Peter Hammerstein

How many species are infected with Wolbachia? – a statistical analysis of current data

Wolbachia are intracellular bacteria found in many species of arthropods and nematodes. They manipulate the reproduction of their arthropod hosts in various ways, may play a role in host speciation and have potential applications in biological pest control. Estimates suggest that at least 20% of all insect species are infected with Wolbachia. These estimates result from several Wolbachia screenings in which numerous species were tested for infection; however, tests were mostly performed on only one to two individuals per species. The actual percent of species infected will depend on the distribution of infection frequencies among species. We present a meta-analysis that estimates percentage of infected species based on data on the distribution of infection levels among species. We used a beta-binomial model that describes the distribution of infection frequencies of Wolbachia, shedding light on the overall infection rate as well as on the infection frequency within species. Our main findings are that (1) the proportion of Wolbachia-infected species is estimated to be 66%, and that (2) within species the infection frequency follows a ‘most-or-few’ infection pattern in a sense that the Wolbachia infection frequency within one species is typically either very high (>90%) or very low (<10%).

Biological markets: supply and demand determine the effect of partner choice in cooperation, mutualism and mating

The formation of collaborating pairs by individuals belonging to two different classes occurs in the contexts of reproduction and intea-specific cooperation as well as of inter-specific mutualism. There is potential for partner choice and for competition for access to preferred partners in all three contexts. These selective forces have long been recognised as important in sexual selection, but their impact is not yet appreciated in cooperative and mutualistic systems. The formation of partnerships between members of different classes has much in common with the conclusion of trade agreements in human markets with two classes of traders, like producers and consumers, or employers and employees. Similar game-theoretical models can be used to predict the behaviour of rational traders in human markets and the evolutionarily stable strategies used in biological markets. We present a formal model in which the influence of the market mechanism on selection is made explicit. We restrict ourselves to biological markets in which: (1) Individuals do not compete over access to partners in an agonistic manner, but rather by outcompeting each other in those aspects that are preferred by the choosing party. (2) The commodity the partner has to offer cannot be obtained by the use of force, but requires the consent of the partner. These two restrictions ensure a dominant role for partner choice in the formation of partnerships. In a biological market model the decision to cooperate is based on the comparison between the offers of several potential partners, rather than on the behaviour of a single potential partner, as is implicitly assumed in currently accepted models of cooperation. In our example the members of one class A offer a commodity of fixed value in exchange for a commodity of variable value supplied by the other class, B. We show that when the B-class outnumbers the A-class sufficiently and the cost for the A-class to sample the offers of the B-class are low, the choosiness of the A-class will lead to selection for the supply of high value commodities by the B-class (Fig. 3a). Under the same market conditions, but with a high sampling cost this may still be the evolutionariy stable outcome, but another pair of strategies proves to be stable too: relaxed choosiness of class A coupled with low value commodities supplied by class B (Fig. 3b). We give a number of examples of mating, cooperative and mutualistic markets that resemble the low sampling cost situation depicted in Fig. 3a.

Evolution of cooperation through indirect reciprocity

How can cooperation through indirect reciprocity evolve and what would it be like? This problem has previously been studied by simulating evolution in a small group of interacting individuals, assuming no gene flow between groups. In these simulations, certain ‘image scoring’ strategies were found to be the most successful. However, analytical arguments show that it would not be in an individuals interest to use these strategies. Starting with this puzzle, we investigate indirect reciprocity in simulations based on an island model. This has an advantage in that the role of genetic drift can be examined. Our results show that the image scoring strategies depend on very strong drift or a very small cost of giving help. As soon as these factors are absent, selection eliminates image scoring. We also consider other possibilities for the evolution of indirect reciprocity. In particular, we find that the strategy of aiming for ‘good standing’ has superior properties. It can be an evolutionarily stable strategy and, even if not, it usually beats image scoring. Furthermore, by introducing quality variation among individuals into the model, we show that the standing strategy can be quality revealing, adding a new dimension to indirect reciprocity. Finally, we discuss general problems with currently popular modelling styles.

Still a Host of Hosts for Wolbachia: Analysis of Recent Data Suggests That 40% of Terrestrial Arthropod Species Are Infected

Wolbachia are intracellular bacteria that manipulate the reproduction of their arthropod hosts in remarkable ways. They are predominantly transmitted vertically from mother to offspring but also occasionally horizontally between species. In doing so, they infect a huge range of arthropod species worldwide. Recently, a statistical analysis estimated the infection frequency of Wolbachia among arthropod hosts to be 66%. At the same time, the authors of this analysis highlighted some weaknesses of the underlying data and concluded that in order to improve the estimate, a larger number of individuals per species should be assayed and species be chosen more randomly. Here we apply the statistical approach to a more appropriate data set from a recent survey that tested both a broad range of species and a sufficient number of individuals per species. Indeed, we find a substantially different infection frequency: We now estimate the proportion of Wolbachia-infected species to be around 40% which is lower than the previous estimate but still points to a surprisingly high number of arthropods harboring the bacteria. Notwithstanding this difference, we confirm the previous result that, within a given species, typically most or only a few individuals are infected. Moreover, we extend our analysis to include several reproductive parasites other than Wolbachia that were also screened for in the aforementioned empirical survey. For these symbionts we find a large variation in estimated infection frequencies and corroborate the finding that Wolbachia are the most abundant endosymbionts among arthropod species.

The asymmetric war of attrition

Abstract The paper, which has an informal discussion at the end, provides a game theoretical analysis of the asymmetric “war of attrition” with incomplete information. This is a contest where animals adopt different roles like “owner” and “intruder” in a territorial conflict, and where the winner is the individual prepared to persist longer. The term incomplete information refers to mistakes in the identification of roles. The idea by Parker & Rubenstein (1981) is mathematically worked out and confirmed that there exists only a single evolutionarily stable strategy (ESS) for the model with a continuum of possible levels of persistence and no discontinuities in the increase of cost during attrition. The ESS prescribes to settle the conflict according to “who has more to gain or less to pay for persistence”. The only evolutionarily stable convention is thus to give the player access to the resource who has the role which is favoured with respect to payoffs. By contrast, it was shown earlier (Hammerstein, 1981) for various asymmetric versions of the “Hawks-Doves” model that an ESS can exist which appears paradoxical with respect to payoffs. The nature of this contrast is further analyzed by introducing elements of discreteness in the asymmetric war of attrition. It turns out that some conditions must be satisfied in order to have the possibility of an alternative ESS which is not of the above simple commonsense type. First, a decision to persist (or escalate) further in a contest must typically commit a contestant to go on fighting for a full “round”, before he can give up without danger. Second, such a “discontinuity” must occur at a level of persistence where the contest is still cheap, and, finally, errors in the identification of roles must be rare.

The role of asymmetries in animal contests

Abstract This paper contains a game theoretical analysis of animal contest situations which are asymmetric in more than one aspect: two opponents may for example be imagined which differ in ‘ownership status’ as well as in ‘relative fighting ability’. The following question is analysed: which aspect may or must be used for conventional settlement in a population ‘playing’ an evolutionarily stable strategy (ESS)? The contestants are assumed to be fully informed about the asymmetric features. In particular, the assessment of relative fighting ability is supposed to be unambiguous and without cost. This assumption of perfect information allows for a decomposition of the ‘evolutionary game’ into sub-games. Therefore an easy procedure for calculating the ESSs can be presented, and simple models are analysed. It is concluded that payoff-irrelevant aspects may be used for conventional settlement of a conflict even if payoff-relevant asymmetric aspects also exist. One of the aspects may, however, be of such strong relevance that, no matter which ESS is played, animals must base their decisions on that ‘dominant’ aspect. It may also occur that two different asymmetric features are each of strong payoff relevance for either of the opponents, such that they have no escalation-suppressing effect. The particular scenario of a conflict between an ‘owner of a resource’ and an ‘intruder’ is used to derive the more general conclusions.

Darwinian adaptation, population genetics and the streetcar theory of evolution.

This paper investigates the problem of how to conceive a robust theory of phenotypic adaptation in non-trivial models of evolutionary biology. A particular effort is made to develop a foundation of this theory in the context ofn-locus population genetics. Therefore, the evolution of phenotypic traits is considered that are coded for by more than one gene. The potential for epistatic gene interactions is not a priori excluded. Furthermore, emphasis is laid on the intricacies of frequency-dependent selection. It is first discussed how strongly the scope for phenotypic adaptation is restricted by the complex nature of ‘reproduction mechanics’ in sexually reproducing diploid populations. This discussion shows that one can easily lose the traces of Darwinsm inn-locus models of population genetics. In order to retrieve these traces, the outline of a new theory is given that I call ‘streetcar theory of evolution’. This theory is based on the same models that geneticists have used in order to demonstrate substantial problems with the ‘adaptationist programme’. However, these models are now analyzed differently by including thoughts about the evolutionary removal of genetic constraints. This requires consideration of a sufficiently wide range of potential mutant alleles and careful examination of what to consider as a stable state of the evolutionary process. A particular notion of stability is introduced in order to describe population states that are phenotypically stable against the effects of all mutant alleles that are to be expected in the long-run. Surprisingly, a long-term stable state can be characterized at the phenotypic level as a fitness maximum, a Nash equilibrium or an ESS. The paper presents these mathematical results and discusses — at unusual length for a mathematical journal — their fundamental role in our current understanding of evolution.

Game theory and evolutionary biology

Publisher Summary The subject matter of evolutionary game theory is the analysis of conflict and cooperation in animals and plants. Originally, game theory was developed as a theory of human strategic behavior based on an idealized picture of rational decision making. Evolutionary game theory does not rely on rationality assumptions but on the idea that the Darwinian process of natural selection drives organisms toward the optimization of reproductive success. Most of evolutionary game theory focuses on those cases where stable equilibrium is reached. However, the dynamics of evolutionary processes in disequilibrium is also an active area of research. In principle, evolutionary game theory deals only with fully symmetric games. Asymmetric conflicts are embedded in symmetric games where each player has the same chance to be on each side of the conflict. The mathematical definition of evolutionary stability refers to symmetric games only. Because asymmetric conflicts can be embedded in symmetric games, this is no obstacle for the treatment of asymmetric conflicts.

Economics in Nature: Social Dilemmas, Mate Choice and Biological Markets

Preface 1. Games and markets: economic behaviour in humans and other animals Peter Hammerstein Part I. Economic Behavior in Social Networks: 2. Social dilemmas and human behaviour Elinor Ostrom 3. Cooperation and collective action in animal behaviour Charles Nunn and Rebecca J. Lewis 4. Conflict, reconciliation and negotiation in non-human primates: the value of long-term relationships Jan A. R. A. M Van Hooff Part II. Biological Markets: 5. Biological markets: partner choice as the driving force behind the evolution of mutualisms Ronald Noe 6. The utility of grooming in baboon troops Louise Barrett and Peter S. Henzi 7. The cleaner fish market Redouan Bshary 8. Modeling interspecific mutualisms as biological markets Jason D. Hoeksema and Mark W. Schwartz Part III. Mating Markets: 9. Human mate choice strategies Boguslaw Pawlowski and Robin I. M. Dunbar 10. How does mate choice contribute to exaggeration and diversity in sexual characters? Andrew Pomiankowski and Yoh Iwasa 11. Information about sperm competition and the economics of sperm allocation Geoffrey A. Parker and Mike A. Ball 12. The economics of male mating strategies Robin I. M. Dunbar.

A new perspective on developmental plasticity and the principles of adaptive morph determination.

Organisms can have divergent paths of development leading to alternative phenotypes, or morphs. The choice of developmental path may be set by environmental cues, the individual’s genotype, or a combination of the two. Using individual‐based simulation and analytical investigation, we explore the idea that from the viewpoint of a developmental switch, genetic morph determination can sometimes be regarded as adaptive developmental plasticity. We compare the possibilities for the evolution of environmental and genetic morph determination and combinations of the two in situations with spatial variation in conditions. We find that the accuracy of environmental cues in predicting coming selective conditions is important for environmental morph determination, in accordance with previous results, and that genetic morph determination is favored in a similar way by the accuracy of genetic cues, in the form of selectively maintained gene frequency differences between local populations. Restricted gene flow and strong selection acting on the phenotypic alternatives produce clearer gene frequency differences and lead to greater accuracy of genetic cues. For combined environmental and genetic morph determination, we show that the developmental machinery can evolve toward efficiently combining information in environmental and genetic cues for the purpose of predicting coming selective conditions.