Symbiont survival and host-symbiont disequilibria under differential vertical transmission

Symbiote transmission and maintenance of extra-genomic associations

Symbiotes can be transmitted from parents to offspring or horizontally from unrelated hosts or the environment. A key question is whether symbiote transmission is similar enough to Mendelian gene transmission to generate and maintain coevolutionary associations between host and symbiote genes. Recent papers come to opposite conclusions, with some suggesting that any horizontal transmission eliminates genetic association. These studies are hard to compare owing to arbitrary differences in modeling approach, parameter values, and assumptions about selection. I show that associations between host and symbiote genes (extra-genomic associations) can be described by the same dynamic model as conventional linkage disequilibria between genes in the same genome. Thus, covariance between host and symbiote genomes depends on population history, geographic structure, selection, and co-transmission rate, just as covariance between genes within a genome. The conclusion that horizontal transmission rapidly erodes extra-genomic associations is equivalent to the conclusion that recombination rapidly erodes associations between genes within a genome. The conclusion is correct in the absence of population structure or selection. However, population structure can maintain spatial associations between host and symbiote traits, and non-additive selection (interspecific epistasis) can generate covariances between host and symbiote genotypes. These results can also be applied to cultural or other non-genetic traits. This work contributes to a growing consensus that genomic, symbiotic, and gene-culture evolution can be analyzed under a common theoretical framework. In terms of coevolutionary potential, symbiotes can be viewed as lying on a continuum between the intimacy of genes and the indifference of casually co-occurring species.

Evolution of transmission mode in obligate symbionts

BACKGROUND

A host obtains symbionts by horizontal transmission when infected from the environment or contagiously from other hosts in the same generation. In contrast, vertical transmission occurs when a host obtains its symbionts directly from its parents. Either vertical or horizontal transmission can sustain an association between a host and its symbiont.

QUESTIONS

What evolutionary forces are necessary to evolve from an ancestral state of horizontal transmission to a derived state of vertical transmission?

MATHEMATICAL METHODS

We explore a general model of fitness interaction, including both additive and epistatic effects, between host and symbiont genes. Recursion equations allow us to analyse the short-term behaviour of the model and to study long-term deterministic effects with numerical iterations.

KEY ASSUMPTIONS

Obligate interaction between a symbiont and a single host species with genetically determined horizontal and vertical transmission. No free-living symbionts or uninfected hosts and each host is infected by only a single symbiont genetic lineage (no multiple infections). No population structure.

CONCLUSIONS

Epistasis for fitness between host and symbiont genes, like that in a matching alleles model, is a necessary condition for the evolution of vertical from horizontal transmission. Stochastic individual-based simulations show that (1) mutation facilitates the switch to vertical transmission and (2) vertical transmission is a stable evolutionary endpoint for a matching alleles model.

Horizontal transmission rapidly erodes disequilibria between organelle and symbiont genomes

We investigate the generation and decay of interspecific disequilibrium (ID) between organelle and symbiont genomes as a function of the rate of horizontal transmission. We show that rare horizontal transmission greatly diminishes the covariance between organelle and symbiont genomes. This result has two important implications. First, a low level of ID does not indicate low levels of vertical transmission. Second, even with low levels of horizontal transmission, the additive effects of host and symbiont loci will determine the response to selection, while epistatic effects will not be selectable.

The effect of Wolbachia on genetic divergence between populations: models with two-way migration

Wolbachia are intracellular bacteria that cause various reproduction alterations in their hosts, including cytoplasmic incompatibility (CI), an incompatibility between sperm and egg that typically results in embryonic death. We investigate theoretically the effects of Wolbachia-induced bidirectional CI on levels of divergence between two populations, where there is migration in both directions and differential selection at a single locus. The main findings are as follows: Wolbachia differences in the two populations are maintained up to a threshold migration rate, above which the system collapses to a single Wolbachia type; differential selection at a nuclear locus increases the threshold migration rate below which Wolbachia polymorphisms are maintained; Wolbachia differences between the populations enhance their genetic divergence at the selected locus by reducing the "effective migration rate," and even moderate levels of CI can cause large population differences in allele frequencies; and asymmetric CI can induce strong asymmetries in effective migration rate and dramatically alter the pattern of genetic divergence compared with the No Wolbachia situation. We derive an analytical approximation for the effective migration rate, which matches the simulation results for most parameter values. These results generally support the view that CI Wolbachia can contribute to genetic divergence between populations.

Exact sample sizes needed to detect dependence in 2 x 3 tables

Many medical and biological studies entail classifying a number of observations according to two factors, where one has two and the other three possible categories. This is the case of, for example, genetic association studies of complex traits with single-nucleotide polymorphisms (SNPs), where the a priori statistical planning, analysis, and interpretation of results are of critical importance. Here, we present methodology to determine the minimum sample size required to detect dependence in 2 x 3 tables based on Fisher's exact test, assuming that neither of the two margins is fixed and only the grand total N is known in advance. We provide the numerical tools necessary to determine these sample sizes for desired power, significance level, and effect size, where only the computational time can be a limitation for extreme parameter values. These programs can be accessed at . This solution of the sample size problem for an exact test will permit experimentalists to plan efficient sampling designs, determine the extent of statistical support for their hypotheses, and gain insight into the repeatability of their results. We apply this solution to the sample size problem to three empirical studies, and discuss the results with specified power and nominal significance levels.

Uniform vertical transmission and selection in a host–symbiont system. Non-random symbiont distribution generates apparent differential selection

We investigate the survival, prevalence, and distribution of a symbiont in its host population when the forces of vertical transmission (beta) and symbiont-induced selection (s) are uniform (invariant across host genotypes). We use host-symbiont disequilibria to quantify the role played by non-random associations between host genotypes and the symbiont in altering host genetic structure. Results show a larger part of the parameter space permits symbiont survival under mutualism (beta>/=0.25) than parasitism (beta>0.5). The nonlinear interaction between beta and s determines symbiont survival and prevalence at equilibrium; initial symbiont prevalence is a factor only in a small number of parameter combinations. The symbiont's non-random distribution generates apparent differential selection, when selective differences across host genotypes and alleles exist under uniform selection. The direction of change in host allele frequencies is determined exclusively by the signs of s and the allelic disequilibrium. Disequilibria cannot be created or maintained, and heterozygote disequilibrium changes sign in a greater number of runs and at higher magnitudes than homozygote disequilibria. This investigation increases our understanding of the interactions between vertical transmission and selection, and their effect on the coevolutionary dynamics and final states of interacting species under different selection regimes.