A new computational system, DOVE (Digital Organisms in a Virtual Ecosystem), to study phenotypic plasticity and its effects in food webs

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1 ecological modelling 205 (2007) available at journal homepage: A new computational system, DOVE (Digital Organisms in a Virtual Ecosystem), to study phenotypic plasticity and its effects in food webs Scott D. Peacor a,b,, Stefano Allesina a,b,c, Rick L. Riolo d, Tim S. Hunter b a Department of Fisheries and Wildlife, Michigan State University, East Lansing, MI 48824, USA b Great Lakes Environmental Research Laboratory (National Oceanic and Atmospheric Administration), Ann Arbor, MI 48105, USA c Department of Ecology and Evolutionary Biology, University of Michigan, Ann Arbor, MI 48109, USA d Center for the Study of Complex Systems, University of Michigan, Ann Arbor, MI 48109, USA article info abstract Article history: Received 5 December 2005 Received in revised form 5 January 2007 Accepted 30 January 2007 Published on line 25 April 2007 Keywords: Individual-based model Genetic algorithm Phenotyipic plasticity Food web Trait-mediated Nonlethal Behavior Nonconsumptive Food webs are abstract models that represent who eats whom relationships in ecosystems. Classical food web representations do not typically include phenotypic plasticity, in which one species responds to changes in density of other species by modifying traits such as behavior and morphology. Such changes, which are presumably adaptive, will affect the magnitude of both direct and indirect effects on species fitness. Empirical evidence suggests that phenotypic plasticity is likely to have large impacts on the structure and dynamics of ecological communities. Whereas theoretical studies support this, there is much that we do not understand that may require new theoretical approaches. We have constructed a computational system, Digital Organisms in a Virtual Ecosystem (DOVE), to address this problem. Its features include an individual-based approach, in which a type of genetic algorithm is used to evolve animal behavior in a dynamic environment. Here we present an overview of the ecological problems motivating the creation of DOVE and its basic structure and operation. We also discuss the kinds of decisions and tradeoffs that were considered to make DOVE as simple as possible but still rich enough to allow us to address our fundamental questions. We then use DOVE to examine optimal foraging strategies of prey in the presence of fluctuating predator risk, and show that activity levels are highly dependent on competitor density in a manner that would be difficult or impossible to explore with traditional techniques. This, and other pilot studies of DOVE, suggests that it can be used to gain insight into the origin and consequences of phenotypic plasticity and other properties of ecological communities Elsevier B.V. All rights reserved. 1. Introduction Developing modeling approaches that capture and elucidate important structural and dynamical properties of food webs is of fundamental importance to further our understanding of natural ecological communities (de Ruiter et al., 2005). It is critical that models accurately capture the underlying mechanisms that are integral to the structure and function of real ecological systems. However an important component of ecological communities, phenotypic plasticity, is often not Corresponding author at: Great Lakes Environmental Research Laboratory (NOAA), 2205 Commonwealth Boulevard, Ann Arbor, MI , USA. Tel.: address: Peacor@msu.edu (S.D. Peacor) /$ see front matter 2007 Elsevier B.V. All rights reserved. doi: /j.ecolmodel

2 14 ecological modelling 205 (2007) included in food web models. Ecologists are becoming increasingly aware of the prevalence and potential consequences to ecological communities of phenotypic plasticity (Tollrain and Harvell, 1999; Agrawal, 2001; West-Eberhard, 2003; Lima, 1998). Organisms often respond to short-term environmental changes by modifying their phenotypes, including traits such as behavior, morphology, or life history. Many prey, for example, respond to predators by reducing their activity, by increasing their use of refuges, or by modifying their movement characteristics such as speed. Clearly prey will respond to predators when attacked, but the phenotypic responses we refer to here are more persistent and pervasive than immediate or initial responses. For example, birds will undoubtedly flee from an attacking predator, but their phenotypic response may be increased vigilance while foraging on longer time scales as a result of a perceived increased in predation threat (Caraco et al., 1980; Lima et al., 1999). Phenotypic plasticity is an important and pervasive feature of ecological communities, and should therefore be incorporated into food web models. Phenotypic plasticity introduces nonlinearities into and strongly affects the functional response of predator-prey interactions (Abrams, 1987, 1990, 2001). Theory suggests these changes can strongly affect population and community dynamics (Abrams, 1987, 1992, 1995; Ives and Dobson, 1987; Křivan, 2003; Luttbeg and Schmitz, 2000; Vos et al., 2004; reviewed in Bolker et al., 2003). In addition, indirect effects can be introduced if the focal species responds to a second species by modifying a trait which in turn alters the nature of the interactions of the focal species with others in the system. For example, in natural systems, the acquisition of resources is often tightly associated with activity level, but activity also relates strongly to vulnerability to predators (Werner and Anholt, 1993; Lima, 1998). This tradeoff means that if a prey responds to a predator by modifying its foraging rate or habitat preference, then any interactions between the prey species and its resources are also affected. In this way, predators can indirectly affect resource species via the prey species, without actually consuming the prey (Turner and Mittelbach, 1990; Abrams et al., 1996; Peacor and Werner, 1997, 2001; Peckarsky and McIntosh, 1998; Trussell et al., 2002). Such indirect interactions are termed trait-mediated indirect interactions (also behavioral indirect interactions, Miller and Kerfoot, 1987, interaction modifications, Wootton, 1993), to distinguish them from density-mediated indirect interactions (Abrams et al., 1996) which are linked direct interactions affecting species density (especially through consumption). Trait-mediated indirect interactions extend to other multiple species interactions (i.e. other than trophic cascades as in the example) and have been demonstrated in diverse systems (reviewed in Werner and Peacor, 2003; Schmitz et al., 2004; Miner et al., 2005). Empirical work and simple theoretical considerations indicate that trait-mediated indirect interactions can contribute strongly to the net effect of species interactions (Abrams, 1984; Peacor and Werner, 2001, 2004; Křivan and Schmitz, 2004; Hölker and Mehner, 2005). The general theoretical approach used to examine the effect of phenotypic plasticity on population and community dynamics is to modify existing theoretical models that use coupled differential equations, by adding and modifying equations that describe the magnitude and functional response of species interactions. Assuming that organisms behave adaptively, parameters that describe phenotype are expressed as a function of species densities and their magnitude is chosen to maximize fitness. For example, Ives and Dobson (1987) introduced parameters that describe foraging effort as a function of predator density. They found that phenotypic plasticity increased predator-prey oscillations, and thereby decreased stability of predator and prey abundance. Luttbeg and Schmitz (2000) used a similar approach that reinforced these findings, but they additionally show that the relative timing of phenotypic responses is important. If, for example, phenotypic responses result from imperfect knowledge of predation risk, phenotypic plasticity can stabilize predator-prey dynamics. The effect of a number of other factors in different food web configurations have also been examined (e.g. Křivan, 2003; Křivan and Schmitz, 2003, 2004; Vos et al., 2004; reviewedin Bolker et al., 2003) so the above examples serve only to illustrate how this general theoretical approach has elucidated the manner in which phenotypic plasticity can influence population dynamics and the magnitude of species direct and indirect interactions. Whereas the theoretical models such as those described above have increased our understanding of the consequences of phenotypic plasticity, limitations arise when using traditional analytic approaches to understand the role of phenotypic plasticity in the evolution and dynamics of food webs. A broad group of limitations arises from general assumptions made about ecological communities in these models. One such assumption is that the dynamics of a few species are tightly coupled and that the effect of phenotypic plasticity therefore arises by influencing the magnitude of the component species population oscillations. However, species densities are typically influenced by multiple biotic and abiotic factors (Lawton, 1989; Cohen et al., 1990; Polis, 1991) that may additionally have large stochastic components. Thus many systems may not have inherent predator-prey oscillations which phenotypic plasticity can dampen or magnify. Assumptions are also required to specify how phenotypic plasticity will affect the functional response of predators, and these assumptions can be critical since theoretical studies indicate that the form of functional responses greatly influences model predictions (Abrams, 2001; Bolker et al., 2003). However our empirical knowledge of these responses is greatly limited at this stage and it is not clear how to derive functional responses from first principles. This is a difficult problem because environmental context, including the presence of other species, will affect the evolution and thus magnitude of species traits, which in turn can affect the magnitude and functional form of species interactions (Hartvigsen and Levin, 1997; Abrams, 2001; Fellowes and Travis, 2000; Uriarte and Reeve, 2003; Beckerman, 2005). A second set of limitations arise when using traditional approaches to model the effects of phenotypic plasticity because they are not well suited to incorporating some potentially influential factors. First, because mean field models are used, the interactions between individual organisms are not explicitly represented. This precludes the potential for discovering and exploring difficult to predict emergent effects that

3 ecological modelling 205 (2007) may occur across organizational scales from the individual to the community (Huston et al., 1988; Railsback, 2001; Grimm and Railsback, 2005). We expect this is especially important because ecological communities are prototypical complex adaptive systems (CAS) (Holland, 1995; Levin, 1998) with adaptation occurring at the within-generation (phenotypic plasticity) and multiple-generation (evolution) timescales. Second, intraspecific variation is not represented. Clearly real populations are composed of heterogeneous individuals that vary both in their physical states (e.g., age and size) and phenotypic traits that dictate the magnitude of species interactions (cf. Lomnicki, 1988; Ebenman and Persson, 1988; Grimm and Uchmanski, 2002; Grimm et al., 2005). Third, models examining the consequence of phenotypic plasticity omit spatial heterogeneity, which is known to affect population and community dynamics. Lastly, traditional techniques cannot determine the adaptive behavior of organisms whose fitness is affected by multiple species, especially if associated feedbacks and ensuing system dynamics affect each species adaptive behavior. As an alternative to traditional analytic population level approaches we have developed a computational modeling system, Digital Organisms in a Virtual Ecosystem (DOVE), to examine the origin and consequences to ecological communities of phenotypic plasticity. In Section 2 we provide an overview of the general goals of and approach used in DOVE. We describe the basic architecture and components of DOVE models in Section 3. We focus on the key components and mechanisms, and on the kinds of decisions and tradeoffs that must be faced when constructing an individual-based model (IBM) that is both as simple as possible, in order to be transparent and tractable, but rich enough to allow us to address our fundamental questions. In order to show a specific application of some of DOVE s features, in Section 4 we provide a simple proof-of-concept example DOVE model. Model runs show how, in a tri-trophic food chain, phenotypic plasticity can evolve in the intermediate consumer species in response to variable predation risk, and show how the presence of a competitor consumer affects that response. In Section 5 we discuss some of the potential benefits and difficulties of using DOVE, and argue that this approach holds promise for uncovering important properties that shape and influence ecological communities. 2. DOVE a computational system for studying phenotypic plasticity Our goal was to build a computational system that enabled us to explore questions concerning the origin and consequences of phenotypic plasticity to food webs. These include: How do various environmental factors, such as competitor presence, affect the evolution (and therefore magnitude and functional form) of phenotypic plasticity (i.e. adaptive responses)? How does phenotypic plasticity affect the structure and dynamics of food webs? Understanding the effect of phenotypic plasticity on the distribution of interaction strengths, the functional response of species interactions, and the topology of the food web network, will all likely be integral to address this question. How do realistic properties of natural communities such as spatial heterogeneity, individual-level variation in phenotype, and age structure, affect the influence of phenotypic plasticity on the above properties? To address these questions, we have developed DOVE, a computational system for implementing individual-based models (IBMs) of food webs that consist of adaptive organisms subject to evolution by natural selection. In DOVE, populations of model plants and animals (including predators, omnivores, herbivores) evolve and interact. This ecosystem is a spatial landscape with multiple habitats that contain resources distributed heterogeneously. Animals can be created with varying degrees of perception of environment factors (e.g., predators) and their own internal state (e.g., hunger), and their behavior can be a function of these perceptions. Species can therefore exhibit phenotypic plasticity, although they need not. Strategies that determine behavioral responses vary between individuals within a population and successful combinations are inherited by offspring, with some small chance of mutation. In this way, optimal behaviors can evolve including those that involve phenotypic plasticity. The basic premise of DOVE is that we can gain insight into the nature of real ecological systems by allowing digital organisms to evolve in a simulated environment (a virtual ecosystem ) that displays particular constraints important to the problem at hand. In short, DOVE models can represent food webs as CAS, in which properties at the population and community level arise from the interactions among individual organisms that adapt to a dynamic environment. As with any modeling approach, there are tensions between creating models that are so simple they don t include important factors and processes, versus overly complicated models that are hard to understand and explain. Thus DOVE includes factors we believe are key to understanding the role of phenotypic plasticity, using mechanisms that are as simple as possible. For example, whereas perceptual capabilities can be arbitrarily complex, studying them is not presently a goal for DOVE models. Thus the perceptual capabilities as described below are fairly simple and once defined, fixed. However, those simple capabilities are rich enough to support experiments that explore a variety of situations in which phenotypic responses to changes in external or internal state may (or may not) be useful. It would be possible to model more complex sensory attributes that include, e.g., imperfect or delayed information, if the questions being addressed by the model require inclusion of those factors. DOVE can best be viewed not as a particular model, but as a software platform for implementing a variety of specific individual-based models of food webs. The different food webs could have different sets of species with different characteristics, capabilities and interactions, embedded in habitats offering different sets of tradeoffs and opportunities for the species to exploit. DOVE s flexibility makes it possible to design and run a range of related computational experiments, each designed to increase our understanding of the dynamics and population level mechanisms exhibited by particular food webs. In the next section we describe the general

4 16 ecological modelling 205 (2007) structure and components of DOVE models. DOVE is written in ObjectiveC using the open-source Swarm class libraries ( 3. DOVE model components and mechanisms At the most abstract level, a DOVE model consists of populations of virtual organisms- plants and animals of different species distributed across one or more habitats. DOVE defines a schedule of activity for the individual organisms, and it provides the user with ways to control model runs and to collect and analyze the model output. Habitats in DOVE represent both (a) the varying trade-offs between resource availability and risk of predation across different habitats and (b) the explicit spatial distribution of plants and animals within each habitat (Fig. 1). Plants in DOVE represent the basal resources of food webs. Each plant species is defined by a growth function and initial distribution across one or more habitats. Plants do not reproduce and are sessile (i.e., they grow, but do not spread). Animals in DOVE represent the focal organisms whose actions, distribution and dynamics are being studied. Each animal species is defined by a set of evolvable traits that determine individual behavioral strategies, a fixed set of plants and/or animals it interacts with (as predator or prey) and a set of fixed characteristics (e.g., resource requirements for reproduction and movement characteristics). Animals select from simple behavioral repertoires (remain inactive, eat/move, or switch habitat see Fig. 1) in order to acquire resources and avoid death. Animal density changes as a result of reproduction and death of individuals. Animals that acquire sufficient resources reproduce sexually and pass their traits to their offspring allowing for evolution of behavior through the recombination and mutation of traits. Animals can die from predation, starvation, age and exogenous factors. Global Predators are a special type of animal whose number is not coupled to the number of other organisms through consumption or predation, but rather is an exogenous stochastic function that is set up by the user to define particular patterns of predator risk. Using global predators allows us to represent variable predation pressure, without the tight coupling between predator and prey densities. By including particular sets of habitats, plants and animals, a DOVE model can represent various abiotic factors and species relationships relevant to the effect of phenotypic plasticity on food-web structure and dynamics. In particular, models can be set up to include key tradeoffs that animals are forced to make, for example between different levels of predation risk and resource acquisition that result from different behavioral choices (e.g., Werner and Anholt, 1993; Lima, 1998). For instance, parameters can be chosen such that eating and moving increase resource acquisition at a cost of increased predation risk, whereas remaining inactive decreases predation risk and decreases resource acquisition. The rest of Section 3 describes in more detail each of the major components in DOVE models habitats, plants, animals and their interactions, as well as the basic activities and processes that generate the dynamical behavior of DOVE models. Parameters and variables are summarized in Table 1. Throughout the text we use italics for model parameters and bold italics for individual variables Habitats Fig. 1 Schematic of DOVE model with 2 habitats occupied by 2 consumer species. Consumer species are identified as blue and red squares, whereas the various shades of green represent different resource levels in cells without a consumer. Multiple consumers may occupy a cell (not displayed in this figure). Individual consumers perform a single action at each time step. They may (1) RemainInactive, (2) Eat (white arrows indicate possible moves for a consumer species with a MoveRadius equal to 1), or (3) SwitchHabitat (black arrow indicates a consumer that has switched from Habitat 2 to a randomly chosen cell in Habitat 1). A DOVE model includes one or more habitats. Each habitat consists of a toroidal grid of discrete locations, with zero or more individual plants or animals in each location. Plant species have habitat-specific growth properties, thus allowing us to represent habitats with different amounts of basal resources. The pattern of variable predation by global predators also can differ between habitats, as can the background death rate. Animals can move from cell to cell within a particular habitat, or they can move from one habitat to another (see Fig. 1 and Section 3.5). Moving among habitats may, for example, represent movement from one region of a pond to another to find more resources or to change their exposure to predators. Thus differential plant and animal densities between different cells (and regions) within habitats explicitly represents spatial heterogeneity facing the moving animals, and models with multiple, different habitats provide a direct way to represent differential trade-offs that animals often face in different parts of a larger region. In order to simplify DOVE models, there is no spatial relationship between different habitats.

5 ecological modelling 205 (2007) Table 1 Parameters and variables of animals, plants, and species interactions Parameter/variable name Description Section Plants state variables Biomass An individual plant s Biomass 3.2 Location Cell occupied 3.2 Plants fixed homogeneous parameters PlantGrowthRate Logistic equation growth rate parameter 3.2 PlantCarryingCapacity Logistic equation carrying capacity parameter 3.2 Animals state variables Biomass Unit used to describe an animal s energy content or size 3.3 Location Cell occupied 3.3 Age Time steps since birth 3.3 StepsSinceReproduction Time steps that have passed since most recent reproduction 3.3 Animals fixed homogeneous characteristics InitialBiomass biomass at birth 3.3 BiomassLoss biomass lost at each time step 3.3 InitialAge age at birth 3.3 MaximumAge age at death due to old age 3.3 BackgroundDeathProbability probability of death due to causes not directly modeled 3.3 EatRadius Distance an animal can eat during Eat action 3.5 MoveRadius Maximum distance moved during Eat action 3.5 FindBestProbability Probability to move to the most profitable cell during the Eat action 3.5 ReproductionThreshold Biomass required to reproduce 3.8 MinStepsForReproduction lower bound on time required to reproduce 3.8 CrossoverProbability probability of crossover during reproduction 3.8 MutationProbability probability that an individual gene will mutate during reproduction 3.8 MutationVariance variance of gene mutation 3.8 Animal action probability parameters ( genes ) RemainInactive Remain on current cell without eating 3.5 Eat Move to cell and eat in cells encompassed by EatRadius 3.5 SwitchHabitat Move to a random location in another habitat 3.5 Species interactions DietList List of prey items of an animal 3.6 Refuge Fraction of a plant s Bimoass not accessible to a particular animal herbivore AvailablePlantBiomass Fraction of a plant s Bimoass accessible to a particular animal herbivore EatFraction Fraction of AvailablePlantBiomass eaten by an herbivore AssimilationEfficiency Fraction of the consumed resources converted into Biomass, 3.6.1, CaptureProbability Probability a predator captures an animal prey during a predation event 3.6.2, Plants Plants represent basal resources in DOVE food web models (Fig. 1). There is at most one plant from each plant species in each discrete location in a habitat. When a DOVE world is created, plant biomass is distributed in cells randomly, i.e., the amount placed in each cell is drawn from a normal distribution with a user-defined mean and variance. Each individual plant is characterized by two state variables, its Biomass and its Location (i.e., the x, y coordinate in the world). The growth of a plant j in habitat i is determined by the Logistic Growth model B ji (t + 1) = B ji (t) (1 + r ji ( 1 B ji(t) K ji )), (1) where B ji is the plant Biomass, r ji is the PlantGrowthRate and K ji is the PlantCarryingCapacity of plant j in a cell belonging to habitat i. Note, for simplicity, parameters describing plant growth are the same for plants in all cells in the same habitat, but introducing heterogeneity into these parameters is a simple and logical extension to DOVE. Plant biomass can be reduced through consumption by herbivorous animals Animals Animals are the focal point of DOVE models. The food web structure is determined by the multiple predator-prey pair-wise interactions that are either animal animal or animal plant interactions. The ability of animals to gain resources and avoid death determines the abundance and dynamics of each population. Each species is defined in terms of (1) variable, heterogeneous characteristics, including state variables and behavioral strategies that can vary across individuals of the species, and (2) fixed, homogeneous characteristics, with common trait values shared by all members of the species. In this section we present a broad overview of these characteristics, before going into more detail in subsequent sections Variable heterogeneous characteristics of animals (state variables and behavioral strategies) Individual state variables. Animal state variables include: (1) Biomass, the unit used to describe an animal s energy content or size. An animal s Biomass is its initial value at birth (InitialBiomass), plus the cumulative amount of

6 18 ecological modelling 205 (2007) resources it has assimilated by eating, less the amount lost to metabolism and reproduction. An individual must increase Biomass (by eating plants and/or animals) in order to reproduce and to avoid death by starvation, (2) A Location in a particular habitat, i.e., in a cell at a discrete (x, y) position, (3) An Age which is its initial age at birth (InitialAge) plus the number of steps it has survived, and (4) StepsSinceReproduction which defines the time passed since the most recent reproduction Individual behavioral strategy. An individual s behavioral strategy determines how that individual responds to each possible combination of perceptual states the individual s (species-defined) sensory capabilities can generate, as described further in Section 3.7. The parameters that dictate the behavioral strategy are not only potentially variable among individuals within a species, but are subject to evolution, and therefore their distribution can change through time (Section 3.8) Fixed homogeneous characteristics of animals (capabilities and constraints) General characteristics. Several parameters define general characteristics of each species. For example, parameters (defined and discussed below) that describe metabolism (Biomass loss), death due to factors other than those directly modeled, and some foraging characteristics, are parameters that are constant and have the same value for all individuals of a given species Reproduction control. An individual becomes a candidate for reproduction when it acquires enough Biomass to reproduce. There are a number of parameters that describe fixed homogeneous characteristics used in the reproduction process Interaction characteristics. Interaction characteristics define which animals can eat which others, and in part determine how effectively they can do so. In short, interaction characteristics define the structure of food webs in DOVE models, as well as specifying (in part) how effectively individuals of each species can (a) find and capture prey (animals or plants) and (b) assimilate what they eat Sensory capabilities. Each species can sense a fixed set of environmental factors (external state, e.g., level of consumable resources) and internal factors (internal state, e.g., Biomass). It is essential for an organism to sense changes in one or more of these factors in order to exhibit phenotypic plasticity Repertoire of basic actions. Species in DOVE are defined to have a fixed repertoire of simple actions from which individuals can select one action to carry out each time step Factors that lead to death. Animals can die due to one of the following optional factors: 1. Old age. An animal dies when it reaches a defined maximum age value, MaximumAge, which was assigned to it when it was born. 2. Starvation. If the Biomass of an animal reaches 0, then it dies of starvation. Biomass is lost at each time step (representing metabolism) by a constant factor, BiomassLoss, independent of behavior. 3. Predation. An animal can die due to predation by another animal (including global predators). 4. Background death. At every step, each animal may undergo random death, given the BackgroundDeathProbability defined for its species. Note that whereas in the current version of DOVE parameters describing particular species characteristics are defined as fixed characteristics for each species, these characteristics could be made more complex or subject to evolution (as with foraging strategy, Section 3.7) if required for exploring particular research questions Global predators Global predators are special types of animals that prey on other (focal) animals. Global predator number is not coupled to the number of other organisms through consumption or predation. Instead, the population dynamics of global predators is controlled by a stochastic function that is set up by the user at the start of each model run. This exogenous specification of predator dynamics makes it possible to examine the effect of predation on animal behavior and system dynamics without the complications added by feedback to the predator s own dynamics. In addition, this approach approximates many systems in which predator number is influenced by multiple biotic and abiotic factors outside of the constructed species assemblage (Lawton, 1989; Cohen et al., 1990; Polis, 1991). Note that global predators also differ from other animals in that their range of influence is the entire habitat that they inhabit (hence the term global ), and they do not consume plants. Global predation is used in the example provided in Section Animal actions At every time step, each animal must select one action to take from a pre-defined repertoire of actions. The repertoire of three actions, which include RemainInactive (or sit ), Eat (after possibly moving), and SwitchHabitat, was chosen to allow the representation of some important, broad categories of activity found in nature, each of which can have associated risks (from predation) and benefits (by enabling an animal to eat). In particular, when an animal performs the RemainInactive action, it remains in its current location (i.e., in the same cell in its current habitat) and does not eat. Because predation efficacy can be a user-defined function of prey activity (Section 3.6.2), this action can represent hiding in a refuge if the chance of predation decreases when prey remain inactive. If an animal selects the SwitchHabitat action (when there are multiple habitats), it moves to a random location in the other habitat (Fig. 1), and again does not eat during that step. The Eat action is more complicated because it involves determining where, what, and how much an animal will eat. In short, if an animal selects to Eat, it first moves to a location in its current habitat (which could be the same location it started at), and then it eats what it can, where eating involves decrementing the Biomass of the

7 ecological modelling 205 (2007) prey (resulting in the death of animal prey, but not necessarily of plant prey) and adding Biomass to the predator (eating) animal. The rest of this section describes the Eat action in more detail. DOVE provides species-level characteristics that determine different foraging abilities defined by parameters that specify the range a predator can search and capture prey, and the predators perception of resource quality/quantity. The MoveRadius (rectilinearly defined) parameter determines how much of the habitat individuals consider when moving. Once an animal has moved (which may be moving to the same location it started in), it then consumes all the resources (plants and animals) it can capture within an EatRadius (rectilinear) range of cells of the location to which it moved. Moving to a cell during the Eat action can be random, or a species can be defined to move to the most profitable cell (in regards to resource acquisition) within its range, with a given probability set by the parameter FindBestProbability. Note that these parameters allow for the simplest possible representation of predator foraging on a spatial grid (moving randomly to eat on one of the nearest neighbor cells), as well as allowing for more effective foraging strategies Species interactions: who eats whom In DOVE, individuals directly interact through predator-prey (including animal animal and animal plant) encounters, in which the predator (animal) consumes animal or plant prey. The animals or plants that a particular animal (including global predators) can eat is listed on the animal s DietList. Thus the collection of DietLists determine all pair-wise species interactions in a model food web. By including different combinations of animals and plants on the DietLists of each animal species, food webs of different sizes and structures (i.e., topology) can be defined. Note that the DietList is not a property of a particular predator, but rather of the interaction between predators and prey, as traits of both species determine whether predation occurs between the two. Whereas the DietList defines the general topology of a food web, predation rates and the population level interaction coefficients (i.e., the per capita effects one species has on the population growth rate of others) are an emergent property of many factors and mechanisms acting at the individual level. The magnitude of the interaction is determined by (1) the distribution of behavioral strategies employed by individuals of the interacting species; (2) fixed characteristics that determine predator foraging characteristics (e.g., MoveRadius as described in Section 3.5); and (3) parameters that are specific to the predator-prey interaction (rather than to either species individually). For example, in nature, the efficiency of converting resources to biomass is a function of both the prey and predator traits, as is the probability of prey capture by a predator. A number of parameters fall under this interaction parameter category in addition to DietList (grouped in Table 1), and are described in more detail in the following subsections. The possibility of examining the influence of such parameters is of great interest, because they influence efficiency which strongly affects food webs dynamics (Gaedke and Straile, 1994; Elser et al., 2000; Nielsen and Ulanowicz, 2000; Valandro et al., 2003). Currently DOVE implements a linear functional response as in classical Lotka Volterra models, in which predators consume prey (animals or plants) with no saturation. It would be a simple matter to modify DOVE so that consumption of prey in a given time step is density dependent and influenced the consumption of other potential prey in that time step. Importantly, however, in the current version of DOVE the benefit of eating may not increase linearly (i.e., reproduction potential) with an increase in resource consumption, as a time constraint may be placed on when resources can be used to reproduce (Section 3.8) Herbivory An animal species that has plant species on its DietList represents an herbivore or omnivore (if it also eats animals). As mentioned in Section 3.2, all the plants from a given plant species at a given x, y location in a habitat are represented by one plant individual in the discrete cell for that location. In nature, a given percentage of a plant s resource is often unavailable to herbivory due to constraints. For example, snails may be limited in how close they can scrape a resource to the substrate surface. In DOVE a refuge is represented by including a Refuge value that is defined as a fraction of the plant species carrying capacity not attainable by the animal. An EatFraction factor specifies the fraction of the available plant Biomass animals of that species will eat. In summary, for a given animal eating a specific plant from a given cell, the animal eats all plants within its EatRadius. The amount eaten on a given cell is equal to the product of the EatFraction and the plant biomass available to the animal (i.e. the Biomass minus the Refuge). The AssimilationEfficiency for this animal plant interaction then determines the conversion (fraction) of the eaten plant Biomass into animal Biomass. When an animal eats a plant, the plant s Biomass is reduced, but the plant does not die (unless EatFraction is 1 and the Refuge is 0). Instead, the plant subsequently increases its Biomass as described by the growth equations in Section Predation on animals During the Eat action, an animal will attempt to eat other animals that are on its DietList and are in a cell encompassed by the predator animal s EatRadius. As with herbivory, parameters that determine predation between animals arise from traits of both the predator and prey, and thus we use parameters that are specific to the predator-prey interaction in addition to parameters that are specific to each individual species. In nature, there are many characteristics of both predator and prey that influence whether a given individual animal will capture and consume a given prey individual. In the current version of DOVE, these factors are combined into a set of CaptureProbability values with one value for each possible prey action (i.e., RemainInactive, Eat, or SwitchHabitat). For example, for predator A and prey B, the CaptureProbability values might be (0.05, 0.5, 0.1), so that if predator A is trying to eat prey B, the probability of capture is 0.05, 0.5 and 0.1, if prey B is inactive, eating, or is switching habitats, respectively. (Note that the action of B is whatever action it last performed). Thus, a DOVE model can be set up such that capture is more likely when the prey is active (e.g., switching habitats or eating) than when it is inactive, as is the case with many animals (Werner

8 20 ecological modelling 205 (2007) and Anholt, 1993; Lima, 1998). If a predator does capture and eat a prey animal, the prey Biomass is converted to predator Biomass, as discounted by the AssimilationEfficiency, and the prey is removed Predation by global predators Global predator animal interactions operate as described above for other predator animal interactions, in that the chance that an individual prey will be eaten depends on the set of prey-action-dependent CaptureProbability values of the global predator and the prey s last action. Global predation differs from other predation in that a global predator range is the entire habitat (and therefore not confined to an EatRadius) Behavioral strategies the basis of phenotypic plasticity in DOVE Animals in DOVE can exhibit different phenotypes as a function of the state of the environment or of its own internal state. This is essential for the representation of phenotypic plasticity. In the current version of DOVE, plasticity is limited to the behavioral strategies the animals use to select basic actions during each time step. In particular, each animal has a behavioral strategy that defines a map from the animal s perception of the environment, denoted the perceived environmental state, to a probability distribution over the basic actions available, denoted the action probability distribution, from which a particular action is selected to be carried out (Table 2). The animal s perceived environmental state defines an environment in a broad sense and includes both the animal s internal state in addition to the external conditions. Animal species can perceive any combination of four environmental variables including: (1) Habitat indicating the habitat the animal is in; (2) Food level available resources it can consume; (3) Predation risk total risk from all predators (including both global predators and specific predators, if any); and (4) its Biomass. The perceived state of each environmental variable is mapped into a discrete value, and these are combined to define the perceived environmental state. For example, animals from a given species could be defined such that they can distinguish (1) two habitat values for each of two habitats; (2) four levels of increasing perceived predation risk; (3) two levels, representing low and high, of perceived Biomass states; and (4) one perceived food level (i.e. they cannot perceive any differences in food level). The concatenation of the perceived state values is then combined to form the perceived environmental state which (in part) determines the action the animal will select. The number of possible perceived environmental states is the product of the number of states perceived for each dimension; e.g., there are = 16 possible perceived environmental states in the above example. Note that translation from detected changes in the environment to what is perceived is often represented as a two (or greater) step process in conceptual or simulation models (Dusenbery, 1992; Holland, 1995), with an intermediate state that distinguishes what is sensed by an organism from how it perceives it. This is indeed the process that takes place in DOVE, where first an animal detects a value in the environmental state (e.g., 10 predators), and then this value is translated into a perception level category (e.g., level 3, or high ). Behavioral strategies are represented as simple tables that map from each possible discrete perceived environmental state to a list of parameters that describe the probably of performing each possible action (RemainInactive, Eat, and SwitchHabitat as described in Section 3.5). That is, each row defines an action probability distribution over possible actions for one perceived environmental state, and the table has rows for all possible perceived environmental states. Table 2 shows one such mapping defining a particular behavioral strategy. The left-hand side of each row contains values that specify a possible perceived environmental state of an animal of a given species. The right hand side specifies an action probability distribution associated with each perceived environmental state. This example animal exists in a world with two habitats (0,1) which it can detect. Animals of this species can detect two predation risk levels (0, low and 1, high), but it cannot differentiate food levels or its own biomass, so there is only one food level and Biomass value (0). This animal will therefore be able to detect four different perceptual states and the action in each state is dictated by the action probability distribution for that state. For example, if the predation risk is low and the animal is in habitat 1, the probabilities that it will chose the actions RemainInactive, Eat or SwitchHabitat will be 0.7, 0.2, and 0.1 respectively. (The probability values in each row must add to 1 since these define the probability distribution over all possible actions.) In this example, the animal s behavioral strategy results in an animal that has a higher propensity to eat in Habitat 0, and responds to high predator presence by becoming less active. The SwitchHabitat genes create a preference for Habitat 0 in predator absence and Habitat 1 in predator presence. Note that conspecifics have the same set of possible perceived environmental states, but may have different values for the action probability distribution. Given this representation, a species exhibits phenotypic plasticity to the extent there are different probability distributions for different perceived environmental states (i.e., in different rows). For example, a species using the behavioral strategy defined in Table 2 exhibits phenotypic plasticity with respect to habitat and predation level, but not food levels. Table 2 Example of a behavioral strategy for a single individual animal Perceived environmental state Action probability distributions Habitat Predation risk level Food level Biomass Remain-Inactive Eat Switch-Habitat

9 ecological modelling 205 (2007) Evolution of strategies through selective reproduction with variation A key element of DOVE is that animal phenotype can evolve, and adaptive behavior is generated using a type of genetic algorithm, an abstract model of Darwinian evolution based on variation and selection of heritable traits (Holland, 1992). While routinely used in engineering and computer science (Goldberg, 1989; Mitchell, 1996), such approaches have also been utilized in ecological models (cf. Hraber and Milne, 1997; Hartvigsen and Levin, 1997; Johst et al., 1999; Lenski et al., 1999; Drossel et al., 2001; Lassig et al., 2001; Strand et al., 2002; Wilke and Adami, 2002). In the current version of DOVE, the only phenotype of animals that is subject to selection is the individuals behavioral strategy (i.e., the parameters describing action probabilities), but it would be a simple matter to extend selection to other parameters if it is required for a given question. The genetic algorithm operates in DOVE as follows. When an animal s Biomass exceeds the ReproductionThreshold (defined for its species), reproduction for that individual is possible. The rate real animals can acquire resources is limited due to processing constraints or handling times. Dove represents this limitation on the benefits associated with resource acquisition with a parameter, MinStepsForReproduction, which sets a lower bound on the number of time steps required to reproduce since birth or since the previous reproductive event for the animal (i.e., the state variable StepsSinceReproduction). When two (or more) animals of the same species are eligible to reproduce at the same time (no matter where they are located), they are paired off randomly to mate. Each pair produces one offspring of the same species that is placed in the habitat of one of the parents chosen randomly. The offspring receives the parameters that describe the fixed homogeneous characteristics of the parents (which are necessarily the same), and receives a subset of the parameters that determine an individual s foraging strategy (behavior) from each parent as described in Fig. 2. These variable parameters, which determine the probability of performing an action as a function of each possible perceived environmental state as described in Table 2, are therefore subject to selection, and denoted genes. In short, the offspring s action probability distributions can be thought of as a genome that is created by recombining the two parents genomes with a single point crossover (Goldberg, 1989). The probability of a crossover event is determined by the parameter CrossoverProbability. There is also a probability for each gene to mutate, i.e., to change the probability value for a given (state,action) gene, as determined by the species-level parameters MutationProbability and MutationVariance. After a mutation or crossover, the genes that define the action probability distribution for a perceived environmental state may no longer sum to one, in which case the genes for that state are renormalized by dividing each value by the new sum of gene values for that state. The value of the gene parameters are constant for a particular individual, but the distribution of values may change for a population due to selection. Note that while our genetic algorithm and associated representation of a genome is very loosely based on biological processes, we do not suggest that the parameters represent natural genes. When a model run is initiated by seeding the world with animals with randomly chosen genes, the low fitness of these animals often leads to rapid extinction before more fit offspring are created by evolution. To avoid this problem, DOVE models can include a species-level AntiExtinctionPeriod at the beginning of model runs, to increase the probability that viable strategies will evolve for that species. During the AntiExtinctionPeriod, whenever the abundance of that species falls below Fig. 2 Adaptation in DOVE. Parameters that dictate behavior, denoted genes, are passed to offspring from two parents using a genetic algorithm. Each individual animal has a list of action probability distributions stored as a set of parameters (denoted genes ) that determine which of its potential actions it will perform at each time step as a function of the perceived environmental state (Table 1). In the example represented here, an individual will RemainInactive ( sit ), Eat, or SwitchHabitat, depending on which habitat it occupies, and the predation risk level. The genes of two individuals from the same population are shown, both passing a segment (determined by a crossover point) of genes to the offspring. There is a small probability of a gene mutation during reproduction, as illustrated; The 6th gene from the left mutated from 0 to 0.2 (and then was renormalized with the value of genes 4 and 5). Over time gene distributions change due to selection (offspring with high fitness will pass on their genes) in a manner similar to that used in genetic algorithms, which are abstract models of Darwinian evolution. In this manner, the population adapts in a dynamic environment.