Biomedical subjects

V Hutson

Publications and source records attributed to V Hutson.

9 recordsLinked to original sources

PubMed2003

The evolution of dispersal.

A non-local model for dispersal with continuous time and space is carefully justified and discussed. The necessary mathematical background is developed and we point out some interesting and challenging problems. While the basic model is not new, a 'spread' parameter (effectively the width of the dispersal kernel) has been introduced along with a conventional rate paramter, and we compare their competitive advantages and disadvantages in a spatially heterogeneous environment. We show that, as in the case of reaction-diffusion models, for fixed spread slower rates of diffusion are always optimal. However, fixing the dispersal rate and varying the spread while assuming a constant cost of dispersal leads to more complicated results. For example, in a fairly general setting given two phenotypes with different, but small spread, the smaller spread is selected while in the case of large spread the larger spread is selected.

Animals↗

PubMed2001

The evolution of dispersal rates in a heterogeneous time-periodic environment.

A reaction-diffusion model for the evolution of dispersal rates is considered in which there is both spatial heterogeneity and temporal periodicity. The model is restricted to two phenotypes because of technical difficulties, but a wide range of mathematical techniques and computational effort are needed to obtain useful answers. We find that the question of selection is a great deal richer than in the autonomous case, where the phenotype with the lowest diffusion is selected for. In the current model either the lower or higher diffuser rate may be selected, or there may be coexistence of phenotypes. The paper raises several open questions and suggests in particular that a mutation-selection multi-phenotypic model would repay study.

Animals↗

PubMed1996

Spatially explicit models for the population dynamics of a species colonizing an island.

We construct reaction-diffusion models for the population dynamics of a species colonizing an island from a source population on a continent. We view the source population as inducing a density or flux of immigrants onto the island and interpret colonization as succeeding if the population on the island is predicted to persist even when immigration from the continent is stopped. To capture the observation that a sufficiently large population or density must be attained for colonization to succeed, we assume Allee (i.e., bistable) dynamics rather than logistic dynamics for the colonizing population. We consider the cases of colonization in both the absence and presence of a competitor. We use reaction-diffusion theory, especially comparison methods and sub- and supersolutions, to determine how parameters such as the distance from the continent to the island and the dispersal, birth and mortality rates, carrying capacity, and minimum viable population density of the colonizing species affect the outcome of the attempted colonization. In the case of colonization in the presence of a competitor we consider a number of scenarios involving different types and strengths of competition. Our analysis permits us to draw conclusions about the characteristics of a species that make it a good colonizer.

Animals↗

PubMed1993

Four steps to two sexes.

Four steps through which parasitic intracellular symbionts could bring about the evolution of two sexes are considered. In the first step, a primitive host population has biparental cytoplasmic inheritance and lacks gametic differentiation: parasitic cytoplasmic elements readily invade and spread by vertical transmission through such host populations, even if they have major deleterious effects on their hosts. The second step leads to the establishment of a nuclear mutant in the host (locus A) that prevents inheritance of the cytoplasm in gametes in which it occurs. This mutant comes to equilibrium at an intermediate frequency, because a double dose of symbionts is more deleterious than a single dose, and zygotes lacking cytoplasm from both gametes are inviable. The third step involves the spread of a mutant at another nuclear locus (B), causing self-incompatibility of gametes in which it occurs. If this is closely linked to locus A, the mutant may become established by preventing the deleterious gamete unions. The mutant at locus B must, however, start both with an appreciable frequency and be in gametic disequilibrium with locus A. In the fourth step a second mutation causing self-incompatibility occurs at locus B. This allele spreads by becoming associated with the other allele at locus A, eventually leaving the population with two gamete types, or sexes, one predominantly transmitting the cytoplasm, and the other eliminating it. It is argued that this is a feasible mechanism for the origin of two sexes.

Animals↗

PubMed1992

Intracellular symbionts and the evolution of uniparental cytoplasmic inheritance.

Uniparental inheritance of cytoplasmic elements is widespread among eukaryotic organisms and is achieved by a diverse range of mechanisms. This paper shows that the cytoplasmic genetic system would be expected to evolve towards uniparental inheritance, given the existence of deleterious symbionts capable of invading the host cytoplasm together with nuclear genes that lead to the elimination of cytoplasmic elements from one of the gamete types. The reason for this is that, under biparental inheritance, foreign symbionts with strong deleterious effects are able to spread through host populations. A nuclear modifier gene which leads to the loss of cytoplasmic elements from one gamete type gains a net advantage as a symbiont spreads, because the modifier sometimes gives rise to a symbiont-free zygote. Insofar as small gametes reduce the rate of symbiont transmission to the zygote, modifier genes causing small gamete size would tend to accumulate, so that cytoplasmic inheritance would become associated with maternal rather than paternal gametes. Once uniparental inheritance predominates in the host population, the population is protected from invasions by a large class of harmful symbionts, but at the same time those symbionts that benefit their hosts are still able to increase in frequency.

Animals↗

PubMed1992

Permanence and the dynamics of biological systems.

A basic question in mathematical biology concerns the long-term survival of each component, which might typically be a population in an ecological context, of a system of interacting components. Many criteria have been used to define the notion of long-term survival. We consider here the subject of permanence, i.e., the study of the long-term survival of each species in a set of populations. These situations may often be modeled successfully by dynamical systems and have led to the development of some interesting mathematical techniques and results. Our intention here is to describe these and to consider their application to several of the most frequently used models occurring in mathematical biology. We particularly wish to include and cover those models leading to problems that are essentially infinite dimensional, for example reaction-diffusion equations, and to make the discussion accessible to a wide audience, we include a chapter outlining the fundamental theory of these.

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PubMed1988

Risk management.

Explore the source record for details and available documents.

Financial Management↗

PubMed1987

Coexistence for systems governed by difference equations of Lotka-Volterra type.

The question of the long term survival of species in models governed by Lotka-Volterra difference equations is considered. The criterion used is the biologically realistic one of permanence, that is populations with all initial values positive must eventually all become greater than some fixed positive number. We show that in spite of the complex dynamics associated even with the simplest of such systems, it is possible to obtain readily applicable criteria for permanence in a wide range of cases.

Animals↗

PubMed1985

Permanent coexistence in general models of three interacting species.

We address the question of the long term coexistence of three interacting species whose dynamics are governed by the ordinary differential equations xi = xifi(i = 1,2,3). In order for any theory in this area to be useful in practice, it must utilize as little information as possible concerning the forms of the fi, in view of the great difficulty of determining these experimentally. Here we obtain, under rather general conditions on the equations, a criterion for judging whether the species will coexist in a biologically realistic manner. This criterion depends only on the behaviour near the one or two species equilibria of the two dimensional subsystems, the behaviour there being relatively easy to examine experimentally. We show that with the exception of one class of cases, which is a generalization of a classical example of May and Leonard [21], invasibility at each such equilibrium suitably interpreted is both necessary and sufficient for a strong form of coexistence to hold. In the exceptional case, a single additional condition at the equilibria is enough to ensure coexistence.

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