How to compare fluctuating asymmetry of different traits

Comparing fluctuating asymmetry (FA) between different traits can be difficult because traits vary at different scales. FA is generally quantified either as the variance of the difference between left and right (σ²_L?R) or the mean of the absolute value of this difference (μ_|R?L|). Corrections for scale differences are obtained by dividing by trait size mean. We show that a third index, one minus the correlation coefficient between left and right (1 ? r_L,R), is equivalent to σ²_L?R standardized by trait size variance. The indices are compared with Monte‐Carlo simulations. All achieve the expected correction for scale differences. High type I error rates (false indication of differences) occur only for σ²_L?R and μ_|R?L| if trait sizes close to or below 0 occur. 1 ? r_L,R with a bootstrap test has always low error rates. Recommendation of the index to be used should be based on whether standardization of FA by trait size mean or trait size variance is preferred. A survey of 36 traits in the Speckled Wood Butterfly (Pararge aegeria) indicated that σ²_L?R is slightly higher correlated to trait size variance than to trait size mean. Thus 1 ? r_L,R seems to be the superior index and should be reported when FA of different traits is compared.     

The effect of trait type and strength of selection on heritability and evolvability in an island bird population

The heritability (h²) of fitness traits is often low. Although this has been attributed to directional selection having eroded genetic variation in direct proportion to the strength of selection, heritability does not necessarily reflect a trait's additive genetic variance and evolutionary potential (“evolvability”). Recent studies suggest that the low h² of fitness traits in wild populations is caused not by a paucity of additive genetic variance (V_A) but by greater environmental or nonadditive genetic variance (V_R). We examined the relationship between h² and variance‐standardized selection intensities (i or β_σ), and between evolvability (I_A:V_A divided by squared phenotypic trait mean) and mean‐standardized selection gradients (β_μ). Using 24 years of data from an island population of Savannah sparrows, we show that, across diverse traits, h² declines with the strength of selection, whereas I_A and I_R (V_R divided by squared trait mean) are independent of the strength of selection. Within trait types (morphological, reproductive, life‐history), h², I_A, and I_R are all independent of the strength of selection. This indicates that certain traits have low heritability because of increased residual variance due to the age at which they are expressed or the multiple factors influencing their expression, rather than their association with fitness.     

r‐ and K‐selection in fluctuating populations is determined by the evolutionary trade‐off between two fitness measures: Growth rate and lifetime reproductive success

In a stable environment, evolution maximizes growth rates in populations that are not density regulated and the carrying capacity in the case of density regulation. In a fluctuating environment, evolution maximizes a function of growth rate, carrying capacity and environmental variance, tending to r‐selection and K‐selection under large and small environmental noise, respectively. Here we analyze a model in which birth and death rates depend on density through the same function but with independent strength of density dependence. As a special case, both functions may be linear, corresponding to logistic dynamics. It is shown that evolution maximizes a function of the deterministic growth rate r₀ and the lifetime reproductive success (LRS) R₀, both defined at small densities, as well as the environmental variance. Under large noise this function is dominated by r₀ and average lifetimes are small, whereas R₀ dominates and lifetimes are larger under small noise. Thus, K‐selection is closely linked to selection for large R₀ so that evolution tends to maximize LRS in a stable environment. Consequently, different quantities (r₀ and R₀) tend to be maximized at low and high densities, respectively, favoring density‐dependent changes in the optimal life history.     

Selection,structure and the heritability of behaviour

Characters which are closely linked to fitness often have low heritabilities (V_A/V_P). Low heritabilities could be because of low additive genetic variation (V_A), that had been depleted by directional selection. Alternatively, low heritabilities may be caused by large residual variation (V_R=V_P – V_A) compounded at a disproportionately higher rate than V_A across integrated characters. Both hypotheses assume that each component of quantitative variation has an independent effect on heritability. However, V_A and V_R may also covary, in which case differences in heritability cannot be fully explained by the independent effects of elimination‐selection or compounded residual variation. We compared the central tendency of published behavioural heritabilities (mean=0.31, median=0.23) with morphological and life history data collected by 26 ). Average behavioural heritability was not significantly different from average life history heritability, but both were smaller than average morphological heritability. We cross‐classified behavioural traits to test whether variation in heritability was related to selection (dominance, domestic/wild) or variance compounding (integration level). There was a significant three‐way interaction between indices of selection and variance compounding, related to the absence of either effect at the highest integration level. At lower integration levels, high dominance variance indicated effects of selection. It was also indicated by the low CV_A of domestic species. At the same time CV_R increased disproportionately faster than CV_A across integration levels, demonstrating variance compounding. However, neither CV_R nor CV_A had a predominant effect on heritability. The partial regression coefficients of CV_R and CV_A on heritability were similar and a path analysis indicated that their (positive) correlation was also necessary to explain variation in heritability. These results suggest that relationships between additive genetic and residual components of quantitative genetic variation can constrain their independent direct effects on behavioural heritability.     

Effect of Intracluster Correlation on the R-Square Statistic

R²-statistic is a popular and very widely used statistic in regression analysis to estimate the square multiple correlation (SMC), ρ², between a response variable Y and p predictor variables, _X1, …, _Xp. Numerous articles are available in the statistical literature on the properties of R² as an estimator of ρ² when the observations are uncorrelated. However, relatively little is known about the behavior of R² when the available observations are correlated such as the data that result from complex sampling schemes. In this paper, we study the behavior R² in the presence of two-stage sampling data. An approximate expressions for the variance and the bias of R² in the presence of two-stage cluster sampling data with positive intracluster correlation (ρ*) are obtained. It is evident from these formulas and from a simulation study that R² is a poor estimator of ρ² except when ρ* is small. As such, we consider several alternative estimators of ρ² and evaluate their theoretical properties and finite sample performance using a simulation study.     

Spatial variance of nutrient limitation of periphyton in montane, headwater streams (McLeod River, Alberta, Canada)

There have been few studies that have examined the spatial variance of nutrient limitation over the scale of an entire set of headwater streams. We used nutrient diffusing substrata experiments (control, nitrogen addition, phosphorus addition, and nitrogen+phosphorus addition) to examine how nutrient limitation varied throughout the five creeks that comprise the McLeod River headwaters (Alberta, Canada). We assessed the variance of chlorophyll a accrual at spatial scales within reach, within creek, among creeks and across linear distance within the entire watershed to assess the consistency and scale of nutrient limitation. We analyzed the importance of the spatial scale using several methods. We assessed the coefficient of variation at different scales, the spatial covariance of nitrogen and phosphorus deficiency indices using a spline correlogram, and the variance through traditional analyses of variance methods. Chlorophyll a accrual responded significantly to nutrients in all creeks, though the response varied in magnitude and in the limiting nutrient among reaches and among creeks. Variance in chlorophyll a accrual was due primarily to the factor of creek (R ²=0.40) and secondarily to reach (R ²=0.07). The CV was 31.4% among creeks, 18.4% among reaches, and 17.9% within reaches. The N deficiency index showed a positive correlation at sites located <4 km apart and a negative correlation at sites greater than 6.5 km apart. The P deficiency index showed no discernible spatial correlation. Our results suggest that nutrient limitation varies on small scales and is often driven by local processes.     

Time-budget data: Log-linear and analysis of variance compared

Analysis of variance (ANOVA) and log-linear analyses of time-budget data from a study of sloth bear enclosure utilization are compared. Two sampling models that plausibly underlie such data are discussed. Either could lead to an analysis of variance, but only one to a log-linear analysis. Given an appropriate sampling model and appropriate data, there is much to recommend log-linear analysis, despite its unfamiliarity to most animal behaviorists. One need not worry whether distribution assumptions are violated. Moreover, the data analyzed are the data collected, not estimates derived from those data, and thus no power is lost through a data reduction step. No matter what analysis is used, effect size should be taken into consideration. Multiple R² can be used for ANOVA, but no directly comparable statistic exists for log-linear analyses. One possible candidate for a log-linear R² analog is discussed here, and appears to give sensible and interpretable results. © 1992 Wiley-Liss Inc.     

A comparison of a deterministic and stochastic model for Hepatitis C with an isolation stage

We formulate a deterministic epidemic model for the spread of Hepatitis C containing an acute, chronic and isolation class and analyse the effects of the isolation class on the transmission dynamics of the disease. We calculate the basic reproduction number R₀ and show that for R₀≤1, the disease-free equilibrium is globally asymptotically stable. In addition, it is shown that for a special case when R₀>1, the endemic equilibrium is locally asymptotically stable. Furthermore, an analogous stochastic epidemic model for Hepatitis C is formulated using a continuous time Markov chain. Numerical simulations are used to estimate the mean, variance and probability distributions of the discrete random variables and these are compared to the steady-state solutions of the deterministic model. Finally, the expected time to disease extinction is estimated for the stochastic model and the impact of isolation on the time to extinction is explored.     

Robustness of statistical tests for multiplicative terms in the additive main effects and multiplicative interaction model for cultivar trials

The additive main effects multiplicative interaction model is frequently used in the analysis of multilocation trials. In the analysis of such data it is of interest to decide how many of the multiplicative interaction terms are significant. Several tests for this task are available, all of which assume that errors are normally distributed with a common variance. This paper investigates the robustness of several tests (Gollob, F _GH1, F_GH2, F_R)to departures from these assumptions. It is concluded that, because of its better robustness, the F _Rtest is preferable. If the other tests are to be used, preliminary tests for the validity of assumptions should be performed.     

Avoiding fallacious significance tests in stepwise regression: a Monte Carlo method applied to a meteorological theory for the Canadian lynx cycle

Stepwise regression is often used in ecology to identify critical factors. From a large number of possible predictors, the procedure selects the subset generating the highest coefficient of determination,R ². This work presents a method for testing the significance of this coefficient. Monte Carlo simulations are used to calculate the statistical distribution ofR ² under the null hypothesis that the response variable is independent of the predictors. The method is illustrated by an application to a previously published analysis of the Canadian lynx population cycle where more than 75% of the variance could be explained by four meteorological factors.     

Correlates of sexual dimorphism in primates: Ecological and size variables

The effects of a series of ecological and size factors on the degree of sexual dimorphism in body weight and canine size were studied among subsets of 70 primate species. Variation in body-weight dimorphism can be almost entirely attributed to body weight (83% of variance R² of weight dimorphism). Much smaller amounts of the variation can be attributed to mating system (R² =6.8%,polygynous species being more dimorphic than monogamous ones) and diet (R² = 2.5%,frugivorous species being more dimorphic than folivorous ones). Habitat (arboreal vs. terrestrial) and activity rhythm (nocturnal vs. diurnal) have only an indirect effect on weight dimorphism. Variation in canine-size dimorphism can be explained in terms of canine size (R² =49%),activity rhythm (R² = 20%,diurnal species being more dimorphic than nocturnal ones), and mating system (R² = 10%).Habitat and diet do not play a significant role in canine-size dimorphism. The unexpectedly high contribution of size to sexual dimorphism coupled with the observation of increased sexual dimorphism with increased size leads us to formulate a new selection model for the evolution of sexual dimorphism. We suggest that if there is selection for size increase, whatever its cause, directional selection in both males and females will lead to an increase in sexual dimorphism based on differences in genetic variance between the sexes. Sexual selection, resource division between the sexes, or lopsided reproductive selection need not play a role in such a model.     

Genetic diversity and differentiation of <Emphasis Type="Italic">Fagus orientalis</Emphasis> Lipsky in Hyrcanian forests revealed by nuclear and chloroplast microsatellite markers

Oriental beech (Fagus orientalis Lipsky) is a widespread monoecious and wind-pollinated tree species. It is one of the major components of the Hyrcanian forests of Iran and it is of both ecological and economical importance. Twelve beech stands were surveyed at 9 chloroplast (cp) and 6 nuclear (n) polymorphic microsatellite loci (simple sequence repeats, SSR) to provide information on distribution of genetic diversity within and among populations and on gene conservation and silvicultural management of this species. High levels of genetic differentiation were detected for the chloroplast genome (F _ST = 0.80 and R _ST = 0.95), in sharp contrast to the nuclear genome (F _ST = 0.06, R _ST = 0.05). The analysis of molecular variance (AMOVA) showed that 48% of the total cpSSR variation was attributable to differences among regions and 30% to differences among populations within regions, suggesting multiple origins of beech populations in Hyrcanian forests. Nuclear SSRs confirmed the presence of significant differentiation among populations and among geographic regions, even if, as expected, this was less pronounced than that found with cpSSRs (based on AMOVA, differences among regions and among populations within regions each contribute 5% to total nSSR variance). A highly significant correlation between genetic (nSSRs) and geographic distances (R ² = 0.522) was estimated, thus showing an isolation by distance effect. The application of spatial analysis of molecular variance (SAMOVA) using both marker data allowed identification of genetically homogeneous groups of populations. Possible applications of these results for the certification of provenances and/or seed lots and for designing conservation programs are presented and discussed.     

A coefficient of determination (R2) for generalized linear mixed models

Extensions of linear models are very commonly used in the analysis of biological data. Whereas goodness of fit measures such as the coefficient of determination (R²) or the adjusted R² are well established for linear models, it is not obvious how such measures should be defined for generalized linear and mixed models. There are by now several proposals but no consensus has yet emerged as to the best unified approach in these settings. In particular, it is an open question how to best account for heteroscedasticity and for covariance among observations present in residual error or induced by random effects. This paper proposes a new approach that addresses this issue and is universally applicable for arbitrary variance‐covariance structures including spatial models and repeated measures. It is exemplified using three biological examples.     

Experience with using Ellenberg’s <Emphasis Type="Italic">R</Emphasis> indicator values in Slovakia: Oligotrophic and mesotrophic submontane broad-leaved forests

Ellenberg’s indicator values have been suggested as useful method of estimating site conditions using plants. We examined whether Ellenberg’s R values are suitable for indicating soil reaction and if calibration to physical pH measurements can improve bioindication in oligotrophic and mesotrophic submontane broad-leaved forests in Slovakia. Vegetation relevés and pH-H₂O and pH-CaCl₂ soil reaction were recorded for this purpose. Ellenberg’s R values (R _e) were compared to Jurko’s indicator values (R _j) and a set of species R values and tolerances (T), which were calibrated with physical pH data using the weighted averaging (R _w, T _w) and Huisman-Olff-Fresco modelling (R _h, T _h). Original R _e values were then recalibrated with measured pH data to establish new, adjusted set of scores (R _c, T _c) at Ellenberg’s scale. The Re values are significantly correlated with the other R values, and they demonstrate similar frequency distribution to R _j and R _w values for the studied species pool. The frequency distribution becomes similar across all the R values when indifferent species were excluded. The performance of all the indicator values in terms of bioindication was tested. Relevé means of the R values were regressed on the field pH measurements. The performance of bioindication varied from 36% to 49% of the explained variance for pH-CaCl₂, with the R _e and R _c values yielding 46% and 49% respectively. The bioindication slightly improved for all calibrated methods (R _w, R _h and R _c) when species were weighted inversely with their tolerances — the performance varied from 42% to 51%, and the R _c values performed most effectively. We concluded that Ellenberg’s R values represent a powerful system for bioindicating soil acidity when compared to the other alternatives, with pH-CaCl₂ showing better results than pH-H₂O. Recalibration of Ellenberg’s values to the measured data improved the indicator system.     

Influence of stand density on soil CO2 efflux for a Pinus densiflora forest in Korea

We investigated the influence of stand density [938 tree ha⁻¹ for high stand density (HD), 600 tree ha⁻¹ for medium stand density (MD), and 375 tree ha⁻¹ for low stand density (LD)] on soil CO₂ efflux (R _S) in a 70-year-old natural Pinus densiflora S. et Z. forest in central Korea. Concurrent with R _S measurements, we measured litterfall, total belowground carbon allocation (TBCA), leaf area index (LAI), soil temperature (ST), soil water content (SWC), and soil nitrogen (N) concentration over a 2-year period. The R _S (t C ha⁻¹ year⁻¹) and leaf litterfall (t C ha⁻¹ year⁻¹) values varied with stand density: 6.21 and 2.03 for HD, 7.45 and 2.37 for MD, and 6.96 and 2.23 for LD, respectively. In addition, R _S was correlated with ST (R ² = 0.77–0.80, P < 0.001) and SWC (R ² = 0.31–0.35, P < 0.001). It appeared that stand density influenced R _S via changes in leaf litterfall, LAI and SWC. Leaf litterfall (R ² = 0.71), TBCA (R ² = 0.64–0.87), and total soil N contents in 2007 (R ² = 0.94) explained a significant amount of the variance in R _S (P < 0.01). The current study showed that stand density is one of the key factors influencing R _S due to the changing biophysical and environmental factors in P. densiflora.     

Environmental variation is directly responsible for short- but not long-term variation in forest-atmosphere carbon exchange

Tower‐based eddy covariance measurements of forest‐atmosphere carbon dioxide (CO₂) exchange from many sites around the world indicate that there is considerable year‐to‐year variation in net ecosystem exchange (NEE). Here, we use a statistical modeling approach to partition the interannual variability in NEE (and its component fluxes, ecosystem respiration, R_eco, and gross photosynthesis, P_gross) into two main effects: variation in environmental drivers (air and soil temperature, solar radiation, vapor pressure deficit, and soil water content) and variation in the biotic response to this environmental forcing (as characterized by the model parameters). The model is applied to a 9‐year data set from the Howland AmeriFlux site, a spruce‐dominated forest in Maine, USA. Gap‐filled flux measurements at this site indicate that the forest has been sequestering, on average, 190 g C m⁻² yr⁻¹, with a range from 130 to 270 g C m⁻² yr⁻¹. Our fitted model predicts somewhat more uptake (mean 270 g C m⁻² yr⁻¹), but interannual variation is similar, and wavelet variance analyses indicate good agreement between tower measurements and model predictions across a wide range of timescales (hours to years). Associated with the interannual variation in NEE are clear differences among years in model parameters for both R_eco and P_gross. Analysis of model predictions suggests that, at the annual time step, about 40% of the variance in modeled NEE can be attributed to variation in environmental drivers, and 55% to variation in the biotic response to this forcing. As model predictions are aggregated at longer timescales (from individual days to months to calendar year), variation in environmental drivers becomes progressively less important, and variation in the biotic response becomes progressively more important, in determining the modeled flux. There is a strong negative correlation between modeled annual P_gross and R_eco (r=−0.93, P≤0.001); two possible explanations for this correlation are discussed. The correlation promotes homeostasis of NEE: the interannual variation in modeled NEE is substantially less than that for either P_gross or R_eco     

Beyond mean allelic effects: A locus at the major color gene MC1R associates also with differing levels of phenotypic and genetic (co)variance for coloration in barn owls

The mean phenotypic effects of a discovered variant help to predict major aspects of the evolution and inheritance of a phenotype. However, differences in the phenotypic variance associated to distinct genotypes are often overlooked despite being suggestive of processes that largely influence phenotypic evolution, such as interactions between the genotypes with the environment or the genetic background. We present empirical evidence for a mutation at the melanocortin‐1‐receptor gene, a major vertebrate coloration gene, affecting phenotypic variance in the barn owl, Tyto alba. The white MC1R allele, which associates with whiter plumage coloration, also associates with a pronounced phenotypic and additive genetic variance for distinct color traits. Contrarily, the rufous allele, associated with a rufous coloration, relates to a lower phenotypic and additive genetic variance, suggesting that this allele may be epistatic over other color loci. Variance differences between genotypes entailed differences in the strength of phenotypic and genetic associations between color traits, suggesting that differences in variance also alter the level of integration between traits. This study highlights that addressing variance differences of genotypes in wild populations provides interesting new insights into the evolutionary mechanisms and the genetic architecture underlying the phenotype.     

QTL analysis of agronomic traits in recombinant inbred lines of sunflower under partial irrigation

The objective of the present research was to map QTLs associated with agronomic traits such as days from sowing to flowering, plant height, yield and leaf-related traits in a population of recombinant inbred lines (RILs) of sunflower (Helianthus annuus). Two field experiments were conducted with well-irrigated and partially irrigated conditions in randomized complete block design with three replications. A map with 304 AFLP and 191 SSR markers with a mean density of 1 marker per 3.7 cM was used to identify QTLs related to the studied traits. The difference among RILs was significant for all studied traits in both conditions. Three to seven QTLs were found for each studied trait in both conditions. The percentage of phenotypic variance (R ²) explained by QTLs ranged from 4 to 49%. Three to six QTLs were found for each yield-related trait in both conditions. The most important QTL for grain yield per plant on linkage group 13 (GYP-P-13-1) under partial-irrigated condition controls 49% of phenotypic variance (R ²). The most important QTL for 1,000-grain weight (TGW-P-11-1) was identified on linkage group 11. Favorable alleles for this QTL come from RHA266. The major QTL for days from sowing to flowering (DSF-P-14-1) were observed on linkage group 14 and explained 38% of the phenotypic variance. The positive alleles for this QTL come from RHA266. The major QTL for HD (HD-P-13-1) was also identified on linkage group 13 and explained 37% of the phenotypic variance. Both parents (PAC2 and RHA266) contributed to QTLs controlling leaf-related traits in both conditions. Common QTL for leaf area at flowering (LAF-P-12-1, LAF-W-12-1) was detected in linkage group 12. The results emphasise the importance of the role of linkage groups 2, 10 and 13 for studied traits. Genomic regions on the linkage groups 9 and 12 are specific for QTLs of leaf-related traits in sunflower.     

Effect of soil water stress on soil respiration and its temperature sensitivity in an 18-year-old temperate Douglas-fir stand

We analyzed 17 months (August 2005 to December 2006) of continuous measurements of soil CO₂ efflux or soil respiration (R_S) in an 18‐year‐old west‐coast temperate Douglas‐fir stand that experienced somewhat greater than normal summertime water deficit. For soil water content at the 4 cm depth (θ) > 0.11 m³ m^?3 (corresponding to a soil water matric potential of ?2 MPa), R_S was positively correlated to soil temperature at the 2 cm depth (T_S). Below this value of θ, however, R_S was largely decoupled from T_S, and evapotranspiration, ecosystem respiration and gross primary productivity (GPP) began to decrease, dropping to about half of their maximum values when θ reached 0.07 m³ m^?3. Soil water deficit substantially reduced R_S sensitivity to temperature resulting in a Q₁₀ significantly < 2. The absolute temperature sensitivity of R_S (i.e. dR_S/dT_S) increased with θ up to 0.15 m³ m^?3, above which it slowly declined. The value of dR_S/dT_S was nearly 0 for θ < 0.08 m³ m^?3, thereby confirming that R_S was largely unaffected by temperature under soil water stress conditions. Despite the possible effects of seasonality of photosynthesis, root activity and litterfall on R_S, the observed decrease in its temperature sensitivity at low θ was consistent with the reduction in substrate availability due to a decrease in (a) microbial mobility, and diffusion of substrates and extracellular enzymes, and (b) the fraction of substrate that can react at high T_S, which is associated with low θ. We found that an exponential (van't Hoff type) model with Q₁₀ and R₁₀ dependent on only θ explained 92% of the variance in half‐hourly values of R_S, including the period with soil water stress conditions. We hypothesize that relating Q₁₀ and R₁₀ to θ not only accounted for the effects of T_S on R_S and its temperature sensitivity but also accounted for the seasonality of biotic (photosynthesis, root activity, and litterfall) and abiotic (soil moisture and temperature) controls and their interactions.