Character displacement in some Cnemidophorus lizards revisited: A phylogenetic analysis

Ecological studies have demonstrated the role of competition in structuring communities; however, the importance of competition as a vehicle for evolution by natural selection and speciation remains unresolved. Study systems of insular faunas have provided several well known cases where ecological character displacement, coevolution of competitors leading to increased morphological separation, is thought to have occurred (e.g., anoline lizards and geospizine finches). Whiptail lizards (genus Cnemidophorus) from the islands of the Sea of Cortez and the surrounding mainland demonstrate a biogeographic pattern of morphological variation suggestive of character displacement. Two species of Cnemidophorus occur on the Baja peninsula, one relatively large (Cnemidophorus tigris) and one smaller (Cnemidophorus hyperythrus). Oceanic islands in the Sea of Cortez contain only single species, five of six having sizes intermediate to both species found on the Baja peninsula. On mainland Mexico C. hyperythrus is absent, whereas C. tigris is the smaller species in whiptail guilds. Here we construct a phylogeny using nucleotide sequences of the cytochrome b gene to infer the evolutionary history of body size change and historical patterns of colonization in the Cnemidophorus system. The phylogenetic analysis indicates that (i) oceanic islands have been founded at least five times from mainland sources by relatives of either C. tigris or C. hyperythrus, (ii) there have been two separate instances of character relaxation on oceanic islands for C. tigris, and (iii) there has been colonization of the oceanic island Cerralvo with retention of ancestral size for Cnemidophorus ceralbensis, a relative of C. hyperythrus. Finally, the phylogenetic analysis reveals potential cryptic species within mainland populations of C. tigris.

Sexually antagonistic coevolution of a postmating-prezygotic reproductive character in desert Drosophila

Rapid divergence in postmating-prezygotic characters suggests that selection may be responsible for generating reproductive barriers between closely related species. Theoretical models indicate that this rapid divergence could be generated by a series of male adaptations and female counteradaptations by means of sexual selection or conflict, but empirical tests of particular mechanisms are generally lacking. Moreover, although a male–female genotypic interaction in mediating sperm competition attests to an active role of females, molecular or morphological evidence of the female's participation in the coevolutionary process is critically needed. Here we show that postmating-prezygotic variation among populations of cactophilic desert Drosophila reflects divergent coevolutionary trajectories between the sexes. We explicitly test the female's role in intersexual interactions by quantifying differences in a specific postmating-prezygotic reproductive character, the insemination reaction mass, in two species, Drosophila mojavensis and Drosophila arizonae. A series of interpopulation crosses confirmed that population divergence was propelled by male–female interactions, a prerequisite if the selective forces derive from sexual conflicts. An association between the reaction mass and remating and oviposition behavior argues that divergence has been propelled by sexually antagonistic coevolution, and potentially has important implications for speciation.

Geometry of the SL(3,ℂ)-character variety of torus knots.

Let G be the fundamental group of the complement of the torus knot of type (m, n). It has a presentation G = . We find a geometric description of the character variety X(G) of characters of representations of G into SL(3,ℂ), GL(3,ℂ) and PGL(3,ℂ).

E-polynomial of the SL(3,C)-character variety of free groups.

We compute the E-polynomial of the character variety of representations of a rank r free group in SL(3,C). Expanding upon techniques of Logares, Muñoz and Newstead (Rev. Mat. Complut. 26:2 (2013), 635-703), we stratify the space of representations and compute the E-polynomial of each geometrically described stratum using fibrations. Consequently, we also determine the E-polynomial of its smooth, singular, and abelian loci and the corresponding Euler characteristic in each case. Along the way, we give a new proof of results of Cavazos and Lawton (Int. J. Math. 25:6 (2014), 1450058).

E-polynomials of the SL(2, C)-character varieties of surface groups

We compute the E-polynomials of the moduli spaces of representations of the fundamental group of a once-punctured surface of any genus into SL(2, C), for any possible holonomy around the puncture. We follow the geometric technique introduced in [12], based on stratifying the space of representations, and on the analysis of the behavior of the E-polynomial under fibrations.