 0.006518

50 -0.002127 -0.00964 0.005092

75 -0.003313 -0.01080 0.004072

100 -0.004500 -0.01192 0.002651

125 -0.005602 -0.01311 0.001596

150 -0.006805 -0.01404 0.000814

175 -0.007768 -0.01521 -0.000685

200 -0.009081 -0.01663 -0.001556

225 -0.010165 -0.01767 -0.003008

250 -0.011345 -0.01868 -0.004021

275 -0.012472 -0.01985 -0.005229

300 -0.013593 -0.02098 -0.006373

325 -0.014797 -0.02205 -0.007526

350 -0.015992 -0.02340 -0.008904

375 -0.017114 -0.02423 -0.010014

400 -0.018242 -0.02549 -0.010970

425 -0.019316 -0.02650 -0.012263

450 -0.020501 -0.02763 -0.013395

475 -0.021681 -0.02890 -0.014746

500 -0.022934 -0.03030 -0.015866


Table A2.6 GX2, breeding, Density Independent. Ratio of median population sizes at 5 year intervals.


0 1.000 1.000 1.000 1.000 1.000

25 0.994 0.987 0.983 0.980 0.975

50 0.991 0.979 0.968 0.958 0.950

75 0.987 0.969 0.953 0.936 0.923

100 0.983 0.960 0.938 0.918 0.899

125 0.977 0.950 0.923 0.897 0.874

150 0.973 0.941 0.909 0.877 0.850

175 0.968 0.931 0.897 0.861 0.830

200 0.965 0.923 0.881 0.842 0.807

225 0.960 0.911 0.868 0.823 0.784

250 0.956 0.903 0.851 0.804 0.762

275 0.952 0.894 0.841 0.789 0.743

300 0.947 0.885 0.826 0.771 0.723

325 0.943 0.873 0.811 0.755 0.703

350 0.938 0.865 0.799 0.738 0.683

375 0.934 0.858 0.787 0.722 0.664

400 0.929 0.847 0.773 0.706 0.646

425 0.926 0.841 0.763 0.693 0.631

450 0.921 0.831 0.751 0.677 0.613

475 0.917 0.822 0.737 0.661 0.595

500 0.913 0.813 0.725 0.646 0.578


Table A2.7 GX2, breeding, Density Dependent: Weibull b=1.2 . Change in population growth rate.


0 0.00000 -0.00509 0.004887

25 -0.00070 -0.00602 0.004301

50 -0.00142 -0.00670 0.003612

75 -0.00219 -0.00750 0.002892

100 -0.00302 -0.00835 0.002084

125 -0.00377 -0.00919 0.001406

150 -0.00460 -0.00984 0.000278

175 -0.00541 -0.01079 -0.000387

200 -0.00618 -0.01161 -0.000968

225 -0.00695 -0.01238 -0.002045

250 -0.00786 -0.01324 -0.002622

275 -0.00874 -0.01392 -0.003486

300 -0.00954 -0.01505 -0.004257

325 -0.01035 -0.01568 -0.005157

350 -0.01116 -0.01658 -0.006110

375 -0.01204 -0.01753 -0.006897

400 -0.01298 -0.01834 -0.007613

425 -0.01393 -0.01931 -0.008732

450 -0.01469 -0.02034 -0.009481

475 -0.01563 -0.02125 -0.010461

500 -0.01645 -0.02201 -0.011154


Table A2.8 GX2, breeding, Density Dependent: Weibull b=1.2 . Ratio of median population sizes at 5

year intervals.


0 1.000 1.000 1.000 1.000 1.000

25 0.995 0.991 0.987 0.984 0.982

50 0.990 0.982 0.975 0.969 0.964

75 0.989 0.976 0.963 0.954 0.947

100 0.982 0.966 0.949 0.936 0.925

125 0.979 0.958 0.938 0.921 0.907

150 0.975 0.950 0.926 0.906 0.890

175 0.972 0.941 0.913 0.892 0.873

200 0.967 0.932 0.901 0.875 0.854

225 0.963 0.925 0.891 0.861 0.837

250 0.958 0.916 0.877 0.844 0.818

275 0.955 0.908 0.865 0.831 0.802

300 0.951 0.900 0.854 0.817 0.786

325 0.947 0.892 0.844 0.803 0.769

350 0.942 0.884 0.832 0.790 0.753

375 0.938 0.876 0.821 0.775 0.736

400 0.934 0.866 0.808 0.760 0.720

425 0.931 0.859 0.799 0.748 0.704

450 0.926 0.851 0.786 0.735 0.690

475 0.923 0.843 0.777 0.721 0.674

500 0.919 0.836 0.766 0.708 0.660


Table A2.9 KI1, breeding, Density Independent. Change in population growth rate.


0 0.000000 -0.0151 0.014621

50 -0.000598 -0.0154 0.014059

100 -0.001277 -0.0159 0.013296

150 -0.001584 -0.0164 0.012577

200 -0.002412 -0.0180 0.012032

250 -0.002885 -0.0172 0.011517

300 -0.003556 -0.0181 0.010688

350 -0.004016 -0.0189 0.009745

400 -0.004686 -0.0195 0.009523

450 -0.005285 -0.0197 0.008697

500 -0.005931 -0.0212 0.008012

550 -0.006593 -0.0213 0.007571

600 -0.006844 -0.0216 0.007770

650 -0.007661 -0.0222 0.006031

700 -0.008307 -0.0232 0.006284

750 -0.008627 -0.0235 0.005457

800 -0.009500 -0.0239 0.004512

850 -0.009893 -0.0248 0.004333

900 -0.010350 -0.0258 0.003759

950 -0.011000 -0.0254 0.003204

1000 -0.011801 -0.0264 0.002759

1050 -0.012127 -0.0278 0.001560

1100 -0.012735 -0.0275 0.001284

1150 -0.013446 -0.0276 0.000274

1200 -0.013799 -0.0293 -0.000130

1250 -0.014766 -0.0296 -0.000208

1300 -0.015111 -0.0299 -0.001217

1350 -0.015575 -0.0300 -0.001792

1400 -0.016334 -0.0312 -0.002042

1450 -0.016858 -0.0315 -0.002964

1500 -0.017466 -0.0323 -0.004225

1550 -0.017944 -0.0328 -0.004030

1600 -0.018651 -0.0327 -0.004938


Table A2.10 KI1, breeding, Density Independent. Ratio of median population sizes at 5 year intervals.


0 1.000 1.000 1.000 1.000 1.000

50 0.999 0.999 0.998 0.995 0.993

100 0.997 0.991 0.987 0.981 0.979

150 0.994 0.989 0.980 0.970 0.968

200 0.991 0.980 0.973 0.962 0.951

250 0.990 0.977 0.967 0.952 0.938

300 0.987 0.972 0.956 0.940 0.926

350 0.983 0.965 0.949 0.928 0.911

400 0.980 0.961 0.940 0.918 0.898

450 0.978 0.955 0.934 0.911 0.888

500 0.978 0.951 0.925 0.901 0.875

550 0.976 0.944 0.918 0.891 0.861

600 0.975 0.944 0.914 0.883 0.856

650 0.972 0.934 0.902 0.868 0.838

700 0.968 0.934 0.897 0.860 0.827

750 0.967 0.928 0.893 0.855 0.823

800 0.964 0.922 0.883 0.841 0.807

850 0.961 0.918 0.876 0.836 0.797

900 0.958 0.912 0.869 0.825 0.787

950 0.957 0.909 0.864 0.819 0.778

1000 0.955 0.901 0.855 0.807 0.763

1050 0.955 0.899 0.849 0.800 0.755

1100 0.953 0.896 0.843 0.792 0.746

1150 0.949 0.888 0.832 0.780 0.732

1200 0.946 0.884 0.828 0.775 0.727

1250 0.944 0.881 0.822 0.764 0.712

1300 0.943 0.875 0.814 0.755 0.704

1350 0.941 0.871 0.811 0.748 0.698

1400 0.939 0.868 0.804 0.740 0.685

1450 0.939 0.863 0.800 0.734 0.677

1500 0.935 0.858 0.790 0.724 0.666

1550 0.933 0.855 0.786 0.718 0.659

1600 0.929 0.848 0.777 0.707 0.648


Table A2.11 KI1, breeding, Density Dependent: Weibull b=1.2 . Change in population growth rate.


0 0.000000 -0.00840 0.00843

50 -0.000193 -0.00876 0.00845

100 -0.000379 -0.00882 0.00827

150 -0.000335 -0.00884 0.00825

200 -0.000528 -0.00911 0.00796

250 -0.000619 -0.00902 0.00801

300 -0.000897 -0.00930 0.00795

350 -0.000961 -0.00935 0.00736

400 -0.000941 -0.00938 0.00756

450 -0.001377 -0.00966 0.00727

500 -0.001316 -0.00996 0.00714

550 -0.001690 -0.00978 0.00701

600 -0.001671 -0.01019 0.00666

650 -0.001834 -0.01007 0.00665

700 -0.002079 -0.01039 0.00662

750 -0.002132 -0.01076 0.00616

800 -0.002352 -0.01068 0.00605

850 -0.002510 -0.01098 0.00593

900 -0.002824 -0.01104 0.00584

950 -0.002749 -0.01113 0.00586

1000 -0.002900 -0.01103 0.00548

1050 -0.003280 -0.01160 0.00531

1100 -0.003201 -0.01154 0.00533

1150 -0.003405 -0.01175 0.00497

1200 -0.003598 -0.01160 0.00474

1250 -0.003706 -0.01193 0.00490

1300 -0.004007 -0.01242 0.00452

1350 -0.004011 -0.01253 0.00416

1400 -0.004266 -0.01256 0.00410

1450 -0.004484 -0.01290 0.00394

1500 -0.004601 -0.01293 0.00367

1550 -0.004754 -0.01307 0.00350

1600 -0.004989 -0.01310 0.00378


Table A2.12 KI1, breeding, Density Dependent: Weibull b=1.2 . Ratio of median population sizes at 5

year intervals.


0 1.000 1.000 1.000 1.000 1.000

50 0.999 0.995 0.996 0.994 0.998

100 0.998 0.994 0.991 0.989 0.992

150 0.994 0.988 0.987 0.986 0.988

200 0.994 0.987 0.985 0.983 0.986

250 0.992 0.983 0.981 0.979 0.980

300 0.989 0.978 0.975 0.973 0.972

350 0.988 0.977 0.972 0.966 0.968

400 0.986 0.975 0.969 0.967 0.967

450 0.985 0.968 0.963 0.959 0.959

500 0.983 0.966 0.961 0.955 0.957

550 0.981 0.963 0.957 0.950 0.952

600 0.979 0.962 0.954 0.948 0.948

650 0.977 0.959 0.949 0.943 0.942

700 0.975 0.955 0.943 0.937 0.935

750 0.975 0.952 0.938 0.933 0.934

800 0.973 0.951 0.937 0.930 0.929

850 0.971 0.945 0.934 0.925 0.923

900 0.968 0.942 0.929 0.921 0.918

950 0.967 0.940 0.925 0.918 0.916

1000 0.964 0.938 0.924 0.914 0.911

1050 0.963 0.933 0.917 0.909 0.904

1100 0.961 0.933 0.916 0.905 0.903

1150 0.961 0.928 0.910 0.900 0.896

1200 0.957 0.924 0.907 0.897 0.890

1250 0.955 0.922 0.903 0.892 0.889

1300 0.955 0.919 0.898 0.886 0.883

1350 0.954 0.917 0.895 0.883 0.880

1400 0.951 0.913 0.892 0.880 0.875

1450 0.951 0.910 0.888 0.874 0.869

1500 0.947 0.905 0.883 0.870 0.864

1550 0.946 0.905 0.881 0.868 0.860

1600 0.943 0.901 0.876 0.862 0.856


Table A2.13 KI2, breeding, Density Independent. Change in population growth rate.


0 0.00000 -0.0199 0.0188507

50 -0.00116 -0.0212 0.0167633

100 -0.00166 -0.0210 0.0173316

150 -0.00192 -0.0222 0.0160303

200 -0.00286 -0.0225 0.0161477

250 -0.00339 -0.0225 0.0152193

300 -0.00373 -0.0239 0.0145759

350 -0.00413 -0.0251 0.0144487

400 -0.00519 -0.0251 0.0134409

450 -0.00541 -0.0261 0.0128374

500 -0.00581 -0.0258 0.0123266

550 -0.00700 -0.0268 0.0117104

600 -0.00749 -0.0269 0.0105236

650 -0.00782 -0.0273 0.0102844

700 -0.00831 -0.0286 0.0102300

750 -0.00916 -0.0289 0.0092613

800 -0.00956 -0.0296 0.0084230

850 -0.01028 -0.0301 0.0081612

900 -0.01108 -0.0302 0.0072966

950 -0.01124 -0.0304 0.0065587

1000 -0.01214 -0.0310 0.0059212

1050 -0.01258 -0.0320 0.0055655

1100 -0.01305 -0.0326 0.0041668

1150 -0.01369 -0.0334 0.0045087

1200 -0.01448 -0.0345 0.0032658

1250 -0.01503 -0.0339 0.0033351

1300 -0.01538 -0.0349 0.0029443

1350 -0.01586 -0.0361 0.0020771

1400 -0.01656 -0.0359 0.0017104

1450 -0.01729 -0.0361 0.0010398

1500 -0.01793 -0.0376 -0.0000353

1550 -0.01822 -0.0375 -0.0000987

1600 -0.01882 -0.0377 -0.0014000


Table A2.14 KI2, breeding, Density Independent. Ratio of median population sizes at 5 year intervals.


0 1.000 1.000 1.000 1.000 1.000

50 0.999 0.990 0.990 0.983 0.980

100 0.995 0.989 0.980 0.973 0.967

150 0.996 0.983 0.973 0.964 0.958

200 0.992 0.977 0.962 0.953 0.944

250 0.993 0.977 0.958 0.943 0.934

300 0.988 0.967 0.951 0.933 0.922

350 0.986 0.963 0.947 0.927 0.907

400 0.984 0.962 0.938 0.915 0.894

450 0.979 0.954 0.933 0.906 0.884

500 0.978 0.951 0.918 0.894 0.872

550 0.975 0.941 0.913 0.885 0.857

600 0.974 0.941 0.907 0.875 0.847

650 0.970 0.932 0.901 0.867 0.838

700 0.973 0.934 0.901 0.863 0.831

750 0.968 0.928 0.885 0.849 0.815

800 0.964 0.921 0.880 0.842 0.807

850 0.966 0.917 0.874 0.833 0.793

900 0.959 0.907 0.860 0.817 0.776

950 0.961 0.909 0.863 0.815 0.775

1000 0.955 0.898 0.850 0.801 0.758

1050 0.955 0.898 0.845 0.796 0.753

1100 0.951 0.890 0.841 0.785 0.740

1150 0.950 0.887 0.834 0.783 0.732

1200 0.950 0.883 0.826 0.770 0.720

1250 0.949 0.882 0.822 0.767 0.710

1300 0.943 0.876 0.814 0.756 0.704

1350 0.942 0.869 0.807 0.746 0.691

1400 0.937 0.866 0.797 0.735 0.681

1450 0.937 0.864 0.797 0.733 0.674

1500 0.935 0.858 0.787 0.721 0.662

1550 0.934 0.853 0.781 0.715 0.656

1600 0.929 0.846 0.771 0.706 0.648


Table A2.15 KI2, breeding, Density Dependent: Weibull b=1.2 . Change in population growth rate.


0 0.000000 -0.00951 0.00967

50 -0.000056 -0.00950 0.00941

100 -0.000312 -0.01018 0.00917

150 -0.000556 -0.01016 0.00888

200 -0.000629 -0.01026 0.00862

250 -0.000813 -0.01052 0.00886

300 -0.000894 -0.01068 0.00904

350 -0.000938 -0.01108 0.00859

400 -0.001260 -0.01095 0.00808

450 -0.001334 -0.01117 0.00810

500 -0.001654 -0.01137 0.00781

550 -0.001722 -0.01149 0.00812

600 -0.001814 -0.01157 0.00783

650 -0.002028 -0.01192 0.00745

700 -0.002106 -0.01179 0.00704

750 -0.002289 -0.01241 0.00723

800 -0.002468 -0.01244 0.00712

850 -0.002668 -0.01244 0.00661

900 -0.002700 -0.01290 0.00687

950 -0.002937 -0.01285 0.00655

1000 -0.003253 -0.01355 0.00640

1050 -0.003331 -0.01329 0.00651

1100 -0.003592 -0.01314 0.00595

1150 -0.003665 -0.01392 0.00634

1200 -0.003991 -0.01368 0.00562

1250 -0.004161 -0.01415 0.00570

1300 -0.004226 -0.01414 0.00526

1350 -0.004466 -0.01442 0.00536

1400 -0.004605 -0.01453 0.00506

1450 -0.004947 -0.01471 0.00508

1500 -0.005072 -0.01525 0.00463

1550 -0.005273 -0.01544 0.00446

1600 -0.005433 -0.01529 0.00454


Table A2.16 KI2, breeding, Density Dependent: Weibull b=1.2 . Ratio of median population sizes at 5

year intervals.


0 1.000 1.000 1.000 1.000 1.000

50 0.995 0.996 0.994 0.993 0.992

100 0.995 0.994 0.990 0.991 0.987

150 0.995 0.991 0.988 0.984 0.982

200 0.991 0.985 0.980 0.980 0.979

250 0.989 0.984 0.978 0.978 0.973

300 0.987 0.983 0.977 0.974 0.969

350 0.987 0.977 0.969 0.969 0.967

400 0.984 0.977 0.966 0.962 0.959

450 0.981 0.970 0.961 0.959 0.955

500 0.980 0.970 0.957 0.952 0.948

550 0.978 0.965 0.954 0.949 0.944

600 0.975 0.963 0.951 0.946 0.941

650 0.975 0.960 0.947 0.943 0.937

700 0.972 0.956 0.943 0.935 0.931

750 0.970 0.951 0.937 0.931 0.926

800 0.970 0.949 0.934 0.925 0.920

850 0.969 0.946 0.933 0.924 0.917

900 0.964 0.943 0.925 0.918 0.913

950 0.964 0.938 0.924 0.913 0.908

1000 0.962 0.937 0.918 0.908 0.901

1050 0.959 0.932 0.913 0.905 0.896

1100 0.958 0.931 0.909 0.898 0.891

1150 0.955 0.925 0.906 0.895 0.887

1200 0.955 0.923 0.904 0.889 0.880

1250 0.953 0.922 0.899 0.886 0.878

1300 0.952 0.918 0.896 0.883 0.875

1350 0.950 0.916 0.891 0.875 0.869

1400 0.949 0.911 0.888 0.874 0.864

1450 0.947 0.909 0.882 0.868 0.857

1500 0.944 0.904 0.878 0.861 0.854

1550 0.942 0.903 0.875 0.858 0.845

1600 0.942 0.901 0.871 0.855 0.845


Table A2.17 GU1, breeding, Density Independent. Change in population growth rate.


0 0.000000 -0.00423 0.0037584

50 -0.000625 -0.00463 0.0032613

100 -0.001252 -0.00536 0.0026350

150 -0.001871 -0.00604 0.0019490

200 -0.002486 -0.00652 0.0013887

250 -0.003156 -0.00731 0.0007536

300 -0.003733 -0.00792 -0.0000349

350 -0.004409 -0.00851 -0.0005460

400 -0.005097 -0.00913 -0.0012592

450 -0.005743 -0.00981 -0.0019076

500 -0.006342 -0.01043 -0.0024302

550 -0.007012 -0.01100 -0.0033639

600 -0.007553 -0.01159 -0.0038442

650 -0.008215 -0.01226 -0.0044449

700 -0.008859 -0.01304 -0.0050824

750 -0.009514 -0.01350 -0.0057209

800 -0.010179 -0.01412 -0.0063211

850 -0.010849 -0.01488 -0.0070568

900 -0.011487 -0.01549 -0.0075924

950 -0.012149 -0.01627 -0.0082914

1000 -0.012744 -0.01672 -0.0090105

1050 -0.013358 -0.01748 -0.0095175

1100 -0.013985 -0.01810 -0.0101902

1150 -0.014643 -0.01865 -0.0108995

1200 -0.015311 -0.01940 -0.0115004

1250 -0.015954 -0.02020 -0.0121439

1300 -0.016597 -0.02063 -0.0127994

1350 -0.017261 -0.02116 -0.0134088

1400 -0.017795 -0.02171 -0.0140734

1450 -0.018444 -0.02263 -0.0147060

1500 -0.019129 -0.02315 -0.0153160

1550 -0.019772 -0.02378 -0.0160351

1600 -0.020355 -0.02437 -0.0166186


Table A2.18 GU1, breeding, Density Independent. Ratio of median population sizes at 5 year

intervals.


0 1.000 1.000 1.000 1.000 1.000

50 0.998 0.995 0.993 0.990 0.987

100 0.995 0.988 0.983 0.978 0.972

150 0.993 0.984 0.976 0.967 0.959

200 0.991 0.978 0.968 0.957 0.945

250 0.988 0.973 0.959 0.945 0.931

300 0.986 0.968 0.952 0.935 0.919

350 0.984 0.963 0.944 0.924 0.905

400 0.981 0.958 0.936 0.913 0.891

450 0.978 0.951 0.927 0.902 0.879

500 0.977 0.947 0.921 0.892 0.867

550 0.973 0.941 0.910 0.881 0.852

600 0.972 0.936 0.905 0.873 0.842

650 0.969 0.931 0.897 0.861 0.829

700 0.967 0.927 0.889 0.853 0.817

750 0.965 0.921 0.882 0.843 0.806

800 0.962 0.916 0.874 0.833 0.793

850 0.960 0.911 0.867 0.822 0.782

900 0.958 0.907 0.860 0.814 0.771

950 0.955 0.901 0.852 0.804 0.759

1000 0.953 0.897 0.845 0.795 0.749

1050 0.950 0.892 0.838 0.786 0.738

1100 0.948 0.887 0.831 0.777 0.727

1150 0.946 0.882 0.824 0.768 0.717

1200 0.943 0.877 0.816 0.759 0.706

1250 0.941 0.872 0.809 0.750 0.696

1300 0.939 0.867 0.803 0.742 0.686

1350 0.937 0.863 0.795 0.733 0.675

1400 0.935 0.858 0.790 0.726 0.666

1450 0.932 0.854 0.783 0.716 0.657

1500 0.930 0.849 0.776 0.708 0.647

1550 0.927 0.844 0.769 0.699 0.637

1600 0.925 0.839 0.763 0.692 0.629


Table A2.19 GU1, breeding, Density Dependent: Weibull b=1.2 . Change in population growth rate.


0 0.000000 -0.00278 0.002664

50 -0.000299 -0.00302 0.002313

100 -0.000569 -0.00335 0.002082

150 -0.000831 -0.00353 0.001758

200 -0.001117 -0.00391 0.001489

250 -0.001366 -0.00409 0.001231

300 -0.001687 -0.00447 0.000940

350 -0.001968 -0.00467 0.000610

400 -0.002293 -0.00502 0.000382

450 -0.002603 -0.00526 0.000104

500 -0.002825 -0.00554 -0.000196

550 -0.003144 -0.00581 -0.000522

600 -0.003437 -0.00612 -0.000873

650 -0.003708 -0.00638 -0.001114

700 -0.003995 -0.00667 -0.001369

750 -0.004278 -0.00703 -0.001715

800 -0.004614 -0.00736 -0.002048

850 -0.004842 -0.00753 -0.002244

900 -0.005208 -0.00794 -0.002609

950 -0.005525 -0.00828 -0.002941

1000 -0.005768 -0.00840 -0.003234

1050 -0.006107 -0.00885 -0.003418

1100 -0.006440 -0.00904 -0.003843

1150 -0.006703 -0.00946 -0.004086

1200 -0.007023 -0.00973 -0.004383

1250 -0.007341 -0.00995 -0.004776

1300 -0.007632 -0.01036 -0.005050

1350 -0.007988 -0.01072 -0.005392

1400 -0.008278 -0.01096 -0.005701

1450 -0.008600 -0.01136 -0.006054

1500 -0.008886 -0.01157 -0.006397

1550 -0.009208 -0.01195 -0.006752

1600 -0.009583 -0.01222 -0.007021


Table A2.20 GU1, breeding, Density Dependent: Weibull b=1.2 . Ratio of median population sizes at

5 year intervals.


0 1.000 1.000 1.000 1.000 1.000

50 0.998 0.996 0.995 0.993 0.993

100 0.996 0.992 0.989 0.987 0.985

150 0.994 0.988 0.984 0.979 0.977

200 0.991 0.984 0.978 0.972 0.969

250 0.989 0.981 0.973 0.967 0.963

300 0.988 0.976 0.967 0.959 0.955

350 0.985 0.973 0.962 0.954 0.947

400 0.984 0.968 0.957 0.947 0.940

450 0.981 0.965 0.951 0.940 0.932

500 0.979 0.961 0.946 0.934 0.925

550 0.978 0.957 0.941 0.928 0.918

600 0.976 0.953 0.936 0.922 0.911

650 0.974 0.949 0.929 0.915 0.903

700 0.971 0.945 0.924 0.908 0.897

750 0.970 0.941 0.919 0.902 0.890

800 0.968 0.938 0.915 0.896 0.882

850 0.965 0.933 0.909 0.890 0.876

900 0.964 0.930 0.904 0.884 0.868

950 0.962 0.926 0.898 0.876 0.860

1000 0.959 0.922 0.894 0.871 0.854

1050 0.957 0.917 0.887 0.865 0.847

1100 0.955 0.914 0.882 0.858 0.840

1150 0.953 0.910 0.877 0.851 0.833

1200 0.951 0.907 0.873 0.846 0.826

1250 0.950 0.903 0.868 0.840 0.820

1300 0.947 0.899 0.863 0.834 0.812

1350 0.946 0.896 0.857 0.828 0.805

1400 0.943 0.892 0.852 0.821 0.799

1450 0.941 0.887 0.847 0.815 0.792

1500 0.940 0.884 0.842 0.810 0.786

1550 0.937 0.880 0.837 0.804 0.779

1600 0.935 0.876 0.831 0.798 0.772


Table A2.21 GU2, breeding, Density Independent. Change in population growth rate.


0 0.000000 -0.00533 0.005065

50 -0.000735 -0.00616 0.004225

100 -0.001321 -0.00676 0.003857

150 -0.001907 -0.00727 0.002977

200 -0.002561 -0.00773 0.002479

250 -0.003143 -0.00843 0.001730

300 -0.003812 -0.00928 0.001231

350 -0.004414 -0.00957 0.000614

400 -0.005078 -0.01055 -0.000110

450 -0.005741 -0.01130 -0.000732

500 -0.006321 -0.01164 -0.001317

550 -0.006933 -0.01220 -0.001875

600 -0.007690 -0.01301 -0.002720

650 -0.008224 -0.01364 -0.003174

700 -0.008869 -0.01416 -0.003877

750 -0.009486 -0.01477 -0.004473

800 -0.010050 -0.01536 -0.005032

850 -0.010720 -0.01601 -0.005641

900 -0.011305 -0.01669 -0.006231

950 -0.011992 -0.01734 -0.006835

1000 -0.012626 -0.01795 -0.007492

1050 -0.013255 -0.01833 -0.008122

1100 -0.013788 -0.01898 -0.008827

1150 -0.014505 -0.01970 -0.009394

1200 -0.015093 -0.02031 -0.010024

1250 -0.015738 -0.02111 -0.010686

1300 -0.016291 -0.02144 -0.011278

1350 -0.016882 -0.02221 -0.011764

1400 -0.017611 -0.02288 -0.012512

1450 -0.018250 -0.02378 -0.013184

1500 -0.018845 -0.02415 -0.013955

1550 -0.019547 -0.02475 -0.014512

1600 -0.020239 -0.02537 -0.015219


Table A2.22 GU2, breeding, Density Independent. Ratio of median population sizes at 5 year

intervals.


0 1.000 1.000 1.000 1.000 1.000

50 0.998 0.993 0.989 0.986 0.984

100 0.995 0.989 0.983 0.977 0.971

150 0.993 0.983 0.974 0.964 0.957

200 0.991 0.977 0.966 0.955 0.945

250 0.988 0.972 0.959 0.944 0.931

300 0.985 0.968 0.950 0.932 0.916

350 0.983 0.962 0.942 0.921 0.904

400 0.981 0.956 0.933 0.911 0.890

450 0.978 0.952 0.926 0.901 0.878

500 0.976 0.947 0.918 0.890 0.865

550 0.974 0.942 0.911 0.880 0.853

600 0.972 0.936 0.902 0.867 0.838

650 0.969 0.931 0.895 0.859 0.827

700 0.966 0.925 0.887 0.849 0.815

750 0.965 0.921 0.881 0.840 0.804

800 0.962 0.916 0.874 0.831 0.793

850 0.959 0.912 0.866 0.821 0.781

900 0.957 0.906 0.858 0.812 0.769

950 0.956 0.901 0.850 0.803 0.759

1000 0.953 0.896 0.844 0.793 0.747

1050 0.951 0.891 0.836 0.784 0.737

1100 0.948 0.887 0.829 0.775 0.726

1150 0.946 0.881 0.822 0.766 0.714

1200 0.943 0.877 0.816 0.758 0.706

1250 0.942 0.872 0.809 0.749 0.694

1300 0.939 0.867 0.802 0.740 0.686

1350 0.938 0.863 0.796 0.732 0.676

1400 0.935 0.858 0.788 0.723 0.666

1450 0.932 0.853 0.780 0.714 0.655

1500 0.930 0.849 0.775 0.706 0.647

1550 0.928 0.843 0.767 0.698 0.636

1600 0.925 0.838 0.761 0.689 0.626


Table A2.23 GU2, breeding, Density Dependent: Weibull b=1.2 . Change in population growth rate.


0 0.000000 -0.00357 0.0033091

50 -0.000326 -0.00396 0.0030326

100 -0.000649 -0.00411 0.0027841

150 -0.000935 -0.00447 0.0023563

200 -0.001202 -0.00482 0.0020978

250 -0.001512 -0.00515 0.0017749

300 -0.001902 -0.00545 0.0015061

350 -0.002110 -0.00570 0.0013222

400 -0.002484 -0.00601 0.0009091

450 -0.002825 -0.00641 0.0005504

500 -0.003088 -0.00664 0.0002482

550 -0.003445 -0.00710 0.0000338

600 -0.003831 -0.00738 -0.0004863

650 -0.004075 -0.00767 -0.0006186

700 -0.004440 -0.00818 -0.0008615

750 -0.004719 -0.00826 -0.0012465

800 -0.005105 -0.00874 -0.0015295

850 -0.005444 -0.00905 -0.0019186

900 -0.005766 -0.00949 -0.0022597

950 -0.006086 -0.00977 -0.0025786

1000 -0.006402 -0.01026 -0.0029417

1050 -0.006729 -0.01040 -0.0031505

1100 -0.007123 -0.01083 -0.0036748

1150 -0.007416 -0.01114 -0.0039646

1200 -0.007808 -0.01128 -0.0042285

1250 -0.008141 -0.01177 -0.0047242

1300 -0.008513 -0.01227 -0.0050247

1350 -0.008870 -0.01260 -0.0053880

1400 -0.009276 -0.01303 -0.0056446

1450 -0.009591 -0.01327 -0.0061714

1500 -0.009973 -0.01371 -0.0064918

1550 -0.010307 -0.01407 -0.0067000

1600 -0.010716 -0.01447 -0.0071438


Table A2.24 GU2, breeding, Density Dependent: Weibull b=1.2 . Ratio of median population sizes at

5 year intervals.


0 1.000 1.000 1.000 1.000 1.000

50 0.998 0.995 0.994 0.992 0.991

100 0.997 0.992 0.989 0.985 0.984

150 0.994 0.989 0.984 0.979 0.977

200 0.992 0.984 0.977 0.972 0.969

250 0.990 0.980 0.971 0.965 0.961

300 0.989 0.977 0.967 0.958 0.951

350 0.985 0.972 0.961 0.952 0.945

400 0.984 0.968 0.955 0.944 0.936

450 0.981 0.964 0.949 0.937 0.928

500 0.979 0.959 0.944 0.930 0.921

550 0.977 0.955 0.938 0.923 0.912

600 0.976 0.951 0.931 0.915 0.904

650 0.973 0.947 0.926 0.910 0.897

700 0.972 0.943 0.920 0.902 0.888

750 0.970 0.940 0.916 0.897 0.882

800 0.967 0.935 0.909 0.889 0.874

850 0.965 0.931 0.905 0.883 0.866

900 0.963 0.927 0.898 0.875 0.858

950 0.961 0.922 0.893 0.868 0.850

1000 0.960 0.920 0.888 0.863 0.844

1050 0.957 0.915 0.883 0.856 0.836

1100 0.956 0.912 0.878 0.850 0.828

1150 0.953 0.907 0.872 0.842 0.821

1200 0.951 0.904 0.867 0.836 0.814

1250 0.949 0.900 0.861 0.830 0.806

1300 0.947 0.896 0.856 0.823 0.799

1350 0.945 0.892 0.850 0.817 0.791

1400 0.943 0.887 0.845 0.810 0.783

1450 0.940 0.883 0.838 0.803 0.776

1500 0.939 0.881 0.835 0.797 0.769

1550 0.937 0.876 0.829 0.791 0.761

1600 0.934 0.873 0.824 0.784 0.753


Table A2.25 RA1, breeding, Density Independent. Change in population growth rate.


0 0.00000 -0.0107 0.010183

50 -0.00251 -0.0136 0.007420

100 -0.00501 -0.0157 0.005175

150 -0.00757 -0.0183 0.002698

200 -0.01015 -0.0208 0.000207

250 -0.01238 -0.0229 -0.002222

300 -0.01502 -0.0260 -0.005161

350 -0.01777 -0.0283 -0.007930

400 -0.02019 -0.0307 -0.010095

450 -0.02275 -0.0333 -0.012792

500 -0.02505 -0.0357 -0.015341

550 -0.02771 -0.0386 -0.017565

600 -0.03006 -0.0404 -0.020440

650 -0.03280 -0.0436 -0.023320

700 -0.03541 -0.0458 -0.025835

750 -0.03787 -0.0482 -0.028246

800 -0.04048 -0.0507 -0.030546

850 -0.04297 -0.0535 -0.033330

900 -0.04532 -0.0559 -0.035856

950 -0.04798 -0.0586 -0.038382

1000 -0.05046 -0.0612 -0.040832


Table A2.26 RA1, breeding, Density Independent. Ratio of median population sizes at 5 year

intervals.


0 1.000 1.000 1.000 1.000 1.000

50 0.991 0.978 0.966 0.957 0.946

100 0.981 0.956 0.936 0.914 0.892

150 0.973 0.936 0.905 0.872 0.842

200 0.963 0.916 0.873 0.834 0.794

250 0.956 0.900 0.847 0.800 0.754

300 0.946 0.880 0.818 0.761 0.709

350 0.936 0.861 0.790 0.726 0.668

400 0.928 0.844 0.766 0.696 0.633

450 0.919 0.823 0.740 0.664 0.596

500 0.909 0.808 0.717 0.636 0.565

550 0.900 0.789 0.691 0.606 0.532

600 0.892 0.771 0.668 0.579 0.503

650 0.883 0.753 0.645 0.552 0.473

700 0.875 0.738 0.624 0.529 0.446

750 0.867 0.723 0.603 0.503 0.420

800 0.858 0.705 0.582 0.479 0.395

850 0.849 0.691 0.564 0.459 0.374

900 0.842 0.677 0.544 0.438 0.353

950 0.833 0.662 0.525 0.418 0.333

1000 0.825 0.646 0.507 0.399 0.313


Table A2.27 RA1, breeding, Density Dependent: Weibull b=1.2 . Change in population growth rate.


0 0.000000 -0.00571 0.005875

50 -0.000693 -0.00648 0.005053

100 -0.001235 -0.00698 0.004487

150 -0.002154 -0.00770 0.003537

200 -0.002774 -0.00860 0.002815

250 -0.003539 -0.00956 0.002215

300 -0.004275 -0.00983 0.001454

350 -0.005214 -0.01098 0.000707

400 -0.005962 -0.01179 -0.000296

450 -0.006767 -0.01267 -0.001196

500 -0.007529 -0.01345 -0.001848

550 -0.008454 -0.01438 -0.002719

600 -0.009421 -0.01529 -0.003652

650 -0.010407 -0.01632 -0.004482

700 -0.011384 -0.01758 -0.005648

750 -0.012469 -0.01825 -0.006619

800 -0.013406 -0.01955 -0.007547

850 -0.014560 -0.02064 -0.008712

900 -0.015697 -0.02191 -0.009826

950 -0.016961 -0.02291 -0.011096

1000 -0.018197 -0.02432 -0.012225


Table A2.28 RA1, breeding, Density Dependent: Weibull b=1.2 . Ratio of median population sizes at 5

year intervals.


0 1.000 1.000 1.000 1.000 1.000

50 0.992 0.984 0.984 0.979 0.980

100 0.983 0.971 0.967 0.961 0.960

150 0.978 0.958 0.950 0.942 0.938

200 0.971 0.944 0.933 0.922 0.918

250 0.962 0.931 0.915 0.903 0.897

300 0.954 0.918 0.899 0.884 0.877

350 0.946 0.905 0.881 0.863 0.855

400 0.939 0.891 0.865 0.844 0.834

450 0.932 0.878 0.848 0.826 0.814

500 0.922 0.863 0.830 0.806 0.793

550 0.916 0.851 0.814 0.787 0.772

600 0.909 0.838 0.798 0.768 0.753

650 0.901 0.825 0.782 0.750 0.732

700 0.894 0.811 0.765 0.732 0.711

750 0.886 0.799 0.748 0.712 0.690

800 0.878 0.787 0.733 0.695 0.671

850 0.872 0.775 0.716 0.676 0.650

900 0.863 0.761 0.701 0.657 0.629

950 0.857 0.749 0.684 0.638 0.609

1000 0.850 0.737 0.669 0.621 0.590


Table A2.29 RA2, breeding, Density Independent. Change in population growth rate.


0 0.00000 -0.0306 0.026934

50 -0.00250 -0.0337 0.023692

100 -0.00485 -0.0348 0.021456

150 -0.00708 -0.0365 0.020350

200 -0.00953 -0.0400 0.017034

250 -0.01190 -0.0418 0.014975

300 -0.01412 -0.0441 0.012183

350 -0.01702 -0.0475 0.009977

400 -0.01909 -0.0491 0.007412

450 -0.02099 -0.0504 0.004501

500 -0.02361 -0.0527 0.002657

550 -0.02624 -0.0553 0.000437

600 -0.02837 -0.0585 -0.003216

650 -0.03051 -0.0601 -0.005298

700 -0.03300 -0.0622 -0.007358

750 -0.03568 -0.0645 -0.009616

800 -0.03837 -0.0663 -0.012022

850 -0.04054 -0.0685 -0.014699

900 -0.04189 -0.0712 -0.016249

950 -0.04511 -0.0743 -0.019218

1000 -0.04733 -0.0759 -0.021931


Table A2.30 RA2, breeding, Density Independent. Ratio of median population sizes at 5 year

intervals.


0 1.000 1.000 1.000 1.000 1.000

50 0.994 0.972 0.967 0.954 0.948

100 0.985 0.954 0.942 0.918 0.895

150 0.976 0.942 0.916 0.875 0.852

200 0.968 0.916 0.886 0.840 0.802

250 0.957 0.896 0.849 0.797 0.752

300 0.947 0.873 0.822 0.763 0.713

350 0.940 0.864 0.802 0.732 0.668

400 0.930 0.844 0.775 0.699 0.632

450 0.921 0.823 0.743 0.668 0.604

500 0.914 0.806 0.725 0.640 0.570

550 0.902 0.787 0.694 0.605 0.529

600 0.896 0.770 0.670 0.579 0.504

650 0.883 0.751 0.651 0.556 0.474

700 0.878 0.733 0.627 0.528 0.448

750 0.871 0.725 0.610 0.507 0.424

800 0.864 0.709 0.589 0.480 0.394

850 0.852 0.689 0.564 0.457 0.371

900 0.843 0.677 0.549 0.438 0.355

950 0.835 0.656 0.525 0.414 0.330

1000 0.827 0.648 0.508 0.395 0.312


Table A2.31 RA2, breeding, Density Dependent: Weibull b=1.2 . Change in population growth rate.


0 0.00000 -0.0241 0.020345

50 -0.00178 -0.0254 0.019074

100 -0.00339 -0.0278 0.016967

150 -0.00500 -0.0287 0.015502

200 -0.00718 -0.0313 0.013636

250 -0.00905 -0.0340 0.011982

300 -0.01112 -0.0355 0.010154

350 -0.01329 -0.0390 0.008770

400 -0.01544 -0.0404 0.006015

450 -0.01771 -0.0419 0.004091

500 -0.01954 -0.0447 0.001799

550 -0.02172 -0.0471 -0.000408

600 -0.02357 -0.0491 -0.001820

650 -0.02598 -0.0511 -0.004569

700 -0.02787 -0.0539 -0.006307

750 -0.03007 -0.0549 -0.008771

800 -0.03253 -0.0578 -0.010060

850 -0.03492 -0.0604 -0.011844

900 -0.03759 -0.0640 -0.014968

950 -0.03954 -0.0647 -0.017247

1000 -0.04179 -0.0670 -0.019738


Table A2.32 RA2, breeding, Density Dependent: Weibull b=1.2 . Ratio of median population sizes at 5

year intervals.


0 1.000 1.000 1.000 1.000 1.000

50 0.992 0.979 0.967 0.960 0.961

100 0.984 0.962 0.942 0.931 0.915

150 0.976 0.945 0.919 0.894 0.878

200 0.965 0.923 0.888 0.854 0.832

250 0.957 0.908 0.867 0.829 0.793

300 0.947 0.887 0.837 0.790 0.753

350 0.936 0.867 0.811 0.760 0.721

400 0.929 0.846 0.780 0.725 0.677

450 0.919 0.831 0.758 0.701 0.645

500 0.915 0.816 0.736 0.664 0.611

550 0.903 0.797 0.715 0.639 0.582

600 0.895 0.786 0.694 0.617 0.553

650 0.884 0.763 0.668 0.589 0.523

700 0.881 0.755 0.648 0.564 0.498

750 0.869 0.735 0.631 0.540 0.471

800 0.858 0.717 0.608 0.514 0.443

850 0.849 0.698 0.585 0.492 0.417

900 0.843 0.686 0.564 0.467 0.391

950 0.835 0.674 0.549 0.449 0.370

1000 0.827 0.655 0.528 0.429 0.351


Table A2.33 PU1, breeding, Density Independent. Change in population growth rate.


0 0.00000 -0.00412 0.00392

5 -0.00272 -0.00683 0.00122

10 -0.00547 -0.00964 -0.00158

15 -0.00821 -0.01240 -0.00411

20 -0.01100 -0.01506 -0.00720

25 -0.01380 -0.01783 -0.00981

30 -0.01661 -0.02073 -0.01262

35 -0.01936 -0.02331 -0.01540

40 -0.02212 -0.02619 -0.01807

45 -0.02489 -0.02888 -0.02096

50 -0.02767 -0.03171 -0.02377

Table A2.34 PU1, breeding, Density Independent. Ratio of median population sizes at 5 year

intervals.


0 1.000 1.000 1.000 1.000 1.000

5 0.990 0.978 0.966 0.953 0.941

10 0.979 0.954 0.931 0.907 0.886

15 0.970 0.933 0.899 0.866 0.834

20 0.960 0.912 0.867 0.824 0.783

25 0.950 0.892 0.836 0.784 0.735

30 0.940 0.870 0.806 0.747 0.690

35 0.930 0.850 0.777 0.711 0.649

40 0.921 0.831 0.750 0.676 0.610

45 0.912 0.811 0.723 0.643 0.573

50 0.901 0.792 0.697 0.612 0.538


Table A2.35 PU1, breeding, Density Dependent: Weibull b=1.2 . Change in population growth rate.


0 0.000000 -0.00309 0.003096

5 -0.000721 -0.00395 0.002375

10 -0.001557 -0.00468 0.001533

15 -0.002323 -0.00537 0.000658

20 -0.003209 -0.00623 -0.000024

25 -0.003995 -0.00708 -0.000885

30 -0.004915 -0.00810 -0.002008

35 -0.005873 -0.00897 -0.002804

40 -0.006876 -0.00986 -0.003783

45 -0.007801 -0.01084 -0.004782

50 -0.008866 -0.01191 -0.005926

Table A2.36 PU1, breeding, Density Dependent: Weibull b=1.2 . Ratio of median population sizes at 5

year intervals.


0 1.000 1.000 1.000 1.000 1.000

5 0.991 0.985 0.982 0.979 0.977

10 0.982 0.969 0.960 0.954 0.952

15 0.974 0.956 0.943 0.935 0.931

20 0.965 0.939 0.922 0.912 0.906

25 0.958 0.924 0.905 0.891 0.884

30 0.949 0.911 0.886 0.869 0.860

35 0.941 0.895 0.867 0.848 0.837

40 0.933 0.880 0.849 0.827 0.813

45 0.924 0.867 0.830 0.806 0.791

50 0.916 0.851 0.811 0.784 0.767


Table A2.37 PU2, breeding, Density Independent. Change in population growth rate.


0 0.00000 -0.0353 0.02837

5 -0.00254 -0.0395 0.02587

10 -0.00528 -0.0398 0.02328

15 -0.00788 -0.0425 0.02094

20 -0.01035 -0.0454 0.01851

25 -0.01241 -0.0461 0.01611

30 -0.01500 -0.0508 0.01322

35 -0.01749 -0.0524 0.01003

40 -0.02069 -0.0555 0.00734

45 -0.02252 -0.0580 0.00580

50 -0.02472 -0.0607 0.00272

Table A2.38 PU2, breeding, Density Independent. Ratio of median population sizes at 5 year

intervals.


0 1.000 1.000 1.000 1.000 1.000

5 0.989 0.975 0.970 0.947 0.942

10 0.981 0.947 0.929 0.913 0.883

15 0.968 0.932 0.893 0.864 0.826

20 0.962 0.915 0.867 0.833 0.782

25 0.954 0.893 0.842 0.792 0.739

30 0.943 0.870 0.806 0.748 0.694

35 0.932 0.851 0.784 0.715 0.659

40 0.922 0.829 0.749 0.677 0.606

45 0.911 0.813 0.724 0.652 0.578

50 0.903 0.797 0.702 0.621 0.543


Table A2.39 PU2, breeding, Density Dependent: Weibull b=1.2 . Change in population growth rate.


0 0.00000 -0.0248 0.01967

5 -0.00160 -0.0256 0.01811

10 -0.00366 -0.0286 0.01610

15 -0.00529 -0.0304 0.01492

20 -0.00707 -0.0321 0.01340

25 -0.00943 -0.0353 0.01114

30 -0.01123 -0.0378 0.00959

35 -0.01326 -0.0393 0.00741

40 -0.01559 -0.0422 0.00541

45 -0.01750 -0.0438 0.00323

50 -0.01998 -0.0473 0.00112

Table A2.40 PU2, breeding, Density Dependent: Weibull b=1.2 . Ratio of median population sizes at 5

year intervals.


0 1.000 1.000 1.000 1.000 1.000

5 0.992 0.980 0.974 0.963 0.958

10 0.984 0.961 0.940 0.923 0.909

15 0.973 0.944 0.919 0.894 0.876

20 0.962 0.922 0.883 0.858 0.833

25 0.950 0.899 0.851 0.813 0.782

30 0.944 0.886 0.834 0.785 0.747

35 0.936 0.867 0.803 0.750 0.711

40 0.921 0.843 0.775 0.714 0.673

45 0.916 0.828 0.755 0.692 0.643

50 0.908 0.809 0.728 0.660 0.603

MacArthur Green Seabird PBA Report August 2015... · This report provides details of population...

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Transcript of MacArthur Green Seabird PBA Report August 2015... · This report provides details of population...