e c o l o g i c a l m o d e l l i n g 2 1 5 ( 2 0 0 8 ) 200–206

avai lab le at www.sc iencedi rec t .com

journa l homepage: www.e lsev ier .com/ locate /eco lmodel

Detrital ontogenic model including decomposer diversity

Madhumita Roy, Sudipto Mandal, Santanu Ray ∗

Ecological Modeling Laboratory, Department of Zoology, Visva-Bharati University, Santiniketan, India

a r t i c l e i n f o

Article history:

Published on line 2 April 2008

Keywords:

Detritus

Recalcitrant

Labile

Fungus

Bacteria

Trophic dynamics

Detritivore

Coexistence

a b s t r a c t

Detritus influences the structure and dynamics of the living species. The quality of detri-

tus tied by the degree of colonization such that it may be more useful in some cases to

consider them as grouped entities as higher consumers in detrital branch may not distin-

guish between the consumption of detritus and micro-organisms that fed on it. Detritus

and producer-based food models both suggest that energy supply limits the length of food

chains. However, in detrital food chain the amount of dead organic matter is needed to

support micro-detritivores (bacteria and fungi) is lower on average than would be required

to support physiological and morphologically comparable herbivores in grazing food chain.

Many questions concerning detritus and diversity are only recently beginning addressed.

These include: (1) what are the factors that determine species richness in detrital commu-

nities? (2) How does diversity of detritivores affects key rates and fate of detritus processing

and ultimately feed back to producer productivity and ecosystem diversity? (3) How does

species diversity of organisms associated with detritus differ at different stages of its

ontogeny?

In this present work a dynamic model of two pools of detritus (recalcitrant and labile pool),

and decomposers (fungus and bacteria) is considered. The behavior is explored after vary-

ing the consumption of labile material by fungi, the transfer rates from one pool of detritus

to another and the amount of recalcitrant material entering the system. The model is also

sensitive to changes in other parameters, for example changes in assimilation and produc-

tion efficiencies of microbes to reflect changes in the quality of detritus. The model behavior

shows the coexistence at equilibrium between fungal and bacterial population is possible

which depicted as a function of the rate of transfer from recalcitrant pool to the labile. At low

rates of fungi mediated transfer of detritus, fungi are favored over bacteria. Coexistence of

bacteria and fungi also depends on the amount of recalcitrant material entering the system;

if inputs are dominated by labile material (that is recalcitrant input is low), fungi cannot sur-

vive. However increasing input of recalcitrant material leads to coexistence and input labile

material that are high relative to other inputs can generate bacteria dominated system.

of detritus exemplifies a quintessential donor controlled pro-

1. Introduction

The non-living nature of detritus influences the structure anddynamics of living species in three ways. Unlike living organ-isms detritus neither reproduces, nor directly affects the input

∗ Corresponding author. Tel.: +91 3463 261 268.E-mail address: sray@visva-bharati.ac.in (S. Ray).

0304-3800/$ – see front matter © 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.ecolmodel.2008.02.020

© 2008 Elsevier B.V. All rights reserved.

of new material. This density independence in the accrual rate

cess (Pimm, 1982), secondly its ontogeny is dependent in parton the actions of other species, in that when consumed detri-tus under goes transformation (i.e. ontogeny) as it decomposes

g 2 1

fersldbnba

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e c o l o g i c a l m o d e l l i n

rom one form to another. Finally detritus does not requirenergy for maintenance, hence has the capacity to serve aseservoirs of energy or supplement the energy needs of con-umers that have been traditionally viewed to rely only oniving organisms for energy. Moreover the naturally evolvedifferences and human induced alterations in material fluxesetween pools of detritus, living organisms and inorganicutrients have had global consequences with respect to car-on storage nutrient translocation, environmental pollutionnd climate change (Cebrian and Duarte, 1995).

Many questions concerning detritus and diversity are onlyecently beginning to be addressed. These include: (1) what arehe factors that determine species richness in detrital commu-ities? (2) How the diversity of detritivores affects key rates

nd fate of detritus processing and ultimately feedback toroducer productivity and ecosystem diversity? (3) How doespecies diversity of organisms associated with detritus differt different stages of its ontogeny? The diversity and abun-

ig. 1 – Conceptual model (drawn with Stella software) rectangleool (RD), labile detritus pool (LD), fungus (Fungi) and bacteria (Bompartments, from outside to the compartments and from insihow all forcing functions.

5 ( 2 0 0 8 ) 200–206 201

dance of microbial population is related to both the diversityand quality of detritus substrates (Moore et al., 2004).

To address some of the above questions particularly the lastquestion and on the basis of theoretical approach a dynamicmodel with two pools of detritus—the recalcitrant and labilepool and two forms of decomposers, i.e. fungi and bacteria isconsidered.

2. The model

As an illustration of the importance of the integrative frame-work for detritus, we present the simple dynamic model usingfour dimension differential equations incorporating detrital

ontogeny and decomposer diversity (Fig. 1). The model con-tains a recalcitrant detrital pool (RD), a labile detrital pool (LD),a bacterial population (Bact), feeding on labile detrital pool(LD), and a fungal population (Fungi) feeding on both recalci-

boxes represent the state variables—recalcitrant detritusact). Bold arrows indicate flow in between thede of the compartment to the outside. Circles with arrows

i n g

202 e c o l o g i c a l m o d e l l

trant (RD) and labile detrital (LD) pools. The model possessesfive pathways of energy flow. The model equations with theirflows and their descriptions are as follows:

dRDdt

= iRD + (n)(dFungi)(Fungi) + (m)(dBact)(Bact) − p(RD)

−(p)(x)(RD)(Fungi) − (1 − aRDFungi)(cRDFungi)(RD)(Fungi)

(1)

where iRD is the input from external sources to the recalcitrant(RD) pool, (n)(dFungi) the fractional inputs (e) from the death(dFungi) of fungal population (Fungi) to recalcitrant (RD) pools(at per unit biomass rates), (m)(dBact) the fractional inputs (m)from the death (dBact) of bacterial population (Bact) to recalci-trant (RD) pools (at per unit biomass rates), p the rate constantwhich governs the flow of material from the recalcitrant (RD) tothe labile (LD) pools due to abiotic factors such as weatheringand leaching, x the rate constant of the flow from recalcitrant(RD) to labile (LD) pools facilitated by extra-cellular enzymaticdegradation by fungi (Fungi), cRDFungi the consumption rate offungi (Fungi) on recalcitrant (RD) pool, aRDFungi the assimila-tion efficiency of fungi (Fungi) on recalcitrant (RD) pool.

dLDdt

= iLD + (1 − n)(dFungi)(Fungi) + (1 − m)(dBact)Bact

+p(RD) + (p)(x)(Fungi)

−(1 − aLDFungi)(cLDFungi)(LD)(Fungi)

−(1 − aLDBact)(cLDBact)(LD)(Bact) (2)

where i is the input from external sources to the labile (LD)

LD

pool, cLDFungi the consumption rate of fungi (Fungi) on labile(LD) pool, aLDFungi the assimilation efficiency of fungi (Fungi)on labile (LD) pool, cLDBact the consumption rate of bacteria(Bact) on labile (LD) pool, aLDBact the assimilation efficiency of

Table 1 – Parameters of the models their symbols, descriptionspopulation and also the equilibrium conditions of both recalcitrfrom Jorgensen et al., 2000)

Symbol Descriptions

p Rate constant for flow from RD to LD due to abix Enzymatic degradation rate by FungiaRDFungi Assimilation rate of Fungi on RDcRDFungi Consumption rate of Fungi on RDcLDFungi Consumption rate of Fungi on LDcRDBact Consumption rate of Bact on LDaLDFungi Assimilation efficiency of Fungi on LDaLDBact Assimilation efficiency of Bact on LDeRDFungi Conversion yield efficiency of Fungi on RDeLDFungi Conversion yield efficiency of Fungi on LDeLDBact Conversion yield efficiency of Bact on LDiRD Input rate of RD from out side.iLD Input rate of LD from out side.edFungi Input rate to RD pool by FungimdBact Input rate to RD pool by BactdFungi Death rate of FungidBact Death rate of BactsFungi Intraspecific competition rate of FungisBact Intraspecific competition rate of Bact

2 1 5 ( 2 0 0 8 ) 200–206

bacteria (Bact) on labile (LD) pool.

dFungidt

= (eRDFungi)(aRDFungi)(cRDFungi)(RD)(Fungi)

+(eLDFungi)(aLDFungi)(cLDFungi)(LD)(Fungi)

−(sFungi)(Fungi)(Fungi) − (dFungi)(Fungi) (3)

where eRDFungi is the conversion yield efficiency of fungi (Fungi)on recalcitrant (RD) pool, eLDFungi the conversion yield effi-ciency of fungi (Fungi) on labile (LD) pool, sFungi the mortalityrate of fungi (Fungi) due to intraspecific competition.

dBactdt

= (eLDBact)(aLDBact)(cLDBact)(LD)(Bact) − (sBact)(Bact)(Bact)

−(dBact)(Bact) (4)

where eLDBact is the conversion yield efficiency of bacteria(Bact) on labile (LD) pool, sBact the mortality rate of bacteria(Bact) due to intraspecific competition.

The model is run on STELLA 6.0 computer software (HighPerformance Systems Inc.) and simulated for the period of 365days to observe the dynamic behaviors of recalcitrant (RD) andlabile (LD) detritus pools and also the coexistence of fungal(Fungi) and bacterial (Bact) population. Parameters and theirsymbols, and values during coexistence of fungal and bacterialpopulation are given in Table 1.

3. Results

3.1. Sensitivity analysis

Sensitivity analysis attempts to provide a measure of the sen-sitivity of either parameter, forcing functions, etc. of greatestinterest in the model. It is usually carried out by changing theparameter values and observing the corresponding response

and values during coexistence of the fungal and bacterialant (RD) and labile detritus (LD) pools (values are obtained

Value Unit

otic factor 0.005 Dimensionless0.5 Dimensionless0.7 Dimensionless0.8 Dimensionless0.5 Dimensionless1.0 Dimensionless0.8 Dimensionless0.9 Dimensionless0.8 Dimensionless0.8 Dimensionless0.8 Dimensionless0.2 gC m−2

2.0 gC m−2

0.2 gC m−2

0.2 gC m−2

0.1 Dimensionless0.1 Dimensionless0.001 Dimensionless0.001 Dimensionless

e c o l o g i c a l m o d e l l i n g 2 1 5 ( 2 0 0 8 ) 200–206 203

Table 2 – Showing the annual average values ofsensitivity (S) of each state variable against eachparameter. Sensitivity analysis is performed bychanging in the parameter values at ±10% level andrecorded the corresponding change in state variable

Parameters State variables

(S) Bact (S) Fungi (S) LD (S) RD

iRD 1.024 −0.481 −0.569 −0.079x 1.025 −0.125 −1.005 −0.150p 1.023 1.043 −1.002 0.157aRDFungi 1.033 0.482 −1.005 0.150cRDFungi 1.031 1.036 −1.002 0.140eRDFungi 1.032 −0.070 −1.003 0.138dFungi 0.010 0.408 −0.078 0.135n 1.030 1.037 −1.003 −0.078cLDFungi 0.230 0.251 0.090 0.374aLDFungi 0.231 0.249 0.109 0.374eLDFungi 0.168 0.251 0.109 0.374m 1.028 1.038 1.003 −0.066dBact 0.116 0.158 −0.047 0.214cLDBact 0.969 0.447 0.172 0.144eLDBact 0.051 0.450 0.172 0.094iLD 0.053 −0.033 −0.098 1.020

oepcsd

S

Ficdn(scss

3

Tbaafcaeb(d(

Fig. 2 – Graph showing the coexistence of fugal andbacterial population. In this condition the equilibrium ofrecalcitrant detritus (RD) and labile detritus pool is also

1990, 1995, 1999; Hendrix et al., 1986; Moore and de Ruiter,2000). Consider for example the equilibrium behavior of thismodel, depicted as a function of the rate of transfer fromthe recalcitrant to labile pools. At low rates of fungi medi-

cLDBact −0.044 0.447 0.172 0.144sBact 1.028 0.163 1.003 −0.071sFungi 0.160 1.037 1.002 0.135

n the important state variable. The relative change in param-ter is chosen on basis of our knowledge of the certainty of thearameters. Here in this model each parameter is chosen tohange at ±10% and recorded the corresponding change in thetate variables (x). Thus, the sensitivity, S, of a parameter, P, isefined as follows (Jorgensen, 1994):

= [∂x/x][∂P/P]

ollowing the above formula sensitivity of each parameters performed, which are shown in Table 2. iRD, aRDFungi, x, p,

RDFungi, eRDFungi, n and sBact are very sensitive to bacterialynamics. So far the fungal population is concerned, cRDFungi,, m and sFungi are very sensitive. In case of labile detritus poolLD), the parameters x, p, aRDFungi, cRDFungi, eRDFungi, n, m, sBact,

Fungi are sensitive than other parameters. Only the parameter

LDBact is sensitive to recalcitrant detritus pool (RD). For overallystem performance six parameters viz., x, p, cRDFungi, n, m and

Bact are sensitive.

.2. Simulation

he model result shows the coexistence at equilibriumetween fungal (Fungi) and bacterial (Bact) population (Fig. 2)nd also both the detrital pools (Fig. 3). From our study itlso shows this coexistence is possible which is depicted as aunction of the rate of transfer parameters (p and x) from recal-itrant pool (RD) to the labile pool (LD). Coexistence of fungind bacteria is more likely to occur within a window of param-ter space where the fungal death rate (dFungi) exceeds the

acterial death rate (dBact), the bacterial assimilation efficiency

aLDBact) exceeds that of fungi (aLDFungi) or the bacterial labileetritus consumption rate (cLDBact) exceeds that of the fungi

cLDFungi). It is also obtained from model results that at low

noticed.

rates of fungi mediated transfer of detritus (n)(dFungi)(Fungi)and (1 − n)(dFungi)(Fungi), fungi are favored over bacteria. Coex-istence of bacteria and fungi also depends on the amountof recalcitrant material entering the system (iRD); if inputsare dominated by labile material (iLD) (and recalcitrant inputis low), fungi cannot survive. Therefore, increasing input ofrecalcitrant material (iRD) only leads to the coexistence of fun-gal and bacterial population and bacteria will rule the systemwhen input of labile material is high relative to recalcitrantinputs. The above observations corroborate with the field andexperimental observations of many authors (Andern et al.,

Fig. 3 – Graph showing the state of equilibrium ofrecalcitrant detritus pool (RD) and labile detritus pool (LD)when coexistence of fungal and bacterial population occurs.

i n g

204 e c o l o g i c a l m o d e l l

ated transfer (x) of detritus, fungi are favored over bacteria,to a point where only fungi are present, because labile pool istoo small to support bacteria. It is possible for both popula-tion to coexist, and for bacteria to overtake fungi whenever (x)increases. This result highlights both the harmony and dis-sonance between the two microbial populations; while theycompete for resources, bacteria are also dependent on fungito create labile material for their consumption and ultimatelysurvival.

4. Discussion

Detritus influences the structure and dynamics of the liv-ing species. Species depend on detritus as an energy sourcein three important ways. First, density independence in theaccrual rate of detritus exemplifies a quintessential donorcontrolled process. Secondly, it does not require any extraenergy for maintenance hence serve as reservoir of energysupplement of consumers. Thirdly, the input rates of detri-tus and detrital pool size have been shown to affect thedynamic stability (resilience) of food web models. Detrituspathways can have strong influences on the structure anddynamics of the grazer pathway by providing energy thatcan sustain higher densities of consumers than would oth-erwise be maintained if these consumers fed exclusively onenergy derived from grazer pathway (Moore et al., 1989). Phyto-plankton relies on mineralized detritus for limiting nutrients.Most of the primary production is not consumed by the her-bivores but rather is returned to the environment as detritusto play critical roles in organizing and sustaining ecosystems(Crawley, 1977; Cyr and Pacr, 1993; Hairston and Hairston, 1993;Polis and Strong, 1996; Wetzel, 1995). In the more immediatetime scales detritus affects trophic structure and dynamics ofcommunities, has the potential to support a grater diversityof species and support larger predator biomass and longerfood chains than would be supported by living autotrophsalone (De Angelis, 1992; De Angelis et al., 1989; Hairstonand Hairston, 1993). Detritus may stabilize both energy fluxand the dynamics of consumer population may alter energyand nutrient transfer efficiencies across trophic levels andincrease species persistence and food web stability in modelconfigurations that are otherwise unstable. In addition toits effect on trophic structure and dynamics, detritus alsophysically alter habitats (Schindler, 1990; Williamson et al.,1999).

The change in the substrate quality can affect the rel-ative abundance of bacteria and fungi, where materials ofhigh C:N ratio (>30:1) favor colonization by fungi while morelabile materials with low C:N ratios (<30:1) favor bacteriaand that with these changes come shift in the abundanceof the consumers of bacteria and fungi (Hendrix et al., 1986;Moore et al., 1993). The biodiversity of detritivores and decom-posers is affected by both quantity and type of detritus andon the other hand the diversity of decomposers and detriti-vores affects the quantity and quality of detritus throughout

decomposition (Lake et al., 2000; Palmer et al., 2000). To inte-grate detritus fully into understanding of factors driving thefunction and diversity of organisms, population, and ecosys-tems, ecologists need to recognize the intimate links between

2 1 5 ( 2 0 0 8 ) 200–206

detritus and other components of living systems, as well as,the heterogeneity and ontogeny of detrital resources. Thepresent work on the ontogeny of detritus reveals both theheterogeneous nature of detritus that is inherent in its con-stant state of flux and change that results from variation insources, and the changes it undergoes during decomposition.The broad changes in particle size and chemical composi-tion, which affects its overall ability as outlined by Swift etal. (1979) are also included in the ontogeny. The more subtleprocess like the immediate uptake of highly labile materi-als by consumers to minimal changes in recalcitrant formsare be of more importance structurally than as food. The rel-ative importance of different forms of detritus, in terms oforigin, size and chemical composition varies across ecosys-tems. Size classifications of detritus range from simple andcomplex organic molecules in dissolve organic matter (DOM),to particulate organic matter (POM), plant litter and coarsewoody debris. These size fractions are dynamic, as coarsedebris converted to fine particulate matter while dissolvedforms of detritus are continually leached from all size frac-tions. Further more, via aggregation, dissolved detritus canbe resynthesized into particulate fractions and small partic-ulate built up in to larger complexes (Moore et al., 2004).Aquatic ecologists subdivide particulate detritus into largeparticles (coarse POM) and small particles (fine POM). In soil,where it is difficult to separate aged detritus from the soilmatrix, density distinguishes more labile (‘light fraction’ orLF) from the less degradable POM fraction that is incorporatedinto aggregates, association with clay and silt and chemi-cal/biological transformation into recalcitrant molecules (Sixet al., 2002). The concept incorporates the association of detri-tus with minerals and other non-detrital material, which inturn affects the physical availability of detritus to organisms.The heterogeneity of detritus as depicted through ontogenyoffers a sound basis to discuss and explore biodiversity, foodweb stability, biogeochemical cycling, organic matter accu-mulation, nutrient retention, energy flow, redox changes andhabitat architecture under natural conditions or disturbed cir-cumstances with a common currency (Moore et al., 2004).The ontogenetic shifts show considerable interdependenceamong carbon sources, microbial decomposers and detriti-vores within detritus pathway. Thus model including detritusneed to make explicit the components of detritus pathwaythat are considered. However the quality of detritus is tiedto the degree of colonization. The amount of dead organicmatter to support bacteria and fungi, if not larger detriti-vores is lower on average than what would be required tosupport physiological and morphologically comparable her-bivores.

It is evident that the impact of detritus is best understoodthrough a focus on the ontogeny of detritus, the changesin detritus from time of its creation until only completelyrecalcitrant material is left. Detritus goes through a series ofchanges through time, and these changes are both mediatedby and have large effects upon the organisms that processthe detritus. This simple model reveals how the ontogeny of

detritus influences decomposers species diversity and theircoexistence. It is important to recognize that bacteria andfungi occupy different ecological niches in detritus controlledecosystem. During detritus formation, initially the leachates

g 2 1

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rom litter favor bacterial colonization and facilitate thereakdown of recalcitrant material (phenolics, tannins, lig-ocellulosic structural polymers, etc.) (Clarholm, 1985). Fungiolonization is promoted by the loss of phenolic from detritusColeman et al., 1983). Fungi are key population to increase inetrital nitrogen owing to the fact that they are found withinhe detritus. This would make the detritus more nutritious.oth bacteria and fungi are a source of vitamins and aminocids, which are extremely essential for the detritus-feedingnimal. Microbial biomass including both bacteria and fungis generally low in detirus. However, they may play an impor-ant role in the biochemical transformation of detritus by theroduction of extracellular enzymes and nitrogen enhance-ent. More experiments are needed that address the effects

f detritus stoichiometry on food webs.

. Conclusions

ast of all we want to mention that the present model is a greatimplification and purely on the basis of theoretical knowl-dge. Even we do not have any data to support the model.ince last 2 years the data have been collecting from Sun-arban mangrove ecosystem (largest mangrove ecosystem ofhe world), India to support the present theoretical model byoing through proper validation with observed data. Duringeld study it is very difficult to isolate detritus from soil in theature and more difficult to separate recalcitrant pool from

abile detritus pool from the sample. However, the count ofacterial and fungal population in unit area is possible and weery much hope that in future the present model will be vali-ated properly at least by the observed data of two variables,

.e. fungus and bacteria. For mathematical simplification somef the details are not incorporated in this model particularlyhe remineralization rate of both the forms of detritus. Theroductivity and existence of the grazing food chain are domi-antly controlled by remineralization rate. After incorporatingll the essential parameters in the present model it can bemphasized that how the impact of detritus is best understoodf differences between the dynamics of detritus, the ‘brown’art of the food web, and the dynamics of the ‘green part’f the food web are recognized and reconciled. Understand-

ng towards solving the ecological questions of the speciesiversity can only be possible by putting together the ‘greenart’ and ‘brown part’ of food webs in a new integrated ecol-gy.

cknowledgements

he authors gratefully acknowledge the Council of Scientificnd Industrial Research (Project Ref. No. 37/1185/04/EMR-II),ovt. of India, New Delhi for financial support to carry out

his work. The authors are also grateful to the Department ofoology, Visva-Bahrati University for giving all sorts of facili-ies to conduct this research. One of the authors (Santanu Ray)

s thankful to the organizers of ICEM for giving him the oppor-unity to present the work in the conference. The authors arelso thankful to the anonymous reviewers of this paper formprovement its quality.

5 ( 2 0 0 8 ) 200–206 205

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