Metamodels for transdisciplinary analysis of wildlife population dynamics.

Wildlife population models have been criticized for their narrow disciplinary perspective when analyzing complexity in coupled biological - physical - human systems. We describe a "metamodel" approach to species risk assessment when diverse threats act at different spatiotemporal scales, interact in non-linear ways, and are addressed by distinct disciplines. A metamodel links discrete, individual models that depict components of a complex system, governing the flow of information among models and the sequence of simulated events. Each model simulates processes specific to its disciplinary realm while being informed of changes in other metamodel components by accessing common descriptors of the system, populations, and individuals. Interactions among models are revealed as emergent properties of the system. We introduce a new metamodel platform, both to further explain key elements of the metamodel approach and as an example that we hope will facilitate the development of other platforms for implementing metamodels in population biology, species risk assessments, and conservation planning. We present two examples - one exploring the interactions of dispersal in metapopulations and the spread of infectious disease, the other examining predator-prey dynamics - to illustrate how metamodels can reveal complex processes and unexpected patterns when population dynamics are linked to additional extrinsic factors. Metamodels provide a flexible, extensible method for expanding population viability analyses beyond models of isolated population demographics into more complete representations of the external and intrinsic threats that must be understood and managed for species conservation

Tackling Biocomplexity with Meta-models for Species Risk Assessment

We describe results of a multi-year effort to strengthen consideration of the human dimension into endangered species risk assessments and to strengthen research capacity to understand biodiversity risk assessment in the context of coupled human-natural systems. A core group of social and biological scientists have worked with a network of more than 50 individuals from four countries to develop a conceptual framework illustrating how human-mediated processes influence biological systems and to develop tools to gather, translate, and incorporate these data into existing simulation models. A central theme of our research focused on (1) the difficulties often encountered in identifying and securing diverse bodies of expertise and information that is necessary to adequately address complex species conservation issues; and (2) the development of quantitative simulation modeling tools that could explicitly link these datasets as a way to gain deeper insight into these issues. To address these important challenges, we promote a "meta-modeling" approach where computational links are constructed between discipline-specific models already in existence. In this approach, each model can function as a powerful stand-alone program, but interaction between applications is achieved by passing data structures describing the state of the system between programs. As one example of this concept, an integrated meta-model of wildlife disease and population biology is described. A goal of this effort is to improve science-based capabilities for decision making by scientists, natural resource managers, and policy makers addressing environmental problems in general, and focusing on biodiversity risk assessment in particular

Metapopulation dynamics influenced by dispersal.

<p>Metapopulation size is projected by (A) a PVA model in <i>Vortex</i> assuming varied rates of dispersal, annual fluctuations in demographic rates, and inbreeding depression; (B) a metamodel that linked a PVA model in <i>Vortex</i> to an infectious disease model in <i>Outbreak</i>, assuming varied rates of dispersal, minimal annual fluctuations in demographic rates, and no inbreeding depression; and (C) a metamodel that linked a PVA in <i>Vortex</i> to an infectious disease model in <i>Outbreak</i>, assuming varied rates of dispersal, annual fluctuations in demographic rates, and inbreeding depression. In (A), higher rates of dispersal increase growth and stability of the metapopulation because stochastic effects in local subpopulations are dampened. When disease was introduced but stochasticity was removed, as in (B), higher rates of dispersal depress population size because of the faster spread of disease. Finally, when stochasticity, disease, and dispersal were considered in (C), higher dispersal initially reduced population size because of the faster spread of disease. In later years, disease was largely eliminated from the system, and higher rates of dispersal stabilized the population against stochastic fluctuations. During a few years in the middle of the simulation, disease and stochastic processes were equally important, and intermediate rates of dispersal led to the highest population size.</p

Examples of data structure and program flow implemented by <i>MetaModel</i><i>Manager</i>.

<p>(A) Nested data representing a species in a metamodel. Global state variables (GSvar), population state variables (PSvar), and individual state variables (ISvar) are descriptors of the overall system, each population, and each individual, respectively. (B) Flow of control among component models. Curved arrows represent access to and modification of data. Block arrows represent control passed among models. (C) A two-species metamodel, with one modifier and one translator model acting on one species and two modifier models acting on the second species. Control alternates between the species, as illustrated by solid block arrows. Each system, modifier, and translator model has access to change any property of its populations and individuals as well as any shared global state variables.</p

Metamodel that integrates demography, landscape change, dispersal, and disease status.

<p>A PVA program acts as the system model (solid outline) to simulate individual survival and reproduction based on individual and population state variables (shown in italics) passed from other models. Modifier models (dashed outlines) simulate habitat dynamics, individual movements, and individual transitions in disease status. A central facilitator program passes state variables between the system and modifier models at appropriate time steps. The ultimate results are measures of population dynamics and extinction risk for a species impacted by habitat change and disease.</p

Population trajectories for a prey species subjected to different levels of predation.

<p>Mean prey population size through time is predicted by a single-species PVA model that assumed a fixed predator population size. Simulations were run for predator populations of 50, 60, 70, 80, and 100 individuals. The prey population was sustained at a size of N = 10000 or more if there were 80 or fewer predators.</p

Population trajectories for a predator species at different levels of prey availability.

<p>Mean predator population size through time is predicted by a single-species PVA model that assumed a fixed prey population size. Simulations were run for prey populations of 5000, 6000, 7000, 8000, 10000, and 15000 individuals. Approximately 6000 prey was sufficient to sustain growth of the predator population from its initial N = 50 to more than 100.</p

Mean predator-prey dynamics in coupled metamodels that (A) did not include and (B) did include stochastic variation.

<p>Mean population densities (N/K) for a predator and a prey species are predicted by a two-species metamodel, which assumed that the density of one species would impact the other species. In (A), externally driven sources of stochasticity (e.g., environmental variation, catastrophes) and inbreeding did not impact either population, and we found that the predator population grew rapidly, causing collapse of the prey population followed by collapse of the predator population. In (B), externally driven stochasticity and inbreeding depression could impact each population. For this scenario, the average trajectory shows that the predator population grew, followed by a decline in prey, causing subsequent decline in the predator, eventually resulting in a possibly stable state in which a reduced prey population sustained a reduced predator population.</p