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.     

Describing Ordinal Odds Ratios for Stratified r × c Tables

For an r × ctable with ordinal responses, odds ratios are commonly used to describe the relationship between the row and column variables. This article shows two types of ordinal odds ratios where local‐global odds ratios are used to compare several groups on a c‐category ordinal response and a global odds ratio is used to measure the global association between a pair of ordinal responses. When there is a stratification factor, we consider Mantel‐Haenszel (MH) type estimators of these odds ratios to summarize the association from several strata. Like the ordinary MH estimator of the common odds ratio for several 2 × 2 contingency tables, the estimators are used when the association is not expected to vary drastically among the strata. Also, the estimators are consistent under the ordinary asymptotic framework in which the number of strata is fixed and also under sparse asymptotics in which the number of strata grows with the sample size. Compared to the maximum likelihood estimators, simulations find that the MH type estimators perform better especially when each stratum has few observations. This article provides variances and covariances formulae for the local‐global odds ratios estimators and applies the bootstrap method to obtain a standard error for the global odds ratio estimator. At the end, we discuss possible ways of testing the homogeneity assumption.     

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.     

Genetic,phenotypic, and environmental correlations in black medic,Medicago lupulina L., grown in three different environments

We have investigated the relationship between phenotypic and genetic correlations among a large number of quantitative traits (36) in three different environments in order to determine their degree of disparity and whether phenotypic correlations could be substituted for their genetic counterparts whatever the environment. We also studied the influence of the environment on genetic and phenotypic correlations. Twenty accessions (full-sib families) ofMedicago luPulina were grown in three environments. In two of these two levels of environmental stress were generated by harvesting plants at flowering and by growing plants in competition with barley, respectively. A third environment, with no treatment, was used as a control with no stress. Average values of pod and shoot weight indicate that competition induces the highest level of stress. The genetic and phenotypic correlations among the 36 traits were compared. Significant phenotypic correlations were obtained easily, while there was no genetic variation for 1 or the 2 characters being correlated. The large positive correlation between the genetic and phenotypic correlation matrices indicated a good proportionality between genetic and phenotypic correlations matrices but not their similarity. In a given environment, when only those traits with a significant genetic variance were taken into account, there were still differences between genetic and phenotypic correlations, even when levels of significance for phenotypic correlations were lowered. Consequently, it is dangerous to substitute phenotypic correlations for genetic correlations. The number of traits that showed genetic variability increased with increasing environmental stress, consequently the number of significant genetic correlations also increased with increasing environmental stress. In contrast, the number of significant phenotypic correlations was not influnced by the environment. The structures of both phenotypic and genetic matrices, however, depended on the environment, and not in the same way for both matrices.     

ANNUAL DIFFERENCES IN FEMALE REPRODUCTIVE SUCCESS AFFECT SPATIAL AND COHORT-SPECIFIC GENOTYPIC HETEROGENEITY IN PAINTED TURTLES

Long-term ecological data were used to evaluate the relative importance of movements, breeding structure, and reproductive ecological factors to the degree of spatial and age-specific variation in genetic characteristics of painted turtles (Chrysemys picta) on the E. S. George Reserve in southeastern Michigan. Estimates of the degree of spatial genetic structuring were based on the proportion of total genotypic variance partitioned within and between subpopulations (inferred from hierarchical F-statistics based on variation at 18 protein loci), and in terms of gene correlations (co-ancestry among individuals derived from reproductive data on full-sib families of females nesting at specific nesting areas). Little variation in allele frequency was observed among turtles from different marshes (F_mt = 0.003), though significant variation was observed among turtles from different nesting areas associated with each marsh (F_nm = 0.046). Gene correlations among individuals within nesting areas varied greatly over years (0.032-0.171; mean = 0.069) and were negatively correlated to the proportion of females that successfully nested during each year. General concordance between independent estimates of genotypic correlations (i.e., F_nm derived from protein electrophoretic variation vs. mean co-ancestry) suggests that allozyme data, when collected over spatial scales consistent with species behavioral characteristics and reproductive ecology, may accurately reflect the apportionment of gene diversity within and among subpopulations. The magnitude and patterning of allelic variation among nesting areas and individuals appears to be primarily a function of gametic correlations among members of full-sib families, irrespective of the degree of gene flow or female nesting-site fidelity. Comparisons of genetic characteristics among 11 cohorts (1974-1984) revealed that heterozygosity (H) and inbreeding coefficients (F) varied greatly. Cohort estimates of H and F were correlated to female nesting success and to estimates of co-ancestry for the same years. Results clearly reflect the concomitant importance of ecological factors (principally the proportion of the female population that successfully produce offspring during each year) in determining the magnitude and patterning of gene correlations within and among groups, and to the genotypic composition of offspring born during each year.     

GENETIC AND SOCIAL INHERITANCE OF BODY AND EGG SIZE IN THE BARNACLE GOOSE (BRANTA LEUCOPSIS)

We present heritability estimates for final size of body traits and egg size as well as phenotypic and genetic correlations between body and egg traits in a recently established population of the barnacle goose (Branta leucopsis) in the Baltic area. Body traits as well as egg size were heritable and, hence, could respond evolutionarily to phenotypic selection. Genetic correlations between body size traits were significantly positive and of similar magnitude or higher than the corresponding phenotypic correlations. Heritability estimates for tarsus length obtained from full-sib analyses were higher than those obtained from midoffspring-midparent regressions, and this indicates common environment effects on siblings. Heritabilities for tarsus length obtained from midoffspring-mother regressions were significantly higher than estimates from midoffspring-father regressions. The results suggest that this discrepancy is not caused by maternal effects through egg size, nor by extra-pair fertilizations, but by a socially inherited foraging site fidelity in females.     

Correlation of endoscopic cytology and histology in oesophageal cancer: results in Porto Alegre,RS—Brazil

A retrospective study of oesophageal cytopathology at the Hospital de Clínicas de Porto Alegre (HCPA), RS, Brazil, from 1989 to 1992 was made to assess the sensitivity, specificity, predictive values and accuracy of endoscopic cytology and biopsy; and study the correlation between cytopathological and histopathological diagnosis. Specimens from 94 patients were available for review. The final diagnosis was based on surgical pathology and follow up. The 81 patients with cancer of the oesophagus had the following sex distribution: 64 males and 17 females (a 3.7–1 ratio). No tumour was found in 13 patients. The following conclusions were made: (i) there is excellent correlation between cytology and histology in oesophageal lesions sampled by endoscopy; (ii) a correct positive cytologic report was obtained in 77 (95%) of the 81 proven oesophageal cancers; a false-negative or unsatisfactory result was given in four patients. A false-positive diagnosis of cancer was not made. There were 13 true-negative reports. These findings result in a sensitivity of 95% with 95% confidence intervals (CI) of 90.26–99.74%; a specificity of 100% (CI of 98.5–100%); a positive predictive value of 100% (CI of 99.3–100%); a negative predictive value of 76% (CI of 55.7–96.3%); (iii) a correct positive histological report was obtained in 67 (83%) of the 81 proven oesophageal cancers; a false-negative or unsatisfactory result was given in 14 patients. A false-positive diagnosis of cancer was not made. There were 13 true-negative reports. These findings result in a sensitivity of 83% with 95% CI of 74.82–91.18%; a specificity of 100% (CI of 98.5–100%); a positive predictive value of 100% (CI of 99.25–100%); a negative predictive value of 48% (CI of 29.16–64.84%); (iv) of 81 patients with proven cancer, in 79 (98%) at least one of the methods was positive. In only two patients with cancer were both methods negative. These findings result in a combined sensitivity of 98% (CI of 94.92–100%); a specificity of 100% (CI of 98.5–100%); a positive predictive value of 100% (CI of 99.31–100%); and a negative predictive value of 87% (CI of 70–100%). Our series confirms the value of the combined use of cytology and biopsy for the investigation of oesophageal lesions. However, it should be remembered that even with the combined use of cytology and biopsy there are some tumours that will be negative by both procedures: we had only two such cases, confirming the rarity of such an event.     

An Analysis of the Metabolic Theory of the Origin of the Genetic Code

A computer program was used to test Wong's coevolution theory of the genetic code. The codon correlations between the codons of biosynthetically related amino acids in the universal genetic code and in randomly generated genetic codes were compared. It was determined that many codon correlations are also present within random genetic codes and that among the random codes there are always several which have many more correlations than that found in the universal code. Although the number of correlations depends on the choice of biosynthetically related amino acids, the probability of choosing a random genetic code with the same or greater number of codon correlations as the universal genetic code was found to vary from 0.1% to 34% (with respect to a fairly complete listing of related amino acids). Thus, Wong's theory that the genetic code arose by coevolution with the biosynthetic pathways of amino acids, based on codon correlations between biosynthetically related amino acids, is statistical in nature. Received: 8 August 1996 / Accepted: 26 December 1996     

PREDICTING MICROEVOLUTIONARY RESPONSES TO DIRECTIONAL SELECTION ON HERITABLE VARIATION

Microevolution of quantitative traits in the wild can be predicted from a knowledge of selection and genetic parameters. Testing the predictions requires measurement of the offspring of the selected group, a requirement that is difficult to meet. We present the results of a study of Darwin's finches on the Galápagos island of Daphne Major where this requirement is met. The study demonstrates microevolutionary consequences of natural selection.