The effects of phenotypic plasticity on genetic correlations

Recent theory suggests that genetic correlations should help to predict the simultaneous response to selection of two or more traits, and much recent research has been directed towards understanding the sources of variation in genetic correlations. Genetic correlations can change from sample to sample, from species to species, from population to population, during the course of development and - within a population, at a fixed stage of development - from one environment to another. These are changes not only in magnitude but also in sign. Theory suggests that genetic correlations should not change sign when the two traits are tightly integrated by physiology or development. Patterns of change of genetic correlations are caused by differences in development and physiology, an understanding of which appears to be necessary to predict the response to selection in natural, heterogeneous environments.     

DESIGNING EXPERIMENTS TO MAXIMIZE THE POWER OF DETECTING CORRELATIONS

Studies investigating correlations among traits are increasingly common in evolutionary biology. By providing power calculations, minimum sample sizes, and standard errors of correlation coefficients in a variety of contexts, this note provides guidelines to insure that nonzero correlations will not be erroneously dismissed as nonsignificant in properly designed experiements. Forty individuals is often sufficient for reasonable estimation of correlation coefficients, although 100 or more individuals may be nexessary if a large number of traits are involved or comparisons are to be made among the coefficients.     

ESTIMATING GENETIC CORRELATIONS FROM MEASUREMENTS OF FIELD-CAUGHT WATERSTRIDERS

Abstract Lynch (1999) proposed a method for estimation of genetic correlations from phenotypic measurements of individuals for which no pedigree information is available. This method assumes that shared environmental effects do not contribute to the similarity of relatives, and it is expected to perform best when sample sizes are large, many individuals in the sample are paired with close relatives, and heritability of the traits is high. We tested the practicality of this method for field biologists by using it to estimate genetic correlations from measurements of field‐caught waterstriders {Aquarius remigis). Results for sample sizes of less than 100 pairs were often unstable or undefined, and even with more than 500 pairs only half of those correlations that had been found to be significant in standard laboratory experiments were statistically significant in this study. Statistically removing the influence of environmental effects (shared between relatives) weakened the estimates, possibly by removing some of the genetic similarity between relatives. However, the method did generate statistically significant estimates for some genetic correlations. Lynch (1999) anticipated the problems found, and proposed another method that uses estimates of relatedness between members of pairs (from molecular marker data) to improve the estimates of genetic correlations, but that approach has yet to be tested in the field.     

A COMPARISON OF GENETIC AND PHENOTYPIC CORRELATIONS

Genetic variances and correlations lie at the center of quantitative evolutionary theory. They are often difficult to estimate, however, due to the large samples of related individuals that are required. I investigated the relationship of genetic- and phenotypic-correlation magnitudes and patterns in 41 pairs of matrices drawn from the literature in order to determine their degree of similarity and whether phenotypic parameters could be used in place of their genetic counterparts in situations where genetic variances and correlations cannot be precisely estimated. The analysis indicates that squared genetic correlations were on average much higher than squared phenotypic correlations and that genetic and phenotypic correlations had only broadly similar patterns. These results could be due either to biological causes or to imprecision of genetic-correlation estimates due to sampling error. When only those studies based on the largest sample sizes (effective sample size of 40 or more) were included, squared genetic-correlation estimates were only slightly greater than their phenotypic counterparts and the patterns of correlation were strikingly similar. Thus, much of the dissimilarity between phenotypic- and genetic-correlation estimates seems to be due to imprecise estimates of genetic correlations. Phenotypic correlations are likely to be fair estimates of their genetic counterparts in many situations. These further results also indicate that genetic and environmental causes of phenotypic variation tend to act on growth and development in a similar manner.     

The correlation of single-particle diffraction patterns as a continuous function of particle orientation

A statistical model for X-ray scattering of a non-periodic sample to high angles is introduced. It is used to calculate analytically the correlation of distinct diffraction measurements of a particle as a continuous function of particle orientation. Diffraction measurements with shot-noise are also considered. This theory provides a general framework for a deeper understanding of single particle imaging techniques used at X-ray free-electron lasers. Many of these techniques use correlations as a measure of diffraction-pattern similarity in order to determine properties of the sample, such as particle orientation.     

Sibling correlations for cranial measurements from serial radiographs

Sibling correlations are presented for nine craniofacial measurements from lateral cephalometric radiographs of participants in the Fels Longitudinal Study of Growth and their siblings. Because the data were collected serially, measurements on sibs at the same age can be compared at one-year intervals. Sibling correlations are generally lowest during the first year of life and highest as adulthood is approached, but no interpretable pattern is established during the intervening years. Most of the correlations are significantly greater than zero, and many exceed 0.5, the value expected for a completely heritable polygenic trait. This suggests that common sibling environment contributes to sibling resemblance for craniofacial dimensions in our sample.     

Attribute correlations in the Poaceae (grasses)

Investigation of correlations between a number of two-state attributes for a sample of grass genera revealed that a high proportion of the correlations were statistically significant. There were proportionately more correlations between attributes from the same organ than between attributes from different organS. Furthermore, attributes associated with the fruit and leaf were found to be more closely correlated with attributes other than those of the flower and spikelet, thereby indicating fruit and leaf attributes to be important in the classification of the grasseS. It is considered that the correlations have arisen in part as a result of the phylogenetic origins of the genera and in part as a response to natural selection determining distribution of genera adapted to present-day habitats.     

Estimating genetic correlations in natural populations

Information on the genetic correlation between traits provides fundamental insight into the constraints on the evolutionary process. Estimates of such correlations are conventionally obtained by raising individuals of known relatedness in artificial environments. However, many species are not readily amenable to controlled breeding programmes, and considerable uncertainty exists over the extent to which estimates derived under benign laboratory conditions reflect the properties of populations in natural settings. Here, non-invasive methods that allow the estimation of genetic correlations from phenotypic measurements derived from individuals of unknown relatedness are introduced. Like the conventional approach, these methods demand large sample sizes in order to yield reasonably precise estimates, and special precautions need to be taken to eliminate bias from shared environmental effects. Provided the sample consists of at least 20% or so relatives, informative estimates of the genetic correlation are obtainable with sample sizes of several hundred individuals, particularly if supplemental information on relatedness is available from polymorphic molecular markers.     

Spatial correlations at different spatial scales are themselves highly correlated in isolation by distance processes

Although many properties of spatial autocorrelation statistics are well characterized, virtually nothing is known about possible correlations among values at different spatial scales, which ultimately would influence how inferences about spatial genetics are made at multiple spatial scales. This article reports the results of stochastic space-time simulations of isolation by distance processes, having a very wide range of amounts of dispersal for plants or animals, and analyses of the correlations among Moran's I-statistics for different mutually exclusive distance classes. In general, the stochastic correlations are extremely large (>0.90); however, the correlations bear a complex relationship with level of dispersal, spatial scale and spatial lag between distance classes. The correlations are so large that any existing or conceived statistical method that employs more than one distance class (or spatial scale) should not ignore them. This result also suggests that gains in statistical power via increasing sample size are limited, and that increasing numbers of assayed loci generally should be preferred. To the extent that sampling error for real data sets can be treated as white noise, it should be possible to account for stochastic correlations in formulating more precise statistical methods. Further, while the current results are for isolation by distance processes, they provide some guidance for some more complex stochastic space-time processes of landscape genetics. Moreover, the results hold for several popular measures other than Moran's I. In addition, in the results, the signal to noise ratios strongly decreased with distance, which also has several implications for optimal statistical methods using correlations at multiple spatial scales.     

Genetic and environmental correlations among serum lipids and apolipoproteins in elderly twins reared together and apart.

Genetic and environmental correlations among five serum-lipid measures were examined in the Swedish Adoption/Twin Study of Aging. The sample included 302 twin pairs; 146 of these twin pairs were separated at an early age and were reared apart. The lipid measures examined include total cholesterol, HDL-cholesterol, triglycerides, and apolipoproteins A-I and B. Genetic and environmental correlations were evaluated for two different age groups, formed by dividing the sample at the median. The younger group included individuals 41.8-65.4 years of age at the midpoint of testing, although only 24 individuals were < 50 years of age. The older group included all those > 65.4 years of age, up to age 87 years of age. Substantial genetic correlations were found within each age group, although there is no evidence for a single genetic factor common to all five lipids. The comparison of twins reared together with twins reared apart allowed estimation of the effects of shared rearing environment; however, shared rearing environment only appears to be a significant mediator of the phenotypic correlation between apolipoprotein B and cholesterol in the older group. Examination of the genetic and environmental covariances suggests that the relative contributions of genetic factors are lower in the older group. Nonshared environmental factors are relatively more important mediators of phenotypic correlations among the serum lipids in individuals > 65.4 years of age than they are for the younger group. Sex differences in the mediation of these serum lipids were not as clear.     

Laboratory Estimates of Heritabilities and Genetic Correlations in Nature

A lower bound on heritability in a natural environment can be determined from the regression of offspring raised in the laboratory on parents raised in nature. An estimate of additive genetic variance in the laboratory is also required. The estimated lower bounds on heritabilities can sometimes be used to demonstrate a significant genetic correlation between two traits in nature, if their genetic and phenotypic correlations in nature have the same sign, and if sample sizes are large, and heritabilities and phenotypic and genetic correlations are high.     

Non-linear relations between selected anthropological predictors and psycho-physiological exercise-responses

In this paper, some very useful non-linear-relation procedures are actualized. The authors have defined the characteristic correlations between a set of anthropological characteristics (14 anthropometric and 14 motor-endurance status variables) and a set of psycho-physiological exercise-responses during the hi-lo and during the step aerobic dance training (heart rate, lactate concentration and rating of the perceived exertion). 60 healthy females served as the sample of subjects (mean age 21 +/- 1.4 years). The experiment consisted of two parts. In the first one, the linear correlations between the two sets of the variables were established. In the second part, non-linear (squared) relations, between the variables of the two sets were calculated. Results confirm the statement that the non-linear correlations, in some cases, better determinate the real nature of the relations between the variables, than linear correlation models.     

Redundancy and synergy arising from pairwise correlations in neuronal ensembles

Multielectrode arrays allow recording of the activity of many single neurons, from which correlations can be calculated. The functional roles of correlations can be revealed by measures of the information conveyed by neuronal activity; a simple formula has been shown to discriminate the information transmitted by individual spikes from the positive or negative contributions due to correlations (Panzeri et al., 1999). Here, this analysis, previously applied to recordings from small ensembles, is developed further by considering a model of a large ensemble, in which correlations among the signal and noise components of neuronal firing are small in absolute value and entirely random in origin. Even such small random correlations are shown to lead to large possible synergy or redundancy, whenever the time window for extracting information from neuronal firing extends to the order of the mean interspike interval. In addition, a sample of recordings from rat barrel cortex illustrates the mean time window at which such corrections dominate when correlations are, as often in the real brain, neither random nor small. The presence of this kind of correlations for a large ensemble of cells restricts further the time of validity of the expansion.     

Heritability and components of phenotypic expression in skin reflectance of Mestizos from the Peruvian Lowlands

Skin reflectance was measured on the inner upper arm and forehead of a sample of 209 Mestizos ranging in age from 2 to 64 years living in the town of Lamas in the Eastern Peruvian Lowlands. The sample consisted of 43 father-son, 42 father-daughter, 62 mother-son, and 70 mother-daughter pairs. The sample also consisted of 57 brother-brother, 60 sister-sister and 139 brother-sister pairs. The reflectance measurements were made with a Photovolt Reflection Meter, model 670. Stepwise polynomial regression techniques were used to derive standardized residual values. Then using these residual values parent-offspring, sibling intraclass correlations and components of the phenotypic expression of skin reflectance were calculated. The study indicates that 1) the parent-offspring and sibling correlation coefficients conformed with the theoretical correlations expected assuming polygenic inheritance; 2) the husband-wife correlations indicate a high degree of assortative mating for skin color, but despite this effect the parent-offspring and sibling correlation coefficients are lower than the values expected under the influence of autosomal genes; 3) estimates of heritability and components of phenotypic expression indicate that about 55% of the total variability in skin reflectance could be attributed to the influence of additive genetic factors; and 4) there is no evidence of X-linkage in the inheritance of skin color.     

When is a correlation between non‐independent variables “spurious”?

Correlations which are artifacts of various types of data transformations can be said to be spurious. This study considers four common types of analyses where the X and Y variables are not independent; these include regressions of the form X/Z vs Y/Z, X×Z vs Y×Z, X vs Y/X, and X+Y vs Y. These analyses were carried out using a series of Monte Carlo simulations while varying sample size and sample variability. The impact of disparities in variability between the shared and non-shared terms and measurement error for the shared term on the magnitude of the spurious correlations was also considered. The accuracy of equations previously derived to predict the magnitude of spurious correlations was also assessed. These results show the risk of producing spurious correlations when analyzing non-independent variables is very large. Spurious correlations occurred in all cases assessed, the mean spurious coefficient of determination (r²) frequently exceeded 0.50, and in some cases the 90% confidence interval for these simulations included all large r² values. The magnitude of spurious correlations was sensitive to differences in the variability of the shared and non-shared terms, with large spurious correlations obtained when the variability for the shared term was larger. Sample size had only a modest impact on the magnitude of spurious correlations. When measurement error for the shared variable was smaller than one half the coefficient of variation for that variable, which is generally the case, the measurement error did not generate large spurious correlations. The equations available to predict expected spurious correlations provided accurate predictions for the case of X×Z vs Y×Z, variable predictions for the case of X vs Y/X, and poor predictions for most cases of X/Z vs Y/Z, and X+Y vs Y.     

Causal inference and large-scale expert validation shed light on the drivers of SDM accuracy and variance

Aim

To develop a causal understanding of the drivers of Species distribution model (SDM) performance.

Location

United Kingdom (UK).

Methods

We measured the accuracy and variance of SDMs fitted for 518 species of invertebrate and plant in the UK. Our measure of variance reflects variation among replicate model fits, and taxon experts assessed model accuracy. Using directed acyclic graphs, we developed a causal model depicting plausible effects of explanatory variables (e.g. species' prevalence, sample size) on SDM accuracy and variance and quantified those effects using a multilevel piecewise path model.

Results

According to our model, sample size and niche completeness (proportion of a species' niche covered by sampling) directly affect SDM accuracy and variance. Prevalence and range completeness have indirect effects mediated by sample size. Challenging conventional wisdom, we found that the effect of prevalence on SDM accuracy is positive. This reflects the facts that sample size has a positive effect on accuracy and larger sample sizes are possible for widespread species. It is possible, however, that the omission of an unobserved confounder biased this effect. Previous studies, which reported negative correlations between prevalence and SDM accuracy, conditioned on sample size.

Main conclusions

Our model explicates the causal basis of previously reported correlations between SDM performance and species/data characteristics. It also suggests that niche completeness has similarly large effects on SDM accuracy and variance as sample size. Analysts should consider niche completeness, or proxies thereof, in addition to sample size when deciding whether modelling is worthwhile.     

Relationship between subunit size and number of rare electrophoretic alleles in human enzymes

Data from published sources were used to compare the numbers of different electrophoretic alleles of 29 monomeric and dimeric human enzymes to their respective subunit molecular weights. Only those human enzymes were considered for which the total sample sizes were in excess of 2000 individuals. Correlations between these two variables were determined within sample size ranges of 2000≤n≤3000 and 4000≤n≤5000 individuals, and separately by quaternary class. There was no statistically significant correlation observed for the smaller sample size range in monomers; however, the correlations for the larger sample size range in monomers and both ranges in dimers were significant. Since there is no relationship between subunit size and heterozygosity, the relationships are due primarily to the incidence of rare alleles. These findings demonstrate the effect of locus-specific mutation rates, expected as a consequence of variation of cistron sizes, and imply that other forces are responsible for the relative frequencies of common alleles at some of the loci.     

Genetic and phenotypic correlations among size-related traits, and heritability variation between body parts in Drosophila buzzatii

Recent studies have shown that body size is a heritable trait phenotypically correlated with several fitness components in wild populations of the cactophilic fly Drosophila buzzatii. To obtain further information on size-related variation, heritabilities as well as genetic and phenotypic correlations among size-related traits of several body parts (head, thorax and wings) were estimated. The study was carried out on an Argentinean natural population in which size-related selection was previously detected. The genetic parameters were estimated using offspring-parent regressions (105 families) in the laboratory G₂ generation of a sample of wild flies. The traits were also scored in Wild-Caught Flies (WCF). Laboratory-Reared Flies (LRF) were larger and less variable than WCF. Although heritability estimates were significant for all traits, heritabilities were higher for thorax-wing traits than for head traits. Phenotypic and genetic correlations were all positive. The highest genetic correlations were found between traits which are both functionally and developmentally related. Genetic and phenotypic correlations estimated in the lab show similar correlation patterns (r = 0.49; TP = 0.02, Mantel's test). However, phenotypic correlations were found to be typically larger in WCF than in LRF. The genetic correlation matrix estimated in the relatively homogeneous lab environment is not simply a constant multiplicative factor of the phenotypic correlation matrix estimated in WCF. This revised version was published online in July 2006 with corrections to the Cover Date.     

Individual‐level leaf trait variation and correlation across biological and spatial scales

Even with increasing interest in the ecological importance of intraspecific trait variation (ITV) for better understanding ecological processes, few studies have quantified ITV in seedlings and assessed constraints imposed by trade‐offs and correlations among individual‐level leaf traits. Estimating the amount and role of ITV in seedlings is important to understand tree recruitment and long‐term forest dynamics. We measured ten different size, economics, and whole leaf traits (lamina and petiole) for more than 2,800 seedlings (height ≥ 10 cm and diameter at breast height < 1 cm) in 283 seedling plots and then quantified the amount of ITV and trait correlations across two biological (intraspecific and interspecific) and spatial (within and among plots) scales. Finally, we explored the effects of trait variance and sample size on the strength of trait correlations. We found about 40% (6%–63%) variation in leaf‐level traits was explained by ITV across all traits. Lamina and petiole traits were correlated across biological and spatial scales, whereas leaf size traits (e.g., lamina area) were weakly correlated with economics traits (e.g., specific lamina area); lamina mass ratio was strongly related to the petiole length. Trait correlations varied among species, plots, and different scales but there was no evidence that the strength of trait relationships was stronger at broader than finer biological and spatial scales. While larger trait variance increased the strength of correlations, the sample size was the most important factor that was negatively related to the strength of trait correlations. Our results showed that a large amount of trait variation was explained by ITV, which highlighted the importance of considering ITV when using trait‐based approaches in seedling ecology. In addition, sample size was an important factor that influenced the strength of trait correlations, which suggests that comparing trait correlations across studies should consider the differences in sample size.