Modeling and Simulation of the Energy Flow Through Root Spring, Massachusetts Author(S): Myron P

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Modeling and Simulation of the Energy Flow Through Root Spring, Massachusetts Author(s): Myron P. Zalucki Source: Ecology, Vol. 59, No. 4 (Summer, 1978), pp. 654-659 Published by: Ecological Society of America Stable URL: http://www.jstor.org/stable/1938766 Accessed: 01-10-2015 05:20 UTC

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This content downloaded from 130.102.82.186 on Thu, 01 Oct 2015 05:20:42 UTC All use subject to JSTOR Terms and Conditions Ecoloxy.59(4), 1978. pp. 654-659 (( 1978by the Ecological Society of America

MODELING AND SIMULATION OF THE ENERGY FLOW THROUGH ROOT SPRING, MASSACHUSETTS1

Myron P. Zalucki2 Departmentof Zoology, Australian National University,Canberra, Australia

Abstract. Four compartmentmodels, each postulatingdistinct forms of interactionsamong the organisms in Root Spring, Massachusetts were developed and compared. None were adequate to simulate the dynamics of energy flux in the spring. A model of the spring which adapted a detritus-processingmatrix developed for stream systems, together with a more precise statement of feeding relationships, reproduced the observed data more faithfully.This model sug- gested that certainfurther information on the biology of the springwould improve understandingof its dynamics. Key words: Compartment;decomposers; detritus;energy flow; Massachusetts; modeling; simulation.

Introduction rived an energy budget, except for the "ooze" compartment. Ooze was considered to be the 4 cen- In recent years, modeling and simulation have been top timetres of the mud which covers the bottom of the applied more and more to whole ecosystems (Patten This mud contained detritus on which 1971, 1972, 1975). These methods are useful tools in spring. organic the organisms fed. Changes in each compartment were studying the involved relationships which characterize described by the general differential such complex systems. A sensible approach is to study equation: as this the relatively simple systems, enables testing m n of differentmodel structures and ideas on interactions = + dX/dt Si ? Iu-^Oki, (1) within ecosystems. With this point in mind, the broad aim and objective of this study was to model and simulate the energy flow in a well-defined simple ecosys- where Ss is input to Xj from a source outside the system, tem, Root Spring, Massachusetts, using the compart? m ment approach. ^ Iij is the sum of inputs to Xjfrom other compartments, flow the biotic j=i Energy through major components n in the spring over a 1-yrperiod was described by Teal and V Oki is the sum of loss terms to other parts of the (1957 a,b). In a chemically and thermally constant k=l spring, the dynamics of energy flux will depend on system. Inputs to the system (POM in Fig. 1) were external inputs together with the interactions occur- added to the ooze compartment. These consisted of net ring among the inhabitants. The success or failure of primary production and the whole apple leaves which a compartment model as a description of such a sys? fell into the spring. It was reasoned that these leaves tem, will depend on how adequately the interactions would not be available for immediate consumption. among the species occurring in the spring can be rep- Whole leaves are colonized and broken down by micro- resented in mathematical terms. During the course of organisms before becoming available to small particle the work, 4 distinct network models were developed, feeders (Cummins and Petersen 1973). This process each containing different forms of interaction among was modeled by delaying leaf input for 60 days. A time the springs species. These 4 models will be described lag of this order would have major effects on the phase and compared briefly. Finally, a detritus-processing behavior of the model. Therefore, an experiment was model, developed for stream ecosystems, was adapted carried out on apple leaves to determine at what rate to the Root Spring situation. This model provided new leaves are broken down in conditions similar to those insights into the functioning of the ecosystem. in the spring (pH 6.5, 9?C). These observations yielded a decomposition rate of 0.006/day (Zalucki 1976). Us? The Network Models of Energy Flow in ing Petersen and Cummins (1974) classification of leaf Root Spring decomposition, this puts apple leaves into the slow- The system is described in the flow diagram in Fig. medium category, with a half-life between 46 and 138 1. The compartments shown correspond to the species days. The 60-day delay incorporated in the model, of organism in the spring for which Teal {\951a) de- therefore, falls within these limits. The mathematical forms given to the interactions 1 7 21 Manuscriptreceived February 1977; accepted Sep? between in the 4 different network tember 1977. compartments 2 Present address: School of Australian Environmental models are given in Table 1. In the linear model all Studies, GriffithUniversity, Nathan, Queensland 4111 Aus- feeding flows were donor dependent. The part-linear tralia. model considered predatory feeding flows to be de-

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Table 1. Summary of models developed and interaction termsused

Form of interactionterm Model name (solid lines in Fig. 1)*** Linear** Fy = 4>aXi Part-linear* Fy = ijXiXj Nonlinear** Fy = uXiXi Controlled nonlinear** Fj, = uX\ * Only predator-preyinteractions. ** All interactions. *** Where F,; = the flow from i to j; Xj and X, are the average biomass levels of compartmentsi and j: uis the flow rate and a is the degree of inhibition.

differential equations using Gears method (Gear 1971). Stability was tested by simulating the dynamics of the system over 5 yr. Any error in a parameter may POM cause an error in calculation of the value of a state Fig. 1. Flow diagram for network description of Root variable. As this erroneous value is then used to cal- Spring,respiration and otherlosses to outside the systemnot culate the magnitude of the next variable, the iterative shown. L = Limnodrilus; P = Pisidium; As = Asellus; Ca solution of the equations can cause significant accu- = C = Caddis; An = Anatopynia; Ph = Phy- Calopsectra; mulation of these errors. A continuous decline, in- sa\ Am = Amphipods; Pl = Planarians (-) feeding of flows;(-) losses to ooze. POM?Particulate organicmatter crease or irregular oscillation in the size a com? (delayed debis + plant matter). partment would suggest that the model is unstable. In deterministic models such as these, stability is pendent on donor and recipient compartments, while achieved when each years output is identical. Stabil? in the nonlinear model, all feeding flows were in this ity was tested, therefore, by comparing the 5th years form. The controlled nonlinear model had self-inhibi- output with that of previous years. tion terms on all nonlinear flows. Where a model was found to be stable using this The biological interpretation of the linear model is criterion, the third year of simulation was compared that feeders are controlled by competition for a limited with TeaFs (1957a) observed values using the follow- food supply, the biomass of feeders having no effect ing 3 methods: (1) visual correspondence of predicted on the amount eaten (Kowal 1971). In the part-linear and observed maximum and minimum values over the and nonlinear models, food supply and feeders control year; (2) the average predicted biomass of each com? each other mutually. Many authors (Holling 1966, Ko? partment was computed and compared to the observed wal 1971, Williams 1971) consider such a formulation average using the /-statistic; and (3) the observed vari- a reasonable description of predator-prey interactions. ance in compartment size was compared with the pre? The controlled nonlinear model introduces a negative dicted value using the variance ratio test Fmax proce- feedback term to represent intraspecific competition. dure (Sokal and Rohlf 1969). These 3 comparisons are Williams (1971) used a similar approach when mod- summarized for the models and 7 selected compart? eling the energy flow through Cedar Bog, Minnesota. ments in Table 2. There are many other compartment interaction terms Both linear and part-linear models are stable. Neither that could have been used (e.g., Park 1975, Wiegert reproduced the dynamics of energy flow through the 1975) however these formulations require a large spring (Table 2). The full nonlinear model failed to amount of information in order to estimate appropriate achieve cyclical behavior. As Wiegert (1974) points parameters. The terms used in this study are among out, models employing such relationships frequently the more common and simple of those used in similar exhibit biologically unrealistic instabilities and sensi- models of ecosystems. In addition, the parameters tivites. By adding self-inhibition terms to all feeding could be estimated from TeaFs (1975a) data, as the flows, the nonlinear model was stabilized. Because of Fu, Xj and Xj are known. All noninteraction losses the method employed in estimating the 4> an(J a terms from compartments were made donor dependent. (Table 1; the method used 1 equation where Fu, Xj Given the inputs and having specified loss and in? and Xj were set to their average value and the other teraction terms, a models behavior over time could using values from that month for which Fy and Xj were be simulated and the output compared with observed at a maximum) compartment predictions were overly fluctuations in the spring. Simulations were made us- large. Minor (60-100%) adjustments to the and a ing an International mathematical and statistical li- terms produced a reasonable fit to the observed com? braries (IMSL) package called DVOGER which solves partment changes over the year (Table 2). No doubt

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Table 2. Comparison between predictedand observed values 4 models and 7 compartments*

L = Linear model, P-L = Part-linear,C-NL = controlledNonlinear, M = Matrix. Yes = correspondence. No = no correspondence. Tested at the 5% level.

more tuning would further improve the correspon? sified according to particle size and extent of microbial dence. This procedure neither validates nor invali- colonization (conditioning), as reflected by community dates the model, nor does it suggest that the dynamics respiration. There were 6 size and 6 conditioning cat- of interaction in the spring are correctly represented egories recognized in this model. The size and con? by the controlled nonlinear formulation. To validate ditioning categories form a 6 x 6 matrix which de- the model would require further time-series data on scribed the detritus pool at any time (Fig. 2). The energy flow through the spring components, and this entries into this descriptive matrix are biomass of de- is not available. Even though none of the feeding for- bris in kilojoules per square metre. Changes in this mulations presented above were sufficient to describe biomass can occur by both vertical and horizontal the spring, this does not necessarily imply that they transitions through this matrix. The direction of the are inadequate descriptions of the interactions. An- horizontal transitions are primarily from left to right. other possibility is that the systems description (Fig. These transitions are a function of fragmentation or 1) is incorrect. In fact, a major criticism of these flaking of particles due to abrasion and animal feeding. models is that all debris is equally available for con- However, right to left transitions are also possible sumption after the specified time delay. Consequently, through flocculation and aggregation. Vertical transi? a filter-feedingclam, Pisidium, is represented as feed? tions occur due to microbial activity and small ing on the same material as an active particle-feeding amounts of energy are converted to heat by microbial chironomid larva, Calopsectra. The models have not respiration. Movement of organic matter from one bin taken into account niche differentiationbased on food of the matrix to another represents a transition func? resource partitioning. It was for these reasons that an tion, fy, where fu is that fraction of birii leaving birii attempt was made to develop a model with more bi? and entering binj in 1 time step. The updating of the ological realism. The basis of this model was a more descriptive matrix is achieved by matrix algebra using precise statement of the feeding relationships of the Eqs. 2, 3 and 4 and the fy values from Boling et al. organisms in the spring. (1975a). The detritus matrix replaces the ooze compartment A Detritus-processing Model for used in previous models. Detritivores remove organic Root Spring matter from the elements of this matrix via feeding, Cummins (1973), Cummins and Petersen (1973), Pe- and return matter in the form of nonpredatory mor? terson and Cummins (1974), Kaushik and Hynes tality, exuviae, mucus, feces and the leftovers of pre- (1968) and Boling et al. (1975#) have shown that de- dation. All feeding flows were considered linear and tritivores show a high degree of preference in the type donor controlled in this model. and size of food particle they will consume. The as- The central problem in coupling the energy flow sumption that predators show no food preferences is model through organisms to the detritus-processing also simplistic. Reynoldson (1966), for example, dem- model was in determining on which particular size and onstrated that lake-dwelling triclads have distinct prey conditioning category of particles the detritivores are preferences. feeding. TeaFs (1957a) statements on the feeding hab- To include the feeding relationships of detritivores its of the spring organisms are very general, and not in greater detail required a better description of the specific enough to assign organisms unequivocally as breakdown of debris into small particles. A model feeding on any particular size/conditioning category of which simulates these processes was developed by detrital particle. The feeding classifications shown in Boling et al. (1975a), for a woodland stream. In this Fig. 2 are hypothetical, rather than being experimen- model, nonliving particulate organic matter was clas- tally determined observations. They are based on in-

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AWOM SWOM LPOM MPOM SPOM FPOM

Ll. -O o o

o Q_ o

Fig. 2. Size/conditioningcategories on which detritivoresfed in the matrixmodel. Bins into which debris, algae and = = = = egesta were added are also shown. Inputs: D debris; P plant net production;Eg egesta. Losses to: L Limnodrilus; Pi = Pisidium; As = Asellus; Ca = Calopsectra; C = Caddis; Ph = Physa; Am = Amphipods; An = Anatopynia. AWOM = aggregatewhole organic matter;SWOM = small whole organic matter;LPOM = large particulateorganic matter;MPOM = medium particulateorganic matter;SPOM = small particulateorganic matter;FPOM = fine particulateorganic matter.

formation in the literature (e.g., Pennak 1953, Minck- gories (MPOM and SPOM, respectively; Fig. 2). The ley 1963), TeaFs (1957a) observations and educated plant input was divided equally among these 2. As the guesses. Factors considered included the size of the bulk of input consisted of whole leaves, 75% of the organism, its mouthparts and methods of feeding: debris was added to the slow small whole organic mat? scraping, collecting, filtering, biting or chewing. In ter (SWOM) category. The remaining 25% was appor- general, organisms give preference to particles heavily tioned among other bins so as to take account of twigs, colonized by bacteria and fungi. Figure 2 also shows branches, leaf veins and midribs. into which elements of the detritus matrix net produc- The predators, planarians and Anatopynia (Chiron- tion of plants and egesta from animals were added. omidae) were assigned prey preferenda. The planarians Egesta was apportioned equally among its bins. Ac- were given a preference for Calopsectra and Asellus. cording to the description of Boling et al. (1975a) of Anatopynia was given a preference for Limnodrilus the constituents of detritus, benthic algae fall into the (Tubificidae). Both predators took Pisidium and Caddis medium and small particulate organic matter cate- larvae equally. The preferences were based on the cor-

This content downloaded from 130.102.82.186 on Thu, 01 Oct 2015 05:20:42 UTC All use subject to JSTOR Terms and Conditions 658 MYRON P. ZALUCKI Ecology, Vol. 59, No. 4 respondence of maximum biomass values for prey and plained solely by describing food resource partitioning predators, e.g., planarians show a biomass peak soon among the component species, is perhaps most appli- after Calopsectra, etc. cable to relatively simple systems, such as a spring. Initial estimates of feeding rates of detritivores were Clearly organisms divide a large set of resources, based on the following assumption: at steady state, which are themselves discontinuously distributed in the average biomass of detritus in each element of the time and space. If the interactions between organisms matrix was set to 280 kilojoules/m2. This assumed that and their environments are to be understood, then the average biomass of the ooze used in previous ecosystem models will have to include better descrip- models was distributed evenly amongst elements of tions of how various resources (other than food) are the matrix. This gave the average biomass of the bins partitioned. on which an organism fed. As the flows into all com? Conclusions partments are known, the transfer rates can be esti? mated. The present study has demonstrated that simple Initial simulations obtained using the model em- compartment models of the Root Spring ecosystem ploying these parameter values were stable but provide inadequate simulation of the system, regard- showed poor correspondence with observed values. less of the precise formulation of the interactions in- However, the model was found to be sensitive to the volved. A more biologically realistic model incorpo- value assigned to the feeding rates of the detritivores rating detail on feeding habits of the organisms and minor adjustments (20-100%) to these produced concerned provides a much more promising approach, a much-improved fit (Table 2). While acknowledging resulting in a tool which can suggest relatively simple this to be an empirically based fittingprocedure, it is information required on the biology of the spring to nevertheless felt that such a procedure has heuristic improve understanding. Ideally, model building of this value. It serves to indicate information required to im- type should occur in the preliminary stages of a piece prove understanding of this system. of research with constant feedback between experi- At this stage, the matrix model may be viewed as ment and model allowing the time wasting task of col- a useful research tool. It suggests information that is lecting masses of irrelevant observations to be avoid- required on the biology of the organisms in the spring. ed. Such information would improve the simulation pro- ACKNOWLEDGMENTS cess and, as a result, indicate more clearly the func- T. tional roles of particular organisms in the spring eco- The author thanks Drs. G. Marples, R. O. Watts and R. L. Kitchingfor theirhelpful advice and criticismsin pre- system. Analysis of the present model indicates, paring this manuscript;Mr. D. W. Kenny for his program- that more is on: specifically, information required (1) minghelp and R. Bootes, W. Lees and C. Sheehan fortyping the feeding habits of the organisms; (2) the rates at the manuscript. which organisms ingest materials; (3) the size and rate Details of equations, output for all models and a copy of the used are in a honors thesis in the of turnover of the organic food available to Limnod- programs deposited Zoology DepartmentLibrary, Australian National Universi? the horizontal transition rates of detritus rilus\ (4) par? ty. ticles in the spring situation; and (5) input data for Literature Cited debris, especially the amount and size spectrum of the debris input and the time taken for leaves to sink to Bates, M. 1958. Food gettingbehaviour. Pages 206-223 in the bottom mud. A. Roe and G. G. Simpson, editors. Behavioural evolution. Yale UniversityPress, New Haven, Connecticut, USA. The model provides a detailed, if incomplete, de- Boling, R. H. Jr., E. D. Goodman, J. A. van Sickle, J. O. scription of detritus-processing and feeding relation- Zimmer, K. W. Cummins, R. C. 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