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M Broom

Publications and source records attributed to M Broom.

17 recordsLinked to original sources
PubMed2006

The evolution of a kleptoparasitic system under adaptive dynamics.

Kleptoparasitism, the stealing of food items, is a common biological phenomenon which has been modelled mathematically in a series of recent papers. A common assumption, following early work, was that mixed strategy solutions were not possible. In this paper we consider the evolution of mixed strategies under adaptive dynamics and show that such mixed strategies can be stable solutions under certain assumptions. In particular we revisit the recent paper of Broom et al. (Bull math Biol 66, 1645-1658, 2004) which assumed pure solutions only, and reanalyze the model under this new formulation.

Animals↗
PubMed2006

Evolutionarily stable defence and signalling of that defence.

We examine the evolution and maintenance of defence and conspicuousness in prey species using a game theoretic model. In contrast to previous works, predators can raise as well as lower their attack probabilities as a consequence of encountering moderately defended prey. Our model predicts four distinct possibilities for evolutionarily stable strategies (ESSs) featuring maximum crypsis. Namely that such a solution can exist with (1) zero toxicity, (2) a non-zero but non-aversive level of toxicity, (3) a high, aversive level of toxicity or (4) that no such maximally cryptic solution exists. Maximally cryptic prey may still invest in toxins, because of the increased chance of surviving an attack (should they be discovered) that comes from having toxins. The toxin load of maximally cryptic prey may be sufficiently strong that the predators will find them aversive, and seek to avoid similar looking prey in future. However, this aversiveness does not always necessarily trigger aposematic signalling, and highly toxic prey can still be maximally cryptic, because the increased initial rate of attack from becoming more conspicuous is not necessarily always compensated for by increased avoidance of aversive prey by predators. In other circumstances, the optimal toxin load may be insufficient to generate aversion but still be non-zero (because it increases survival), and in yet other circumstances, it is optimal to make no investment in toxins at all. The model also predicts ESSs where the prey are highly defended and aversive and where this defence is advertised at a cost of increased conspicuousness to predators. In many circumstances there is an infinite array of these aposematic ESSs, where the precise appearance is unimportant as long as it is highly visible and shared by all members of the population. Yet another class of solutions is possible where there is strong between-individual variation in appearance between conspicuous, poorly defended prey.

Adaptation, Biological↗
PubMed2003

A framework for modelling and analysing conspecific brood parasitism.

Recently several papers that model parasitic egg-laying by birds in the nests of others of their own species have been published. Whilst these papers are concerned with answering different questions, they approach the problem in a similar way and have a lot of common features. In this paper a framework is developed which unifies these models, in the sense that they all become special cases of a more general model. This is useful for two main reasons; firstly in order to aid clarity, in that the assumptions and conclusions of each of the models are easier to compare. Secondly it provides a base for further similar models to start from. The basic assumptions for this framework are outlined and a method for finding the ESSs of such models is introduced. Some mathematical results for the general, and more specific, models are considered and their implications discussed. In addition we explore the biological consequences of the results that we have obtained and suggest possible questions which could be investigated using models within or very closely related to our framework.

Algorithms↗
PubMed2003

Rapid convergence to an equilibrium state in kleptoparasitic populations.

Previous papers have modelled the behaviour of populations which are subject to kleptoparasitism, and found those ecological situations in which kleptoparasitism should occur. Individuals were considered to be in one of several states, and an equilibrium distribution for the population was found. It was then assumed, for analytical purposes but without proof, that the population was actually in that equilibrium. In this paper, we show that the equilibrium is a stable one, and that it is reached in a relatively short time for all reasonable values of the ecological parameters. Thus, a population may be expected to spend most of the time in equilibrium, and this assumption of these previous works is justified.

Algorithms↗
PubMed2003

Mathematical analysis of a model describing evolution of an asexual population in a changing environment.

We investigate a mathematical model for an asexual population with non-overlapping (discrete) generations, that exists in a changing environment. Sexual populations are also briefly discussed at the end of the paper. It is assumed that selection occurs on the value of a single polygenic trait, which is controlled by a finite number of loci with discrete-effect alleles. The environmental change results in a moving fitness optimum, causing the trait to be subject to a combination of stabilising and directional selection. This model is different from that investigated by Waxman and Peck [Genetics 153 (1999) 1041] where overlapping generations and continuous effect alleles were considered. In this paper, we consider non-overlapping generations and discrete effect alleles. However in [Genetics 153 (1999) 1041] and the present work, there is the same pattern of environmental change, namely a constant rate of change of the optimum. From [Genetics 153 (1999) 1041], no rigorous theoretical conclusion can be drawn about the form of the solutions as t grows large. Numerical work carried out in [Genetics 153 (1999) 1041] suggests that the solution is a lagged travelling wave solution, but no mathematical proof exists for the continuous model. Only partial results, regarding existence of travelling wave solutions and perturbed solutions, have been established (see [Nonlin. Anal. 53 (2003) 683; An integral equation describing an asexual population in a changing environment, Preprint]). For the discrete case of this paper, under the assumption that the ratio between the unit of genotypic value and the speed of environment change is a rational number, we are able to give rigorous proof of the following conclusion: the population follows the environmental change with a small lag behind, moreover, the lag is represented using a calculable quantity.

Biological Evolution↗
PubMed2002

Modelling dominance hierarchy formation as a multi-player game.

Animals who live in groups need to divide available resources amongst themselves. This is often achieved by means of a dominance hierarchy, where dominant individuals obtain a larger share of the resources than subordinate individuals. This paper introduces a model of dominance hierarchy formation using a multi-player extension of the classical Hawk-Dove game. Animals play non-independent pairwise games in a Swiss tournament which pairs opponents against those which have performed equally well in the conflict so far, for a fixed number of rounds. Resources are divided according to the number of contests won. The model, and its emergent properties, are discussed in the context of experimental observations.

Animals↗
PubMed2002

A unified model of dominance hierarchy formation and maintenance.

In many different species it is common for animals to spend large portions of their lives in groups. Such groups need to divide available resources amongst the individuals they contain and this is often achieved by means of a dominance hierarchy. Sometimes hierarchies are stable over a long period of time and new individuals slot into pre-determined positions, but there are many situations where this is not so and a hierarchy is formed out of a group of individuals meeting for the first time. There are several different models both of the formation of such dominance hierarchies and of already existing hierarchies. These models often treat the two phases as entirely separate, whereas in reality, if there is a genuine formation phase to the hierarchy, behaviour in this phase will be governed by the rewards available, which in turn depends upon how the hierarchy operates once it has been formed. This paper describes a method of unifying models of these two distinct phases, assuming that the hierarchy formed is stable. In particular a framework is introduced which allows a variety of different models of each of the two parts to be used in conjunction with each other, thus enabling a wide range of situations to be modelled. Some examples are given to show how this works in practice.

Animals↗
PubMed2001

Modelling antipredator vigilance and flight response in group foragers when warning signals are ambiguous.

The trade-off between feeding and vigilance in flocks of birds has been extensively studied and modelled. An assumption of many models is that if one bird spots the predator, it gives a signal and the rest of the flock takes flight. However, it has been observed that birds do not always respond to signals and in fact many signals turn out to be false alarms. Since taking flight is both costly in time and energy, it may be advantageous for birds not to respond to all alarm calls. A model is developed to show under what circumstances birds should respond to a signal. The model predicts that under most, but not all, circumstances, birds should respond to multiple detections but not to single detections. The model also predicts that if birds respond to all flights, they will have to compensate for the time lost to feeding and the greater energy requirement of spending more time in flight, by being less vigilant, and they have a lower probability of survival than birds which only respond to multiple detections.

Animals↗
PubMed2000

A sequential-arrivals model of territory acquisition II.

Birds arrive sequentially at their breeding ground where the nest sites vary in value (measured by reproductive success). Each bird may choose a vacant site or challenge an occupier for its site. In the latter case, the occupier is presumed to be the more-likely winner; the loser incurs a cost and must go to a vacant site. In a previous paper (Broom et al., 1997, J. theor. Biol.189, 257-272), we considered the optimal strategy. However, that optimal strategy was complex and perhaps could not be realized in real bird populations, making possibly costly demands both perceptually and at the coding level. With this in mind we introduce certain restricted classes of strategy, and consider how populations might evolve. Computer simulations of various populations have been performed to model the competition amongst several strategies in the presence of recurrent mutations. Certain combinations of strategies persisted and corresponded approximately to the ESSs found in Broom et al. (1997).

Animals↗
PubMed2000

Evolution in knockout conflicts: the fixed strategy case.

A group of individuals resolve their disputes by a knockout tournament. In each round of the tournament, the remaining contestants form pairs which compete, the winners progressing to the next round and the losers being eliminated. The payoff received depends upon how far the player has progressed and a cost is incurred only when it is defeated. We only consider strategies in which individuals are constrained to adopt a fixed play throughout the successive rounds. The case where individuals can vary their choice of behaviour from round to round will be treated elsewhere. The complexity of the system is investigated and illustrated both by special cases and numerical examples.

Agonistic Behavior↗
PubMed2000

Patterns of evolutionarily stable strategies: the maximal pattern conjecture revisited.

A conflict is defined by a set of pure strategies [1,..., n] and a payoff matrix, and may have many evolutionarily stable strategies (ESSs). A collection of subsets of the set of pure strategies is called a pattern. If there is an n x n matrix which has ESSs whose supports match those of the pattern, then that pattern is said to be attainable. Much of the work on patterns of ESSs relied upon an unproved conjecture. Subject to some relaxation of the definition of attainability, this conjecture is proved.

Animals↗
PubMed2000

Bounds on the number of ESSs of a matrix game.

It is well known that for any evolutionary game there may be more than one evolutionarily stable strategy (ESS). In general, the more ESSs there are, the more difficult it is to work out how the population will behave (unless there are no ESSs at all). If a matrix game has an ESS which allows all possible pure strategies to be played, referred to as an internal ESS, then no other ESS can exist. In fact, the number of ESSs possible is highly dependent upon how many of the pure strategies each allow to be played, their support size. It is shown that if alpha is the ratio of the mean support size to the number of pure strategies n, then as n tends to infinity the greatest number of ESSs can be represented by a continuous function f(alpha) with useful regularity properties, and bounds are found for both f(alpha) and the value alpha(*), where it attains its maximum. Thus we can obtain a limit on the complexity of any particular system as a function of its mean support size.

Animals↗
PubMed2000

A spatial model of antipredator vigilance.

Many species of animals have to perform two contradictory tasks: feeding, and avoiding becoming food for others. A large number of theoretical and empirical studies have investigated the trade-off between feeding and antipredator vigilance, especially in birds. An important factor which has been neglected in these studies is that of the area occupied by the flock. If individuals feed close together, competition increases and feeding rates decrease. However, if individuals space themselves widely, then vigilance efficiency goes down and there is an increased predation risk. We develop a vigilance model which allows birds to control the area the flock occupies as well as their vigilance rate. The optimal strategy is found for the birds under a variety of environmental conditions. In particular the effect of each environmental parameter on this optimum is considered in turn. How the model can be adapted for different bird species is also investigated.

Animals↗
PubMed1997

A sequential-arrivals model of territory acquisition

Birds arrive sequentially at their breeding ground where the nest sites vary in value (measured by reproductive success). Each bird must either choose a vacant site or challenge an occupier for its site. In the latter case we assume the occupier to be the more likely winner. The loser of the contest incurs a cost and must go to a vacant site. The rational strategy for such a contest is found. There is a threshold phenomenon; early arrivals occupy vacant sites, late arrivals fight. This result is intuitively reasonable, but the sequence of sites chosen is complex. A recursive method for specifying the solution is described and applied explicitly to some illustrative cases.Copyright 1997 Academic Press Limited Copyright 1997 Academic Press Limited

Journal Article↗
PubMed1996

ESS patterns: adding pairs to an ESS.

The notion of a pattern of evolutionarily stable strategies was introduced by Cannings and Vickers in 1988 (J. Theor. Biol. 132:387-420). In this paper a specific class of patterns is considered. Suppose that there is an evolutionarily stable strategy (ESS) on some set of n strategies {1,2,...,n} and that new strategies {n + 1,n + 2,...,n + k} are added. Supposing that for this new enlarged conflict there is still an ESS on {1,2,...,n} and also that there are ESSs on {n + i,j} for 1 < or = i < or = k and j epsilon Si [symbol: see text] {1,2,...,n}, the authors investigate the restrictions on the Si. These restrictions are related to certain properties of strong tournaments introduced by Reid and Beineke. We also specify, given the Si, what ESSs of the form {n + i,n + j} can be added.

Animals↗