- Email: [email protected]
The evolutionary stability of mixed strategies
NEWS & COMMENT hybrid incompatibility factors by the introgression of marked segments of Drosophila mauritiana chromosomes into Drosophila simulans. Genetics 144, 819–837 14 Hollocher, H. and Wu, C-I. (1996) The genetics of reproductive isolation in the Drosophila
simulans clade: X vs. autosomal effects and male vs. female effects. Genetics 143, 1243–1255 15 Turelli, M. and Orr, H.A. (1995) The dominance theory of Haldane’s rule. Genetics 140, 389–402 16 Kascer, H. and Burns, J.A. (1981) The molecular basis of dominance. Genetics 97, 639–666
The evolutionary stability of mixed strategies
U
nderstanding the causes and consequences of phenotypic variation is a central goal of evolutionary biology. Variation persists in many cases because the phenotype that will maximize the fitness of an individual often depends upon the condition of the individual, the condition of its environment and the phenotypes expressed by other individuals. Organisms have evolved mechanisms for assessing these important conditions and for using this information to determine the phenotypes they express. How do organisms assess conditions? Crowley1 now shows that the answer to this question has important implications for the patterns of phenotypic variation that we expect to see in nature. One method of understanding the causes of phenotypic variability is to use evolutionary game theory to predict the contexts that select for expression of alternative phenotypes. In the language of game theory, a mechanism that specifies the phenotype expressed by an organism in a particular condition is called a strategy (Box 1). There has been considerable debate about the evolutionary stability of mixed (stochastic) strategies in situations where an organism’s assessment of itself or its surroundings influences the phenotype it expresses. Gross2 argued that mixed strategies
cannot be evolutionarily stable when organisms use assessments of such conditions and suggested that mixed strategies are rare or nonexistent. This idea has gained wide acceptance, even though other theoretical and empirical studies suggest that mixed strategies that incorporate condition assessments have evolved and can be evolutionarily stable3–7. Until recently, the reasons for this discrepancy and the precise factors favoring pure or mixed strategies have not been clear. Crowley’s rigorous analysis provides a major step forward in this area: (1) bringing attention to the importance of condition-assessment mechanisms; (2) showing that mixed strategies can be stable even when organisms use condition assessment; and (3) showing the limits of the latter stability.
Strategies in animal contests Crowley constructed a game-theoretic model of a contest between two animals (such as a territorial dispute), where the behavior an animal expresses depends upon its size. Animal contests were some of the earliest situations to be analysed using evolutionary game theory8. Early analyses revealed that models of symmetric contests (i.e. the contestants are equivalent in all relevant aspects) often predict that mixed strategies are
Box 1. Defining and classifying types of strategy A strategy is a rule that specifies what phenotype an organism should express in a particular condition. All strategies can be categorized as either pure or mixed4. A pure strategy specifies the expression of exactly one phenotype for each condition in which an organism can be. A strategy is mixed if, in one condition, more than one phenotype has a positive probability of being expressed. Consider the following two examples of strategies for determining clutch size. First, ‘If food is abundant, lay five eggs; otherwise, lay four eggs.’ Second, ‘If food is abundant, lay five eggs with probability 0.81 and four eggs with probability 0.19; otherwise, lay four eggs.’ The first strategy is pure, whereas the second is mixed. Strategies of either type can be condition dependent (also called ‘conditional’ or ‘state dependent’). That is, the phenotype expressed by an organism might depend upon its assessment of some aspect of its condition or the condition of its environment. In the example just given, clutch size (the phenotype) depends upon food availability (the condition). Note that ‘strategies’, ‘assessments’ and ‘decisions’, as used here, do not necessarily connote conscious thought. These terms are merely convenient for describing the process and mechanisms of variable phenotypic expression. (Definitions of pure, mixed and condition-dependent strategies follow those given by Maynard Smith4.)
482
0169-5347/00/$ – see front matter © 2000 Elsevier Science Ltd. All rights reserved.
17 Orr, H.A. (1995) The population genetics of speciation: the evolution of hybrid incompatibilities. Genetics 139, 1805–1813 18 Gavrilets, S. (1997) Evolution and speciation on holey adaptive landscapes. Trends Ecol. Evol. 12, 307–312
evolutionarily stable, whereas models of asymmetric contests (i.e. contestants differ in one or more ways that are perceptible and assessed without error by the contestants) predict that only pure, condition-dependent strategies (Box 1) are stable4,9. Models of symmetric contests predict stable mixed strategies because of negative frequency dependence4 – in a symmetric contest, all individuals have the same assessments of any relevant conditions and, therefore, all express the same phenotype if they all follow the same pure strategy. Hence, if the fitness of each phenotype decreases as it becomes more common in the population, the only stable strategy might be one that causes probabilistic expression of multiple phenotypes. However, contestants facing one another in asymmetric contests always differ and have different condition assessments, and can therefore express different phenotypes even if they follow the same pure (conditional) strategy. For this reason, asymmetric contests lack the frequency dependence necessary for stable mixed strategies. However, modeling interactions between organisms as either symmetric or asymmetric is biologically unrealistic, because organisms nearly always differ in some aspect but they will never have complete information about the asymmetries between them. Biologically plausible models must therefore incorporate variation in condition, assessment of condition and uncertainty in that assessment. Crowley constructed a general model having these three elements and used it to show how different assumptions about the empirical system being modeled led to different predictions about whether pure or mixed strategies are evolutionarily stable.
The key factor: mechanisms of assessment The mechanism of condition assessment is the crucial factor that determines whether it is possible for mixed strategies to be stable. Suppose, as Crowley does, that, in a contest between two animals, a contestant can assess its relative resource-holding potential (as indicated by size) in one of two ways – it can place itself in a discrete category, such as ‘larger’, ‘same size’ or ‘smaller’, or it can
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TREE vol. 15, no. 12 December 2000
NEWS & COMMENT estimate itself to be at a point on a continuum of relative size. (a) (b) When modeling condition Phenotype Careful Mixed Daring Phenotype Careful Daring assessment, use of discrete cat* Relative size egories3 or continuous distriSame size Larger Relative size Smaller butions10 is often a matter Trends in Ecology & Evolution of mathematical convenience, Fig. 1. Examples of predictions made by models with different assumptions about mechanisms of condition but it also has real biological assessment (after Crowley1). The figure depicts two condition-dependent strategies for determining an action in significance. Variables that are an animal contest. Both strategies use the relative size of an individual (the condition) to determine whether it is naturally classified as categori‘careful’ or ‘daring’ (the possible alternative phenotypes). In both cases, assessments need not be accurate. (a) cal (e.g. male and female, self When size assessments are points on a continuum, the only stable strategy is a pure one, which is to be daring and others, full sibling and half above a certain threshold value of assessment (indicated by ‘*’) and careful below it. (b) When assessments fall into discrete categories, mixed strategies can be stable. Note that the strategy is actually mixed for only one of sibling, and number of individthe categories. Indeed, as Crowley proves, even when mixed strategies can be stable, at most one category can uals in a group) or continuous express a mix of phenotypes; the strategy will necessarily be pure for the other categories. (e.g. size, nutrient abundance and temperature) are both common, and both types are likely to be used in determining condition- dependence necessary for stable mixed have two main implications for the ways dependent expression of phenotypes. As strategies. The fitness consequences of in which we model, predict and analyse Crowley shows, our assumptions about each of the possible phenotypes will then phenotypic variability in nature. First, whether the assessments made by organ- determine whether the frequency of several questions must be answered isms are discrete or continuous have symmetric, relative to asymmetric, inter- before constructing any model involving profound consequences on the strategies actions is sufficient for a mixed strategy condition-dependent strategies. What are that we predict to see in nature. When to be stable. the relevant conditions that the organism assessments fall into finite numbers of is assessing? Is it assessing the condidiscrete categories, mixed strategies can Implications and directions tion(s) as a discrete or continuous varibe stable; but, as the number of categories Although Crowley developed his models able(s)? If discrete, how many categories becomes infinite (i.e. assessments be- specifically around contests between two do assessments fall into? How accurate come points on a continuum), only pure animals, the results can be generalized to are assessments? Unfortunately, these any situation where the phenotype that questions might be difficult to answer, strategies are stable (Fig. 1). The intuitive logic underlying this maximizes the fitness of an individual especially if little is known about the senresult is as follows. Suppose that two depends upon the phenotypes expressed sory biology or cognitive mechanisms of individuals that truly differ in size are by other organisms with which it inter- the organism under investigation. Howcompeting over a resource and each acts, be it directly (e.g. animal contests ever, knowing that different conditionassesses itself to be ‘larger’ (one has and predator–prey interactions) or indi- assessment mechanisms give rise to disassessed the condition incorrectly). To rectly (e.g. games against the field). tinct patterns of phenotypic expression, an outside observer, the contest appears Important extensions await exploration. we can work backwards and use observaasymmetric because of the difference in For example, one context in which mixed tions of these patterns in nature to learn size, but the contest is actually symmet- strategies are frequently predicted is ‘bet- about the mechanisms that organisms ric because the individuals have identical hedging’; that is, reducing variance in fit- use. This is an exciting development assessments and therefore express the ness even at the possible expense of because it creates new links between evosame phenotype if they both use the arithmetic mean fitness11,12. By increasing lutionary biology, sensory biology and same strategy. This creates frequency- variance in phenotypic expression, a cognition. Second, Crowley’s results faldependent selection on strategies and, mixed strategy can decrease variance in sify the claim that mixed strategies canhence, the opportunity for stable mixed the reproductive success of an individual. not be stable in nature3 and, because strategies. However, if assessments were Many life history models use measures of many biological variables naturally fall points on a continuum in this scenario, fitness that are sensitive to variance in into discrete categories (examples no two individuals would ever assess reproductive success13,14 and conse- mentioned previously), mixed strategies themselves identically and, as a result, quently predict stable mixed strategies as might actually be common. there would be no frequency depen- ways of dealing with uncertainty6,7. Howdence because all competitions would ever, variation in both individual and Acknowledgements environmental condition in these models I thank H.K. Reeve, R.J. Safran, A. Lotem, be asymmetric. Gross2 argued that because two is usually broken down into categories and members of the Behavior Lunch Bunch organisms are never exactly the same, the (e.g. age classes, ‘good years’ and ‘bad for useful discussions, input and frequency-dependent selection neces- years’). Furthermore, fitness measures in commentary. P.W. Sherman provided helpful comments on a preliminary draft. I sary for stable mixed strategies is elimi- these models are implicitly frequency thank P.H. Crowley for helpful suggestions nated when organisms assess relevant dependent because the best phenotype and for checking the accuracy of this report aspects of their condition. However, as for an individual to express depends on his work. Crowley’s analysis shows, Gross’s argu- upon those expressed by other members ment applies only to situations where the of the same genotype that are in the same Samuel M. Flaxman assessments made by organisms are condition14. It will be instructive to see if Dept of Neurobiology and Behavior, Cornell points on a continuum. When assessments these types of models no longer predict University, Ithaca, NY 14853, USA fall into discrete categories, there is a stable mixed strategies when condition ([email protected]) chance that interacting individuals will variables are modeled as points on a conassess themselves identically; that is, tinuum instead. References there is a chance that interactions might Crowley’s general findings about the 1 Crowley, P.H. (2000) Hawks, doves, and mixedsymmetry games. J. Theoret. Biol. 204, 543–563 be symmetric, creating the frequency stability of pure and mixed strategies TREE vol. 15, no. 12 December 2000
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NEWS & COMMENT 2 Gross, M.R. (1996) Alternative reproductive strategies and tactics: diversity within the sexes. Trends Ecol. Evol. 11, 92–98 3 Hammerstein, P. and Parker, G.A. (1981) The asymmetric war of attrition. J. Theoret. Biol. 96, 647–682 4 Maynard Smith, J. (1982) Evolution and the Theory of Games, Cambridge University Press 5 Parker, G.A. and Courtney, S.P. (1983) Seasonal incidence adaptive variation in the timing of life history stages. J. Theoret. Biol. 105, 147–156 6 Haccou, P. and Iwasa, Y. (1995) Optimal mixed strategies in stochastic environments. Theoret. Popul. Biol. 47, 212–243
7 Heino, M. et al. (1997) Evolution of mixed maturation strategies in semelparous life histories: the crucial role of dimensionality of feedback environment. Philos. Trans. R. Soc. London Ser. B 352, 1647–1655 8 Maynard Smith, J. and Price, G.R. (1973) The logic of animal conflict. Nature 246, 15–18 9 Selten, R. (1980) A note on evolutionarily stable strategies in asymmetrical animal conflicts. J. Theoret. Biol. 84, 93–101 10 Repka, J. and Gross, M.R. (1995) The evolutionarily stable strategy under individual condition and tactic frequency. J. Theoret. Biol. 176, 27–31
Biodiversity, hotspots and defiance
A
n astounding 44% of the known global biodiversity of plants and 35% of all non-fish vertebrates are endemic to just 25 separate ‘hotspots’ on 12% of the earth’s surface1,2. These areas are under acute threat, principally through forest clearing – overall, only about 12% remains in its original state. Add the adjacent tropical forest ‘wildernesses’ of the Amazon/Orinoco and Congo Basins, and the island of New Guinea, and the immediate task for the preservation of global biodiversity becomes spatially focused. These ‘Holocene refugia’ could bring global biodiversity through the bottleneck of peak human impact that is expected over the next couple of centuries, just as their Pleistocene counterparts preserved diversity through the last glacial maximum. Of course, there is more to biodiversity conservation than simply preserving refugia, but if we do not preserve these most diverse areas then, regardless of how ‘right’ or ‘wrong’ we get the management of the surrounding matrix, we will have lost the plot along with the biodiversity. In principle, the task is achievable. Adding reserves that total approximately the size of Texas will do the trick…but what about the cost? As it turns out, the cost will be rather less than for a single Amazonian or Yangtse hydroelectricity project. Thus, how to proceed with this task, with the awareness that the next five or ten years are crucial? This was the central question put to the thirty or so biodiversity scientists, from more than 17 countries, gathered together at a recent meeting on biodiversity and conservation*. This group was joined by the staff of Conservation International (CI; Washington, DC, USA) and a small but, we hope, influential set of business leaders, to define and to cost an
484
action plan that will be used by CI as a basis for fund-raising and conservation action. Biodiversity conservation is too important to be left to governments alone, and, we are told, the private sector is willing and able to support major international conservation efforts given competent and informed direction (Peter Seligmann, CI). ‘The whole conservation agenda needs to be cranked up a notch’ and it was the task of this meeting to turn the handle (or at least put the handle into the machine). Essentially a think-tank, the actual cerebration was prefaced by scene-setting presentations by Russ Mittermeier (CI), Geoff McNeely (IUCN, Gland, Switzerland), Norman Myers (Green College, Oxford, UK) and Stuart Pimm (Columbia University, New York, USA). Pre-meeting inputs from six thematic working groups had converged on three general principles. • Greater land area needs to be placed under formal protection. • Formal protection must coincide with the building of local capacity and commitment. • Long-term solutions must be pursued. Subsequently, the meeting formed into working groups to expand, prioritize and cost the actions required within the broader agenda, and these subsequent sessions canvassed a wide range of issues. • The need for local ‘biodiversity facilitation centres’ in each target area (Roger Kitching, Griffith University, Brisbane, Australia, and colleagues). • The ongoing development of our knowledge base must occur as we *Defying Nature’s End: A Practical Agenda for Saving Life on the Planet, California Institute of Technology, Pasadena, CA, USA, 22–26 August 2000.
0169-5347/00/$ – see front matter © 2000 Elsevier Science Ltd. All rights reserved.
11 Seger, J. and Brockmann, H.J. (1987) What is bet-hedging? In Oxford Surveys in Evolutionary Biology, Volume 4 (Harvey, P.H. and Partridge, L., eds), pp. 182–211, Oxford University Press 12 Philippi, T. and Seger, J. (1989) Hedging one’s evolutionary bets, revisited. Trends Ecol. Evol. 4, 41–44 13 Roff, D.A. (1992) The Evolution of Life Histories, Chapman & Hall 14 McNamara, J.M. (1997) Optimal life histories for structured populations in fluctuating environments. Theoret. Popul. Biol. 51, 94–108
conserve, not before (Peter Raven, Missouri Botanic Gardens, St Louis, USA, and colleagues). • A hotspot assessment of global freshwater ecosystems is missing – the assumption that the terrestrial assessment is a viable surrogate needs to be tested (Melanie Stiassny, American Museum of Natural History, New York, USA, and colleagues). • Any action on land needs to be paralleled in a set of marine foci for conservation action (Callum Roberts, York University, UK, and colleagues). • Strategies to expand reserved areas, and to ensure the effectiveness of existing reserves in both the hotspots themselves (Thomas Brooks and Gustavo da Fonseca, CI, and colleagues) and in the tropical forest wilderness areas (Russ Mittermeier and Anthony Rylands, CI, and colleagues), are required. • The connection between biodiversity, ecosystem services and human health must be understood (Robert Constanza, University of Maryland, Solomons, USA, and colleagues). • A range of economic incentives and disincentives to biodiversity conservation exist. So-called perverse subsidies3, which threaten biodiversity, must be reduced and positive incentives increased (Bradley Raffle, Baker Botts LLP, Houston, USA, and colleagues). • Finally, as in any global campaign, awareness in the broadest sense must be cultivated through the media (Ivan Hattingh, WWF, Godalming, UK). This brief treatment of outcomes inevitably glosses over points of debate, disagreement and uncertainty. Hovering, as it did, at the interface between science and society this meeting certainly had its fair share of disagreements – any further discussion is necessarily a personal one, but here goes! First, put any group of scientists in a room and mention ‘agendas’ and ‘money’, and they will likely come up with research agendas. These are not the same as conservation agendas.
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simulans clade: X vs. autosomal effects and male vs. female effects. Genetics 143, 1243–1255 15 Turelli, M. and Orr, H.A. (1995) The dominance theory of Haldane’s rule. Genetics 140, 389–402 16 Kascer, H. and Burns, J.A. (1981) The molecular basis of dominance. Genetics 97, 639–666
The evolutionary stability of mixed strategies
U
nderstanding the causes and consequences of phenotypic variation is a central goal of evolutionary biology. Variation persists in many cases because the phenotype that will maximize the fitness of an individual often depends upon the condition of the individual, the condition of its environment and the phenotypes expressed by other individuals. Organisms have evolved mechanisms for assessing these important conditions and for using this information to determine the phenotypes they express. How do organisms assess conditions? Crowley1 now shows that the answer to this question has important implications for the patterns of phenotypic variation that we expect to see in nature. One method of understanding the causes of phenotypic variability is to use evolutionary game theory to predict the contexts that select for expression of alternative phenotypes. In the language of game theory, a mechanism that specifies the phenotype expressed by an organism in a particular condition is called a strategy (Box 1). There has been considerable debate about the evolutionary stability of mixed (stochastic) strategies in situations where an organism’s assessment of itself or its surroundings influences the phenotype it expresses. Gross2 argued that mixed strategies
cannot be evolutionarily stable when organisms use assessments of such conditions and suggested that mixed strategies are rare or nonexistent. This idea has gained wide acceptance, even though other theoretical and empirical studies suggest that mixed strategies that incorporate condition assessments have evolved and can be evolutionarily stable3–7. Until recently, the reasons for this discrepancy and the precise factors favoring pure or mixed strategies have not been clear. Crowley’s rigorous analysis provides a major step forward in this area: (1) bringing attention to the importance of condition-assessment mechanisms; (2) showing that mixed strategies can be stable even when organisms use condition assessment; and (3) showing the limits of the latter stability.
Strategies in animal contests Crowley constructed a game-theoretic model of a contest between two animals (such as a territorial dispute), where the behavior an animal expresses depends upon its size. Animal contests were some of the earliest situations to be analysed using evolutionary game theory8. Early analyses revealed that models of symmetric contests (i.e. the contestants are equivalent in all relevant aspects) often predict that mixed strategies are
Box 1. Defining and classifying types of strategy A strategy is a rule that specifies what phenotype an organism should express in a particular condition. All strategies can be categorized as either pure or mixed4. A pure strategy specifies the expression of exactly one phenotype for each condition in which an organism can be. A strategy is mixed if, in one condition, more than one phenotype has a positive probability of being expressed. Consider the following two examples of strategies for determining clutch size. First, ‘If food is abundant, lay five eggs; otherwise, lay four eggs.’ Second, ‘If food is abundant, lay five eggs with probability 0.81 and four eggs with probability 0.19; otherwise, lay four eggs.’ The first strategy is pure, whereas the second is mixed. Strategies of either type can be condition dependent (also called ‘conditional’ or ‘state dependent’). That is, the phenotype expressed by an organism might depend upon its assessment of some aspect of its condition or the condition of its environment. In the example just given, clutch size (the phenotype) depends upon food availability (the condition). Note that ‘strategies’, ‘assessments’ and ‘decisions’, as used here, do not necessarily connote conscious thought. These terms are merely convenient for describing the process and mechanisms of variable phenotypic expression. (Definitions of pure, mixed and condition-dependent strategies follow those given by Maynard Smith4.)
482
0169-5347/00/$ – see front matter © 2000 Elsevier Science Ltd. All rights reserved.
17 Orr, H.A. (1995) The population genetics of speciation: the evolution of hybrid incompatibilities. Genetics 139, 1805–1813 18 Gavrilets, S. (1997) Evolution and speciation on holey adaptive landscapes. Trends Ecol. Evol. 12, 307–312
evolutionarily stable, whereas models of asymmetric contests (i.e. contestants differ in one or more ways that are perceptible and assessed without error by the contestants) predict that only pure, condition-dependent strategies (Box 1) are stable4,9. Models of symmetric contests predict stable mixed strategies because of negative frequency dependence4 – in a symmetric contest, all individuals have the same assessments of any relevant conditions and, therefore, all express the same phenotype if they all follow the same pure strategy. Hence, if the fitness of each phenotype decreases as it becomes more common in the population, the only stable strategy might be one that causes probabilistic expression of multiple phenotypes. However, contestants facing one another in asymmetric contests always differ and have different condition assessments, and can therefore express different phenotypes even if they follow the same pure (conditional) strategy. For this reason, asymmetric contests lack the frequency dependence necessary for stable mixed strategies. However, modeling interactions between organisms as either symmetric or asymmetric is biologically unrealistic, because organisms nearly always differ in some aspect but they will never have complete information about the asymmetries between them. Biologically plausible models must therefore incorporate variation in condition, assessment of condition and uncertainty in that assessment. Crowley constructed a general model having these three elements and used it to show how different assumptions about the empirical system being modeled led to different predictions about whether pure or mixed strategies are evolutionarily stable.
The key factor: mechanisms of assessment The mechanism of condition assessment is the crucial factor that determines whether it is possible for mixed strategies to be stable. Suppose, as Crowley does, that, in a contest between two animals, a contestant can assess its relative resource-holding potential (as indicated by size) in one of two ways – it can place itself in a discrete category, such as ‘larger’, ‘same size’ or ‘smaller’, or it can
PII: S0169-5347(00)01966-2
TREE vol. 15, no. 12 December 2000
NEWS & COMMENT estimate itself to be at a point on a continuum of relative size. (a) (b) When modeling condition Phenotype Careful Mixed Daring Phenotype Careful Daring assessment, use of discrete cat* Relative size egories3 or continuous distriSame size Larger Relative size Smaller butions10 is often a matter Trends in Ecology & Evolution of mathematical convenience, Fig. 1. Examples of predictions made by models with different assumptions about mechanisms of condition but it also has real biological assessment (after Crowley1). The figure depicts two condition-dependent strategies for determining an action in significance. Variables that are an animal contest. Both strategies use the relative size of an individual (the condition) to determine whether it is naturally classified as categori‘careful’ or ‘daring’ (the possible alternative phenotypes). In both cases, assessments need not be accurate. (a) cal (e.g. male and female, self When size assessments are points on a continuum, the only stable strategy is a pure one, which is to be daring and others, full sibling and half above a certain threshold value of assessment (indicated by ‘*’) and careful below it. (b) When assessments fall into discrete categories, mixed strategies can be stable. Note that the strategy is actually mixed for only one of sibling, and number of individthe categories. Indeed, as Crowley proves, even when mixed strategies can be stable, at most one category can uals in a group) or continuous express a mix of phenotypes; the strategy will necessarily be pure for the other categories. (e.g. size, nutrient abundance and temperature) are both common, and both types are likely to be used in determining condition- dependence necessary for stable mixed have two main implications for the ways dependent expression of phenotypes. As strategies. The fitness consequences of in which we model, predict and analyse Crowley shows, our assumptions about each of the possible phenotypes will then phenotypic variability in nature. First, whether the assessments made by organ- determine whether the frequency of several questions must be answered isms are discrete or continuous have symmetric, relative to asymmetric, inter- before constructing any model involving profound consequences on the strategies actions is sufficient for a mixed strategy condition-dependent strategies. What are that we predict to see in nature. When to be stable. the relevant conditions that the organism assessments fall into finite numbers of is assessing? Is it assessing the condidiscrete categories, mixed strategies can Implications and directions tion(s) as a discrete or continuous varibe stable; but, as the number of categories Although Crowley developed his models able(s)? If discrete, how many categories becomes infinite (i.e. assessments be- specifically around contests between two do assessments fall into? How accurate come points on a continuum), only pure animals, the results can be generalized to are assessments? Unfortunately, these any situation where the phenotype that questions might be difficult to answer, strategies are stable (Fig. 1). The intuitive logic underlying this maximizes the fitness of an individual especially if little is known about the senresult is as follows. Suppose that two depends upon the phenotypes expressed sory biology or cognitive mechanisms of individuals that truly differ in size are by other organisms with which it inter- the organism under investigation. Howcompeting over a resource and each acts, be it directly (e.g. animal contests ever, knowing that different conditionassesses itself to be ‘larger’ (one has and predator–prey interactions) or indi- assessment mechanisms give rise to disassessed the condition incorrectly). To rectly (e.g. games against the field). tinct patterns of phenotypic expression, an outside observer, the contest appears Important extensions await exploration. we can work backwards and use observaasymmetric because of the difference in For example, one context in which mixed tions of these patterns in nature to learn size, but the contest is actually symmet- strategies are frequently predicted is ‘bet- about the mechanisms that organisms ric because the individuals have identical hedging’; that is, reducing variance in fit- use. This is an exciting development assessments and therefore express the ness even at the possible expense of because it creates new links between evosame phenotype if they both use the arithmetic mean fitness11,12. By increasing lutionary biology, sensory biology and same strategy. This creates frequency- variance in phenotypic expression, a cognition. Second, Crowley’s results faldependent selection on strategies and, mixed strategy can decrease variance in sify the claim that mixed strategies canhence, the opportunity for stable mixed the reproductive success of an individual. not be stable in nature3 and, because strategies. However, if assessments were Many life history models use measures of many biological variables naturally fall points on a continuum in this scenario, fitness that are sensitive to variance in into discrete categories (examples no two individuals would ever assess reproductive success13,14 and conse- mentioned previously), mixed strategies themselves identically and, as a result, quently predict stable mixed strategies as might actually be common. there would be no frequency depen- ways of dealing with uncertainty6,7. Howdence because all competitions would ever, variation in both individual and Acknowledgements environmental condition in these models I thank H.K. Reeve, R.J. Safran, A. Lotem, be asymmetric. Gross2 argued that because two is usually broken down into categories and members of the Behavior Lunch Bunch organisms are never exactly the same, the (e.g. age classes, ‘good years’ and ‘bad for useful discussions, input and frequency-dependent selection neces- years’). Furthermore, fitness measures in commentary. P.W. Sherman provided helpful comments on a preliminary draft. I sary for stable mixed strategies is elimi- these models are implicitly frequency thank P.H. Crowley for helpful suggestions nated when organisms assess relevant dependent because the best phenotype and for checking the accuracy of this report aspects of their condition. However, as for an individual to express depends on his work. Crowley’s analysis shows, Gross’s argu- upon those expressed by other members ment applies only to situations where the of the same genotype that are in the same Samuel M. Flaxman assessments made by organisms are condition14. It will be instructive to see if Dept of Neurobiology and Behavior, Cornell points on a continuum. When assessments these types of models no longer predict University, Ithaca, NY 14853, USA fall into discrete categories, there is a stable mixed strategies when condition ([email protected]) chance that interacting individuals will variables are modeled as points on a conassess themselves identically; that is, tinuum instead. References there is a chance that interactions might Crowley’s general findings about the 1 Crowley, P.H. (2000) Hawks, doves, and mixedsymmetry games. J. Theoret. Biol. 204, 543–563 be symmetric, creating the frequency stability of pure and mixed strategies TREE vol. 15, no. 12 December 2000
483
NEWS & COMMENT 2 Gross, M.R. (1996) Alternative reproductive strategies and tactics: diversity within the sexes. Trends Ecol. Evol. 11, 92–98 3 Hammerstein, P. and Parker, G.A. (1981) The asymmetric war of attrition. J. Theoret. Biol. 96, 647–682 4 Maynard Smith, J. (1982) Evolution and the Theory of Games, Cambridge University Press 5 Parker, G.A. and Courtney, S.P. (1983) Seasonal incidence adaptive variation in the timing of life history stages. J. Theoret. Biol. 105, 147–156 6 Haccou, P. and Iwasa, Y. (1995) Optimal mixed strategies in stochastic environments. Theoret. Popul. Biol. 47, 212–243
7 Heino, M. et al. (1997) Evolution of mixed maturation strategies in semelparous life histories: the crucial role of dimensionality of feedback environment. Philos. Trans. R. Soc. London Ser. B 352, 1647–1655 8 Maynard Smith, J. and Price, G.R. (1973) The logic of animal conflict. Nature 246, 15–18 9 Selten, R. (1980) A note on evolutionarily stable strategies in asymmetrical animal conflicts. J. Theoret. Biol. 84, 93–101 10 Repka, J. and Gross, M.R. (1995) The evolutionarily stable strategy under individual condition and tactic frequency. J. Theoret. Biol. 176, 27–31
Biodiversity, hotspots and defiance
A
n astounding 44% of the known global biodiversity of plants and 35% of all non-fish vertebrates are endemic to just 25 separate ‘hotspots’ on 12% of the earth’s surface1,2. These areas are under acute threat, principally through forest clearing – overall, only about 12% remains in its original state. Add the adjacent tropical forest ‘wildernesses’ of the Amazon/Orinoco and Congo Basins, and the island of New Guinea, and the immediate task for the preservation of global biodiversity becomes spatially focused. These ‘Holocene refugia’ could bring global biodiversity through the bottleneck of peak human impact that is expected over the next couple of centuries, just as their Pleistocene counterparts preserved diversity through the last glacial maximum. Of course, there is more to biodiversity conservation than simply preserving refugia, but if we do not preserve these most diverse areas then, regardless of how ‘right’ or ‘wrong’ we get the management of the surrounding matrix, we will have lost the plot along with the biodiversity. In principle, the task is achievable. Adding reserves that total approximately the size of Texas will do the trick…but what about the cost? As it turns out, the cost will be rather less than for a single Amazonian or Yangtse hydroelectricity project. Thus, how to proceed with this task, with the awareness that the next five or ten years are crucial? This was the central question put to the thirty or so biodiversity scientists, from more than 17 countries, gathered together at a recent meeting on biodiversity and conservation*. This group was joined by the staff of Conservation International (CI; Washington, DC, USA) and a small but, we hope, influential set of business leaders, to define and to cost an
484
action plan that will be used by CI as a basis for fund-raising and conservation action. Biodiversity conservation is too important to be left to governments alone, and, we are told, the private sector is willing and able to support major international conservation efforts given competent and informed direction (Peter Seligmann, CI). ‘The whole conservation agenda needs to be cranked up a notch’ and it was the task of this meeting to turn the handle (or at least put the handle into the machine). Essentially a think-tank, the actual cerebration was prefaced by scene-setting presentations by Russ Mittermeier (CI), Geoff McNeely (IUCN, Gland, Switzerland), Norman Myers (Green College, Oxford, UK) and Stuart Pimm (Columbia University, New York, USA). Pre-meeting inputs from six thematic working groups had converged on three general principles. • Greater land area needs to be placed under formal protection. • Formal protection must coincide with the building of local capacity and commitment. • Long-term solutions must be pursued. Subsequently, the meeting formed into working groups to expand, prioritize and cost the actions required within the broader agenda, and these subsequent sessions canvassed a wide range of issues. • The need for local ‘biodiversity facilitation centres’ in each target area (Roger Kitching, Griffith University, Brisbane, Australia, and colleagues). • The ongoing development of our knowledge base must occur as we *Defying Nature’s End: A Practical Agenda for Saving Life on the Planet, California Institute of Technology, Pasadena, CA, USA, 22–26 August 2000.
0169-5347/00/$ – see front matter © 2000 Elsevier Science Ltd. All rights reserved.
11 Seger, J. and Brockmann, H.J. (1987) What is bet-hedging? In Oxford Surveys in Evolutionary Biology, Volume 4 (Harvey, P.H. and Partridge, L., eds), pp. 182–211, Oxford University Press 12 Philippi, T. and Seger, J. (1989) Hedging one’s evolutionary bets, revisited. Trends Ecol. Evol. 4, 41–44 13 Roff, D.A. (1992) The Evolution of Life Histories, Chapman & Hall 14 McNamara, J.M. (1997) Optimal life histories for structured populations in fluctuating environments. Theoret. Popul. Biol. 51, 94–108
conserve, not before (Peter Raven, Missouri Botanic Gardens, St Louis, USA, and colleagues). • A hotspot assessment of global freshwater ecosystems is missing – the assumption that the terrestrial assessment is a viable surrogate needs to be tested (Melanie Stiassny, American Museum of Natural History, New York, USA, and colleagues). • Any action on land needs to be paralleled in a set of marine foci for conservation action (Callum Roberts, York University, UK, and colleagues). • Strategies to expand reserved areas, and to ensure the effectiveness of existing reserves in both the hotspots themselves (Thomas Brooks and Gustavo da Fonseca, CI, and colleagues) and in the tropical forest wilderness areas (Russ Mittermeier and Anthony Rylands, CI, and colleagues), are required. • The connection between biodiversity, ecosystem services and human health must be understood (Robert Constanza, University of Maryland, Solomons, USA, and colleagues). • A range of economic incentives and disincentives to biodiversity conservation exist. So-called perverse subsidies3, which threaten biodiversity, must be reduced and positive incentives increased (Bradley Raffle, Baker Botts LLP, Houston, USA, and colleagues). • Finally, as in any global campaign, awareness in the broadest sense must be cultivated through the media (Ivan Hattingh, WWF, Godalming, UK). This brief treatment of outcomes inevitably glosses over points of debate, disagreement and uncertainty. Hovering, as it did, at the interface between science and society this meeting certainly had its fair share of disagreements – any further discussion is necessarily a personal one, but here goes! First, put any group of scientists in a room and mention ‘agendas’ and ‘money’, and they will likely come up with research agendas. These are not the same as conservation agendas.
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