This book is the second of two volumes in a series on terrestrial and marine comparisons, focusing on the temporal complement of the earlier spatial analysis of patchiness and pattern (Levin et al. 1993). The issue of the relationships among pattern, scale, and patchiness has been framed forcefully in John Steele’s writings of two decades (e.g., Steele 1978). There is no pattern without an observational frame. In the words of Nietzsche, “There are no facts… only interpretations.”

https://esajournals.onlinelibrary.wiley.com/doi/pdf/10.2307/1941447

The Problem of Pattern and Scale in Ecology: The Robert H. MacArthur Award Lecture

▪ Abstract The focus of most ideas on diversity maintenance is species coexistence, which may be stable or unstable. Stable coexistence can be quantified by the long-term rates at which community members recover from low density. Quantification shows that coexistence mechanisms function in two major ways: They may be (a) equalizing because they tend to minimize average fitness differences between species, or (b) stabilizing because they tend to increase negative intraspecific interactions relative to negative interspecific interactions. Stabilizing mechanisms are essential for species coexistence and include traditional mechanisms such as resource partitioning and frequency-dependent predation, as well as mechanisms that depend on fluctuations in population densities and environmental factors in space and time. Equalizing mechanisms contribute to stable coexistence because they reduce large average fitness inequalities which might negate the effects of stabilizing mechanisms. Models of unstable coexitence...

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Mechanisms of Maintenance of Species Diversity

This review summarizes theoretical progress in the field of active matter, placing it in the context of recent experiments. This approach offers a unified framework for the mechanical and statistical properties of living matter: biofilaments and molecular motors in vitro or in vivo, collections of motile microorganisms, animal flocks, and chemical or mechanical imitations. A major goal of this review is to integrate several approaches proposed in the literature, from semimicroscopic to phenomenological. In particular, first considered are ``dry'' systems, defined as those where momentum is not conserved due to friction with a substrate or an embedding porous medium. The differences and similarities between two types of orientationally ordered states, the nematic and the polar, are clarified. Next, the active hydrodynamics of suspensions or ``wet'' systems is discussed and the relation with and difference from the dry case, as well as various large-scale instabilities of these nonequilibrium states of matter, are highlighted. Further highlighted are various large-scale instabilities of these nonequilibrium states of matter. Various semimicroscopic derivations of the continuum theory are discussed and connected, highlighting the unifying and generic nature of the continuum model. Throughout the review, the experimental relevance of these theories for describing bacterial swarms and suspensions, the cytoskeleton of living cells, and vibrated granular material is discussed. Promising extensions toward greater realism in specific contexts from cell biology to animal behavior are suggested, and remarks are given on some exotic active-matter analogs. Last, the outlook for a quantitative understanding of active matter, through the interplay of detailed theory with controlled experiments on simplified systems, with living or artificial constituents, is summarized.

Hydrodynamics of soft active matter

■ Abstract Contributions from the field of population biology hold promise for understanding and managing invasiveness; invasive species also offer excellent opportunities to study basic processes in population biology. Life history studies and demographic models may be valuable for examining the introduction of invasive species and identifying life history stages where management will be most effective. Evolutionary processes may be key features in determining whether invasive species establish and spread. Studies of genetic diversity and evolutionary changes should be useful for

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The Population Biology of Invasive Species

Community ecology theory can be used to understand biological invasions by applying recent niche concepts to alien species and the communities that they invade. These ideas lead to the concept of ‘niche opportunity', which defines conditions that promote invasions in terms of resources, natural enemies, the physical environment, interactions between these factors, and the manner in which they vary in time and space. Niche opportunities vary naturally between communities but might be greatly increased by disruption of communities, especially if the original community members are less well adapted to the new conditions. Recent niche theory clarifies the prediction that low niche opportunities (invasion resistance) result from high species diversity. Conflicting empirical patterns of invasion resistance are potentially explained by covarying external factors. These various ideas derived from community ecology provide a predictive framework for invasion ecology.

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Community ecology theory as a framework for biological invasions

The spatio-temporal dynamics of three competitive species is considered. Mathematically, the community is described by a system of partial differential equations of Lotka-Volterra type. The properties of the system are investigated both numerically and analytically. We show that for finite initial conditions the dynamics of the system is typically reduced to a succession of travelling diffusive waves, some of which demonstrate rather an unusual behaviour. Particularly, a locally unstable equilibrium can become stable in the wake of a diffusive front. After propagation of the waves, the domain is invaded by irregular spatiotemporal population oscillations that can be classified as spatio-temporal chaos.

Diffusive waves, dynamical stabilization and spatio-temporal chaos in a community of three competitive species

Range expansions of invading species in homogeneous environments have been extensively studied since the pioneer works by Fisher (Ann Eugen 7:255–369, 1937) and Skellam (Biometrika 38:196–218, 1951). However, environments for living organisms are often fragmented by natural or artificial habitat destruction. Here we address how such environmental heterogeneity affects the range expansion of invading species. We consider a single-species invasion in heterogeneous environments whose habitat parameters vary in a sinusoidal or quasi-sinusoidal manner. Accordingly, Fisher’s model is modified to make the intrinsic growth rate and diffusion coefficient spatially variable. By numerically solving the model, we examine the spatio-temporal pattern of propagating waves, and predict the speed as a function of the amplitude and the wave length of the diffusion coefficient and the intrinsic growth rate. Firstly, the results demonstrate that in the sinusoidally varying environment, if the intrinsic growth rate solely oscillates, the speed increases with increases in the amplitude of oscillation. Conversely, if the diffusion coefficient solely oscillates, the speed decreases with increases in the amplitude of oscillation. When both the intrinsic growth rate and diffusion coefficient oscillate, the speed is synergistically accelerated if the oscillations are in anti-phase, whereas it is decelerated if the oscillations are in same phase. Secondly, the increase in the wave length in either the intrinsic growth rate or the diffusion coefficient leads to decreases in the speed. Thirdly, in the irregularly varying environment, the irregularity in the amplitude of the intrinsic growth rate enhances the speed, while that of the diffusion coefficient attenuates the speed.

Spatial dynamics of invasion in sinusoidally varying environments

The problem of biological invasion in a model single-species community is considered, the spatiotemporal dynamics of the system being described by a modified Fisher equation. For a special case, we obtain an exact solution describing self-similar growth of the initially inhabited domain. By comparison with numerical solutions, we show that this exact solution may be applicable to describe an early stage of a biological invasion preceding the propagation of the stationary travelling wave. Also, the exact solution is applied to the problem of critical aggregation to derive sufficient conditions of population extinction. Finally, we show that the solution we obtain is in agreement with some data from field observations.

Some exact solutions of a generalized fisher equation related to the problem of biological invasion

An idea used by Thieme (J. Math. Biol. 8, 173–187, 1979) is extended to show that a class of integro-difference models for a periodically varying habitat has a spreading speed and a formula for it, even when the recruitment function R(u, x) is not nondecreasing in u, so that overcompensation occurs. Numerical simulations illustrate the behavior of solutions of the recursion whose initial values vanish outside a bounded set.

Spreading speeds of spatially periodic integro-difference models for populations with nonmonotone recruitment functions

An interference competition model for a many species system is presented, based on Lotka-Volterra equations in which some restrictions are imposed on the parameters. The competition coefficients of the Lotka-Volterra equations are assumed to be expressed as products of two factors: the intrinsic interference to other individuals and the defensive ability against such interference. All the equilibrium points of the model are obtained explicitly in terms of its parameters, and these equilibria are classified according to the concept of sector stability. Thus survival or extinction of species at a stable equilibrium point can be determined analytically. The result of the analysis is extended to the successional processes of a community. A criterion for invasion of a new species is obtained and it is also shown that there are some characteristic quantities which show directional changes as succession proceeds.

Nanako Shigesada

Papers

Diffusive waves, dynamical stabilization and spatio-temporal chaos in a community of three competitive species

Spatial dynamics of invasion in sinusoidally varying environments

Some exact solutions of a generalized fisher equation related to the problem of biological invasion

Spreading speeds of spatially periodic integro-difference models for populations with nonmonotone recruitment functions

The effects of interference competition on stability, structure and invasion of a multi-species system