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Social interactions, nonlinear dynamics and task allocation in groups
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This new work also sheds light on the outstanding conceptual problem in the study of groups. At the present time, we know much about the evolutionaryor functional advantagesof group livingr. However,as Niko Tinbergensnotedyearsago,it is valuableto understandnot only the ultiwith other individuals.The last criterion is matecauseof a behaviorbut its proximate especiallyimportant: changesin the rate of mechanism. Currently, we know much social interaction with population density less about the proximate mechanismsfor and changes of density with group size group formation and fission. The work of (so that group size may influencethe rate Pacala et al., especially if it is extended at which individuals switch tasks) under- from the context of social insects,has the lie their work. The mathematical models potential to provide a conceptualfoundathen focus on the dynamicsof the fraction tion for the study of the proximate mechof the total populationinvolvedin different anismsof group formation. Theseinsights tasks. The models involve the local popu- are complementedby recent work of Gene which prolation density and a simple individual Robinsonand his colleaguesgJ0, assessmentrule that determineswhether vides an understandingof the actual (versus mathematical)mechanismsby which or not the current task is profitable. Pacala et al. begin with evolutionary social regulations of behavioral develop(ultimate) arguments concerning maxi- ment occurs in honeybeecolonies.These mization of individual or colony fitness. biological mechanisms involve workerThey show that the evolutionary optimum worker interactions that mediate hormo for individuals is a form of the ideal free nally regulatedplasticity in the division of distribution in which all tasksthat are per- laborswithin an overarchinggeneticcomformed provide the samefitness pay-offto ponent to behavioraldevelopmentlo. In summary, then, Pacalaet al. show individuals. On the other hand, the evolutionary optimum for the colony is one that by regulating the rate of interaction in which tasks that are performed yield with conspecifics, individuals can solve equal marginal benefits. One limitation of the problem of balancing environmental evolutionary argumentsis that proximate stimuli and information transfer. This is a mechanisms for attaining them are usu- welcomeresult. ally not describeds.However,one focus of the paper by Pacalaet al. is exactly that Marc Mangel question.They show, in fact, that different mechanisms for regulating group inter- Sectionof Evolution and Ecology,Universityof actions and for determiningthe successof California, Davis, CA 95616,USA the current task can lead to either the indi- References vidual optimum or to the colony optimum, 1 Lasota, A. and Mackey, M.C. (1994) Chaos, or very close to these. Fractals and Noise: Stochastic Aspects of Another of their results, that larger Dynamics (2nd edn), Springer-Verlag groups are likely to be more efficient in Pacala,SW., Gordon, D.M. and Godfray, H.C.J. tracking a changing environment than Euol. Ecol. (in press) Szathmary,E. and Maynard Smith, J. (1995) smallerones,is well known4.A less-appre Nature 374,227-232 ciated corollary that they also show is Clark, C.W. and Mangel, M. (1984)Am. Nat. that large groups may experience a dis123,626-647 advantagewhen information from social Putters, F. and Vonk, M. (1990)Behaoiour 114, interactionsoverwhelmsthat from the en148-159 vironment, and individuals consequently Mangel, M. (1990).I. Math. Biol. 28,237-256 continue in unprofitable tasks when they Pulliam, H.R. and Caraco,T. (1984) in should switch. Behavioural Ecology: An Evolutionary Their other main results are extremely Approach (Krebs, JR. and Davies, N.B., eds), exciting. First, simple interactions among pp. 122-147,Blackwell individualswith limited abilility to process 8 Tinbergen,N. (1963)Z. Tierpsychol. 20,410-433 information often leadsto group behavior 9 Huang,Z-Y. and Robinson, GE. (1992)Proc. Nat1Acad. Sci. USA 89,11726-l 1729 that is close to the behavior predicted by evolutionaryoptimizationmodels.This re- 10 Giray, T. and Robinson,G.E.(1994)Behau. Ecol. Sociobiol. 35, 13-20 sult helps fortify the conclusion that simple proximate mechanisms can achieve nearly optimal fitnesse@. Second,Pacala Students! I et al. predict that organismswill regulate 50% discount on per capita rates of social interaction as a TREE subscriptions! function of group size. Third, the effects For details see subscription card that they observecan occur in stochastic bound in this issue models with groups even as small as ten individuals.
Social interactions, nonlinear dynamics and task allocation in groups ne of the great intellectual revolutions of the past 20 years - led in part by 0ecologists like Robert May and former ecologistslike GeorgeOster- has beenthe development of nonlinear dynamics and deterministic chaos’. A main messageof this work is that relatively simple but nonlinearmathematicalrelationshipsbetween different state variables may lead to incredibly complexdynamicalrelations,and that predicting the behavior of nonlinear systems is fraught with difficulty. These messagesare somewhat depressing for those who want to understand biology using mathematicsas a tool (versusthose who want to use biology to motivate mathematicalstudies). A new paper by Stephen Pacala, DeborahGordon and CharlesGodfray*in Evolutionary Ecology is a refreshingalternative. In this work, they show that social interactions, which are inherently nonlinear, may lead to order and division of labor within groups.Although the motivations for their work are the social insects, the conceptual foundations of this paper are very broad. The approach of Pacalaet al. is based on models that use relative standard mathematicalmethods of ordinary different equations (reminiscent, in fact, of the Lorenz equationsthat generatedeterministic chaos)and elementarystochasticpro cesses.This meansthat the results should be accessibleto a wide readership, even though it may be tough going at some points to understandfully what they have done. Although I might quibble with the choice of assumptions,someof the results are quite new and extremely interesting. The models involve individuals that can perform one of a number of tasks (e.g. foragingat different kinds of sites) for the group. The behavior of a target individual is determined by social interactions and by environmentalstimuli. Rather than assuming that individuals are fixed in the task that they perform, Pacalaet al. allow switching, which is commonly observed in social insects in response to changes in food supply, predation rates or nest structure. It is also known that social insects regulatethe rate of interactions with conspecifics.Interactionsleadto the exchange of informationand this can affectboth individual fitness and colony fitness.Whether an individual switches or not dependson the successof the current task, an assessment of the environment,and interactions TREE
vol.
10, no.
9 September
1995
0 1995, Elsevier Science Ltd
347
&
COMMENT
This new work also sheds light on the outstanding conceptual problem in the study of groups. At the present time, we know much about the evolutionaryor functional advantagesof group livingr. However,as Niko Tinbergensnotedyearsago,it is valuableto understandnot only the ultiwith other individuals.The last criterion is matecauseof a behaviorbut its proximate especiallyimportant: changesin the rate of mechanism. Currently, we know much social interaction with population density less about the proximate mechanismsfor and changes of density with group size group formation and fission. The work of (so that group size may influencethe rate Pacala et al., especially if it is extended at which individuals switch tasks) under- from the context of social insects,has the lie their work. The mathematical models potential to provide a conceptualfoundathen focus on the dynamicsof the fraction tion for the study of the proximate mechof the total populationinvolvedin different anismsof group formation. Theseinsights tasks. The models involve the local popu- are complementedby recent work of Gene which prolation density and a simple individual Robinsonand his colleaguesgJ0, assessmentrule that determineswhether vides an understandingof the actual (versus mathematical)mechanismsby which or not the current task is profitable. Pacala et al. begin with evolutionary social regulations of behavioral develop(ultimate) arguments concerning maxi- ment occurs in honeybeecolonies.These mization of individual or colony fitness. biological mechanisms involve workerThey show that the evolutionary optimum worker interactions that mediate hormo for individuals is a form of the ideal free nally regulatedplasticity in the division of distribution in which all tasksthat are per- laborswithin an overarchinggeneticcomformed provide the samefitness pay-offto ponent to behavioraldevelopmentlo. In summary, then, Pacalaet al. show individuals. On the other hand, the evolutionary optimum for the colony is one that by regulating the rate of interaction in which tasks that are performed yield with conspecifics, individuals can solve equal marginal benefits. One limitation of the problem of balancing environmental evolutionary argumentsis that proximate stimuli and information transfer. This is a mechanisms for attaining them are usu- welcomeresult. ally not describeds.However,one focus of the paper by Pacalaet al. is exactly that Marc Mangel question.They show, in fact, that different mechanisms for regulating group inter- Sectionof Evolution and Ecology,Universityof actions and for determiningthe successof California, Davis, CA 95616,USA the current task can lead to either the indi- References vidual optimum or to the colony optimum, 1 Lasota, A. and Mackey, M.C. (1994) Chaos, or very close to these. Fractals and Noise: Stochastic Aspects of Another of their results, that larger Dynamics (2nd edn), Springer-Verlag groups are likely to be more efficient in Pacala,SW., Gordon, D.M. and Godfray, H.C.J. tracking a changing environment than Euol. Ecol. (in press) Szathmary,E. and Maynard Smith, J. (1995) smallerones,is well known4.A less-appre Nature 374,227-232 ciated corollary that they also show is Clark, C.W. and Mangel, M. (1984)Am. Nat. that large groups may experience a dis123,626-647 advantagewhen information from social Putters, F. and Vonk, M. (1990)Behaoiour 114, interactionsoverwhelmsthat from the en148-159 vironment, and individuals consequently Mangel, M. (1990).I. Math. Biol. 28,237-256 continue in unprofitable tasks when they Pulliam, H.R. and Caraco,T. (1984) in should switch. Behavioural Ecology: An Evolutionary Their other main results are extremely Approach (Krebs, JR. and Davies, N.B., eds), exciting. First, simple interactions among pp. 122-147,Blackwell individualswith limited abilility to process 8 Tinbergen,N. (1963)Z. Tierpsychol. 20,410-433 information often leadsto group behavior 9 Huang,Z-Y. and Robinson, GE. (1992)Proc. Nat1Acad. Sci. USA 89,11726-l 1729 that is close to the behavior predicted by evolutionaryoptimizationmodels.This re- 10 Giray, T. and Robinson,G.E.(1994)Behau. Ecol. Sociobiol. 35, 13-20 sult helps fortify the conclusion that simple proximate mechanisms can achieve nearly optimal fitnesse@. Second,Pacala Students! I et al. predict that organismswill regulate 50% discount on per capita rates of social interaction as a TREE subscriptions! function of group size. Third, the effects For details see subscription card that they observecan occur in stochastic bound in this issue models with groups even as small as ten individuals.
Social interactions, nonlinear dynamics and task allocation in groups ne of the great intellectual revolutions of the past 20 years - led in part by 0ecologists like Robert May and former ecologistslike GeorgeOster- has beenthe development of nonlinear dynamics and deterministic chaos’. A main messageof this work is that relatively simple but nonlinearmathematicalrelationshipsbetween different state variables may lead to incredibly complexdynamicalrelations,and that predicting the behavior of nonlinear systems is fraught with difficulty. These messagesare somewhat depressing for those who want to understand biology using mathematicsas a tool (versusthose who want to use biology to motivate mathematicalstudies). A new paper by Stephen Pacala, DeborahGordon and CharlesGodfray*in Evolutionary Ecology is a refreshingalternative. In this work, they show that social interactions, which are inherently nonlinear, may lead to order and division of labor within groups.Although the motivations for their work are the social insects, the conceptual foundations of this paper are very broad. The approach of Pacalaet al. is based on models that use relative standard mathematicalmethods of ordinary different equations (reminiscent, in fact, of the Lorenz equationsthat generatedeterministic chaos)and elementarystochasticpro cesses.This meansthat the results should be accessibleto a wide readership, even though it may be tough going at some points to understandfully what they have done. Although I might quibble with the choice of assumptions,someof the results are quite new and extremely interesting. The models involve individuals that can perform one of a number of tasks (e.g. foragingat different kinds of sites) for the group. The behavior of a target individual is determined by social interactions and by environmentalstimuli. Rather than assuming that individuals are fixed in the task that they perform, Pacalaet al. allow switching, which is commonly observed in social insects in response to changes in food supply, predation rates or nest structure. It is also known that social insects regulatethe rate of interactions with conspecifics.Interactionsleadto the exchange of informationand this can affectboth individual fitness and colony fitness.Whether an individual switches or not dependson the successof the current task, an assessment of the environment,and interactions TREE
vol.
10, no.
9 September
1995
0 1995, Elsevier Science Ltd
347