Animal dispersal modelling: Handling landscape features and related animal choices

Animal dispersal in a fragmented landscape depends on the complex interaction between landscape structure and animal behavior. To better understand how individuals disperse, it is important to explicitly represent the properties of organisms and the landscape in which they move. A common approach to modelling dispersal includes representing the landscape as a grid of equal sized cells and then simulating individual movement as a correlated random walk. This approach uses a priori scale of resolution, which limits the representation of all landscape features and how different dispersal abilities are modelled.We develop a vector-based landscape model coupled with an object-oriented model for animal dispersal. In this spatially explicit dispersal model, landscape features are defined based on their geographic and thematic properties and dispersal is modelled through consideration of an organism's behavior, movement rules and searching strategies (such as visual cues). We present the model's underlying concepts, its ability to adequately represent landscape features and provide simulation of dispersal according to different dispersal abilities. We demonstrate the potential of the model by simulating two virtual species in a real Swiss landscape. This illustrates the model's ability to simulate complex dispersal processes and provides information about dispersal such as colonization probability and spatial distribution of the organism's path.     

Parameterizing,evaluating and comparing metapopulation models with data from individual-based simulations

Due to the lack of sufficient data and appropriate ecological information parameterizing predictive population dynamical models usually is a difficult task. The approach proposed in this study is meant to overcome this problem by using detailed individual-based simulations to generate artificial data. With short-term data samples, the models to be investigated can be parameterized and their predictions be compared. The flexibility of individual-based simulations as experimental tools also facilitates the evaluation and comparison of different (aggregated) model types. The presented approach is a step towards unifying models of different complexity. As an example we applied it to two metapopulation models of insect species in a highly fragmented landscape: the well-known incidence function model with a patch-based representation of space and a grid-based analogue. The models are tested with respect to their data requirement and recommendations for a better data sampling are derived.     

Modeling individual and population dynamics in a consumer–resource system: Behavior under food limitation and crowding and the effect on population cycling in Daphnia

In population modeling, a considerable level of complexity is often required to provide trustworthy results, comparable with field observations. By assuring sufficient detail at the individual level while preserving the potential to explore the consequences at higher levels, individual-based modeling may thus provide a useful tool to investigate dynamics at different levels of organization. Still, population dynamics resulting from such models are often at odds with observations from the field. This may be partly caused by a lack of focus on the individual dynamics under conditions of food stress and starvation. I developed a physiologically structured, individual-based simulation model to investigate life history of Daphnia and its effect on population dynamics in response to the productivity of the system. In verifying model behavior with available literature data on life history and physiology, I paid special attention to the dynamics of food intake and the verification of individual level results under conditions of food limitation and starvation. I show that the maximum filtering rates under low food levels used in the current model are much closer to measured filtering rates than the ones used in other models. Being consistent with results on physiology and life history from experiments at a wide range of food availability (including starvation), the model generates low amplitude or high amplitude population density cycles depending on the productivity of the system, as observed in field and experimental populations of Daphnia and with the minimum population densities being one to two orders of magnitude lower in the high amplitude than in the low amplitude cycles. To generate results which are not only qualitatively but also quantitatively comparable to experimental and field observations, however, a crowding effect on the filtering response has to be incorporated in the model.     

A bunch of tiny individuals—Individual-based modeling for microbes

The individual-based (aka agent-based) approach is now well established in ecological modeling. Traditionally, most applications have been to organisms at higher trophic levels, where the importance of population heterogeneity (intra-population variability), complete life cycles and behavior adapted to internal and external conditions has been recognized for some time. However, advances in molecular biology and biochemistry have brought about an increase in the application of individual-based modeling (IBM) to microbes as well. This literature review summarizes 46 IBM papers for bacteria in wastewater treatment plants, phytoplankton in ocean and inland waters, bacteria in biofilms, bacteria in food and other environs, and “digital organisms” and “domesticated computer viruses” in silico. The use of IBM in these applications was motivated by population heterogeneity (45%), emergence (24%), absence of a continuum (5%), and other unknown reasons (26%). In general, the challenges and concepts of IBM modeling for microbes and higher trophic levels are similar. However, there are differences in the microbe population dynamics and their environment that create somewhat different challenges, which have led to somewhat different modeling concepts. Several topics are discussed, including producing, maintaining and changing population heterogeneity (different life histories, internal variability, positive feedback, inter-generation memory), dealing with very large numbers of individuals (different up-scaling methods, including representative space vs. super-individual, number vs. biomass based, discrete vs. continuous kinetics, various agent accounting methods), handling space, simulating interactions with the extracellular environment (hybrid Eulerian–Lagrangian approach), modeling agent–agent interaction (self-shading, predation, shoving) and passive transport (random walk with spatially variable diffusivity, well-mixed reactors). Overall, the literature indicates that the application of IBM to microbes is developing into a mature field. However, several challenges remain, including simulating various types of agent–agent interactions (formation and function of colonies or filaments, sexual reproduction) and even smaller individuals (viruses, genes). Further increases in intracellular detail and complexity in microbe IBMs may be considered the combination of systems biology and systems ecology, or the new field of systems bioecology.     

Optimal annual routines: new tools for conservation biology?

Many applied problems in ecology and conservation require prediction, and population models are important tools for that purpose. Formerly, the majority of predictive population models were based on matrix models. As the limitations of classical matrix models have become clearer, the use of individual-based models has increased. These models use behavioral rules imposed at the level of the individual to establish the emergent consequences of those rules at the population level. Individual behaviors in such models use an array of different rule types, from empirically derived probabilities to long-term fitness considerations. There has been surprisingly little discussion of the strengths and weaknesses of these different rule types. Here, we consider different strategies for modeling individual behaviors, together with some problems associated with individual-based models. We propose a novel approach based on modeling optimal annual routines. Annual routines allow individual behaviors to be predicted over a whole annual cycle within the context of long-term fitness considerations. Temporal trade-offs between different behaviors are automatically included in annual routine models, overcoming some of the primary limitations of other individual-based models. Furthermore, as well as population predictions, individual behaviors and indices of condition are emergent features of annual routine models. We show that these can be more sensitive to environmental change than population size, offering alternative, repeatable metrics for monitoring population status. Annual routine models provide no panacea for the problems of data limitations in predictive population modeling. However, as a result of their ability to deal with life-history trade-offs, as well as their potential for relatively rapid and accurate validation and parameterization, we suggest that annual routine models have strong potential for predictive population modeling in applied conservation settings.     

Appreciating Ecological Complexity: Habitat Contours as a Conceptual Landscape Model

Abstract:  Organisms respond to their surroundings at multiple spatial scales, and different organisms respond differently to the same environment. Existing landscape models, such as the "fragmentation model" (or patch-matrix-corridor model) and the "variegation model," can be limited in their ability to explain complex patterns for different species and across multiple scales. An alternative approach is to conceptualize landscapes as overlaid species-specific habitat contour maps. Key characteristics of this approach are that different species may respond differently to the same environmental conditions and at different spatial scales. Although similar approaches are being used in ecological modeling, there is much room for habitat contours as a useful conceptual tool. By providing an alternative view of landscapes, a contour model may stimulate more field investigations stratified on the basis of ecological variables other than human-defined patches and patch boundaries. A conceptual model of habitat contours may also help to communicate ecological complexity to land managers. Finally, by incorporating additional ecological complexity, a conceptual model based on habitat contours may help to bridge the perceived gap between pattern and process in landscape ecology. Habitat contours do not preclude the use of existing landscape models and should be seen as a complementary approach most suited to heterogeneous human-modified landscapes.     

Community processes as emergent properties: Modelling multilevel interaction in small mammals communities

Community interactions of small rodents have attracted the attention of ecologists for many years due to their abrupt changes in population numbers, their impact on the whole biocoenosis and also because of immense damages to agricultural production and forestry. In particular, regularly oscillating rodent populations in Scandinavia have been subject of discussions among theoretically and empirically working ecologists for many decades. Spatial and temporal restrictions in empirical work led to various attempts to model these dynamics to understand large scale effects resulting from complex interactions in variable cause-effect networks of the numerous involved system components.The presented individual-based model for the first time described small rodent communities as a set of interacting autonomously acting agents with a detailed life history and behavioural repertoire in a food-web setup composed of three trophic levels (rodents, rodents food and predators). It thus allowed to integrate all relevant factors accounting for the dynamics of rodents which acted in a simulated environment containing the spatial arrangement of habitats and seasonal changing conditions. Due to the representation with interacting entities, the dynamics on higher levels resulted in a self-organisation process as emergent properties. This differentiation between the focal and the operational level allowed to investigate processes interacting between different integration levels and to adapt the model to different scenarios easily as well as to specify it for a large range of rodents species.Simulations have been executed for two different scenarios. The Bornhöved scenario simulating the situation of a Northern German rodent community in a beech forest represented bottom-up effects of mast events on population dynamics. The Scandinavian scenario which depicted the most important actors of these oscillating rodent communities, gave new insights into the processes causing the sudden decline of rodent populations. Both, lack of resources and predation, contributed to about 90% of mortality, but no pattern could be found when relating either cause with the properties of the respective cycle. Bottom up and top down control vary unpredictably and chaotically in the model. These results may explain considerable parts of contradicting empirical findings.     

Continuous versus binary representations of landscape heterogeneity in spatially-explicit models of mobile populations

How a landscape is represented is an important structural assumption in spatially-explicit simulation models. Simple models tend to specify just habitat and non-habitat (binary), while more complex models may use multiple levels or a continuum of habitat quality (continuous). How these different representations influence model projections is unclear. To assess the influence of landscape representation on population models, I developed a general, individual-based model with local dispersal and examined population persistence across binary and continuous landscapes varying in the amount and fragmentation of habitat. In binary and continuous landscapes habitat and non-habitat were assigned a unique mean suitability. In continuous landscapes, suitability of each individual site was then drawn from a normal distribution with fixed variance. Populations went extinct less often and abundances were higher in continuous landscapes. Production in habitat and non-habitat was higher in continuous landscapes, because the range of habitat suitability sampled by randomly dispersing individuals was higher than the overall mean habitat suitability. Increasing mortality, dispersal distance, and spatial heterogeneity all increased the discrepancy between continuous and binary landscapes. The effect of spatial structure on the probability of extinction was greater in binary landscapes. These results show that, under certain circumstances, model projections are influenced by how variation in suitability within a landscape is represented. Care should be taken to assess how a given species actually perceives the landscape when conducting population viability analyses or empirical validation of theory.     

Evaluating approaches for scaling-up community-based marine-protected areas into socially equitable and ecologically representative networks

Marine-protected areas (MPAs) are vital to marine conservation, but their coverage and distribution is insufficient to address declines in global biodiversity and fisheries. In response, many countries have committed through the Aichi Target 11 of the Convention on Biological Diversity to conserve 10% of the marine environment through ecologically representative and equitably managed MPAs by 2020. The rush to fulfill this commitment has raised concerns on how increasing MPA coverage will affect other elements of Target 11, including representation and equity. We examined a Philippines case study to assess and compare 3 MPA planning approaches for biodiversity representation and equitable distribution of costs to small-scale fishers. In the opportunistic approach, MPAs were identified and supported by coastal communities. The donor-assisted approach used local knowledge to select MPAs through a national-scale and donor-assisted conservation project. The systematic conservation planning approach identified MPA locations with the spatial prioritization software Marxan with Zones to achieve biodiversity objectives with minimal costs to fishers. We collected spatial data on biodiversity and fisheries features and performed a gap analysis to evaluate MPAs derived from different approaches. We assessed representation based on the proportion of biodiversity features conserved in MPAs and distribution equity by the distribution of opportunity costs (fishing areas lost in MPAs) among fisher stakeholder groups. The opportunistic approach did not ineffectively represent biodiversity and resulted in inequitable costs to fishers. The donor-assisted approach affected fishers disproportionately but provided near-optimal regional representation. Only the systematic approach achieved all representation targets with minimal and equitable costs to fishers. Our results demonstrate the utility of systematic conservation planning to address key elements of Target 11 and highlight opportunities (e.g., integration of local and scientific knowledge can address representation and equity concerns) and pitfalls (e.g., insufficient stakeholder considerations can exacerbate social inequalities) for planning MPAs in similar contexts.     

An individual-oriented model for ecological risk assessment of wading birds

The contribution of certain contaminants to reproductive failure in many avian species has been an ongoing concern. Appropriate quantitative techniques have focused either on the individual organisms by providing explicit bioaccumulation dynamics or on whole ecosystems by looking at the fate of the contaminant but fail to make the necessary link via population dynamics of interacting individuals. We used the individual-oriented approach in an effort to quantify effects of chronic contaminant exposure on individual birds. This was made possible by the use of an object-oriented model, where individual birds are interacting objects, and their actions are implemented by passing to them appropriate messages. Using this modeling approach a breeding colony of Great Blue Herons (Ardea herodias) is simulated as an assemblage of interacting individuals whose daily actions (foraging, growth, feeding of the young) are simultaneously followed over short time intervals for a nesting season. Spatial distribution of the contaminants in prey resources is used on a cell by cell basis and their effects on certain behavior characteristics of adult birds (e.g. foraging efficiency, effects on flying efficiency, parental care) are taken into account. Results showed that sublethal effects could have a considerable effect on colony success. Appropriate selection of endpoints for risk assessment yields a variety of scenarios for colony success.     

Exploring community assembly through an individual-based model for trophic interactions

Traditionally, the dynamics of community assembly has been analyzed by means of deterministic models of differential equations. Despite the theoretical advances provided by such models, they are restricted to questions about community-wide features. The individual-based modeling offers an opportunity to link bionomic features to patterns at the community scale, allowing us to understand how trait-based assembly rules can arise by dynamical processes. The present paper introduces an individual-based model of community assembly, and discusses some of the major advantages and drawbacks of this approach. The model was framed to deal with predation among size-structured populations, incorporating allometric constraints to energetic requirements, movement, life-history features and interaction relationships among individuals. A protocol of assembly procedure is proposed, in which a period of intense species introductions is followed by a period without introductions. The resultant communities did not present any pattern of trait over-dispersion, meaning that the multivariate distances of bionomic features among co-occurring species were neither larger nor more regular than expected in a random collection of species. It suggests a weak influence of interspecific interactions in the model environment and individualistic rules of coexistence, driven mainly by the spatial structure. This highlights that trait over-dispersion and resource partitioning should not be considered a necessary condition for coexistence, even in communities entirely structured by internal processes like predation and competition.     

SEIB–DGVM: A new Dynamic Global Vegetation Model using a spatially explicit individual-based approach

We report the development of a new spatially explicit individual-based Dynamic Global Vegetation Model (SEIB–DGVM), the first DGVM that can simulate the local interactions among individual trees within a spatially explicit virtual forest. In the model, a sample plot is placed at each grid box, and then the growth, competition, and decay of each individual tree within each plot is calculated by considering the environmental conditions for that tree as it relates to the trees that surround it. Based on these parameters only, the model simulated time lags between climate change and vegetation change. This time lags elongated when original biome was forest, because existing trees prevent newly establish trees from receiving enough sunlight and space to quickly replace the original vegetation. This time lags also elongated when horizontal heterogeneity of sunlight distribution was ignored, indicating the potential importance of horizontal heterogeneity for predicting transitional behavior of vegetation under changing climate. On a local scale, the model reproduced climate zone-specific patterns of succession, carbon dynamics, and water flux, although on a global scale, simulations were not always in agreement with observations. Because the SEIB–DGVM was formulated to the scale at which field biologists work, the measurements of relevant parameters and data comparisons are relatively straightforward, and the model should enable more robust modeling of terrestrial ecosystems.     

How might we model an ecosystem?

Predicting ecosystem effects is of crucial importance in a world at threat from natural and human-mediated change. Here we propose an ecologically defensible representation of an ecosystem that facilitates predictive modelling. The representation has its roots in the early trophic and energetic theory of ecosystem dynamics and more recent functional ecology and network theory. Using the arable ecosystem of the UK as an example, we show that the representation allows simplification from the many interacting plant and invertebrate species, typically present in arable fields, to a more tractable number of trophic-functional types. Our compound hypothesis is that “trophic-functional types of plants and invertebrates can be used to explain the structure, diversity and dynamics of arable ecosystems”. The trophic-functional types act as containers for individuals, within an individual-based model, sharing similar trophic behaviour and traits of biomass transformation. Biomass, or energy, flows between the types and this allows the key ecological properties of individual abundance and body mass, at each trophic height, to be followed through simulations. Our preliminary simulation results suggest that the model shows great promise. The simulation output for simple ecosystems, populated with realistic parameter values, is consistent with current laboratory observations and provides exciting indications that it could reproduce field scale phenomena. The model also produces output that links the individual, population and community scales, and may be analysed and tested using community, network (food web) and population dynamic theory. We show that we can include management effects, as perturbations to parameter values, for modelling the effects of change and indicating management responses to change. This model will require robust analysis, testing and validation, and we discuss how we will achieve this in the future.     

Virtual Corridors for Conservation Management

Abstract:  Corridors are usually perceived as clearly visible, linear landscape elements embedded in a hostile environment that connect two or more larger blocks of habitat. Animal response to certain aspects of landscape heterogeneity, however, can channel their movements into specific routes that may appear similar to their surroundings. These routes can be described as "virtual corridors" (VCs). Here we contribute to the foundation of the concept of VCs and highlight their implications for conservation management. We used an individual-based model to analyze the formation of VCs in the case of hilltopping in butterflies—where males and virgin females ascend to hilltops and mate. We simulated butterfly movements in two different topographically heterogeneous landscapes. We analyzed the movement patterns with respect to one parameter, the intensity of response to topography. Virtual corridor structure depended on the behavioral parameter, landscape, and location of the source patch. Within a realistic range of the behavioral parameter and in a realistic landscape, VC structures may be complex and require individual-based models for their elucidation.     

Evaluating the outcomes of genetic rescue attempts

Augmenting gene flow is a powerful tool for the conservation of small, isolated populations. However, genetic rescue attempts have largely been limited to populations at the brink of extinction, in part due to concerns over negative outcomes (e.g., outbreeding depression). Increasing habitat fragmentation may necessitate more proactive genetic management. Broader application of augmented gene flow will, in turn, require rigorous evaluation to increase confidence and identify pitfalls in this approach. To date, there has been no assessment of best monitoring practices for genetic rescue attempts. We used genomically explicit, individual-based simulations to examine the effectiveness of common approaches (i.e., tests for increases in fitness, migrant ancestry, heterozygosity, and abundance) for determining whether genetic rescue or outbreeding depression occurred. Statistical power to detect the effects of gene flow on fitness was high (≥0.8) when effect sizes were large, a finding consistent with those from previous studies on severely inbred populations. However, smaller effects of gene flow on fitness can appreciably affect persistence probability but current evaluation approaches fail to provide results from which reliable inferences can be drawn. The power of the metrics we examined to evaluate genetic rescue attempts depended on the time since gene flow and whether gene flow was beneficial or deleterious. Encouragingly, the use of multiple metrics provided nonredundant information and improved inference reliability, highlighting the importance of intensive monitoring efforts. Further development of best practices for evaluating genetic rescue attempts will be crucial for a responsible transition to increased use of translocations to decrease extinction risk.     

Development and validation of an individual based Daphnia magna population model: The influence of crowding on population dynamics

An individual-based model was developed to predict the population dynamics of Daphnia magna at laboratory conditions from individual life-history traits observed in experiments with different feeding conditions. Within the model, each daphnid passes its individual life cycle including feeding on algae, aging, growing, developing and – when maturity is reached – reproducing. The modelled life cycle is driven by the amount of ingested algae and the density of the Daphnia population. At low algae densities the population dynamics is mainly driven by food supply, when the densities of algae are high, the limiting factor is “crowding” (a density-dependent mechanism due to chemical substances released by the organisms or physical contact, but independent of food competition).     

Patterns in swimming by a scyphomedusa: a novel approach to quantifying behavior in individuals

Behavior is commonly studied at the group level using several individuals, but there is increasing evidence that the behavior of a few individuals often has a disproportionate effect on the response of a population to its environment. The present study used a suite of statistical techniques, random series analysis, analysis of variance, spectral analysis, and goodness-of-fit tests of frequency histograms, to quantitatively describe the time-dependent changes in individual behavior. Each technique reveals a different facet of the behavior and, when simultaneously applied to the data, distinguishes significant differences among the behaviors of several individuals. The approach was developed and tested on the swimming behavior of four specimens of the scyphomedusa Aurelia aurita (Linnaeus, 1758), which were observed for 19 days, beginning 16 January 1998, and videotaped under identical environmental conditions during that period. The analyses showed that each medusa swam in a unique pattern, varying swimming at characteristic frequencies. Application of the approach to individual-based numerical modeling, to the role of endogenous stimuli in the behavioral repertoire, and to in situ studies of animal behavior is discussed.Communicated by J.P. Grassle, New Brunswick     

Using network centrality measures to manage landscape connectivity

We use a graph-theoretical landscape modeling approach to investigate how to identify central patches in the landscape as well as how these central patches influence (1) organism movement within the local neighborhood and (2) the dispersal of organisms beyond the local neighborhood. Organism movements were theoretically estimated based on the spatial configuration of the habitat patches in the studied landscape. We find that centrality depends on the way the graph-theoretical model of habitat patches is constructed, although even the simplest network representation, not taking strength and directionality of potential organisms flows into account, still provides a coarse-grained assessment of the most important patches according to their contribution to landscape connectivity. Moreover, we identify (at least) two general classes of centrality. One accounts for the local flow of organisms in the neighborhood of a patch, and the other accounts for the ability to maintain connectivity beyond the scale of the local neighborhood. Finally, we study how habitat patches with high scores on different network centrality measures are distributed in a fragmented agricultural landscape in Madagascar. Results show that patches with high degree and betweenness centrality are widely spread, while patches with high subgraph and closeness centrality are clumped together in dense clusters. This finding may enable multispecies analyses of single-species network models.     

Improving inverse model fitting in trees—Anisotropy,multiplicative effects,and Bayes estimation

Model fitting for individual-based effects in forests has some problems. Because samples measuring the separate influence of each individual are rarely available, the measured value in the sample represents the influence of all surrounding individual trees. Therefore, it is helpful to build inverse models that use the spatial pattern of the variable as well as that of the source trees. For example, since seed dispersal is influenced by wind effects, a model is discussed describing anisotropic effects to ensure an unbiased estimate of the total fruit number. Further, we present a model describing the absorption of radiation by trees. In this case a multiplicative combination of individual effects yields the total effect. Our approach uses logarithmic transformations of the original data to model multiplicative combinations as sum of transformed single effects. For fitting model parameters we propose an approach based on Bayesian statistics, to ensure ecologically interpretable parameters.