R Pekelney | Search PubMed

PubMed1982

Stochastic information processing biological systems.

We propose a simple, biochemically-based model for stochastic information processing in brain, genetic, and, consequently, evolutionary modelling. The essential features of reaction-diffusion processes are realized by intrinsically stochastic probabilistic automata (Shannon and Weaver, 1948; see also Ashby, 1958, von Neumann, 1966; Burks, 1970; Paz, 1971) whose definition extends that of classical automata. (Classical automata are deterministic; earlier work on probabilistic automata focused on error correction and at least approximating deterministic behavior.) We call these probabilistic automata biochemical to emphasize the role of intrinsically stochastic process in biological information processing. Our model yields descriptions of gradualism (Conrad, 1974), learning, and apparent inefficiencies in the brain, and partially resolves the near impossibility of simultaneous point mutations (Conrad, 1972, 1978) in genetics. The genetic model implies an evolutionary dynamics of punctuated equilibria (Gould and Eldredge, 1977).

Animals↗

PubMed1982

Time scales, persistence and patchiness.

We consider competition in patch-dynamical and more general diffusion-extinction models. These models identify three time scales in ecology. We begin with a reformulation of Levin's 1978 basic model, using a geometric description of diffusion. As in Levin's model, diffusion drives short-term dynamics, and longer-term dynamics depends upon a diffusion-extinction ratio; maximizing this ratio is shown to be an Evolutionarily Stable Strategy. Over still longer times, the effect of organisms upon their environments becomes paramount. We use Mandelbrot's 1977 fractals to develop these models, and thus relate persistence with relative patchiness. Finally, we propose a numerical measure, the fractal exponent H, of successional stage.

Biological Evolution↗