Robert W. Jernigan

Evolutionary implications of divergent clines in an avian (Manacus: Aves) hybrid zone

Abstract A previous study of the hybrid zone in western Panama between white‐collared (Manacus candei) and golden‐collared manakins (M. vitellinus) documented the unidirectional introgression of vitellinus male secondary sexual traits across the zone. Here, we examine the hybrid zone in greater genetic and morphological detail. Statistical comparisons of clines are performed using maximum‐likelihood and nonparametric bootstrap methods. Our results demonstrate that an array of six molecular and two morphometric markers agree in cline position and width. Clines for male collar and belly color are similar in width to the first eight clines, but are shifted in position by at least five cline widths. The result is that birds in intervening populations are genetically and morphometrically very like parental candei, but males have the plumage color of parental vitellinus. Neither neutral diffusion nor nonlinearity of color scales appear to be viable explanations for the large cline shifts. Genetic dominance of vitellinus plumage traits is another potential explanation that will require breeding experiments to test. Sexual selection remains a plausible explanation for the observed introgression of vitellinus color traits in these highly dimorphic, polygynous, lek‐mating birds. Two other clines, including a nondiagnostic isozyme locus, are similar in position to the main cluster of clines, but are broader in width. Thus, introgression at some loci is greater than that detected with diagnostic markers. Assuming that narrow clines are maintained by selection, variation in cline width indicates that selection is not uniform throughout the genome and that diagnostic markers are under more intense selective pressure. The traditional focus on diagnostic markers in studies of hybrid zones may therefore lead to underestimates of average introgression. This effect may be more pronounced in organisms with low levels of genetic divergence between hybridizing taxa.

THE DUAL ROLE OF SELECTION AND EVOLUTIONARY HISTORY AS REFLECTED IN GENETIC CORRELATIONS

The patterns of genetic correlations between a series of eye and antenna characters were compared among two sets of spring‐dwelling and cave‐dwelling populations of Gammarus minus. The two sets of populations originate from different drainages and represent two separate invasions of cave habitats from surface‐dwelling populations. Matrix correlations, using permutation tests, indicated significant correlations both between populations in the same basin and from the same habitat. The technique of biplot, which allows for the simultaneous consideration of relationships between different genetic correlations and different populations, was used to further analyze the correlation structure. A rank‐3 biplot indicated that spring and cave populations were largely differentiated by eye‐antennal correlations, whereas basins were differentiated by both eye‐antennal and antennal‐antennal correlations. Eye‐antennal correlations, which are likely to be subject to selection, were most similar within habitats, which are likely to have similar selective regimes.

The effect of marker choice on estimated levels of introgression across an avian (Pipridae: Manacus) hybrid zone

Hybrid zones are often characterized by narrow, coincident clines for diverse traits, suggesting that little introgression occurs across them. However, this pattern may result from a bias in focussing on traits that are diagnostic of parental populations. Such choice of highly differentiated traits may cause us to overlook differential introgression in nondiagnostic traits and to distort our perception of hybrid zones. We tested this hypothesis in an avian hybrid zone by comparing cline structure in two sets of molecular markers: isozyme and restriction fragment length polymorphism markers chosen for differentiation between parental forms, and microsatellite markers chosen for polymorphism. Two cline‐fitting methods showed that cline centre positions of microsatellite alleles were more variable than those of isozyme and restriction fragment length polymorphism markers, and several were significantly shifted from those of the diagnostic markers. Cline widths of microsatellite alleles were also variable and two‐ to eightfold wider than those of the diagnostic markers. These patterns are consistent with the idea that markers chosen for differentiation are more likely to be under purifying selection, and studies focussed on these markers will underestimate overall introgression across hybrid zones. Our results suggest that neutral and positively selected alleles may introgress freely across many hybrid zones without altering perceived boundaries between hybridizing forms.

Species Interactions in Cave Stream Communities: Experimental Results and Microdistribution Effects

-The interspecific interactions of three pairs of cave isopods and amphipods, previously thought to be competitors, were examined by analyzing washouts and losses from laboratory streams and from manipulation experiments in streams of Organ Cave, West Virginia. None of the pairs were in fact competitors. The isopod Caecidotea holsingeri was an amensalist of the amphipod Stygobromus spinatus in the laboratory, but the two did not interact in the field. The amphipod Gammarus minus was a predator on C. holsingeri both in laboratory streams and in the field, and C. holsingeri was a competitor of G. minus, at least in laboratory streams. Stygobromus emarginatus was an amensalist of G. minus in laboratory streams and in the field; but in the field G. minus was a commensalist of S. emarginatus. This combination of commensalism and amensalism produces the dynamics of a predator-prey system. Interactions in both laboratory streams and cave streams were asymmetric and often had characteristics of several kinds of interspecific interactions. Negative interactions dominated in laboratory streams while positive interactions were more common in the field experiments. Negative interactions had an effect on microdistribution only at the level of individual stones in a riffle. Positive interactions may contribute to the positive association of some species at larger scales.

Testing the equality of correlation matrices

We present results that extend an existing test of equality of correlation matrices. A new test statistic is proposed and is shown to be asymptotically distributed as a linear combination of independent x 2 random variables. This new formulation allows us to find the power of the existing test and our extensions by deriving the distribution under the alternative using a linear combination of independent non-central x 2 random variables. We also investigate the null and the alternative distribution of two related statistics. The first one is a quadratic form in deviations from a control group with which the remaining k-1 groups are to be compared. The second test is designed for comparing adjacent groups. Several approximations for the null and the alternative distribution are considered and two illustrative examples are provided.

Testing lumpability in Markov chains

The chi-squared test of Markov chain lumpability is shown to operate reliably under a corrected derivation of the degrees of freedom. The test is used to screen out lumping schemes that corrupt the Markov property and give rise to higher order dependence.

Genomic variation in cline shape across a hybrid zone.

Hybrid zones are unique biological interfaces that reveal both population level and species level evolutionary processes. A genome-scale approach to assess gene flow across hybrid zones is vital, and now possible. In Mexican towhees (genus Pipilo), several morphological hybrid gradients exist. We completed a genome survey across one such gradient (9 populations, 140 birds) using mitochondrial DNA, 28 isozyme, and 377 AFLP markers. To assess variation in introgression among loci, cline parameters (i.e., width, center) for the 61 clinally varying loci were estimated and compiled into genomic distributions for tests against three empirical models spanning the range of observed cline shape. No single model accounts for observed variation in cline shape among loci. Numerous backcross individuals near the gradient center confirm a hybrid origin for these populations, contrary to a previous hypothesis based on social mimicry and character displacement. In addition, the observed variation does not bin into well-defined categories of locus types (e.g., neutral vs. highly selected). Our multi-locus analysis reveals cross-genomic variation in selective constraints on gene flow and locus-specific flexibility in the permeability of the interspecies membrane.

A robust test for comparing correlation matrices

The purpose of this paper is to make an empirical investigation of the robustness of the likelihood ratio test for comparing correlation matrices. It is shown that, in addition to the computational difficulties associated with the likelihood ratio test, this test is very sensitive to the assumption of multivariate normality. It is also shown that Q, a test based solely on the asymptotic normality of the vector of correlation coefficients, performs better under non-normal distributions. Unlike the likelihood ratio test, this test is asymptotically distribution robust.

A linear stochastic model for phytoplankton production in a marine ecosystem

Abstract A linear stochastic process is formulated as an approximation to a nonlinear ecosystem model. The formulation traces a chemical nutrient as it undergoes random exchanges between the phytoplankton, zooplankton, and the euphotic zone of an aquatic ecosystem. The formulation of a linear process allows the derivation of a partial-differential equation for the cumulant-generating function of the process. The use of this equation leads to a system of linear, deterministic differential equations for the cumulants of the process. Closed-form solutions are obtained for the means of the ecosystem components. These means display the characteristic oscillations and phase-plane spirals of predator-prey models. A variance which increases almost linearly with time suggests a non-stable probability distribution. Predation dynamics are reflected in the correlation structure of the solutions.

Spatial Correlation Models as Applied to Evolutionary Biology

One of the keys to comparative analyses in evolutionary biology is the ability to model phylogenetic influence on trait variation among related taxa. In recent years spatial autocorrelation models have become more popular in such analyses. In the context of evolutionary biology, spatially correlated is akin to “phylogenetically related”. We consider two of the current methods for “controlling” or “subtracting out” the effects due to phylogeny. The methods of interest are a mixed MANOVA model (Lynch, 1991, Evolution) and a spatial autocorrelation model with a fixed, known weight matrix (Ord, 1975, JASA). In the MANOVA model, the phylogeny is included via an n × n matrix of phylogenetic relationships, G, that is incorporated into the variance-covariance matrix of the random effects. In the univariate spatial autocorrelation model, the phylogenetic information enters into the analysis via a weight matrix W. We compare the two models using data on several morphometric traits among four populations of an amphipod, Gammarus minus. DNA sequence data is employed as the measure of relatedness. The models have been modified to allow for replicate observations in each trait and population combination. We show that these two models are substantively different in that the quantities remaining after subtraction do not contain the same information about the trait. The spatial autocorrelation model partitions the trait values into two components, P, the phylogenetic effect, and (S+E) the site-specific plus noise effects. Conversely, Lynch’s mixed model partitions the effects as (P+S), a “heritable” value, and E, the random noise. These differences have important implications for evolutionary comparative studies.