Brian C. Goodwin

A Parallel Distributed Model of the Behaviour of Ant Colonies

Members of an ant colony perform a variety of tasks outside the nest, such as foraging and nest maintenance work. The number of ants actively performing each task changes, because workers switch from one task to another and because workers are sometimes active, sometimes inactive. In field experiments with harvester ants ( Gordon, 1986 , Gordon, 1987 ), a perturbation that directly affects only the number of workers engaged in one task, causes changes in the numbers engaged in other activities. These dynamics must be the outcome of interactions among individuals; an ant cannot be expected to assess and respond to colony-level changes of behaviour. Here we present a parallel distributed model of the processes regulating changes in numbers of workers engaged in various tasks. The model is based on a Hopfield net, but differs from conventional Hopfield models in that when a unit or ant changes state, it changes its interaction patterns. Simulation results resemble experimental results; perturbations of one activity propagate to others. Depending on the pattern of interactions among worker groups, the distribution of active workers in different tasks either settles into a single, global attractor, or shows the dynamics associated with a landscape containing multiple attractors.

Drosophila segmentation: supercomputer simulation of prepattern hierarchy.

Spontaneous prepattern formation in a two level hierarchy of reaction-diffusion systems is simulated in three space co-ordinates and time, mimicking gap gene and primary pair-rule gene expression. The model rests on the idea of Turing systems of the second kind, in which one prepattern generates position dependent rate constants for a subsequent reaction-diffusion system. Maternal genes are assumed responsible for setting up gradients from the anterior and posterior ends, one of which is needed to stabilize a double period prepattern suggested to underly the read out of the gap genes. The resulting double period pattern in turn stabilizes the next prepattern in the hierarchy, which has a short wavelength with many characteristics of the stripes seen in actual primary pair-rule gene expression. Without such hierarchical stabilization, reaction-diffusion mechanisms yield highly patchy short wave length patterns, and thus unreliable stripes. The model yields seven stable stripes located in the middle of the embryo, with the potential for additional expression near the poles, as observed experimentally. The model does not rely on specific chemical reaction kinetics, rather the effect is general to many such kinetic schemes. This makes it robust to parameter changes, and it has good potential for adapting to size and shape changes as well. The study thus suggests that the crucial organizing principle in early Drosophila embryogenesis is based on global field mechanisms, not on particular local interactions.

The Role of Development in Macroevolutionary Change Group Report

B. C. Goodwin’s comments provided an appropriate preamble to the raison d’etre and format of our group’s discussions and report. All scientific theories incorporate both contingencies (particulars) and laws (universals) in their explanatory structure. In biology, the emphasis on one or the other has shifted dramatically over the past two centuries depending upon whether the biological realm is perceived as one of systematic order and regularity, or as one which is dominated by historical and environmental contingencies. Before Darwin, the focus of attention was on laws of biological form and morphological transformations (as expressed in the research program of rational morphology), whereas Darwin’s emphasis on inheritance and adaptation brought historical and environmental factors into prominence.

Spatial harmonics and pattern specification in early Drosophila development. Part I. Bifurcation sequences and gene expression.

Molecular probes have now provided an unprecedented wealth of detail revealing the changing spatial patterns of gene products in early Drosophila development. This is examined for dynamic properties which might provide insights into the underlying behaviour of the patterning process. What emerges is that transcripts and protein products of members of the major categories of zygotically active genes involved in segmentation pass through transient spatial patterns that are suggestive of harmonic sequences arising from spatial frequency-doubling bifurcations. That is to say, these patterns are typically periodic in space and show a doubling in the number of domains of spatial expression as development proceeds. One of these patterns reflects the primary functional role of the gene in the establishment of the spatial pattern. The different categories of segmentation gene pass through these transients at different rates, those with the longest functional wavelength progressing most slowly. Each gene in a category has its own unique phase relationship to other members, as well as particular variations on the harmonic sequence theme. The result is that the developing embryo experiences a spatial hierarchy of phase-shifted patterning influences that span the range from the whole embryo to single segments, providing progressively more spatial resolution in the patterning process. The characteristic transients and the dynamic relationships between genes of the different categories suggest that gene products expressed in longer-wavelength patterns act as bifurcation parameters on the dynamic system generating the next shorter wavelength category. Such parametric influences are known to result in frequency-doubling bifurcations in Turing reaction-diffusion systems. A general model is proposed of a hierarchically-nested set of quasi-autonomous dynamic systems involving gene activities that can generate the progressively finer spatial order that emerges during embryogenesis. This model has implications for the general stability properties of evolving epigenetic systems.

Geometry and dynamics of tip morphogenesis in Acetabularia

A detailed study of the relationship between the geometry of the regenerating tip in Acetabularia mediterranea and the dynamics of a mechanochemical model of the process is presented. The tip is described as a viscoelastic shell having two layers: an underlying cytogel with calcium-regulated strain fields, and an external cell wall, treated as an elastic body. When parameter values are chosen to satisfy the bifurcation condition in the cytogel field, spatially non-uniform solutions occur whose patterns depend upon geometry. When growth is included in the model by allowing plastic as well as elastic deformation, tip formation is initiated.

Collective behavior of random-activated mobile cellular automata

Abstract Dynamical properties of 2D cellular automata with mobile elements are examined qualitatively. Results show that a system containing elements with local interactions but with no fixed connections, due to movement and connection breaking, are able to display periodic oscillations by collective synchronization of non-periodical randomly activated elements. The system studied is found to be robust. Spatial dynamics is shown to generate interesting spatial structures suggesting the presence of self-organization. Moreover, maximum Lyapunov exponents and fractal dimension of attractors have been calculated in order to show that the dynamics of interaction among elements is chaotic.

Developing Organisms as Self-Organizing Fields

The way in which parts are related to wholes is crucial to any theory of self-organization, since it is necessary to know what is being organized and what collective properties they reveal. The analytic tradition of science uses an atomistic description of this relationship: parts (“atoms”) are assumed to be primary and the whole is generated by their interaction. This approach dominates modern embryology and evolutionary biology. However, there is an alternative view that is very useful in understanding complex order, which is the structuralist tradition: a whole entity is defined by invariant relations within which parts emerge and behave in accordance with transformational principles. Evidence that the constraints determining biological form arise from organizational levels other than the genome and gene products emphasizes the primacy of morphogenetic principles at the level of the organism, and the inadequacy of atomistic theories on which the concept of the genetic program is based.

Ether-induced segmentation disturbances in Drosophila melanogaster

SummaryDrosophila embryos, exposed to ether between 1 and 4 h after oviposition, develop defects ranging from the complete lack of segmentation to isolated gaps in single segments. Between these extremes are varying extents of incomplete and abnormal segmentation. On the basis of both their temporal and spatial characteristics, five major phenotype classes may be distinguished: headless — unsegmented or incompletely segmented anteriorly; gap — interruptions of segmentation not obviously periodic; alternating segment gaps — interruptions with double segment periodicities; fused segments; and short segments — truncations with single segment periodicities. Many defects resemble known mutant phenotypes. The disturbances in segmentation are predominantly global and frequently accompanied by alterations in segment specification, such that the segments obtained show no resemblance to the normal homologues. These features, together with the distinctive spatiotemporal characteristics of the defects, all point to segmentation as a dynamic process. The regular spacing of the segments and the fact that the entire range of defects is inducible by ether are further consistent with the hypothesis that at least part of the segmentation process may consist of physicochemical reactions coordinated over the whole body. The relationship between our data and data from genetic and other analyses are briefly discussed.

NEURAL NETWORKS AS SOURCES OF CHAOTIC MOTOR ACTIVITY IN ANTS AND HOW COMPLEXITY DEVELOPS AT THE SOCIAL SCALE

We discuss a Neural Network model generating activation signals for locomotion in ants. The signals are chaotic and so are the temporal patterns of spontaneous activations in single ants. Active ants are able to move and interact with other nest mates. This process of movement-interaction generates periodic pulses of activity once the number of individuals reaches a certain density value. An algorithmic complexity measure is used for identifying accurately the transition from chaos into order. Finally, an Iterated Function System analysis reveals the richness of dynamical behavior that emerges when ant colonies are self-poised near such a transition.

Emergent Behavior in Insect Societies: Global Oscillations, Chaos and Computation

Insect societies are formed by a huge number of individuals in interaction. Ant behavior is simple and, apparently, predictable, but recent results suggest that low-dimensional chaotic dynamics would be implicated at the individual level dynamics. In this paper, we explore several recent experimental results concerning global properties of ant societies, with the individuals defined as chaotic automata