Building adaptive and flexible individual-based ecological models for a changing world via pattern-guided evolution
S. Haythorne, A. Skabar
Procedia Environmental Sciences
In a changing world, ecologists have an important role in examining the impacts of environmental changes, and formulating strategies for adapting to these changes, such as engineering sustainable ecosystems that are integrated with human society. Some ecological models supporting these processes need to model species' adaptive responses to changing conditions. Individual-based models (IBMs) can be used to simulate intergenerational adaptation by implementing model organisms parameterized with
... ructures analogous to genetic chromosomes. IBMs may be calibrated and validated using the pattern-oriented approach, in which model outputs are compared to field data patterns, generally at the end of each simulation. In some circumstances this approach may be limited and computationally expensive when applied to IBMs with adaptive mechanisms. This research explores an approach for using field data patterns, obtained from published research, to guide the evolution of model organisms within each model simulation. An adaptive IBM of an old-field ecosystem consisting of spiders, grasshoppers and plants was constructed using Repast Simphony to demonstrate the approach. The approach produced persistent ecosystem simulations matching aspects of field data patterns, and yielded populations of virtual organisms with phenotypic diversity. The approach produces flexible IBMs and may contribute towards improving model and data sharing within the ecological modelling community. building adaptive, resilient, and sustainable ecosystems that are integrated with human society, such as those explored in the field of ecological engineering (described in ), present humanity with some of its greatest challenges. Ecological models to support these processes are likely to be diverse, including and expanding upon existing modelling approaches (summarized in  ). Some of these models however, will undoubtedly need to simulate the adaptive responses of biological organisms to changing conditions. Individual-based models (IBMs) have the capacity to model organism adaptation, both intergenerational (evolutionary) adaptation and adaptive behavioral responses that occur within the lifetime of individual organisms (discussed in ). IBMs model individual variability, heterogeneous distribution, local interactions and organism behaviors (described in  ). Within an IBM, individual organism attributes and behaviors may be parameterized with inheritable 'genetic' structures, thus facilitating intergenerational adaptation via modeled reproductive life-cycles. This approach has been used to construct evolutionary IBMs for studying life-history and behavior evolution of various ecosystems, including those described in [5, 6] . IBMs may be developed and validated using the pattern-oriented modelling (POM) approach (described in  ), whereby the model outputs are compared to known patterns, often sourced from field data. The process of calibrating the parameters of an IBM using the POM approach generally involves examining the final output of many simulation runs, and is generally limited by computational resources (discussed in  ). IBMs with evolutionary mechanisms have been validated using the POM approach (in  ). However, in many circumstances, evolutionary trajectories in simulated ecosystems are unlikely to result in final simulation outputs that reflect real-world pattern data (discussed in ), particularly without limiting the number or ranges of inheritable parameters. The POM approach may be especially limited for use with many IBMs that incorporate intergenerational adaptation. This research explores an approach for using field data patterns to guide the evolution of model organisms within each model simulation, rather than comparing patterns to final model outputs of multiple simulations, as is typical of the POM approach. To demonstrate the pattern-guided evolution approach, an adaptive IBM of an old-field ecosystem located in Connecticut, USA was constructed, based on an IBM described in  . The model consisted of spider predators (Pisaurina mira), grasshopper prey (Melanoplus femurrubrum), and their plant habitat and food resource, represented simply as grass and herbs. As in , the model aims to replicate observed dietary shifts that grasshoppers tend to make in response to predation risk from spiders. The pattern-guided evolution approach provides, to the best of the authors' knowledge, a novel method for developing IBMs that incorporate intergenerational adaptation, and whose outputs match field data patterns. The approach also yields populations of model organisms with parametric diversity, thereby reducing model rigidity, and potentially allowing model components to be reused in different models (as discussed in [11, 12] ). The next section presents an overview of the pattern-guided evolution method. Following that, Section 3 describes the model used to demonstrate the approach. Section 4 outlines the simulations performed with the demonstration model. The results from these simulations are presented in Section 5 and discussed in Section 6. Finally, Section 7 presents conclusions that have been made so far within the research, and explores possibilities for future research. The pattern-guided evolution method involved augmenting an individual-based model (IBM) with selective mechanisms for guiding the evolution of model organisms using field data patterns. To facilitate intergenerational adaptation, organism reproductive life-cycles were modeled. Inheritable organism attributes, including parameters that govern behaviors, were stored in evolutionary structures analogous to genetic chromosomes, and passed between generations via reproductive functionality that utilized genetic operators such as crossover (detailed in  ). An additional model component for guiding evolution, denoted the gardener, was implemented to periodically remove individual organisms, their reproductive products (eggs), or local communities of organisms. Removal was conducted when entity or community properties excessively deviated from expected patterns, as derived from field experiment data and observations from published research. The organisms and eggs that remained after removal contributed to subsequent generations via reproductive functions. The method is summarized in Fig. 1 . Model description The following sections describe the model following the ODD protocol for describing individual-based models (IBMs) outlined in [14, 15] . The model was constructed with the Repast Simphony agent-based modelling and simulation development toolkit (http://repast.sourceforge.net/). Purpose The purpose of the model was to demonstrate the proposed pattern-guided evolution method for developing an IBM that incorporates intergenerational adaptation, outlined in Section 2. An old-field ecosystem, consisting of grasshoppers, spiders, grass and herbs, was chosen as a suitable model domain. It was a simple, yet nontrivial, ecosystem to model, and has previously been modeled via an IBM based on field research (described in  ). When applying the method with the modeled ecosystem, the aim was to evolve organisms with parameterized phenotypic diversity to facilitate intergenerational adaptation, whilst maintaining congruence with field data patterns and ecosystem observations. In particular, the model aimed to evolve adaptive feeding behaviors in grasshoppers in order to reproduce observed dietary shifts, that is, a reduction in the proportion of grass eaten, thus an increase in herb consumed, by grasshoppers when spiders are present (described in ). Entities, state variables, and scales The model consists of ecosystem entities representing the organisms and their reproductive products situated in a spatial grid-based environment. Additional non-situated entities, or agents, were constructed for performing seasonal tasks, imposing mortality, managing evolutionary structures, and performing selective activities for pattern-guided evolution. Ecosystem entities Entities specific to the ecosystem include grasshoppers, grasshopper egg pods, spiders, spider eggs, grass and herbs. The organisms were all modeled with sexual reproduction whereby the inheritable attributes of parent organisms, stored in genetic chromosomes, were combined using the genetic crossover operator to produce offspring chromosomes (detailed in  ).