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Ian Stewart

Publications and source records attributed to Ian Stewart.

6 recordsLinked to original sources
PubMed2003

Self-organization in evolution: a mathematical perspective.

The neo-Darwinian view of evolution centres upon the role of the gene. Here there seems to be little scope for self-organization. This conclusion is reinforced by traditional models of polymorphism in terms of allele frequencies in a mean-field gene-pool. However, models based on phenotypes, and including nonlinear and collective effects, suggest that evolution can indeed be viewed as a process whereby the ecosystem self-organizes. Here we focus on the phenomenon of speciation, and discuss a series of phenotypic models which together illuminate some of the issues surrounding the role of self-organization, including new approaches to fitness landscapes and species selection. All of these models represent speciation as a symmetry-breaking bifurcation, but in different mathematical contexts including deterministic dynamical systems, stochastic dynamical systems, and iterated function schemes. The main conclusions are surprisingly robust, despite the diversity of the models.

Adaptation, Physiological↗
PubMed2002

A functional-analytic model of analogy: a relational frame analysis.

The aim of this study was to explore a behavior-analytic model of analogical reasoning, defined as the discrimination of formal similarity via equivalence-equivalence responding. In Experiment 1, adult humans were trained and tested for the formation of four three-member equivalence relations: A1-B1-C1, A2-B2-C2, A3-B3-C3, and A4-B4-C4. The B and C stimuli were three-letter nonsense syllables, and the A stimulus was a colored shape. Subjects were then successfully tested for equivalence-equivalence responding (e.g., matching B1/C1 to B2/C2 rather than B3/C4). These tasks were designed such that equivalence-equivalence responding might allow subjects to discriminate a physical similarity between the relations involved. Some participants (color subjects) received only equivalence-equivalence tasks in which they might discriminate a color relation, whereas others (shape subjects) were given tasks in which they might discriminate a shape relation. A control group received both types of task. In a subsequent test for the discrimination of formal similarity, color subjects matched according to color, shape subjects matched according to shape, and the control group showed no consistent matching pattern. In Experiment 2, adult humans showed a transformation of the functions of a block-sorting task via this basic model of analogy. Empirical and conceptual issues related to these results are discussed.

Adolescent↗