Search

We present a novel method for the estimation of variance parameters in generalised linear mixed models. The method has its roots in Harville (1977)'s work, but it is able to deal with models that have a precision matrix for the random-effect vector that is linear in the inverse of the variance parameters (i.e., the precision parameters). We call the method SOP (Separation of Overlapping Precision matrices). SOP is based on applying the method of successive approximations to easy-to-compute estimate updates of the variance parameters. These estimate updates have an appealing form: they are the ratio of a (weighted) sum of squares to a quantity related to effective degrees of freedom. We provide the sufficient and necessary conditions for these estimates to be strictly positive. An important application field of SOP is penalised regression estimation of models where multiple quadratic penalties act on the same regression coefficients. We discuss in detail two of those models: penalised splines for locally adaptive smoothness and for hierarchical curve data. Several data examples in these settings are presented., MTM2014-55966-P MTM2014-52184-P

Background Random regression models (RRM) are widely used to analyze longitudinal data in genetic evaluation systems because they can better account for time-course changes in environmental effects and additive genetic values of animals by fitting the test-day (TD) specific effects. Our objective was to implement a random regression model for the evaluation of dairy production traits in French goats. Results The data consisted of milk TD records from 30,186 and 32,256 first lactations of Saanen and Alpine goats. Milk yield, fat yield, protein yield, fat content and protein content were considered. Splines were used to model the environmental factors. The genetic and permanent environmental effects were modeled by the same Legendre polynomials. The goodness-of-fit and the genetic parameters derived from functions of the polynomials of orders 0 to 4 were tested. Results were also compared to those from a lactation model with total milk yield calculated over 250 days and to those of a multiple-trait model that considers performance in six periods throughout lactation as different traits. Genetic parameters were consistent between models. Models with fourth-order Legendre polynomials led to the best fit of the data. In order to reduce complexity, computing time, and interpretation, a rank reduction of the variance covariance matrix was performed using eigenvalue decomposition. With a reduction to rank 2, the first two principal components correctly summarized the genetic variability of milk yield level and persistency, with a correlation close to 0 between them. Conclusions A random regression model was implemented in France to evaluate and select goats for yield traits and persistency, which are independent i.e. no genetic correlation between them, in first lactation. Electronic supplementary material The online version of this article (10.1186/s12711-019-0485-3) contains supplementary material, which is available to authorized users.

SNP heritability, the proportion of phenotypic variance explained by SNPs, has been reported for many hundreds of traits. Its estimation requires strong prior assumptions about the distribution of heritability across the genome, but the assumptions in current use have not been thoroughly tested. By analyzing imputed data for a large number of human traits, we empirically derive a model that more accurately describes how heritability varies with minor allele frequency, linkage disequilibrium and genotype certainty. Across 19 traits, our improved model leads to estimates of common SNP heritability on average 43% (standard deviation 3) higher than those obtained from the widely-used software GCTA, and 25% (standard deviation 2) higher than those from the recently-proposed extension GCTA-LDMS. Previously, DNaseI hypersensitivity sites were reported to explain 79% of SNP heritability; using our improved heritability model their estimated contribution is only 24%.

BackgroundEfficient communication requires that signals are well transmitted and perceived in a given environment. Natural selection therefore drives the evolution of different signals in different environments. In addition, environmental heterogeneity at small spatial or temporal scales may favour phenotypic plasticity in signaling traits, as plasticity may allow rapid adjustment of signal expression to optimize transmission. In this study, we explore signal plasticity in the nuptial coloration of Lake Victoria cichlids,Pundamilia pundamiliaandPundamilia nyererei.These two species differ in male coloration, which mediates species-assortative mating. They occur in adjacent depth ranges with different light environments. Given the close proximity of their habitats, overlapping at some locations, plasticity in male coloration could contribute to male reproductive success but interfere with reproductive isolation.MethodsWe rearedP. pundamilia,P. nyererei,and their hybrids under light conditions mimicking the two depth ranges in Lake Victoria. From photographs, we quantified the nuptial coloration of males, spanning the entire visible spectrum. In experiment 1, we examined developmental colour plasticity by comparing sibling males reared in each light condition. In experiment 2, we assessed colour plasticity in adulthood, by switching adult males between conditions and tracking coloration for 100 days.ResultsWe found that nuptial colour inPundamiliadid respond plastically to our light manipulations, but only in a limited hue range. Fish that were reared in light conditions mimicking the deeper habitat were significantly greener than those in conditions mimicking shallow waters. The species-specific nuptial colours (blue and red) did not change. When moved to the opposing light condition as adults, males did not change colour.DiscussionOur results show that species-specific nuptial colours, which are subject to strong divergent selection by female choice, are not plastic. We do find plasticity in green coloration, a response that may contribute to visual conspicuousness in darker, red-shifted light environments. These results suggest that light-environment-induced plasticity in male nuptial coloration inP. pundamiliaandP. nyerereiis limited and does not interfere with reproductive isolation.

Local adaptation can be a potent force in speciation, with environmental heterogeneity leading to niche specialization and population divergence. However, local adaption often requires nonrandom mating to generate reproductive isolation. Population divergence in sensory properties can be particularly consequential in speciation, affecting both ecological adaptation and sexual communication. Pundamilia pundamila and Pundamilia nyererei are two closely related African cichlid species that differ in male coloration, blue vs. red. They co-occur at rocky islands in southern Lake Victoria, but inhabit different depth ranges with different light environments. The species differ in colour vision properties, and females exert species-specific preferences for blue vs. red males. Here, we investigated the mechanistic link between colour vision and preference, which could provide a rapid route to reproductive isolation. We tested the behavioural components of this link by experimentally manipulating colour perception – we raised both species and their hybrids under light conditions mimicking shallow and deep habitats – and tested female preference for blue and red males under both conditions. We found that rearing light significantly affected female preference: shallow-reared females responded more strongly to P. pundamilia males and deep-reared females favoured P. nyererei males – implying that visual development causally affects mate choice. These results are consistent with sensory drive predictions, suggesting that the visual environment is key to behavioural isolation of these species. However, the observed plasticity could also make the species barrier vulnerable to environmental change: speciesassortative preferences were weaker in females that were reared in the other species’ light condition.

The objectives of this study were 1) to propose a profit function for Italian Chianina beef cattle; 2) to derive economic values for some biological variables in beef cows, specifically, production expressed as the number of calves born alive per year (NACY), age at the insemination that resulted in the birth of the first calf (FI), and length of productive life (LPL); and 3) to investigate the relationship between the phenotypic profit function and type traits as early predictors of profitability in the Chianina beef cattle population. The average profit was 196/(cow·yr) for the length of productive life (LPL) and was obtained as the difference between the average income of 1,375/(cow·yr) for LPL and costs of 1,178/(cow·yr) of LPL. The mean LPL was equal to 5.97 yr, so the average total phenotypic profit per cow on a lifetime basis was 1,175. A normative approach was used to derive the economic weights for the biological variables. The most important trait was the number of calves born alive (+4.03·cow¿1·yr¿1 and +24.06/cow). An increase of 1 d in LPL was associated with an increase of +0.19/(cow·yr) and +1.65/cow on a lifetime basis. Increasing FI by 1 d decreased profit by 0.42/(cow·yr) and 2.51/cow. Phenotypic profit per cow had a heritability of 0.29. Heritabilities for eight muscularity traits ranged from 0.16 to 0.23, and for the seven body size traits between 0.21 and 0.30. The conformation trait final score can be used as an early predictor of profitability. The sale price of the animal and differences in the revenue and costs of offspring due to muscularity should be included in a future profit function

The objectives of this study were 1) to propose a profit function for Italian Chianina beef cattle; 2) to derive economic values for some biological variables in beef cows, specifically, production expressed as the number of calves born alive per year (NACY), age at the insemination that resulted in the birth of the first calf (FI), and length of productive life (LPL); and 3) to investigate the relationship between the phenotypic profit function and type traits as early predictors of profitability in the Chianina beef cattle population. The average profit was 196 Euros/(cow.yr) for the length of productive life (LPL) and was obtained as the difference between the average income of 1,375 Euros/(cow.yr) for LPL and costs of 1,178 Euros/(cow.yr) of LPL. The mean LPL was equal to 5.97 yr, so the average total phenotypic profit per cow on a lifetime basis was 1,175 Euros. A normative approach was used to derive the economic weights for the biological variables. The most important trait was the number of calves born alive (+4.03.cow(-1).yr(-1) and +24.06 Euros/cow). An increase of 1 d in LPL was associated with an increase of +0.19 Euros/(cow.yr) and +1.65 Euros/cow on a lifetime basis. Increasing FI by 1 d decreased profit by 0.42 Euros/(cow.yr) and 2.51 Euros/cow. Phenotypic profit per cow had a heritability of 0.29. Heritabilities for eight muscularity traits ranged from 0.16 to 0.23, and for the seven body size traits between 0.21 and 0.30. The conformation trait final score can be used as an early predictor of profitability. The sale price of the animal and differences in the revenue and costs of offspring due to muscularity should be included in a future profit function.