Noelle G. Beckman, firstname.lastname@example.org
Richard Schugart, email@example.com
In this talk, I will provide an introduction to using dynamic models (ODEs) as statistical models, and to some tools and approaches for overcoming mathematical and statistical challenges that can arise in applications. I will illustrate different uses of dynamic models as statistical models using multiple ecological examples, using both empirical and synthetic (simulated) data. I will present different methods for parameter estimation and uncertainty analysis, including our recent work on integrating bifurcation information into some of these methods, and how these can be used in conjunction with an assessment of a model’s statistical properties to inform experimental design or data collection protocols. I will conclude the talk by briefly mentioning how our current toolset might benefit from future research. 368
Stochasticity influences single species population dynamics, typically elevating extinction risk. On the other hand, stochasticity can also allow for multi-species coexistence when competition would otherwise lead to exclusion. However, many forms of stochasticity exist, and there is currently no consensus on how each form of stochasticity may influence competitive outcome. In many cases, stochasticity can cause competitive indeterminacy, in which the outcome of competition varies in replicate communities. Here, we examine the role of stochasticity on competitive indeterminacy and extinction risk by extending a set of eight stochastic Ricker models incorporating combinations of four distinct forms of stochasticity; environmental stochasticity, demographic stochasticity, demographic heterogeneity, and stochastic sex determination. Using replicated populations of two Tribolium species, we competed the set of stochastic models, finding that demographic stochasticity, environmental stochasticity, and stochastic sex determination were the prominent causes of population variability. While the standard Poisson Ricker model incorporating demographic stochasticity does not allow for competitive indeterminacy or transient coexistence given fitness differences between competitors, our best fit model suggests that stochastic processes allow to transient coexistence and competitive indeterminacy. This probabilistic view of competitive outcome dependent on the initial abundance of competing species could explain the anomalous long term co-occurrence observed in previous Tribolium experiments at moderately long timescales. Further, the incorporation of the various stochastic forces into demographic models suggest that current estimates of extinction risk, coexistence, and biological invasion probabilities may be inaccurate when based on models only incorporating demographic stochasticity.
Global change affects the ecology and evolution of dispersal, limiting the ability of species to move or adapt to global change events. Due to the long-term and spatially-complex dynamics of plant populations, understanding and predicting their responses to global change is empirically and mathematically challenging. We apply recent advances in the study of species’ movement and develop a general classification scheme to assess the risk of plant extinction in response to climate change in continuous landscapes. Using a Bayesian approach, we synthesize existing data on dispersal, functional traits, and demography to generate virtual species with realistic dispersal kernels and life-history strategies. We sample these virtual species to parameterize integrodifference equations and approximate population spread in continuous landscapes. Using this approach, we obtain predictors of risk that are related to easily measurable functional traits that will inform the types of species least likely to track a shifting climate. In future research, this approach will be extended to predict extinction risk of plant species in fragmented landscapes. This research will help identify species at greatest risk and aid the development of conservation strategies to ensure their persistence under global change.
After being brought in by pioneers for agricultural reasons, European earthworms have been taking North America by storm and are starting to change the Alberta Boreal forests. This talk uses an invasive species model to the rate of new worm introductions and how quickly they spread with the goal of predicting the future extent of the great Canadian worm invasion. To estimate the introduction and spread rates we need to deal with an unknown number of introductions, which in turn results in an unknown number of model parameters. The complexity of the model means that we need to turn to Approximate Bayesian Computation methods. Approximate Bayesian Computation is a step in the right direction when it's just not possible to actually do the right thing- in this case using the exact invasive species model is infeasible.
In recent years, large areas of lodgepole pine forest inWestern North America have been disturbed by a series of severe and widespread outbreaks of a native insect, the mountain pine beetle (Dendroctonus ponderosae). The dramatic and unprecedented consequences of this epidemic on forest ecosystem services have motivated many researchers to investigate the causes and dynamics of pine beetle outbreaks. For decades now, government officials in British Columbia (BC) have been using remote sensing to acquire spatially referenced data on pine mortality and associated environmental covariates. With yearly data spanning 2000-2017 at a resolution of 1 km 2 and a spatial extent of nearly 1 million km 2 , this ecological time series is unusually large and complete. How can we connect such a massively detailed dataset with nonlinear population models? In this talk I will explain how spatial statistical techniques can be used to tackle this modelling problem. The core model combines a novel formulation of nonlinear discrete-time growth and dispersal patterns for eruptive forest pests with a stochastic component capturing the environmental noise shared by nearby pine stands. Because of the high-dimensionality, traditional maximum likelihood based inference can be computationally infeasible. I will discuss techniques for speeding up computations of the likelihood function, as well as pseudolikelihood-based alternatives. I will also discuss the model’s potential for regional planning of future pine beetle control efforts in BC.