Ecological Invasion: Spatial Clustering and the Critical Radius (original) (raw)

Nucleation and global time scales in ecological invasion under preemptive competition

The breakdown of biogeographic barriers allows some invasive species to reshape ecological communities and threaten local biodiversity. Most introductions of exotic species fail to generate an invasion. However, once introduction succeeds, invader density increases rapidly. We apply nucleation theory to describe spatio-temporal patterns of the invasion process under preemptive competition. The predictions of the theory are confirmed by Monte Carlo simulations of the underlying discrete spatial stochastic dynamics. In particular, for large enough spatial regions, invasion occurs through the nucleation and subsequent growth of many clusters of the invasive species, and the global densities are well approximated by Avrami’s law for homogeneous nucleation. For smaller systems or very small introduction rates, invasion typically occurs through a single cluster, whose appearance is inherently stochastic.

Invasion Dynamics in Spatially Heterogeneous Environments

The American Naturalist, 2009

Biological invasions, including infectious disease outbreaks and biocontrol introductions, often involve small numbers of individuals arriving in spatially heterogeneous environments. Small numbers lead to demographic stochasticity, and spatial heterogeneity means that establishment success depends critically on the introduction sites and movement patterns of invaders. We present a general stochastic modeling framework to address how spatial heterogeneity and movement patterns determine establishment success, population growth, and rates of spatial spread. For dispersal-limited populations, our analysis reveals that spatial heterogeneity increases the expected population growth rate and that local reproductive numbers determine establishment success. Higher dispersal rates decrease the expected population growth rate but can enhance establishment success, particularly when movement patterns are positively correlated with local reproductive numbers. We also find that several small, randomly distributed propagules of invaders are more likely to succeed than a single large propagule. Even if invasions are ultimately successful, there may be substantial time lags before an invader reaches observable densities. These time lags are longer for invasions into patches where extinction risk is high and in landscapes where metapopulation-scale population growth rate is low, while the opposite holds true for rates of spatial spread. Sensitivity analysis of our models provides guidance for control efforts.

Invasion under a trade-off between density dependence and maximum growth rate

Population Ecology, 2008

The invasion of alien species and genotypes is an increasing concern in contemporary ecology. A central question is, what life-history traits enable invasion amidst populations of wild species and conventional cultivars? In order to invade, the initially rare species must perform better than their resident competitors. We conducted a mathematical analysis and simulation of a two-species extension of the Maynard Smith and Slatkin model for population dynamics in discrete time to study the role of density dependence as different types of competition in the invasion of new species. The type of density dependence ranged from scramble to contest competition. This led to intrinsic dynamics of the species range from point equilibrium to cycles and chaos. The traits were treated either as free parameters or constrained by a trade-off resulting from a common fixed strength of density dependence or equilibrium density. Resident and intruder traits had up to tenfold differences in all of the parameters investigated. Higher equilibrium density of the intruder allowed invasion. Under constrained equilibrium density, an intrinsically stable intruder could invade an unstable resident population. Scramble competition made a population more susceptible to invasion than contest competition (e.g., limitation by light or territory availability). This predicts that a population which is mainly limited by food (or nutrients in plants) is more likely to be invaded than a population limited by a hierarchical competition, such as light among plants. The intruder population may have an effect on the resident population's dynamics, which makes the traditional invasion analysis unable to predict invasion outcome.

Invasion speeds for structured populations in fluctuating environments

Theoretical Ecology, 2011

We live in a time where climate models predict future increases in environmen-1 tal variability and biological invasions are becoming increasingly frequent. A key 2 to developing effective responses to biological invasions in increasingly variable en-3 vironments will be estimates of their rates of spatial spread and the associated un-4 certainty of these estimates. Using stochastic, stage-structured, integro-difference 5 equation models, we show analytically that invasion speeds are asymptotically nor-6 mally distributed with a variance that decreases in time. We apply our methods to 7 a simple juvenile-adult model with stochastic variation in reproduction and an il-8 lustrative example with published data for the perennial herb, Calathea ovandensis. 9 These examples buttressed by additional analysis reveal that increased variability 10 in vital rates simultaneously slow down invasions yet generate greater uncertainty 11 about rates of spatial spread. Moreover, while temporal autocorrelations in vital 12 rates inflate variability in invasion speeds, the effect of these autocorrelations on the 13 average invasion speed can be positive or negative depending on life history traits 14 and how well vital rates "remember" the past. 15 Word count: 4,649 without Appendix; 4,807 with Appendix Figures: 4 Tables: 0 References: 50 arXiv:1006.2490v1 [q-bio.PE] 12 Jun 2010 65 tuations and demographic structure on invasion speeds. We begin by reviewing the work of 66 Neubert and Caswell (2000) in constant environments. We extend these models to allow for 67 temporal variation in the projection matrices and dispersal kernels and provide a formula for 68 asymptotic invasion speeds and normal approximations that describe the variation in these inva-69 sion speeds over finite time horizons. Applying these results to two examples, we illustrate how 70 our results allow one to address questions like "how does the magnitude of variability influence 71 asymptotic invasion speeds?" and "how do temporal autocorrelations influence the uncertainty 72 in predicting invasion speeds?" 73 Constant environments 74 Neubert and Caswell (2000) analyzed invasion speeds for IDE models for stage-structured 75 populations in constant environments. These models consider structured populations living on 76

Temporally variable dispersal and demography can accelerate the spread of invading species

Theoretical Population Biology, 2012

We analyze how temporal variability in local demography and dispersal combine to affect the rate of spread of an invading species. Our model combines state-structured local demography (specified by an integral or matrix projection model) with general dispersal distributions that may depend on the state of the individual or its parent. It allows very general patterns of stationary temporal variation in both local demography and in the frequency and distribution of dispersal distances. We show that expressions for the asymptotic spread rate and its sensitivity to parameters, which have been derived previously for less general models, continue to hold. Using these results we show that random temporal variability in dispersal can accelerate population spread. Demographic variability can further accelerate spread if it is positively correlated with dispersal variability, for example if high-fecundity years are also years in which juveniles tend to settle further away from their parents. A simple model for the growth and spread of patches of an invasive plant (perennial pepperweed, Lepidium latifolium) illustrates these effects and shows that they can have substantial impacts on the predicted speed of an invasion wave. Temporal variability in dispersal has received very little attention in both the theoretical and empirical literature on invasive species spread. Our results suggest that this needs to change.

Species Invasion in a Network Population Model

2016

The introduction and spread of invasive species is increasingly driven by the expansion of human-made transportation routes. We formulate a network model of biotic invasion incorporating logistic growth and dispersal along a network, and present analyses of the model. We introduce small world networks and use them to investigate the role of network properties and long-distance dispersal on spread dynamics. Lastly we present comparisons between the stochastic and deterministic models to illustrate the effects of stochasticity on invasive species spread dynamics.

Permanence via invasion graphs: incorporating community assembly into modern coexistence theory

Journal of Mathematical Biology

To understand the mechanisms underlying species coexistence, ecologists often study invasion growth rates of theoretical and data-driven models. These growth rates correspond to average per-capita growth rates of one species with respect to an ergodic measure supporting other species. In the ecological literature, coexistence often is equated with the invasion growth rates being positive. Intuitively, positive invasion growth rates ensure that species recover from being rare. To provide a mathematically rigorous framework for this approach, we prove theorems that answer two questions: (i) When do the signs of the invasion growth rates determine coexistence? (ii) When signs are sufficient, which invasion growth rates need to be positive? We focus on deterministic models and equate coexistence with permanence, i.e., a global attractor bounded away from extinction. For models satisfying certain technical assumptions, we introduce invasion graphs where vertices correspond to proper subs...