Sex and death: a model of density-dependent virulence

Providing evidence that supports the role of parasites driving the maintenance of sex (i.e. the Red Queen hypothesis) has been a challenge ever since it was proposed. Both theoreticians and empiricists have tackled this hypothesis with vigor to mixed results. This week we read Lively (2009) which focuses on a singular effect to help build a theoretical argument for the Red Queen, density-dependent virulence. Here virulence is defined as the effect of the parasite on the host population growth rate. The density-dependent part comes into play in that the virulence increases with host population size.

The main argument of the paper is that as an asexual population invades a sexual population, the level of virulence changes and this can in turn change the outcome of the overall winner. Parasites with large density-dependent effects can change the balance and allow the maintenance of sexual populations. Presented in several graphs, virulence is a population measure of the effect of the parasites on the hosts. I'm still curious about the magnitude of selection on the individual genotypes in the model. When interpreting the results of this model, I was only able to see what happens when a group of asexual organisms invades a sexual one.

Lively provides an excellent ion description and understanding of the cost of sex. Of course the cost of sex has been detailed before, but the mathematical explanation helps with a basic intuition. The model described in the paper identifies two populations of hosts: asexual and sexually reproducing individuals. What he identifies is that in a sexual population, males provide little and females must produce at least two offspring to replace themselves. These males are using up resources. They are also decreasing the overall density of hosts that could be achieved in a complete female (or asexual) population.

One of the topics that came up during out discussion was how sex ratio may change or evolve during the evolution of sex. The simulation results presented in Lively (2009) assumes a sex ratio of 50/50 which makes sense in an evolutionary context. This has the effect of setting the advantage of the asexual population to be two fold over the sexual population. What happens when instead of two separate populations that do not interbreed, we have females choosing to produce offspring via sex or parthenogenesis? Will rare males in such a population change the early dynamics enough to produce different results?

References

Lively, C. M. 2009. The maintenance of sex: host-parasite coevolution with density-dependent virulence. J Evolution Biol 22:2086-2093.

LIVELY, C. (2009). The maintenance of sex: host-parasite coevolution with density-dependent virulence Journal of Evolutionary Biology, 22 (10), 2086-2093 DOI: 10.1111/j.1420-9101.2009.01824.x

Is the Red Queen showing her face? Evidence of negative frequency dependent selection by parasites

Recently Wolinska and Spaak (2009) provide a survey of Daphnia infections by genotype across a number of lakes in Italy and Switzerland. They present their results as empirical evidence of Red Queen dynamics in which coevolution with virulent parasites generates continued evolution. Although Van Valen (1973) originally presented a macroevolutionary argument where by reciprocal selection of hosts and their parasites generates conditions for continuous change, Bell (1982) narrowed the focus as a mechanistic explanation for the evolution or maintenance of sexual reproduction through cyclical changes in genotype frequencies. Wolinska and Spaak (2009) are not addressing the evolution of sex, but looking for evidence that parasites in Daphnia populations are generating negative frequency dependent selection such that a rare genotype has an advantage. Evidence consistent with the Red Queen has been found in other systems using spatially distributed samples (e.g. Dybdahl and Lively 1995) to look non-random infection rates as well as more directly looking at changes in frequencies of common genotypes (e.g. Dybdahl and Lively 1998).

Wolinska and Spaak (2009) propose three hypotheses to test with their data. The first is that common genotypes should be either over or under infected compared to a random sample. This prediction is based on stereotyped cyclical dynamics of genotypes of hosts and parasites (image two out of sync sine waves). At some points, the common clones will be targeted by the parasites and become overly infected. As a genotype becomes common, parasites haven't started attacking this genotype yet (i.e. time lagged), so it is under infected. In their survey, the found that indeed, some of the populations showed over infection (n = 1) and other showed under infection (n = 11), although the majority of cases did show no significant difference from random infection probabilities which is predicted as being a rare event. Their second hypothesis was that common genotypes should over the course of time decline if they are being tracked by parasites. The previous sample included only different lakes; where as the data needed to test this hypothesis are temporal samples from the same location. Their additional data is consistent with common genotypes declining over time (9 out of 10 cases). However, it is unclear to me how the general trend in this data of common genotypes decreasing over time, leads to the evidence supporting the first hypothesis. Shouldn't they find many more over infected common clones? A third hypothesis that they tested regarded host-parasite interactions maintaining diversity and an evenness of genotype frequencies which their data supported.

When discussing this paper, we were interested in what happens to predictions based on Red Queen dynamics when more than one parasite is involved. Previous empirical papers and theory seems to be generally focused on a host and a common parasite, but we know hosts are attacked by all kinds of parasites and pathogens. The system described by Wolinska and Spaak (2009) involves a host hybrid complex as well as four different parasites and questions about host specialization and hybrid maintenance were addressed in a previous paper (Wolinska et al. 2007). Where is the companion theoretical work to provide testable hypotheses?

References

Bell, G. 1982. The Masterpiece of Nature: The Evolution and Genetics of Sexuality. University of California Press, Berkeley.

Dybdahl, M. F., and C. M. Lively. 1995. Host-Parasite Interactions: Infection of Common Clones in Natural Populations of a Freshwater Snail (Potamopyrgus antipodarum). Proceedings of the Royal Society of London. Series B: Biological Sciences 260:99-103.

Dybdahl, M. F., and C. M. Lively. 1998. Host-parasite coevolution: Evidence for rare advantage and time-lagged selection in a natural population. Evolution 52:1057-1066.

Van Valen, L. 1973. A new evolutionary law. Evolutionary Theory 1:1-30.

Wolinska, J., B. Keller, M. Manca, and P. Spaak. 2007. Parasite survey of a Daphnia hybrid complex: host-specificity and environment determine infection. Journal of Animal Ecology 76:191-200.

Wolinska, J., and P. Spaak. 2009. The cost of being common: evidence from natural Daphnia populations. Evolution 63:1893-1901.

Wolinska, J., & Spaak, P. (2009). The cost of being common: evidence from natural Daphnia populations Evolution, 63 (7), 1893-1901 DOI: 10.1111/j.1558-5646.2009.00663.x

Can the Red Queen keep running? A case against recombination

In 2004, Otto and Nuismer published a theoretical paper on the evolution of sex where they examined a range of stereotyped models (e.g. gene-for-gene) of species interactions (both antagonistic and beneficial) that are often used by theoreticians. Their results indicated that sex and recombination were generally selected against regardless of the model of interaction given the assumptions of the quasi linkage equilibrium (QLE, in this case, weak selection and strong recombination). In their numerical simulations that explored parameter space potentially outside the assumptions of the QLE, they found that some cases of the matching-genotypes model (or a strict matching alleles model) of interactions would favor sex and recombination.

Kouyos et al (2007) looked at a wide range of matching alleles models (MAM) and found that when selection was strong, some models would favor sex and recombination. Salathé et al (2008b) also provide evidence of strong selection favoring recombination under the MAM. However, both did find that the closer these models were to a multiplicative form of the MAM, sex and recombination were selected against. These multiplicative matching alleles models (MMAM) were described by Otto and Nuismer (2004) as the negative control in their numerical simulations because they never favored recombination. Their QLE results also indicated that this model of interaction should not generate linkage disequilibrium and therefore neither favor nor select against recombination. Contrary to this, in a surprising result by Kouyos et al (2007), their simulations found that there was strong selection against recombination (rather than no selection at all) in the parameter space near a MMAM.

It was this surprising result that was explained in the paper that we read this past week for Coevolvers (Kouyos et al 2009). Here the authors investigated why this parameter space shows strong selection again recombination. In a MMAM, there are no epistatic interactions between the loci involved in the fitness of the interaction between host and parasite. Despite this, previous observations (Kouyos et al 2007) and the current simulations have shown that strong linkage disequilibrium is built up and maintained. It turns out that here that an interaction governed by the MMAM can equilibrate to a region of high complementarity. The importance of this is that this equilibrium is such that any recombination among the loci will generate genotypes that have a lower fitness and recombination should be selected against.

I think that this recent paper (Kouyos et al 2009) sheds more light on specific potential microevolutionary mechanisms that drive the maintenance of recombination. We still need empirical test of some more of these new predictions. The challenge for empiricists is to find the right kind of systems and a challenge for the theoreticians is to help design the right kinds of experiments.

While I have just touched on a couple of recent results testing aspects of the Red Queen Hypothesis, Salathé et al (2008a) produced a wonderful review of many of many recent theoretical results on the evolution of sex and recombination driven by host-parasite interactions. In addition, this group has another paper on this topic out recently in the American Naturalist (Salathé et al 2009) that I'm looking forward to reading.

References

Kouyos, R., M. Salathe, and S. Bonhoeffer. 2007. The Red Queen and the persistence of linkage-disequilibrium oscillations in finite and infinite populations. BMC Evolutionary Biology 7:211.

Kouyos, R. D., M. Salathé, S. P. Otto, and S. Bonhoeffer. 2009. The role of epistasis on the evolution of recombination in host-parasite coevolution. Theoretical Population Biology 75:1-13.

Otto, S. P., and S. L. Nuismer. 2004. Species interactions and the evolution of sex. Science 304:1018-1020.

Salathé, M., R. D. Kouyos, and S. Bonhoeffer. 2008a. The state of affairs in the kingdom of the Red Queen. Trends in Ecology & Evolution 23:439-445.

Salathé, M., R. D. Kouyos, and S. Bonhoeffer. 2009. On the Causes of Selection for Recombination Underlying the Red Queen Hypothesis. The American Naturalist 174:S31-S42.

Salathé, M., R. D. Kouyos, R. R. Regoes, and S. Bonhoeffer. 2008b. Rapid parasite adaptation drives selection for high recombination rates. Evolution 62:295-300.

KOUYOS, R., SALATHE, M., OTTO, S., & BONHOEFFER, S. (2009). The role of epistasis on the evolution of recombination in host–parasite coevolution Theoretical Population Biology, 75 (1), 1-13 DOI: 10.1016/j.tpb.2008.09.007

How to optimize host transmission in a complex parasite

Hammerschmidt and colleagues (2009) recently published an empirical investigation of optimal host switching. Parasites that must infect multiple hosts to complete their life cycle face a complex set of challenges. One of these is determining the timing of the switch. The authors of this paper look at the trade-off involved in staying in an intermediate host so as to become larger and more fecund in the next host and the increased chance of mortality in the current host. The authors conduct two different experiments with a tapeworm parasite, Schistocephalus solidus. In one experiment they examined the behavior of the first intermediate host, cyclopoid copepods (Macrocyclops albidus). In the second experiment they directly measured differences in fecundity among different host switch timing between the first and second intermediate hosts (in this case the three-spine stickleback, Gasterosteus aculeatus). The authors also build an optimality model and use the data from these experiments as well as some previously published data to confirm that the switch from the first to second host occurs at an optimal time for parasite fecundity.

What was most novel about this paper to me was the modification of the host behavior that had the effect of reducing parasite transmission, at least in the short run. Since the parasite was transmitted trophically, the next host eats the previous host, predation enhancement or avoidance directly influences the rate of transmission. The authors found some evidence of predation enhancement after the optimal switch time, but the stronger evidence was at least a shift in behavior of the current host. Before the parasite is mature in the first intermediate host, or before the optimal switching time to the second intermediate host, there was a reduction in movement which translates into predator avoidance behavior. Manipulating the host so as to allow the parasite a longer time to grow is a very clever strategy. In hosts that have a high potential mortality, this strategy may be found among a diversity of trophically transmitted parasites.

Reference

Hammerschmidt, K., K. Koch, M. Milinski, J. C. Chubb, and G. A. Parker. 2009. When to go: Optimization of host switching in parasites with complex life cycles. Evolution 63:1976-1986.

Hammerschmidt, K., Koch, K., Milinski, M., Chubb, J., & Parker, G. (2009). Whe to go: Optimzation of host switching in parasites with complex life cycles Evolution, 63 (8), 1976-1986 DOI: 10.1111/j.1558-5646.2009.00687.x