THE EVOLUTION OF GENETIC CORRELATIONS: AN ANALYSIS OF PATTERNS

The genetic correlation is a central parameter of quantitative genetics, providing a measure of the rate at which traits respond to indirect selection (i.e., selection that does not act upon the traits under study, but some other trait with which they have genes in common). In this paper, I review the pattern of variation among four combinations of traits: life history × life history (L × L), morphological × morphological (M × M), life history × morphological (L × M), and behavioral × behavioral (B × B). A few other combinations were investigated, but insufficient data were obtained for separate analysis. A total of 1798 correlations, distributed over 51 different animal and plant species, were analyzed. The analysis was conducted at two levels: first by dividing the data set solely by trait combination, and second by blocking the data by trait combination and species. Because selection will tend to fix alleles that show positive correlations with fitness traits faster than those that are negative and because the latter are expected to arise more frequently by mutation, correlations between life-history traits are predicted to be more often negative than those between morphological traits. This prediction was supported, with the ranking in decreasing proportion of negative correlations being: L × L > L × M > B × B > M × M. The mean magnitude of the genetic correlation shows little variation among morphological and life-history combinations, and the distribution of values is remarkably flat. However, the estimated standard errors and the coefficient of variation (SE/r_G) are large, making it difficult to separate biological factors influencing the pattern of dispersion from experimental error. Analysis of the phenotypic and genetic correlations suggest that for the combinations M × M and L × M, but not L × L or B × B, the phenotypic correlation is an adequate estimate of the genetic correlation.     

Imprints of glacial history and current environment on correlations between endemic plant and invertebrate species richness

Aim We evaluate how closely diversity patterns of endemic species of vascular plants, beetles, butterflies, molluscs and spiders are correlated with each other, and to what extent similar environmental requirements or survival in common glacial refugia and comparable dispersal limitations account for their existing congruence. Location Austria. Methods We calculated pairwise correlations among species numbers of the five taxonomic groups in 1405 cells of a 3′ × 5′ raster (c. 35 km²) using the raw data as well as the residuals of regression models that accounted for: (1) environmental variables, (2) environmental variables and the occurrence of potential refugia during the Last Glacial Maximum, or (3) environmental variables, refugia and spatial filters. Results Pairwise cross‐taxonomic group Spearman’s rank correlations in the raw data were significantly positive in most cases, but only moderate (0.3 < ρ < 0.5) to weak (ρ < 0.3) throughout. Correlations were closest between plants and beetles, plants and butterflies, and plants and snails, respectively, whereas the distribution of endemic spiders was largely uncorrelated with those of the other groups. Environmental variables explained only a moderate proportion of the variance in endemic richness patterns, and the response of individual groups to environmental gradients was only partly consistent. The inclusion of refugium locations and the spatial filters increased the goodness of model fit for all five taxonomic groups. Moreover, removing the effects of environmental conditions reduced congruence in endemic richness patterns to a lesser extent than did filtering the influence of refugium locations and spatial autocorrelation, except for spiders, which are probably the least dispersal‐limited of the five groups. Main conclusions The moderate to weak congruence of endemic richness patterns clearly limits the usefulness of a surrogacy approach for designating areas for the protection of regional endemics. On the other hand, our results suggest that dispersal limitations still shape the distributions of many endemic plant, snail, beetle and butterfly species, even at the regional scale; that is, survival in shared refugia and subsequent restricted spread retain a detectable signal in existing correlations. Concentrating conservation efforts on well‐known Pleistocene refugia hence appears to be a reasonable first step towards a strategy for protecting regional endemics of at least the less mobile invertebrate groups.     

On Testing Equality of Means of Correlated Variates with Incomplete Data

A statistic is proposed for testing the hypothesis of equality of the means of a bivariate normal distribution with unknown common variance and correlation coefficient when observations are missing on one of the variates. Expressions for the second and fourth central moments of the statistic are obtained. These moments are used to approximate the distribution of the statistic by a Student's t distribution under the null hypothesis. The powers of the test are computed and compared with those of the conventional paired t and the other known statistics.     

On Comparing Correlated Means in the Presence of Incomplete Data

Two statistics are proposed for testing the hypothesis of equality of the means of a bivariate normal distribution with unknown common variance and correlation coefficient when observations are missing on both variates. One of the statistics reduces to the one proposed by Bhoj (1978, 1984) when the unpaired observations on the variates are equal. The distributions of the statistics are approximated by well known distributions under the null hypothesis. The empirical powers of the tests are computed and compared with those of some known statistics. The comparison supports the use of one of the statistics proposed in this paper.     

Cranial variation in European populations: a spatial autocorrelation study at three time periods

This study reports on spatial variation of 10 cranial variables in European populations at 3 time periods. Means for these variables, based on 137, 108, and 183 samples from the Early Medieval, Late Medieval, and Recent periods, were subjected to one-dimensional and directional spatial autocorrelation analyses. Significant spatial structure was found for most variables. It becomes more pronounced as time progresses. The spatial patterns are not strongly clinal. Correlograms based on distances computed from all variables are monotonic only to 900, 1,650, and 1,350 km for the three periods. Regional patterns are seen for most variables and become more structured and significant with time. There is little similarity among the correlograms of the variables at any one period and virtually none among periods. Inferences about spatial structure of these populations, based on spatial autocorrelation analysis, suggest a pattern dominated by migration, followed by expansion and admixture rather than selection or chance fluctuations. The patterns of morphometric change seem to reflect the patterns of linguistic change in these areas.     

Phenotypic plasticity in Phlox

Summary Three species of Phlox (Polemoniaceae) were grown in 6 greenhouse treatments. A variety of traits were recorded and the correlations among them were computed for each treatment. The phenotypic correlations between characters are significantly altered when plants are grown under different environmental conditions. These changes in correlation structure result from the differential phenotypic plasticity of traits. Partial correlations between flower production and other traits are also environment-dependent. Such changes can alter the intensity of, and possibly the response to, selection on traits correlated with fitness in natural plant populations.     

Theoretical studies on the necessary number of components in mixtures

Summary Theoretical studies on the necessary numbers of components in mixtures (for example multiclonal varieties or mixtures of lines) have been performed according to the relations between the juvenile-mature correlations of mixtures and their number of components. For the juvenile-mature correlation r_E based upon the values of the single components (= component means at juvenile and mature ages) and the juvenile-mature correlation r_M based upon the means of mixtures of different components we usually will have r_M>r_E. Furthermore, r_M will increase with an increasing number of components in the mixtures. The effectiveness of an early selection will be mainly determined by the magnitude of the juvenile-mature correlation. If we have r_M>r_E an improvement of early testing can be realized by using mixtures instead of single components. But, what are the necessary numbers of components so that r_M will be sufficiently high to enable an effective early selection of mixtures? Some relations between r_E and r_M can be obtained and conclusions have been derived.The statistical approach significant difference between r_E and r_M for a given numerical value of r_M leads to estimates for the necessary number n of components dependent on r_M, , r_E and N where: N = total number of components, which are available for the composition of mixtures and = error probability. For different tree species r_E can be estimated by an appropriate formula which depends on T with T = time (in years) from planting date until the mature age.Lambeth's formula, for example, has been developed for height growth in pines. For this situation numerical calculations are performed using r_M=0.90 and =0.05. The necessary numbers n for T=5, T=10, T=20 and T=50 are: 6, 9, 10 and 12 (for N=50); 13, 17, 20 and 23 (for N=100); 26, 34, 40 and 46 (for N=200); 38, 51, 60 and 69 (for N=300); 64, 85, 100 and 114 (for N=500) and 128, 171, 199 and 228 (for N=1,000). The dependence of these necessary numbers n of components on different type I errors and different levels of r_M have been investigated numerically.