Evolutionarily stable strategies of diploid populations with semi-dominant inheritance patterns

1984 ◽  
Vol 21 (1) ◽  
pp. 1-9 ◽  
Author(s):  
R. Cressman ◽  
W. G. S. Hines
Keyword(s):  
Evolutionarily Stable Strategy ◽  
Correct Choice ◽  
Population Models ◽  
Dominant Inheritance ◽  
Evolutionarily Stable Strategies ◽  
Stable Strategy ◽  
Inheritance Patterns ◽  
Evolutionarily Stable ◽  
Diploid Populations

The assumption of arbitrary and biologically implausible inheritance patterns in sexual diploid populations can yield population models in which convergence of a population's mean strategy to an evolutionarily stable strategy will not occur, even though this strategy is attainable with the correct choice of gametic frequencies. The present paper investigates the effect of imposing a simplifying and biologically reasonable restriction on the assumed inheritance patterns; namely, that dominance or underdominance occurs.

Evolutionarily stable strategies of diploid populations with semi-dominant inheritance patterns

1984 ◽  
Vol 21 (01) ◽  
pp. 1-9 ◽  
Author(s):  
R. Cressman ◽  
W. G. S. Hines
Keyword(s):  
Evolutionarily Stable Strategy ◽  
Correct Choice ◽  
Population Models ◽  
Dominant Inheritance ◽  
Evolutionarily Stable Strategies ◽  
Stable Strategy ◽  
Inheritance Patterns ◽  
Evolutionarily Stable ◽  
Diploid Populations

The assumption of arbitrary and biologically implausible inheritance patterns in sexual diploid populations can yield population models in which convergence of a population's mean strategy to an evolutionarily stable strategy will not occur, even though this strategy is attainable with the correct choice of gametic frequencies. The present paper investigates the effect of imposing a simplifying and biologically reasonable restriction on the assumed inheritance patterns; namely, that dominance or underdominance occurs.

Evolutionarily stable strategies in diploid populations with general inheritance patterns

1983 ◽  
Vol 20 (2) ◽  
pp. 395-399 ◽  
Author(s):  
W. G. S. Hines ◽  
D. T. Bishop
Keyword(s):  
Sexual Selection ◽  
Evolutionarily Stable Strategy ◽  
Evolutionarily Stable Strategies ◽  
Stable Strategy ◽  
Simple Argument ◽  
Sexual Population ◽  
Inheritance Patterns ◽  
The Mean ◽  
Evolutionarily Stable ◽  
Diploid Populations

A simple argument demonstrates that the mean strategy of a diploid sexual population at evolutionary equilibrium can be expected to be an evolutionarily stable strategy (ESS) in the formal sense. This result follows under a wide set of models of genetic inheritance of strategy (including sexual selection) provided that the ESS is both attainable and maintainable.

Evolutionarily stable strategies in diploid populations with general inheritance patterns

1983 ◽  
Vol 20 (02) ◽  
pp. 395-399 ◽  
Author(s):  
W. G. S. Hines ◽  
D. T. Bishop
Keyword(s):  
Sexual Selection ◽  
Evolutionarily Stable Strategy ◽  
Evolutionarily Stable Strategies ◽  
Stable Strategy ◽  
Simple Argument ◽  
Sexual Population ◽  
Inheritance Patterns ◽  
The Mean ◽  
Evolutionarily Stable ◽  
Diploid Populations

A simple argument demonstrates that the mean strategy of a diploid sexual population at evolutionary equilibrium can be expected to be an evolutionarily stable strategy (ESS) in the formal sense. This result follows under a wide set of models of genetic inheritance of strategy (including sexual selection) provided that the ESS is both attainable and maintainable.

Strategy stability in complex randomly mating diploid populations

1982 ◽  
Vol 19 (03) ◽  
pp. 653-659 ◽  
Author(s):  
W. G. S. Hines
Keyword(s):  
Convex Hull ◽  
Lyapunov Functions ◽  
Evolutionarily Stable Strategy ◽  
Stable Strategy ◽  
Convergence In Mean ◽  
Evolutionarily Stable ◽  
Diploid Populations ◽  
Better Than

A class of Lyapunov functions is used to demonstrate that strategy stability occurs in complex randomly mating diploid populations. Strategies close to the evolutionarily stable strategy tend to fare better than more remote strategies. If convergence in mean strategy to an evolutionarily stable strategy is not possible, evolution will continue until all strategies in use lie on a unique face of the convex hull of available strategies. The results obtained are also relevant to the haploid parthenogenetic case.

ESS modelling of diploid populations II: stability analysis of possible equilibria

1994 ◽  
Vol 26 (2) ◽  
pp. 361-376 ◽  
Author(s):  
W. G. S. Hines
Keyword(s):  
Stability Analysis ◽  
Evolutionarily Stable Strategy ◽  
Companion Paper ◽  
Stable Strategy ◽  
Local Attractors ◽  
The Mean ◽  
Arbitrary Frequency ◽  
Probability Simplex ◽  
Evolutionarily Stable ◽  
Diploid Populations

In order to determine the robustness of the mean-covariance approach to exploring behavioural models of sexual diploid biological populations which are based on the evolutionarily stable strategy (ESS) concept, a companion paper explored relevant features of the probability simplex of allelic frequencies for a population which is genetically homogeneous except possibly at a single locus.The Shahshahani metric is modified in this paper to produce a measure of distance near an arbitrary frequency F in the allelic simplex which can be used when some alleles are given zero weight by F. The equation of evolution for the modified metric can then be used to show that certain sets of frequencies (corresponding to equilibrium mean strategies) act as local attractors, as long as the mean strategies corresponding to those sets are non-singular or even, in most cases, singular. We identify conditions under which the measure of distance from an initial frequency to a nearby set of equilibrium frequencies corresponding to exceptional mean strategies might increase, either temporarily or for a protracted length of time.

On the local stability of an evolutionarily stable strategy in a diploid population

1984 ◽  
Vol 21 (02) ◽  
pp. 215-224 ◽  
Author(s):  
W. G. S. Hines ◽  
D. T. Bishop
Keyword(s):  
Local Stability ◽  
Evolutionarily Stable Strategy ◽  
Payoff Matrix ◽  
Stable Strategy ◽  
Diploid Population ◽  
Haploid Population ◽  
The Mean ◽  
Evolutionarily Stable ◽  
Diploid Populations

The evolutionarily stable strategy for a given payoff matrix contest, although originally determined in terms of a haploid population, has been shown elsewhere to correspond to an equilibrium of the mean strategy of a diploid population. In this note, the equilibrium is shown to be locally stable for diploid populations. This local stability is demonstrated primarily by relating the behaviour of the perturbed diploid population to one, or in some cases two, associated haploid populations.

Joint Nesting in a Digger Wasp as an Evolutionarily Stable Preadaptation To Social Life

Behaviour ◽  
1979 ◽  
Vol 71 (3-4) ◽  
pp. 203-244 ◽  
Author(s):  
H. Jane Brockmann ◽  
Richard Dawkins
Keyword(s):  
Social Life ◽  
Evolutionarily Stable Strategy ◽  
Group Living ◽  
Egg Laying ◽  
Brood Cell ◽  
Evolutionarily Stable Strategies ◽  
Stable Strategy ◽  
A Cell ◽  
Insect Sociality ◽  
Evolutionarily Stable

AbstractOne suggested evolutionary origin of insect sociality is joint nesting by females of the same generation. Long before selection favoured joint nesting itself, it might have favoured some other incidental preadaptation such as the habit of 'entering' abandoned burrows, found in the usually solitary wasp Splaex ichneumoneus. We have comprehensive economic records of individually marked wasps. There is little evidence of consistent individual variation in nesting success. Wasps often abandon the nests they have dug, and other individuals adopt or 'enter' these empty burrows. 'Dig/Enter' is a good candidate for a mixed evolutionarily stable strategy : digging and entering decisions are not characteristic of particular individuals; the probability of entering is not conditional upon whether it is early or late in the season; there is no correlation between an individual's size and her tendency to dig or enter; there is no correlation between an individual's egg-laying success and her tendency to dig or enter; individuals do not choose to dig or enter on the basis of immediate past success; individuals do not dig and enter in runs, nor do they alternate; wasps do not choose to dig or enter on the basis of how long they have been searching. At one study site digging and entering decisions are roughly equally successful, but at another entering decisions are perhaps slightly more successful. Entering wasps seem not to distinguish empty, abandoned burrows from burrows that are still occupied. As a consequence of indiscriminate entering, two females sometimes co-occupy the same burrow. Co-occupation should not be called 'communal' because the wasps usually share the same brood cell, not just the same burrow. One might expect that wasps would gain some benefit from co-occupying, but they do not, for a number of reasons: only one egg is laid in a shared cell, and obviously only one of the two wasps can lay it; two wasps together do not fetch noticeably more food than one alone; two wasps together are no quicker at provisioning a cell than one wasp alone; wasps sometimes duplicate each others' efforts when they co-occupy a nest; co-occupying wasps often have costly fights. About all that can be said for joint nesting is that it may reduce parasitism. The risk of joint nesting is the price wasps pay for the advantages of taking over an already dug and abandoned burrow. A mathematical model assuming 'dig/enter' as a mixed evolutionarily stable strategy has some predictive success. If the parameters changed quantitatively, the Sphex model could come to predict selection in favour of joint nesting as such. The selection pressures would have to be very strong to overcome the demonstrated disadvantages of co-occupying. Variants of the Sphex model may be applicable to other species, and may help our understanding of the evolution of group living. The theory of evolutionarily stable strategies is relevant not just to the maintenance of behaviour but to its evolutionary change.

Three characterizations of population strategy stability

1980 ◽  
Vol 17 (2) ◽  
pp. 333-340 ◽  
Author(s):  
W. G. S. Hines
Keyword(s):  
Nash Equilibrium ◽  
Dynamical Systems ◽  
Evolutionarily Stable Strategy ◽  
Evolutionarily Stable Strategies ◽  
Stable Strategy ◽  
Standard Population ◽  
Population Strategy ◽  
Operative Strategies ◽  
Nash Equilibrium Strategies ◽  
Evolutionarily Stable

In addition to the concept of the evolutionarily stable strategy (ESS), developed specifically for considering intraspecific conflicts, concepts such as the Nash equilibrium from game theory and the attractor or sink from dynamical systems theory appear relevant to the problem of characterizing populations of stable composition. The three concepts mentioned are discussed for one simple standard population model. It is found that evolutionarily stable strategies of one type are necessarily Nash equilibrium strategies, although the converse is not true. The dynamical systems characterization is found to provide a model for populations susceptible to invasion by ‘co-operative' strategies, but capable of evolving back in average to the original equilibrium.

ESS modelling of diploid populations I: anatomy of one-locus allelic frequency simplices

1994 ◽  
Vol 26 (02) ◽  
pp. 341-360 ◽  
Author(s):  
W. G. S. Hines
Keyword(s):  
Genetic Variability ◽  
Evolutionarily Stable Strategy ◽  
Companion Paper ◽  
Allelic Frequency ◽  
Stable Strategy ◽  
The Mean ◽  
Probability Simplex ◽  
Weaker Conditions ◽  
Evolutionarily Stable ◽  
Diploid Populations

In order to determine the robustness of the mean-covariance approach to exploring behavioural models of sexual diploid biological populations which are based on the evolutionarily stable strategy (ESS) concept, relevant features of the probability simplex of allelic frequencies for a population with genetic variability at a single locus are explored. Singularities and related properties of mappings from the space of allele frequencies to the space of strategy frequencies are examined, and related to a certain covariance measure of variability present in the population.A companion paper builds on this characterization to establish that previous claims of stability in fact hold under slightly weaker conditions than initially indicated. The pair of papers also determines conditions under which unstable equilibria can occur, and establishes that these conditions are exceptional in practice.

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