Journal of Theoretical Biology 

Abstract: A genetical mathematical model is described which allows for interactions between relatives on one another's fitness. Making use of Wright's Coefficient of Relationship as the measure of the proportion of replica genes in a relative, a quantity is found which incorporates the maximizing property of Darwinian fitness. This quantity is named “inclusive fitness”. Species following the model should tend to evolve behaviour such that each organism appears to be attempting to maximize its inclusive fitness. This implies a limited restraint on selfish competitive behaviour and possibility of limited self-sacrifices. Special cases of the model are used to show (a) that selection in the social situations newly covered tends to be slower than classical selection, (b) how in populations of rather non-dispersive organisms the model may apply to genes affecting dispersion, and (c) how it may apply approximately to competition between relatives, for example, within sibships. Some artificialities of the model are discussed.

Abstract: It is suggested that characters which develop through mate preference confer handicaps on the selected individuals in their survival. These handicaps are of use to the selecting sex since they test the quality of the mate. The size of characters selected in this way serve as marks of quality. The understanding that a handicap, which tests for quality, can evolve as a consequence of its advantage to the individual, may provide an explanation for many puzzling evolutionary problems. Such an interpretation may provide an alternative to other hypotheses which assumed complicated selective mechanisms, such as group selection or kin selection, which do not act directly on the individual.

Abstract: Proto-organisms probably were randomly aggregated nets of chemical reactions. The hypothesis that contemporary organisms are also randomly constructed molecular automata is examined by modeling the gene as a binary (on-off) device and studying the behavior of large, randomly constructed nets of these binary “genes”. The results suggest that, if each “gene” is directly affected by two or three other “genes”, then such random nets: behave with great order and stability; undergo behavior cycles whose length predicts cell replication time as a function of the number of genes per cell; possess different modes of behavior whose number per net predicts roughly the number of cell types in an organism as a function of its number of genes; and under the stimulus of noise are capable of differentiating directly from any mode of behavior to at most a few other modes of behavior. Cellular differentation is modeled as a Markov chain among the modes of behavior of a genetic net. The possibility of a general theory of metabolic behavior is suggested.

Abstract: Information content may be used as a measure of the diversity of a many-species biological collection. The diversity of small collections, all of whose members can be identified and counted, is defined by Brillouin's measure of information. With larger collections it becomes necessary to estimate diversity; what is estimated is Shannon's measure of information which is a function of the population proportions of the several species. Different methods of estimation are appropriate for different types of collections. If the collection can be randomly sampled and the total number of species is known, Basharin's formula may be used. With a random sample from a population containing an unknown number of species, Good's method is sometimes applicable. With a patchy population of sessile organisms, such as a plant community, random samples are unobtainable since the contents of a randomly placed quadrat are not a random sample of the parent population. To estimate the diversity of such a community a method is proposed whereby the sample size is progressively increased by addition of new quadrats; as this is done the diversity of the pooled sample increases and then levels off. The mean increment in total diversity that results from enlarging the sample still more then provides an estimate of the diversity per individual in the whole population.

Abstract: This paper presents an antithesis to the view that gregarious behaviour is evolved through benefits to the population or species. Following Galton (1871) and Williams (1964) gregarious behaviour is considered as a form of cover-seeking in which each animal tries to reduce its chance of being caught by a predator. It is easy to see how pruning of marginal individuals can maintain centripetal instincts in already gregarious species; some evidence that marginal pruning actually occurs is summarized. Besides this, simply defined models are used to show that even in non-gregarious species selection is likely to favour individuals who stay close to others. Although not universal or unipotent, cover-seeking is a widespread and important element in animal aggregation, as the literature shows. Neglect of the idea has probably followed from a general disbelief that evolution can be dysgenic for a species. Nevertheless, selection theory provides no support for such disbelief in the case of species with outbreeding or unsubdivided populations. The model for two dimensions involves a complex problem in geometrical probability which has relevance also in metallurgy and communication science. Some empirical data on this, gathered from random number plots, is presented as of possible heuristic value.