Spatially-explicit Individual-based Models Research Articles

An integrated modeling approach for considering wildlife reintroduction in the face of climate uncertainty: A case for the North Cascades grizzly bear

As Earth faces a crisis of biodiversity loss, reintroduction of imperiled species has become an important tool toward mitigating extirpation. Current habitat quality for a reintroduced species may change dramatically under future climate scenarios, undermining or supporting species conservation efforts. Models designed to understand such change must consider the niche plasticity of a species to assess the costs and benefits of reintroduction. We integrated spatially-explicit individual-based population models with a dynamic vegetation model, using combinations of global climate models and greenhouse gas scenarios to better understand potential future carrying capacity for grizzly bears in the North Cascades Ecosystem (NCE). We estimated the ecosystem could support a grizzly bear population under several climate change scenarios through the 2080s, with the amount of high quality habitat increasing across all models, scenarios, and time periods, as compared to current conditions. Projected future habitat quality remained consistent or increased slightly along the eastern portion of the ecosystem, and increased along its central and western portions, for a net increase in high quality habitat through time. At the most plausible female home range size of 280 km2, we estimated carrying capacity would increase from a baseline of 139 female bears to 241–289 female bears. Estimated changes in habitat over time could increase grizzly bear density to 20–22 bears/1000 km2 (males and females) from the previous estimate of 17 bears/1000 km2. Species with broad ecological niches (i.e., generalists), such as grizzly bears, may be especially good candidates for reintroduction efforts in some ecosystems. Our integrated model structure provides an innovative tool for advancing reintroduction initiatives while considering some long-term risks for species.

A spatially-explicit, individual-based demogenetic simulation framework for evaluating hybridization dynamics

Spatially-explicit individual-based simulation models provide a valuable tool for exploring complex ecological and evolutionary processes that are not easily empirically measured. Here, we present modifications of a spatially-explicit individual-based simulation model (CDMetaPOP) to accommodate a two-species system and simulations involving interspecific hybridization. We first describe how a hybrid (H) index is used to distinguish individuals of interspecific descent from those of either parental species. User-defined thresholds provide flexibility in the degree of admixture tolerated for classifying ‘pure’ individuals. We then detail relationships further informed by the H index, including individual growth, temperature-based fitness and selection, and mate preference behavior. Empirically derived species- and system-specific information can be incorporated into these relationships, for example, to produce differential growth among hybrids and parental species. Lastly, we demonstrate an application of this simulation framework by exploring the relative effects of temperature-based selection, mate preference behavior, and hybrid fitness on the rate and spatial extent of sympatric hybridization between two native riverine fish species, bull trout (Salvelinus confluentus) and Dolly Varden (Salvelinus malma), in the upper Skagit River system (United States and Canada). Results from this demonstration provide guidance for future empirical studies of bull trout, a federally threatened species. Understanding factors that contribute to the initiation and maintenance of hybridization, as well as the ecological and evolutionary consequences of this phenomenon, is of increasing importance given shifting species ranges due to large-scale landscape modification and a changing global climate. Our framework can be used to study a wide range of hybridization dynamics in any terrestrial or aquatic system, including comparisons of distinct environmental conditions or potential management responses.

Modeling as a Decision Support Tool for Bovine TB Control Programs in Wildlife.

Computer modeling has a long history of association with epidemiology, and has improved our understanding of the theory of disease dynamics and provided insights into wildlife disease management. A summary of badger bovine TB models and their role in decision making is presented, from a simple initial SEI model, to SEIR (inclusion of a recovered category) and SEI1I2 (inclusion of two stages of disease progression) variants, and subsequent spatially-explicit individual-based models used to assess historical badger management strategies. The integration of cattle into TB models allowed comparison of the predicted impacts of different badger management strategies on cattle herd breakdown rates, and provided an economic dimension to the outputs. Estimates of R0 for bovine TB in cattle and badgers are little higher than unity implying that the disease should be relatively easy to control, which is at odds with practical experience. A cohort of recent models have suggested that combined strategies, involving management of both host species and including vaccination may be most effective. Future models of badger vaccination will need to accommodate the partial protection from infection and likely duration of immunity conferred by the currently available vaccine (BCG). Descriptions of how models could better represent the ecological and epidemiological complexities of the badger-cattle TB system are presented, along with a wider discussion of the utility of modeling for bovine TB management interventions. This includes consideration of the information required to maximize the utility of the next generation of models.

How effective are buffer zones in managing invasive beavers in Patagonia? A simulation study

In an age of invasions, it is critical to design and test management strategies to more efficiently control foreign species. Spatially explicit individual based models (SEIBMs) are a powerful tool to explore different management scenarios to control invaders, but we rarely have enough data to parameterize these models, particularly for relatively long-lived species. Here we take advantage of our previous work estimating demographic rates of invasive beavers in Patagonia, and develop an SEIBM to model the spread of beavers in Patagonia. We used our SEIBM both to estimate dispersal distances by fitting their observed rate of spread and to test how placing a buffer zone (a longitudinal strip of land perpendicular to the direction of spread within which a fraction of beavers are culled) beyond the invasion front would work as a control strategy. Specifically, we explored six different scenarios with two different culling rates and two buffer zone widths. We found that beavers in Patagonia must disperse long distances on average to account for the observed rate of spread, and thus our model predicts that a 100 km buffer zone will be needed to slow (but likely not halt) the spread of beavers. Interestingly, culling a higher proportion of beavers within a 100 km buffer zone (90 vs. 60%) did not improve buffer zone performance. Our study shows that wide buffer zones can slow (but likely not halt) continental spread of beavers in Patagonia and potentially pave the way for beaver eradication.

Simulating individual-based movement in dynamic environments

The accuracy of spatially-explicit individual-based models (IBMs) often depends on the realistic simulation of the movement of organisms, which is especially challenging when movement cues (e.g., environmental conditions; prey and predator abundances) vary in time and space. A number of approaches or sub-models have been developed for simulating movement in IBMs. We evaluated four movement sub-models (restricted-area search, kinesis, event-based, and run and tumble) in a spatially-explicit cohort IBM in which the prey and predators were both dynamic (varying across cells and over time) and responsive to the dynamics of the cohort individuals. Movement, growth, and mortality were simulated every 25min for 30 12-h days (single generation) on a 2.7×2.7km2 grid with 625m2 cells, and egg production was calculated based on weight and survival of individuals at the end of 30days. We based the cohort model on small pelagic coastal fish, and the prey was based on zooplankton and the predators based on a typical piscivorous fish. Movement sub-models were calibrated with a genetic algorithm in dynamic and static versions of the prey and predator-defined environments. Prey and predator fields were fixed in the static environment; in the dynamic environment, prey density was reduced based on consumption and predators actively sought out cohort individuals. Static-trained sub-models were then tested in the dynamic environments and vice versa. The four movement sub-models were successfully trained and performed reasonably well in terms of egg production (a measure of individual fitness) when trained and tested in the same type of environment. However, the type of environment affected calibration success, and static-trained models did not perform well when tested in dynamic environments because cohort individuals moved in response to both prey and predator cues rather than primarily avoiding fixed-in-space high mortality cells. Use of movement sub-models in IBMs should carefully consider how the conditions assumed for calibration relates to the dynamic conditions the model will be used to address.

Overcoming challenges of sparse telemetry data to estimate caribou movement

Spatially explicit individual-based models (SE-IBMs) can simulate species’ movement behaviors. Although such models allow many applications to ecology and conservation biology and are useful for management purposes, they are difficult to parameterize directly from the kinds of observational data that are generally available. Coupled with pattern-oriented modeling strategy, SE-IBMs can be parameterized and assess alternate hypotheses on movement behaviors by comparing simulated to observed patterns of movement. We illustrated this with the endangered Atlantic-Gaspésie caribou population while using sparse Very High Frequency (VHF) telemetry data. We formulated alternative movement hypotheses built around proximate movement mechanisms and coded them into an SE-IBM to explain and predict caribou movement. These mechanisms were: a random walk, a biased correlated random walk, a foray loop to reproduce caribou extra-range movement patterns, and caribou fidelity during mating season. We combined these to test single- and two-behavior movement models regarding landscape quality. The best fitted model successfully reproduced most of the movement patterns derived from the VHF locations. We found that caribou movement in low quality habitat was better reproduced by a foray loop behavior than by a biased correlated random walk or a random walk. Adding an attraction to the individuals’ mating area during the mating season also improved the model. We used the selected model to estimate and map potential landscape use by the Atlantic-Gaspésie caribou. We confirmed areas of high use seen in the VHF data and identified some potential areas where no caribou locations were recorded. We also found that large areas of moderate to high quality habitat were unused because they could not be reached by caribou. We conclude that sparse data sets, such as VHF collar locations, can be used to fit movement models whose parameters could not be estimated directly from the data. SE-IBMs coupled with pattern-oriented modeling can reveal new insights about landscape use beyond what can be defined with habitat selection models, and can identify habitat locations where management actions could be taken to facilitate species persistence or recovery of endangered populations.

Landscape fragmentation and pollinator movement within agricultural environments: a modelling framework for exploring foraging and movement ecology.

Pollinator decline has been linked to landscape change, through both habitat fragmentation and the loss of habitat suitable for the pollinators to live within. One method for exploring why landscape change should affect pollinator populations is to combine individual-level behavioural ecological techniques with larger-scale landscape ecology. A modelling framework is described that uses spatially-explicit individual-based models to explore the effects of individual behavioural rules within a landscape. The technique described gives a simple method for exploring the effects of the removal of wild corridors, and the creation of wild set-aside fields: interventions that are common to many national agricultural policies. The effects of these manipulations on central-place nesting pollinators are varied, and depend upon the behavioural rules that the pollinators are using to move through the environment. The value of this modelling framework is discussed, and future directions for exploration are identified.

Simulating the evolution of a clonal trait in plants with sexual and vegetative reproduction

Aims Phenotypic optimality models neglect genetics. However, especially when heterozygous genotypes are fittest, evolving allele, genotype and phenotype frequencies may not correspond to predicted optima. This was not previously addressed for organisms with complex life histories. Methods Therefore, we modelled the evolution of a fitness-relevant trait of clonal plants, stolon internode length. We explored the likely case of an asymmetric unimodal fitness profile with three model types. In constant selection models (CSMs), which are gametic, but not spatially explicit, evolving allele frequencies in the one-locus and fiveloci cases did not correspond to optimum stolon internode length predicted by the spatially explicit, but not gametic, phenotypic model. This deviation was due to the asymmetry of the fitness profile. Gametic, spatially explicit individual-based (SEIB) modeling allowed us relaxing the CSM assumptions of constant selection with exclusively sexual reproduction. Important findings For entirely vegetative or sexual reproduction, predictions of the gametic SEIB model were close to the ones of spatially explicit nongametic phenotypic models, but for mixed modes of reproduction they approximated those of gametic, not spatially explicit CSMs. Thus, in contrast to gametic SEIB models, phenotypic models and, especially for few loci, also CSMs can be very misleading. We conclude that the evolution of traits governed by few quantitative trait loci appears hardly predictable by simple models, that genetic algorithms aiming at technical optimization may actually miss the optimum and that selection may lead to loci with smaller effects in derived compared with ancestral lines.

Hydrology, habitat change and population demography: an individual‐based model for the endangered Cape Sable seaside sparrow Ammodramus maritimus mirabilis

Summary Habitat destruction and fragmentation have led to precipitous declines in a number of species of concern. For these species, traditional models that group individuals into age or stage cohorts may not accurately capture the stochasticity associated with small populations. Additionally, traditional models do not explicitly incorporate landscape‐level structure, which becomes increasingly important at small population sizes. Thus, for declining species, spatially explicit individual‐based models (SEIBM) can be used to understand both population demography and the impacts of habitat destruction, and to guide management practices to increase the chances of species survival. To gauge the impacts of changes in habitat and also demographic rates on a US endangered species, we constructed an SEIBM for the Cape Sable seaside sparrow (Ammodramus maritimus mirabilis Howell) of the South Florida Everglades. The model simulates temporal and spatial dynamics of individual sparrows using local GIS‐based topography, vegetation and hydrology along with behavioural and demographic rates derived from field studies. When adult mortality and, to a lesser extent, juvenile mortality were increased in model simulations, there was an increase in extinction risk and a decrease in population size, whereas changes in number of clutches or female mating range had little impact. In contrast to the effects of simulating changes in mortality rates, simulated landscape‐level changes (increasing water levels or decreasing habitat availability) were associated with dramatic population declines and increases in extinction risk. The sparrow appears to be particularly sensitive to the loss of higher‐elevation breeding habitat. These results highlight the importance of proper water‐ and land‐use management in assuring the species’ survival. Synthesis and applications. Although changes in demographic rates affect population growth and are often the focus of conservation efforts, changes in habitat structure can also dramatically alter population viability. When both landscape‐level and demographic data are available, spatially explicit models are particularly advantageous. Not only do they allow researchers and resource managers to prioritize areas for habitat restoration and species management, but they can also be used to help focus future research efforts.

Population-level Assessment of Risks of Pesticides to Birds and Mammals in the UK

It is generally acknowledged that population-level assessments provide a better measure of response to toxicants than assessments of individual-level effects. Population-level assessments generally require the use of models to integrate potentially complex data about the effects of toxicants on life-history traits, and to provide a relevant measure of ecological impact. Building on excellent earlier reviews we here briefly outline the modelling options in population-level risk assessment. Modelling is used to calculate population endpoints from available data, which is often about individual life histories, the ways that individuals interact with each other, the environment and other species, and the ways individuals are affected by pesticides. As population endpoints, we recommend the use of population abundance, population growth rate, and the chance of population persistence. We recommend two types of model: simple life-history models distinguishing two life-history stages, juveniles and adults; and spatially-explicit individual-based landscape models. Life-history models are very quick to set up and run, and they provide a great deal of insight. At the other extreme, individual-based landscape models provide the greatest verisimilitude, albeit at the cost of greatly increased complexity. We conclude with a discussion of the implications of the severe problems of parameterising models.