Optimal flower lifetimes

Summary ESS floral lifetimes satisfy the product theorem from sex allocation theory. The dimensionless time investment per flower is a symmetric function of two dimensionless gain : cost ratios, one for each gender function.     

Evolutionary dynamics of predator-prey systems: an ecological perspective

 Evolution takes place in an ecological setting that typically involves interactions with other organisms. To describe such evolution, a structure is needed which incorporates the simultaneous evolution of interacting species. Here a formal framework for this purpose is suggested, extending from the microscopic interactions between individuals – the immediate cause of natural selection, through the mesoscopic population dynamics responsible for driving the replacement of one mutant phenotype by another, to the macroscopic process of phenotypic evolution arising from many such substitutions. The process of coevolution that results from this is illustrated in the context of predator–prey systems. With no more than qualitative information about the evolutionary dynamics, some basic properties of predator–prey coevolution become evident. More detailed understanding requires specification of an evolutionary dynamic; two models for this purpose are outlined, one from our own research on a stochastic process of mutation and selection and the other from quantitative genetics. Much of the interest in coevolution has been to characterize the properties of fixed points at which there is no further phenotypic evolution. Stability analysis of the fixed points of evolutionary dynamical systems is reviewed and leads to conclusions about the asymptotic states of evolution rather different from those of game-theoretic methods. These differences become especially important when evolution involves more than one species. Received 10 November 1993; received in revised form 25 July 1994     

Coexistence of Banksia species in southwestern Australia: the role of regional and local processes

Abstract. 60 of the 75 Banksia species are confined to southwestern Australia where five or six species often coexist. We explored the role of regional species richness, niche differentiation, and habitat specialization in structuring banksia assemblages. The diversity of growth forms and categories of seed production and response to fire were assessed in actual assemblages at 40 sites throughout southwestern Australia. Diversity indices at each site were compared with those from null communities assembled on the basis of the abundance and sociability of taxa in regional species pools. The relationship between local and regional species richness suggests that processes at the scale of 100-m² quadrats limit local richness and therefore coexistence. However, there was no consistent evidence that taxa are differentiated by growth form or regeneration strategy. No particular biological profile makes a banksia adept at coexisting with a wide range of other taxa. Habitat specialization is an important factor contributing to lower local richness than would be predicted from niche differentiation of taxa in regional pools. There is recent empirical evidence of several mechanisms whereby the number of coexisting banksias is increased beyond the limits suggested by simple niche theories. Variability in the fire regime also provides a mechanism for maintaining local species richness because different fires favour recruitment of different taxa.     

The Hawk—Dove game revisited: Effects of continuous variation in resource-holding potential on the frequency of escalation

Summary The classic Hawk—Dove game is extended to deal with continuous variation in resource-holding potential or RHP, when RHP is observable (via any sensory modality) but RHP difference is less than perfectly reliable as a predictor of the outcome of an escalated contest. The relationship between sensory and physical magnitudes of RHP is assumed to be governed by Fechner's psychophysical law, whose effect is that contestants interact as if they had perfect information about their relative RHP (as opposed to RHP difference). Thus, an animal is aggressive if its RHP exceeds a certain fraction, called its threshold, of its opponent's RHP and otherwise is non-aggressive; and the classic Hawk and Dove strategies correspond to zero and infinite thresholds, respectively. For RHPs drawn at random from an arbitrary Gamma distribution there is a unique evolutionarily stable strategy or ESS, which depends on a parameter measuring the reliability of RHP as a predictor of the outcome of a fight, on the ratio of the valueV of winning to the costC of losing (both measured in units of reproductive fitness) and on the mean µ and variance ² of the RHP distribution. In a population at this ESS, ifV/C < 1 then the threshold is 1 and there is no fighting. AsV/C increases beyond 1 to a second critical value , however, the threshold decreases steadily from 1 to 0 and remains 0 forV/C > ; is an increasing function of , but a decreasing function of ². That a lower variance of RHP can imply a lower escalation frequencyp is a novel insight of the analysis. The prediction is at first counterintuitive, because if the aggression threshold were fixed then larger variance would imply lowerp (dispersion effect of variance). When natural selection acts on the threshold, however, increasing the variance not only reduces the probability that an animal with larger RHP will be attacked by an animal with lower RHP at the existing threshold, but also reduces the expected costs of adopting that particular threshold, so that a mutant with a somewhat lower threshold can invade the population (selection effect of variance). Forp, the selection effect dominates toward the upper end of the interval 1 V/C .     

Altruism,tit for tat and ‘outlaw’ genes

Summary In a prior study we combined game theory and inclusive fitness models to examine whether the guarded altruism that can evolve among non-relatives (tit for tat, TFT) might also evolve among close relatives, supplanting unconditional altruism. In most cases, TFT replaced unconditional altruism in family-structured models. Even when TFT is selected at a single locus, however, by withholding altruism from non-reciprocating relatives it may qualify as an outlaw from the standpoint of modifier genes at other loci. Here we examine this possibility with a series of haploid, two-locus models in which a modifier gene transforms TFT into unconditional altruism. The modifier allele spreads to fixation whenever Hamilton's Rule is satisfied, resulting in an unconditional altruist replacing the TFT strategy. As such, TFT may be regarded as an outlaw vulnerable to suppression by alleles at other loci.     

Complex ecological models with simple dynamics: From individuals to populations

The aim of this work is to study complex ecological models exhibiting simple dynamics. We consider large scale systems which can be decomposed into weakly coupled subsystems. Perturbation Theory is used in order to get a reduced set of differential equations governing slow time varying global variables. As examples, we study the influence of the individual behaviour of animals in competition and predator-prey models. The animals are assumed to do many activities all day long such as searching for food of different types. The degree of competition as well as the predation pressure are dependent upon these activities. Preys are more vulnerable when doing some activities during which they are very exposed to predators attacks rather than for others during which they are hidden. We study the effect of a change in the average individual behaviour of the animals on interspecific relationships. Computer simulations of the whole sets of equations are compared to simulations of the reduced sets of equations.     

SUBSTITUTION PROCESSES IN MOLECULAR EVOLUTION. II. EXCHANGEABLE MODELS FROM POPULATION GENETICS

Substitution processes are of two sorts: origination processes record the times at which nucleotide mutations that ultimately fix in the population first appear, and fixation processes record the times at which they actually fix. Substitution processes may be generated by combining models of population genetics—here the symmetrical-neutral, overdominance, underdominance, TIM, and SAS-CFF models—with the infinite-sites, no-recombination model of the gene. This paper is mainly concerned with a computer simulation study of these substitution processes. The rate of substitution is shown to be remarkably insensitive to the strength of selection for models with strong balancing selection caused by the genealogical drift of mutations through alleles held in the population by selection. The origination process is shown to be more regular than Poisson for the overdominance, TIM, and SAS-CFF models but more clustered for the underdominance model. A class of point processes called Sawyer processes is introduced to help explain these observations as well as the observation that the times between successive originations are nearly uncorrelated. Fixation processes are shown to be more complex than origination processes, with regularly spaced bursts of multiple fixations. An approximation to the fixation process is described. One important conclusion is that protein evolution is not easily reconciled with any of these models without adding perturbations that recur on a time scale that is commensurate with that of molecular evolution.     

Root movements: Towards an understanding through attempts to model the processes involved

Roots have the ability to change the direction of their forward growth. Sometimes these directional changes are rapid, as in mutations, or they are slower, as in tropisms. The gravitational force is always present and roots have an efficient graviperception mechanism which enables them to initiate gravitropic movements. In trying to model and simulate the course of gravitropic root movements with a view to analyse the component processes, the following aspects of the plant's interaction with gravity have been considered: (1) The level of organization (organism, organ, cell) at which the movement process is expressed; (2) whether the gravity stimulation event is dynamic or static (i.e. whether or not physiologically significant displacements take place with respect to the gravity vector); (3) the sub-systems involved in movement and the processes which they regulate; (4) the mathematical characterization of the relevant sub-systems. A further allied topic is the nature of nutational movements and whether they are linked with gravitropic movements in some way. In considering how they can best be modelled, two types of nutational movements are proponed: stochastic nutation and circumnutation. Most, if not all, natural movements developed in response to static gravistimulation can be viewed as gravimorphisms. This applies at the levels of cell, organ and organism. However, when a system at any one of these levels experiences dynamic gravistimulation, because of its inherent homeostatic properties, it is induced to regenerate a state similar to that previously held. Thus, gravitropism is a regenerative gravimorphic process at the level of the organ.     

An optimal foraging and migration model for juvenile plaice

Summary A state-dependent model has been used to predict daily and tidal patterns of migration, feeding and inactivity in juvenile plaice (Pleuronectes platessa L.) in their intertidal and shallow subtidal nursery areas. Vertical position, quantity of energy reserves and fullness of the gut characterized the state of individual fishes. If feeding is visually mediated, the model predicts that, by night, plaice should move to areas of low predation risk and become inactive, whereas by day, plaice should migrate to feed in areas of high prey encounter rate. Vertical zones adopted by day and night and, hence, patterns of migration, should depend on the distributions of predators and prey. When prey are more abundant in the intertidal zone, plaice should move onshore to feed as the tide rises and when prey are more abundant offshore, plaice should move offshore to feed by day. If predators are equally abundant in all zones, the fish should behave as if no predators were present, having no effective refuge. An increase in the abundance of predators with depth results in the restriction of plaice activities to shallower vertical zones, depending on the magnitude of the predation threat. Zones adopted thus depend on the trade-off between energy intake and predation risk. Concordance between predicted behaviour and observed patterns is evident in contrasting habitats. Migration and feeding in the Wadden Sea, where prey are more abundant on intertidal flats, is dominated by the tidal component, whereas on impoverished exposed beaches of the west coast of Scotland, the diurnal component is dominant. Tidally related behaviour persists in the latter environment, not predicted by the model and may be a consequence of using endogenous rhythms to approach optimal behavioural patterns.