Karen C. Abbott

A dispersal‐induced paradox: synchrony and stability in stochastic metapopulations

Understanding how dispersal influences the dynamics of spatially distributed populations is a major priority of both basic and applied ecologists. Two well-known effects of dispersal are spatial synchrony (positively correlated population dynamics at different points in space) and dispersal-induced stability (the phenomenon whereby populations have simpler or less extinction-prone dynamics when they are linked by dispersal than when they are isolated). Although both these effects of dispersal should occur simultaneously, they have primarily been studied separately. Herein, I summarise evidence from the literature that these effects are expected to interact, and I use a series of models to characterise that interaction. In particular, I explore the observation that although dispersal can promote both synchrony and stability singly, it is widely held that synchrony paradoxically prevents dispersal-induced stability. I show here that in many realistic scenarios, dispersal is expected to promote both synchrony and stability at once despite this apparent destabilising influence of synchrony. This work demonstrates that studying the spatial and temporal impacts of dispersal together will be vital for the conservation and management of the many communities for which human activities are altering natural dispersal rates.

Analysis of ecological time series with ARMA(p,q) models.

Autoregressive moving average (ARMA) models are useful statistical tools to examine the dynamical characteristics of ecological time-series data. Here, we illustrate the utility and challenges of applying ARMA (p,q) models, where p is the dimension of the autoregressive component of the model, and q is the dimension of the moving average component. We focus on parameter estimation and model selection, comparing both maximum likelihood (ML) and restricted maximum likelihood (REML) parameter estimation. While REML estimation performs better (has less bias) than ML estimation for ARMA (p,q) models with p = 1 (as has been found previously), for models with p > 1 the performance of the estimators is complicated by multimodal likelihood functions. The resulting difficulties in estimation lead to our recommendation that likelihood functions be routinely investigated when applying ARMA (p,q) models. To aid this investigation, we provide MATLAB and R code for the ML and REML likelihood functions. We further explore the consequences of measurement error, showing how it can be explicitly and implicitly incorporated into estimation. In addition to parameter estimation, we also examine model selection for identifying the correct model dimensions (p and q). Finally, we estimate the characteristic return rate of the stochastic process to its stationary distribution, a quantity that describes a key property of population dynamics, and investigate bias that results from both estimation and model selection. While fitting ARMA models to ecological time series with complex dynamics has challenges, these challenges can be surmounted, making ARMA a useful and broadly applicable approach.

Evolution of plant?pollinator mutualisms in response to climate change

Climate change has the potential to desynchronize the phenologies of interdependent species, with potentially catastrophic effects on mutualist populations. Phenologies can evolve, but the role of evolution in the response of mutualisms to climate change is poorly understood. We developed a model that explicitly considers both the evolution and the population dynamics of a plant–pollinator mutualism under climate change. How the populations evolve, and thus whether the populations and the mutualism persist, depends not only on the rate of climate change but also on the densities and phenologies of other species in the community. Abundant alternative mutualist partners with broad temporal distributions can make a mutualism more robust to climate change, while abundant alternative partners with narrow temporal distributions can make a mutualism less robust. How community composition and the rate of climate change affect the persistence of mutualisms is mediated by two‐species Allee thresholds. Understanding these thresholds will help researchers to identify those mutualisms at highest risk owing to climate change.

Weak population regulation in ecological time series

How strongly natural populations are regulated has a long history of debate in ecology. Here, we discuss concepts of population regulation appropriate for stochastic population dynamics. We then analyse two large collections of data sets with autoregressive-moving average (ARMA) models, using model selection techniques to find best-fitting models. We estimated two metrics of population regulation: the characteristic return rate of populations to stationarity and the variability of the stationary distribution (the long-term distribution of population abundance). Empirically, longer time series were more likely to show weakly regulated population dynamics. For data sets of length > or = 20, more than 35% had characteristic return times > 6 years, and more than 29% had stationary distributions whose coefficients of variation were more than two times greater than would be the case if they were maximally regulated. These results suggest that many natural populations are weakly regulated.

Spatial Heterogeneity in Soil Microbes Alters Outcomes of Plant Competition

Plant species vary greatly in their responsiveness to nutritional soil mutualists, such as mycorrhizal fungi and rhizobia, and this responsiveness is associated with a trade-off in allocation to root structures for resource uptake. As a result, the outcome of plant competition can change with the density of mutualists, with microbe-responsive plant species having high competitive ability when mutualists are abundant and non-responsive plants having high competitive ability with low densities of mutualists. When responsive plant species also allow mutualists to grow to greater densities, changes in mutualist density can generate a positive feedback, reinforcing an initial advantage to either plant type. We study a model of mutualist-mediated competition to understand outcomes of plant-plant interactions within a patchy environment. We find that a microbe-responsive plant can exclude a non-responsive plant from some initial conditions, but it must do so across the landscape including in the microbe-free areas where it is a poorer competitor. Otherwise, the non-responsive plant will persist in both mutualist-free and mutualist-rich regions. We apply our general findings to two different biological scenarios: invasion of a non-responsive plant into an established microbe-responsive native population, and successional replacement of non-responders by microbe-responsive species. We find that resistance to invasion is greatest when seed dispersal by the native plant is modest and dispersal by the invader is greater. Nonetheless, a native plant that relies on microbial mutualists for competitive dominance may be particularly vulnerable to invasion because any disturbance that temporarily reduces its density or that of the mutualist creates a window for a non-responsive invader to establish dominance. We further find that the positive feedbacks from associations with beneficial soil microbes create resistance to successional turnover. Our theoretical results constitute an important first step toward developing a general understanding of the interplay between mutualism and competition in patchy landscapes, and generate qualitative predictions that may be tested in future empirical studies.

Using Mechanistic Models to Understand Synchrony in Forest Insect Populations : The North American Gypsy Moth as a Case Study

In many forest insects, subpopulations fluctuate concurrently across large geographical areas, a phenomenon known as population synchrony. Because of the large spatial scales involved, empirical tests to identify the causes of synchrony are often impractical. Simple models are, therefore, a useful aid to understanding, but data often seem to contradict model predictions. For instance, chaotic population dynamics and limited dispersal are not uncommon among synchronous forest defoliators, yet both make it difficult to achieve synchrony in simple models. To test whether this discrepancy can be explained by more realistic models, we introduced dispersal and spatially correlated stochasticity into a mechanistic population model for the North American gypsy moth Lymantria dispar. The resulting model shows both chaotic dynamics and spatial synchrony, suggesting that chaos and synchrony can be reconciled by the incorporation of realistic dynamics and spatial structure. By relating alterations in model structure to changes in synchrony levels, we show that the synchrony is due to a combination of spatial covariance in environmental stochasticity and the origins of chaos in our multispecies model.

Environmental variation in ecological communities and inferences from single-species data.

Data are often collected for a single species within an ecological community, so quantitative tools for drawing inferences about the unobserved portions of the community from single-species data are valuable. In this paper, we present and examine a method for estimating community dimension (the number of strongly interacting species or groups) from time series data on a single species. The dynamics of one species can be strongly affected by environmental stochasticity acting not only on itself, but also on other species with which it interacts. By fully accounting for the effects of stochasticity on populations embedded in a community, our approach gives better estimates of community dimension than commonly used methods. Using a combination of time series data and simulations, we show that failing to properly account for stochasticity when attempting to relate population dynamics to attributes of the community can give misleading information about community dimension.

Stochasticity and bistability in insect outbreak dynamics

There is a long history in ecology of using mathematical models to identify deterministic processes that may lead to dramatic population dynamic patterns like boom-and-bust outbreaks. Stochasticity is also well-known to have a significant influence on the dynamics of many ecological systems, but this aspect has received far less attention. Here, we study a stochastic version of a classic bistable insect outbreak model to reveal the role of stochasticity in generating outbreak dynamics. We find that stochasticity has strong effects on the dynamics and that the stochastic system can behave in ways that are not easily anticipated by its deterministic counterpart. Both the intensity and autocorrelation of the stochastic environment are important. Stochasticity with higher intensity (variability) generally weakens bistability, causing the dynamics to spend more time at a single state rather than jumping between alternative stable states. Which state the population tends toward depends on the noise color. High-intensity white noise causes the insect population to spend more time at low density, potentially reducing the severity or frequency of outbreaks. However, red (positively autocorrelated) noise can make the population spend more time near the high density state, intensifying outbreaks. Under neither type of noise do early warning signals reliably predict impending outbreaks or population crashes.

Trade-Offs and Coexistence in Fluctuating Environments: Evidence for a Key Dispersal-Fecundity Trade-Off in Five Nonpollinating Fig Wasps

The ecological principle of competitive exclusion states that species competing for identical resources cannot coexist, but this principle is paradoxical because ecologically similar competitors are regularly observed. Coexistence is possible under some conditions if a fluctuating environment changes the competitive dominance of species. This change in competitive dominance implies the existence of trade-offs underlying species’ competitive abilities in different environments. Theory shows that fluctuating distance between resource patches can facilitate coexistence in ephemeral patch competitors, given a functional trade-off between species dispersal ability and fecundity. We find evidence supporting this trade-off in a guild of five ecologically similar nonpollinating fig wasps and subsequently predict local among-patch species densities. We also introduce a novel colonization index to estimate relative dispersal ability among ephemeral patch competitors. We suggest that a dispersal ability–fecundity trade-off and spatiotemporally fluctuating resource availability commonly co-occur to drive population dynamics and facilitate coexistence in ephemeral patch communities.

Moving forward in circles: challenges and opportunities in modelling population cycles

Population cycling is a widespread phenomenon, observed across a multitude of taxa in both laboratory and natural conditions. Historically, the theory associated with population cycles was tightly linked to pairwise consumer-resource interactions and studied via deterministic models, but current empirical and theoretical research reveals a much richer basis for ecological cycles. Stochasticity and seasonality can modulate or create cyclic behaviour in non-intuitive ways, the high-dimensionality in ecological systems can profoundly influence cycling, and so can demographic structure and eco-evolutionary dynamics. An inclusive theory for population cycles, ranging from ecosystem-level to demographic modelling, grounded in observational or experimental data, is therefore necessary to better understand observed cyclical patterns. In turn, by gaining better insight into the drivers of population cycles, we can begin to understand the causes of cycle gain and loss, how biodiversity interacts with population cycling, and how to effectively manage wildly fluctuating populations, all of which are growing domains of ecological research.