Genetic interactions, or epistasis, are a central feature of population biology, affecting how genetic variation within populations is translated into observable differences among populations and how reproductive isolation evolves between incipient species. Both of these aspects of epistasis will be studied using a combination of mathematical and computational analyses. Over the past decade, it has become increasingly clear that deleterious interactions between genetic variants that have been favored by natural selection within independently evolving lineages often cause inviability and sterility of hybrids. These genetic incompatibilities produce repeatable patterns of hybrid dysfunction. By relating mathematical models to more than 100 years of data on hybrid dysfunction, one can understand the number and nature of the genetic incompatibilities that are a key aspect of the origin of species. The existing genetic models describing both hybrid dysfunction and population change are highly idealized. Hence, the robustness of their conclusions must be tested with more general models.
This research will develop biologically informed mathematical models that make testable predictions that can be used by researchers studying the origin of species and the responses of populations to natural and artificial selection. The research will be integrated with an NSF-funded ?mathematics and biology? training grant for undergraduates and will foster international collaboration and the training of graduate students and postdoctorals in the US and abroad.
Wolbachia research in Australia and California Very few empirical examples of Wolbachia spread in nature are known. Kriesner et al. (2013) describes the sequential spread over approximately 20 years of two Wolbachia variants (wAu and wRi) in natural populations of D. simulans in eastern Australia. Only wRi (the Wolbachia variant found in California D. simulans and throughout North and South America, Europe, Asia and much of Africa) causes significant CI, hence wAu must spread by increasing host fitness (Hoffmann and Turelli 1997). wRi invaded Australia and rapidly displaced wAu in eastern Australia since 2004. Wolbachia and mtDNA frequency data and theoretical analyses suggest that these dynamics, as well as the earlier spread of wRi in California, are best understood as Fisherian waves of favorable variants, in which local spread tends to occur from arbitrarily low frequencies (Fisher 1937). This is a significant change in our understanding of how wRi, and presumably many other Wolbachia variants, spread in nature. Interestingly, our initial interpretation of wRi spread as a "Bartonian wave" (Turelli and Hoffmann 1991), in which local frequencies increase deterministically only after a critical threshold frequency is exceeded, is unquestionably the correct model for analyzing Wolbachia infections artificially introduced to populations for disease control (Hoffmann et al. 2011). Our initial (Bartonian) interpretation of spatial spread for wRi rested on the fact that we had documented two factors, imperfect maternal transmission and reduced (laboratory) fecundity for infected females (Hoffmann, Turelli and Harshman 1990), that would lead to deterministic reductions of Wolbachia frequency when it is very low (note that CI does not appreciably harm uninfected females when Wolbachia infection is very rare). Until 2008, when it was discovered that Wolbachia can increase host fitness by protecting them from other microbes (Hedges et al. 2008; Teixeira et al. 2008), no deterministic mechanism was known in Drosophila that might lead very rare Wolbachia to increase in frequency. Application of Wolbachia to control vector-borne disease Hoffmann and Turelli (2013) provides a simple theoretical analysis of facilitating Wolbachia introduction by transiently introducing nuclear-encoded resistance to pesticides for which resistance has previously evolved. Pesticides are widely used to control disease vectors. As resistance evolves, new pesticides are introduced and resistance alleles to the initial pesticides generally fall to low frequencies because of their deleterious pleiotropic effects. We show that by simultaneously re-using an outdated pesticide and introducing Wolbachia-transformed mosquitoes resistant to it, population transformation with Wolbachia can be facilitated. Once the Wolbachia infection is established, pesticide application stops and resistance alleles return to low frequencies. Bull and Turelli (2013) attempts to predict the (co)evolutionary responses of Wolbachia, the dengue virus and the dengue vector Ae. aegypti to Wolbachia introductions (as documented in Hoffmann et al. 2011). Our discussion deals with mathematical predictions, but it emphasizes comparative data describing what is known about disease incidence, relative virulence and vector competence in situations in which mosquitoes are or are not naturally infected with Wolbachia. Meta-analyses related to speciation Turelli, Lipkowitz and Brandvain (in press) addresses the contributions of intrinsic hybrid inviability and sterility, ecological divergence, X chromosome size and geographical isolation to the origin of Drosophila species. We find no significant signal associated with X chromosome size or levels of intrinsic postzygotic isolation or ecological divergence. In contrast, we find strong evidence for non-allopatric speciation. Although Coyne and Orr (2004) have been some of the vocal supporters of allopatric speciation, their most famous papers Coyne and Orr (1989, 1997) provide the best evidence for frequent non-allopatric speciation. Obviously, if reinforcement is pervasive, non-allopatric speciation must be common (cf. Yukilevich 2012). Brandvain, May, Pauly and Turelli (in prep.) examines the role of epistatic incompatibilities between nuclear genes and mitochondrial genes in contributing to the common pattern of differences between the viability or fertility of F1 hybrids produced from reciprocal crosses (i.e., "Darwin’s corollary to Haldane’s rule," Turelli and Moyle 2007). We test the robustness of the finding of Bolnick, Turelli et al. (2008) that directional asymmetry in hybrid performance can be predicted from the relative rates of plastid versus nuclear evolution. Turelli and Moyle (2007) described conditions under which this might be true. The question is whether Bolnick, Turelli et al. (2008) were "lucky" or whether we uncovered a general phenomenon. Our new analysis does not support a general role for relative rates of mtDNA and nuclear evolution in explaining the pervasive patterns of reciprocal-cross asymmetry in hybrid inviability. This final NSF-supported manuscript will be submitted by the end of the year.
