Biological markets

In biological markets, two classes of traders exchange commodities to their mutual benefit. Characteristics of markets are: competition within trader classes by contest or outbidding; preference for partners offering the highest value; and conflicts over the exchange value of commodities. Biological markets are currently studied under at least three different headings: sexual selection, intraspecific cooperation and interspecific mutualism. The time is ripe for the development of game theoretic models that describe the common core of biological markets and integrate existing knowledge from the separate fields.

Epidemiology in evolutionary time: the case of Wolbachia horizontal transmission between arthropod host species

Wolbachia are bacterial endosymbionts that manipulate the reproduction of their arthropod hosts. Although theory suggests that infections are frequently lost within host species due to the evolution of resistance, Wolbachia infect a huge number of species worldwide. This apparent paradox suggests that horizontal transmission between host species has been a key factor in shaping the global Wolbachia pandemic. Because Wolbachia infections are thus acquired and lost like any other infection, we use a standard epidemiological model to analyse Wolbachia horizontal transmission dynamics over evolutionary time. Conceptually modifying the model, we apply it not to transmission between individuals but between species. Because, on evolutionary timescales, infections spread frequently between closely related species and occasionally over large phylogenetic distances, we represent the set of host species as a small-world network that satisfies both requirements. Our model reproduces the effect of basic epidemiological parameters, which demonstrates the validity of our approach. We find that the ratio between transmission rate and recovery rate is crucial for determining the proportion of infected species (incidence) and that, in a given host network, the incidence may still be increasing over evolutionary time. Our results also point to the importance of occasional transmission over long phylogenetic distances for the observed high incidence levels of Wolbachia. In conclusion, we are able to explain why Wolbachia are so abundant among arthropods, although selection for resistance within hosts often leads to infection loss. Furthermore, our unorthodox approach of using epidemiology in evolutionary time can be applied to all symbionts that use horizontal transmission to infect new hosts.

The evolution of endosymbiont density in doubly infected host species

Multiple infection of individual hosts with several species or strains of maternally inherited endosymbionts is commonly observed in animals, especially insects. Here, we address theoretically the effect of co-infection on the optimal density of the endosymbionts in doubly infected hosts. Our analysis is based on the observation that a maternally inherited double infection is only stable if doubly infected females produce more doubly infected daughters than singly infected or uninfected females produce daughters. We consider both a general model and a model involving two endosymbionts inducing bidirectional cytoplasmic incompatibility (CI). We demonstrate that the optimal replication rate of endosymbionts in doubly infected hosts can be expected to be similar to or below the optimal replication rate in singly infected hosts. This is in contrast to some theoretical predictions for horizontally transmitted parasites and stems from the two strains of endosymbionts having coupled fitness. We discuss our results with respect to recent empirical results on endosymbiont densities, the evolution of CI-inducing bacteria and, more generally, the evolution of cooperation through direct fitness benefits.

Wolbachia-induced unidirectional cytoplasmic incompatibility and the stability of infection polymorphism in parapatric host populations

Wolbachia are intracellular, maternally inherited bacteria that are widespread among arthropods and commonly induce a reproductive incompatibility between infected male and uninfected female hosts known as unidirectional cytoplasmic incompatibility (CI). If infected and uninfected populations occur parapatrically, CI acts as a post-zygotic isolation barrier. We investigate the stability of such infection polymorphisms in a mathematical model with two populations linked by migration. We determine critical migration rates below which infected and uninfected populations can coexist. Analytical solutions of the critical migration rate are presented for mainland-island models. These serve as lower estimations for a more general model with two-way migration. The critical migration rate is positive if either Wolbachia causes a fecundity reduction in infected female hosts or its transmission is incomplete, and is highest for intermediate levels of CI. We discuss our results with respect to local adaptations of the Wolbachia host, speciation, and pest control.

Asymmetric gene flow and constraints on adaptation caused by sex ratio distorters

Asymmetric gene flow is generally believed to oppose natural selection and potentially impede adaptation. Whilst the cause of asymmetric gene flow has been seen largely in terms of variation in population density over space, asymmetric gene flow can also result from varying sex ratios across subpopulations with similar population sizes. We model the process of adaptation in a scenario in which two adjacent subpopulations have different sex ratios, associated with different levels of infection with maternally inherited endosymbionts that selectively kill male hosts. Two models are analyzed in detail. First, we consider one host locus with two alleles, each of which possesses a selective advantage in one of the subpopulations. We found that local adaptation can strongly be impeded in the subpopulation with the more female biased population sex ratio. Second, we analyze host alleles that provide resistance against the male-killing (MK) endosymbionts and show that asymmetric gene flow can prevent the spread of such alleles under certain conditions. These results might have important implications for the coevolution of MK bacteria and their hosts.

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 individual's 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.

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 of n-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 Darwinism in n-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.