Biomedical subjects

Timothy Killingback

Publications and source records attributed to Timothy Killingback.

7 recordsLinked to original sources

PubMed2006

Evolution in group-structured populations can resolve the tragedy of the commons.

Public goods are the key features of all human societies and are also important in many animal societies. Collaborative hunting and collective defence are but two examples of public goods that have played a crucial role in the development of human societies and still play an important role in many animal societies. Public goods allow societies composed largely of cooperators to outperform societies composed mainly of non-cooperators. However, public goods also provide an incentive for individuals to be selfish by benefiting from the public good without contributing to it. This is the essential paradox of cooperation-known variously as the Tragedy of the Commons, Multi-person Prisoner's Dilemma or Social Dilemma. Here, we show that a new model for evolution in group-structured populations provides a simple and effective mechanism for the emergence and maintenance of cooperation in such a social dilemma. This model does not depend on kin selection, direct or indirect reciprocity, punishment, optional participation or trait-group selection. Since this mechanism depends only on population dynamics and requires no cognitive abilities on the part of the agents concerned, it potentially applies to organisms at all levels of complexity.

Animals↗

PubMed2006

Scale-free extinction dynamics in spatially structured host-parasitoid systems.

Much of the work on extinction events has focused on external perturbations of ecosystems, such as climatic change, or anthropogenic factors. Extinction, however, can also be driven by endogenous factors, such as the ecological interactions between species in an ecosystem. Here we show that endogenously driven extinction events can have a scale-free distribution in simple spatially structured host-parasitoid systems. Due to the properties of this distribution there may be many such simple ecosystems that, although not strictly permanent, persist for arbitrarily long periods of time. We identify a critical phase transition in the parameter space of the host-parasitoid systems, and explain how this is related to the scale-free nature of the extinction process. Based on these results, we conjecture that scale-free extinction processes and critical phase transitions of the type we have found may be a characteristic feature of many spatially structured, multi-species ecosystems in nature. The necessary ingredient appears to be competition between species where the locally inferior type disperses faster in space. If this condition is satisfied then the eventual outcome depends subtly on the strength of local superiority of one species versus the dispersal rate of the other.

Animals↗

PubMed2005

Evolution of cooperation by generalized reciprocity.

The evolution of cooperation by direct reciprocity requires that individuals recognize their present partner and remember the outcome of their last encounter with that specific partner. Direct reciprocity thus requires advanced cognitive abilities. Here, we demonstrate that if individuals repeatedly interact within small groups with different partners in a two person Prisoner's Dilemma, cooperation can emerge and also be maintained in the absence of such cognitive capabilities. It is sufficient for an individual to base their decision of whether or not to cooperate on the outcome of their last encounter--even if it was with a different partner.

Altruism↗

PubMed2004

Spatial models of virus-immune dynamics.

To date, the majority of theoretical models describing the dynamics of infectious diseases in vivo are based on the assumption of well-mixed virus and cell populations. Because many infections take place in solid tissues, spatially structured models represent an important step forward in understanding what happens when the assumption of well-mixed populations is relaxed. Here, we explore models of virus and virus-immune dynamics where dispersal of virus and immune effector cells was constrained to occur locally. The stability properties of our spatial virus-immune dynamics models remained robust under almost all biologically plausible dispersal schemes, regardless of their complexity. The various spatial dynamics were compared to the basic non-spatial dynamics and important differences were identified: When space was assumed to be homogeneous, the dynamics generated by non-spatial and spatially structured models differed substantially at the peak of the infection. Thus, non-spatial models may lead to systematic errors in the estimates of parameters underlying acute infection dynamics. When space was assumed to be heterogeneous, spatial coupling not only changed the equilibrium properties of the uncoupled populations but also equalized the dynamics and thereby reduced the likelihood of dynamic elimination of the infection. In line with experimental and clinical observations, long-lasting oscillation periods were virtually absent. When source-sink dynamics were considered, the long-term outcome of the infection depended critically on the degree of spatial coupling. The infection collapsed when emigration from source sites became too large. Finally, we discuss the implications of spatially structured models on medical treatment of infectious diseases, and note that a huge gap exists in data accurately describing infection dynamics in solid tissues.

Chronic Disease↗

PubMed2004

Effects of neighbourhood size and connectivity on the spatial Continuous Prisoner's Dilemma.

The Prisoner's Dilemma, a two-person game in which the players can either cooperate or defect, is a common paradigm for studying the evolution of cooperation. In real situations cooperation is almost never all or nothing. This observation is the motivation for the Continuous Prisoner's Dilemma, in which individuals exhibit variable degrees of cooperation. It is known that in the presence of spatial structure, when individuals "play against" (i.e. interact with) their neighbours, and "compare to" ("learn from") them, cooperative investments can evolve to considerable levels. Here, we examine the effect of increasing the neighbourhood size: we find that the mean-field limit of no cooperation is reached for a critical neighbourhood size of about five neighbours on each side in a Moore neighbourhood, which does not depend on the size of the spatial lattice. We also find the related result that in a network of players, the critical average degree (number of neighbours) of nodes for which defection is the final state does not depend on network size, but only on the network topology. This critical average degree is considerably (about 10 times) higher for clustered (social) networks, than for distributed random networks. This result strengthens the argument that clustering is the mechanism which makes the development and maintenance of the cooperation possible. In the lattice topology, it is observed that when the neighbourhood sizes for "interacting" and "learning" differ by more than 0.5, cooperation is not sustainable, even for neighbourhood sizes that are below the mean-field limit of defection. We also study the evolution of neighbourhood sizes, as well as investment level. Here, we observe that the series of the interaction and learning neighbourhoods converge, and a final cooperative state with considerable levels of average investment is achieved.

Animals↗

PubMed2004

The evolutionary origin of cooperators and defectors.

Coexistence of cooperators and defectors is common in nature, yet the evolutionary origin of such social diversification is unclear. Many models have been studied on the basis of the assumption that benefits of cooperative acts only accrue to others. Here, we analyze the continuous snowdrift game, in which cooperative investments are costly but yield benefits to others as well as to the cooperator. Adaptive dynamics of investment levels often result in evolutionary diversification from initially uniform populations to a stable state in which cooperators making large investments coexist with defectors who invest very little. Thus, when individuals benefit from their own actions, large asymmetries in cooperative investments can evolve.

Altruism↗

PubMed2003

Metapopulation dynamics with quasi-local competition.

Stepping-stone models for the ecological dynamics of metapopulations are often used to address general questions about the effects of spatial structure on the nature and complexity of population fluctuations. Such models describe an ensemble of local and spatially isolated habitat patches that are connected through dispersal. Reproduction and hence the dynamics in a given local population depend on the density of that local population, and a fraction of every local population disperses to neighboring patches. In such models, interesting dynamic phenomena, e.g. the persistence of locally unstable predator-prey interactions, are only observed if the local dynamics in an isolated patch exhibit non-equilibrium behavior. Therefore, the scope of these models is limited. Here we extend these models by making the biologically plausible assumption that reproductive success in a given local habitat not only depends on the density of the local population living in that habitat, but also on the densities of neighboring local populations. This would occur if competition for resources occurs between neighboring populations, e.g. due to foraging in neighboring habitats. With this assumption of quasi-local competition the dynamics of the model change completely. The main difference is that even if the dynamics of the local populations have a stable equilibrium in isolation, the spatially uniform equilibrium in which all local populations are at their carrying capacity becomes unstable if the strength of quasi-local competition reaches a critical level, which can be calculated analytically. In this case the metapopulation reaches a new stable state, which is, however, not spatially uniform anymore and instead results in an irregular spatial pattern of local population abundance. For large metapopulations, a huge number of different, spatially non-uniform equilibrium states coexist as attractors of the metapopulation dynamics, so that the final state of the system depends critically on the initial conditions. The existence of a large number of attractors has important consequences when environmental noise is introduced into the model. Then the metapopulation performs a random walk in the space of all attractors. This leads to large and complicated population fluctuations whose power spectrum obeys a red-shifted power law. Our theory reiterates the potential importance of spatial structure for ecological processes and proposes new mechanisms for the emergence of non-uniform spatial patterns of abundance and for the persistence of complicated temporal population fluctuations.

Competitive Behavior↗