A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media. The theoretical starting point is usually a set of deterministic equations of motion, typically in the form of nonlinear partial differential equations. These are sometimes supplemented by stochastic terms representing thermal or instrumental noise, but for macroscopic systems and carefully designed experiments the stochastic forces are often negligible. An aim of theory is to describe solutions of the deterministic equations that are likely to be reached starting from typical initial conditions and to persist at long times. A unified description is developed, based on the linear instabilities of a homogeneous state, which leads naturally to a classification of patterns in terms of the characteristic wave vector q0 and frequency ω0 of the instability. Type Is systems (ω0=0, q0≠0) are stationary in time and periodic in space; type IIIo systems (ω0≠0, q0=0) are periodic in time and uniform in space; and type Io systems (ω0≠0, q0≠0) are periodic in both space and time. Near a continuous (or supercritical) instability, the dynamics may be accurately described via "amplitude equations," whose form is universal for each type of instability. The specifics of each system enter only through the nonuniversal coefficients. Far from the instability threshold a different universal description known as the "phase equation" may be derived, but it is restricted to slow distortions of an ideal pattern. For many systems appropriate starting equations are either not known or too complicated to analyze conveniently. It is thus useful to introduce phenomenological order-parameter models, which lead to the correct amplitude equations near threshold, and which may be solved analytically or numerically in the nonlinear regime away from the instability. The above theoretical methods are useful in analyzing "real pattern effects" such as the influence of external boundaries, or the formation and dynamics of defects in ideal structures. An important element in nonequilibrium systems is the appearance of deterministic chaos. A greal deal is known about systems with a small number of degrees of freedom displaying "temporal chaos," where the structure of the phase space can be analyzed in detail. For spatially extended systems with many degrees of freedom, on the other hand, one is dealing with spatiotemporal chaos and appropriate methods of analysis need to be developed. In addition to the general features of nonequilibrium pattern formation discussed above, detailed reviews of theoretical and experimental work on many specific systems are presented. These include Rayleigh-Benard convection in a pure fluid, convection in binary-fluid mixtures, electrohydrodynamic convection in nematic liquid crystals, Taylor-Couette flow between rotating cylinders, parametric surface waves, patterns in certain open flow systems, oscillatory chemical reactions, static and dynamic patterns in biological media, crystallization fronts, and patterns in nonlinear optics. A concluding section summarizes what has and has not been accomplished, and attempts to assess the prospects for the future.

/pdf/pattern-formation-outside-of-equilibrium-1601b9znum.pdf

Pattern formation outside of equilibrium

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

Rho, Rac, and Cdc42 GTPases regulate the assembly of multimolecular focal complexes associated with actin stress fibers, lamellipodia, and filopodia

Acts in what Hutchinson (1965) has called the 'ecological theatre' are played out on various scales of space and time. To understand the drama, we must view it on the appropriate scale. Plant ecologists long ago recognized the importance of sampling scale in their descriptions of the dispersion or distribution of species (e.g. Greig-Smith, 1952). However, many ecologists have behaved as if patterns and the processes that produce them are insensitive to differences in scale and have designed their studies with little explicit attention to scale. Kareiva & Andersen (1988) surveyed nearly 100 field experiments in community ecology and found that half were conducted on plots no larger than 1 m in diameter, despite considerable differences in the sizes and types of organisms studied. Investigators addressing the same questions have often conducted their studies on quite different scales. Not surprisingly, their findings have not always matched, and arguments have ensued. The disagreements among conservation biologists over the optimal design of nature reserves (see Simberloff, 1988) are at least partly due to a failure to appreciate scaling differences among organisms. Controversies about the role of competition in structuring animal communities (Schoener, 1982; Wiens, 1983, 1989) or about the degree of coevolution in communities (Connell, 1980; Roughgarden, 1983) may reflect the

https://www.jstor.org/stable/info/2389612

Spatial Scaling in Ecology

Cell Migration: A Physically Integrated Molecular Process

In this pathbreaking and far-reaching work George Oster and Edward Wilson provide the first fully developed theory of caste evolution among the social insects. Furthermore, in studying the effects of natural selection in generally increasing the insects' ergonomic efficiency, they go beyond the concentration of previous researchers on the physiological mechanisms of the insects and turn our attention instead to the scale and efficiency of the insects' division of labor.Recognizing that the efficiency of the insect colony is based on a complex fitting of the division of labor to many simultaneous needs, including those imposed by the distribution of resources and enemies around the nest, Professors Oster and Wilson are able to construct a series of mathematical models to characterize the agents of natural selection that promote particular caste systems.The social insects play a key role in the subject of sociobiology because their social organization is so rigid and can be related to genetic evolution. Because of this important consideration, the authors' work has consequences not only for entomology but also for general evolutionary theory.

Caste and ecology in the social insects

Caste and Ecology in the Social Insects

We present a quantitative method for describing how heterochronic changes in ontogeny relate to phyletic trends. This is a step towards creating a unified view of developmental biology and evolu- tionary ecology in the study of morphological evolution. Using this representation, we obtain a greatly simplified and logical scheme of classification. We believe that this scheme will be particularly useful in studying the data of paleontology and comparative morphology and in the analysis of processes leading to adaptive radiation. We illustrate this scheme by examples drawn from the literature and our own work.

Size and shape in ontogeny and phylogeny

Many biological populations breed seasonally and have nonoverlapping generations, so that their dynamics are described by first-order difference equations, Nt+1 = F (Nt). In many cases, F(N) as a function of N will have a hump. We show, very generally, that as such a hump steepens, the dynamics goes from a stable point, to a bifurcating hierarchy of stable cycles of period 2n, into a region of chaotic behavior where the population exhibits an apparently random sequence of "outbreaks" followed by "crashes." We give a detailed account of the underlying mathematics of this process and review other situations (in two- and higher dimensional systems, or in differential equation systems) where apparently random dynamics can arise from bifurcation processes. This complicated behavior, in simple deterministic models, can have disturbing implications for the analysis and interpretation of biological data.

Bifurcations and Dynamic Complexity in Simple Ecological Models

https://www.cims.nyu.edu/~mogilner/actin.pdf

George Oster

Papers

Caste and ecology in the social insects

Caste and Ecology in the Social Insects

Size and shape in ontogeny and phylogeny

Bifurcations and Dynamic Complexity in Simple Ecological Models

Cell motility driven by actin polymerization