We introduce a new statistical computing method, called data cloning, to calculate maximum likelihood estimates and their standard errors for complex ecological models. Although the method uses the Bayesian framework and exploits the computational simplicity of the Markov chain Monte Carlo (MCMC) algorithms, it provides valid frequentist inferences such as the maximum likelihood estimates and their standard errors. The inferences are completely invariant to the choice of the prior distributions and therefore avoid the inherent subjectivity of the Bayesian approach. The data cloning method is easily implemented using standard MCMC software. Data cloning is particularly useful for analysing ecological situations in which hierarchical statistical models, such as state-space models and mixed effects models, are appropriate. We illustrate the method by fitting two nonlinear population dynamics models to data in the presence of process and observation noise.

We derive conditions for persistence and spread of a population where individuals are either immobile or dispersing by advection and diffusion through a one-dimensional medium with a unidirectional flow. Reproduction occurs only in the stationary phase. Examples of such systems are found in rivers and streams, marine currents, and areas with prevalent wind direction. In streams, a long-standing question, dubbed 'the drift paradox', asks why aquatic insects faced with downstream drift are able to persist in upper stream reaches. For our two-phase model, persistence of the population is guaranteed if, at low population densities, the local growth rate of the stationary component of the population exceeds the rate of entry of individuals into the drift. Otherwise the persistence condition involves all the model parameters, and persistence requires a critical (minimum) domain size. We calculate the rate at which invasion fronts propagate up-and downstream, and show that persistence and ability to spread are closely connected: if the population cannot advance upstream against the flow, it also cannot persist on any finite spatial domain. By studying two limiting cases of our model, we show that residence in the immobile state always enhances population persistence. We use our findings to evaluate a number of mechanisms previously proposed in the ecological literature as resolutions of the drift paradox. r 2004 Elsevier Inc. All rights reserved.

What is the effect of landscape heterogeneity on the spread rate of populations? Several spatially-explicit simulation models address this question for particular cases and find qualitative insights (e.g., extinction thresholds) but no quantitative relationships. We use a time-discrete analytic model and find general quantitative relationships for the invasion threshold, i.e., the minimal percentage of suitable habitat required for population spread. We investigate how, on the relevant spatial scales, this threshold depends on the relationship between dispersal ability and fragmentation level. The invasion threshold increases with fragmentation level when there is no Allee effect, but it decreases with fragmentation in the presence of an Allee effect. We obtain simple formulas for the approximate spread rate of a population in heterogeneous landscapes from averaging techniques. Comparison with spatially explicit simulations shows an excellent agreement between approximate and true values. We apply our results to the spread of trees and give some implications for the control of invasive species.

Individuals in streams are constantly subject to predominantly unidirectional flow. The question of how these populations can persist in upper stream reaches is known as the "drift paradox." We employ a general mechanistic movement-model framework and derive dispersal kernels for this situation. We derive thin-as well as fat-tailed kernels. We then introduce population dynamics and analyze the resulting integrodifferential equation. In particular, we study how the critical domain size and the invasion speed depend on the velocity of the stream flow. We give exact conditions under which a population can persist in a finite domain in the presence of stream flow, as well as conditions under which a population can spread against the direction of the flow. We find a critical stream velocity above which a population cannot persist in an arbitrarily large domain. At exactly the same stream velocity, the invasion speed against the flow becomes zero; for larger velocities, the population retreats with the flow.

We construct and analyze a nonlocal continuum model for group formation with application to self-organizing collectives of animals in homogeneous environments. The model consists of a hyperbolic system of conservation laws, describing individual movement as a correlated random walk. The turning rates depend on three types of social forces: attraction toward other organisms, repulsion from them, and a tendency to align with neighbors. Linear analysis is used to study the role of the social interaction forces and their ranges in group formation. We demonstrate that the model can generate a wide range of patterns, including stationary pulses, traveling pulses, traveling trains, and a new type of solution that we call zigzag pulses. Moreover, numerical simulations suggest that all three social forces are required to account for the complex patterns observed in biological systems. We then use the model to study the transitions between daily animal activities that can be described by these different patterns.

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Online enhancements: appendixes. abstract: How individual-level movement decisions in response to habitat edges influence population-level patterns of persistence and spread of a species is a major challenge in spatial ecology and conservation biology. Here, we integrate novel insights into edge behavior, based on habitat preference and movement rates, into spatially explicit growth-dispersal models. We demonstrate how crucial ecological quantities (e.g., minimal patch size, spread rate) depend critically on these individual-level decisions. In particular, we find that including edge behavior properly in these models gives qualitatively different and intuitively more reasonable results than those of some previous studies that did not consider this level of detail. Our results highlight the importance of new empirical work on individual movement response to habitat edges.

Understanding the movement of species' ranges is a classic ecological problem that takes on urgency in this era of global change. Historically treated as a purely ecological process, range expansion is now understood to involve eco-evolutionary feedbacks due to spatial genetic structure that emerges as populations spread. We synthesize empirical and theoretical work on the eco-evolutionary dynamics of range expansion, with emphasis on bridging directional, deterministic processes that favor evolved increases in dispersal and demographic traits with stochastic processes that lead to the random fixation of alleles and traits. We develop a framework for understanding the joint influence of these processes in changing the mean and variance of expansion speed and its underlying traits. Our synthesis of recent laboratory experiments supports the consistent role of evolution in accelerating expansion speed on average, and highlights unexpected diversity in how evolution can influence variability in speed: results not well predicted by current theory. We discuss and evaluate support for three classes of modifiers of eco-evolutionary range dynamics (landscape context, trait genetics, and biotic interactions), identify emerging themes, and suggest new directions for future work in a field that stands to increase in relevance as populations move in response to global change.

The question how aquatic populations persist in rivers when individuals are constantly lost due to downstream drift has been termed the "drift paradox." Recent modeling approaches have revealed diffusion-mediated persistence as a solution. We study logistically growing populations with and without a benthic stage and consider spatially varying growth rates. We use idealized hydrodynamic equations to link river cross-sectional area to flow speed and assume heterogeneity in the form of alternating patches, i.e., piecewise constant conditions. We derive implicit formulae for the persistence boundary and for the dispersion relation of the wave speed. We explicitly discuss the influence of flow speed, cross-sectional area and benthic stage on both persistence and upstream invasion speed.