Genetic Covariance Research Articles

Selection and the direction of phenotypic evolution.

Predicting adaptive phenotypic evolution depends on invariable selection gradients and on the stability of the genetic covariances between the component traits of the multivariate phenotype. We describe the evolution of six traits of locomotion behavior and body size in the nematode Caenorhabditis elegans for 50 generations of adaptation to a novel environment. We show that the direction of adaptive multivariate phenotypic evolution can be predicted from the ancestral selection differentials, particularly when the traits were measured in the new environment. Interestingly, the evolution of individual traits does not always occur in the direction of selection, nor are trait responses to selection always homogeneous among replicate populations. These observations are explained because the phenotypic dimension with most of the ancestral standing genetic variation only partially aligns with the phenotypic dimension under directional selection. These findings validate selection theory and suggest that the direction of multivariate adaptive phenotypic evolution is predictable for tens of generations.

Host genomic variation shapes gut microbiome diversity in threespine stickleback fish.

A major focus of host-microbe research is to understand how genetic differences, of various magnitudes, among hosts translate to differences in their microbiomes. This has been challenging for animal hosts, including humans, because it is difficult to control environmental variables tightly enough to isolate direct genetic effects on the microbiome. Our work in stickleback fish is a significant contribution because our experimental approach allowed strict control over environmental factors, including standardization of the microbiome from the earliest stage of development and unrestricted co-housing of fish in a truly common environment. Furthermore, we measured host genetic variation over 2,000 regions of the stickleback genome, comparing this information and microbiome composition data among fish from very similar and very different genetic backgrounds. Our findings highlight how differences in the host genome influence microbiome diversity and make a case for future manipulative microbiome experiments that use host systems with naturally occurring genetic variation.

Genetic Correlations Among Corneal Biophysical Parameters and Anthropometric Traits.

The genetic architecture of corneal dysfunction remains poorly understood. Epidemiological and clinical evidence suggests a relationship between corneal structural features and anthropometric measures. We used global and local genetic similarity analysis to identify genomic features that may underlie structural corneal dysfunction. We assembled genome-wide association study summary statistics for corneal features (central corneal thickness, corneal hysteresis [CH], corneal resistance factor [CRF], and the 3 mm index of keratometry) and anthropometric traits (body mass index, weight, and height) in Europeans. We calculated global genetic correlations (rg) between traits using linkage disequilibrium (LD) score regression and local genetic covariance using ρ-HESS, which partitions the genome and performs regression with LD regions. Finally, we identified genes located within regions of significant genetic covariance and analyzed patterns of tissue expression and pathway enrichment. Global LD score regression revealed significant negative correlations between height and both CH (rg = -0.12; P = 2.0 × 10-7) and CRF (rg = -0.11; P = 6.9 × 10-7). Local analysis revealed 68 genomic regions exhibiting significant local genetic covariance between CRF and height, containing 2874 unique genes. Pathway analysis of genes in regions with significant local rg revealed enrichment among signaling pathways with known keratoconus associations, including cadherin and Wnt signaling, as well as enrichment of genes modulated by copper and zinc ions. Corneal biophysical parameters and height share a common genomic architecture, which may facilitate identification of disease-associated genes and therapies for corneal ectasias. Local genetic covariance analysis enables the identification of associated genes and therapeutic targets for corneal ectatic disease.

Digest: Multivariate genetic variation constrains adaptation to environmental changes during range expansion.

How do selection and standing genetic variation shape population divergence across landscapes? Henry and Stinchcombe estimated selection gradients on traits in the ivy-leaved morning glory (Ipomoea hederacea) in the field and compared them with the G-matrix and population divergence for four populations in North America. The authors show that population divergence and genetic covariances are largely unaligned with the selection gradient at the species' range edge. These findings raise the question of whether limited evolvability or multivariate genetic variation of populations at range edges prevent species from range expansion, which is important for understanding the role of genetic constraint in population divergence and predicting local adaptation in the face of climate change.

Estimation and consequences of direct-maternal genetic and environmental covariances in models for genetic evaluation in broilers

BackgroundMaternal effects influence juvenile traits such as body weight and early growth in broilers. Ignoring significant maternal effects leads to reduced accuracy and inflated predicted breeding values. Including genetic and environmental direct-maternal covariances into prediction models in broilers can increase the accuracy and limit inflation of predicted breeding values better than simply adding maternal effects to the model. To test this hypothesis, we applied a model accounting for direct-maternal genetic covariance and direct-maternal environmental covariance to estimate breeding values.ResultsThis model, and simplified versions of it, were tested using simulated broiler populations and then was applied to a large broiler population for validation. The real population analyzed consisted of a commercial line of broilers, for which body weight at a common slaughter age was recorded for 41 selection rounds. The direct-maternal genetic covariance was negative whereas the direct-maternal environmental covariance was positive. Simulated populations were created to mimic the real population. The predictive ability of the models was assessed by cross-validation, where the validation birds were all from the last five selection rounds. Accuracy of prediction was defined as the correlation between the predicted breeding values estimated without the phenotypic records of the validation population and a predictor. The predictors were the breeding values estimated using all the phenotypic information and the phenotypes corrected for the fixed effects, and for the simulated data, the true breeding values. In the real data, adding the environmental covariance, with or without also adding the genetic covariance, increased the accuracy, or reduced deflation of breeding values compared with a model not including dam–offspring covariance. Nevertheless, in the simulated data, reduction in the inflation of breeding values was possible and was associated with a gain in accuracy of up to 6% compared with a model not including both forms of direct-maternal covariance.ConclusionsIn this paper, we propose a simple approach to estimate the environmental direct-maternal covariance using standard software for REML analysis. The genetic covariance between dam and offspring was negative whereas the corresponding environmental covariance was positive. Considering both covariances in models for genetic evaluation increased the accuracy of predicted breeding values.

Genome-wide association study on coordination and agility in 461 Chinese Han males

PurposeThere is growing evidence that genetic factors can influence human athletic performance. In many sports performances, excellent coordination and agility are the keys to mastery. However, few studies have been devoted to identifying genetic influences on athletic performance. Methods: We generated a derived measure of coordination and agility from the data of hexagonal jumps and T-runs and conducted genome-wide association and meta-analysis studies focused on coordination and agility. Results: The phenotypic correlation and genetic covariance analysis indicated that hexagonal jumps and T-runs were possibly influenced by the same set of genetic factors (R = 0.27, genetic covariance = 0.59). Meta-analysis identified rs117047321 genome-wide significant association (N = 143, P < 10E-5) with coordination and agility, and this association was replicated in the replication group (N = 318, P < 0.05). The CG genotype samples of this single nucleotide polymorphism (SNP) required a longer average movement time than the CC genotype samples, and the CG genotype only exists in Asia, which may belong to the East Asia-specific variation. This SNP is located on MYO5B, which is highly expressed in tissues such as the brain, heart, and muscle, suggesting that this locus might be a genetic factor related to human energy metabolism. Conclusion: Our study indicated that genetic factors can affect the athletic performance of coordination and agility. These findings may provide valuable insights for using genetic factors to evaluate sports characteristics.

Family History of Age-Related Macular Degeneration and Genetics Predict Progression to Advanced Age-Related Macular Degeneration Adjusting for Macular Status, Demographic, and Lifestyle Factors

To determine if a family history of age-related macular degeneration (AMD) and genetic variants identify eyes at higher risk for progression to advanced AMD (AAMD), after controlling for baseline demographics, behavioral factors, and macular status. Prospective, longitudinal cohort study. Eyes were classified using the Age-Related Eye Disease Study severity scale. Non-genetic and genetic predictors for progression to AAMD, geographic atrophy, and neovascular disease were evaluated. Cox proportional hazards models using the eye as the unit of analysis were used to calculate hazard ratios (HRs), accounting for correlated data. Discrimination between progressing and non-progressing eyes was assessed using C-statistics and net reclassification improvement (NRI). Among 4910 eyes, 863 progressed to AAMD over 12 years. Baseline AMD severity scale and status of the fellow eye were important predictors; genes provided additional discrimination. A family history of AMD also independently predicted progression after accounting for genetic and other covariates: 1 family member versus none (HR 1.21 [95% confidence interval {CI} 1.02-1.43]; P=0.03); ≥2 family members versus none (HR 1.55 [95% CI 1.26-1.90]; P < 0.001). A composite risk score calculated using β estimates of both non-genetic and significant genetic factors predicted progression to AAMD (HR 5.57; 90th vs 10th percentile; area under the receiver operating characteristic curve [AUC] = 0.92), providing superior fit compared with other models, including one with only ocular variables (NRI=0.34; P < 0.001; AUC = 0.87, ΔAUC 0.05 ± 0.005; P < 0.001). Genetic variants and family history provided additional discrimination for predicting progression to AAMD, after accounting for baseline macular status and other covariates.

Multivariate extension of penalized regression on summary statistics to construct polygenic risk scores for correlated traits.

Genetic correlations between human traits and disorders such as schizophrenia (SZ) and bipolar disorder (BD) diagnoses are well established. Improved prediction of individual traits has been obtained by combining predictors of multiple genetically correlated traits derived from summary statistics produced by genome-wide association studies, compared with single trait predictors. We extend this idea to penalized regression on summary statistics in Multivariate Lassosum, expressing regression coefficients for the multiple traits on single nucleotide polymorphisms (SNPs) as correlated random effects, similarly to multi-trait summary statistic best linear unbiased predictors (MT-SBLUPs). We also allow the SNP contributions to genetic covariance and heritability to depend on genomic annotations. We conducted simulations with two dichotomous traits having polygenic architecture similar to SZ and BD, using genotypes from 29,330 subjects from the CARTaGENE cohort. Multivariate Lassosum produced polygenic risk scores (PRSs) more strongly correlated with the true genetic risk predictor and had better discrimination power between affected and non-affected subjects than previously published sparse multi-trait (PANPRS) and univariate (Lassosum, sparse LDpred2, and the standard clumping and thresholding) methods in most simulation settings. Application of Multivariate Lassosum to predict SZ, BD, and related psychiatric traits in the Eastern Quebec SZ and BD kindred study revealed associations with every trait stronger than those obtained with univariate sparse PRSs, particularly when heritability and genetic covariance depended on genomic annotations. Multivariate Lassosum thus appears promising to improve prediction of genetically correlated traits with summary statistics for a selected subset of SNPs.

Dissecting shared genetic architecture between obesity and multiple sclerosis.

Observational studies have associated obesity with an increased risk of multiple sclerosis (MS). However, the role of genetic factors in their comorbidity remains largely unknown. Our study aimed to investigate the shared genetic architecture underlying obesity and MS. By leveraging data from genome-wide association studies, we investigated the genetic correlation of body mass index (BMI) and MS by linkage disequilibrium score regression and genetic covariance analyser. The casualty was identified by bidirectional Mendelian randomisation. Linkage disequilibrium score regression in specifically expressed genes and multimarker analysis of GenoMic annotation was utilised to explore single-nucleotide polymorphism (SNP) enrichment at the tissue and cell-type levels. Shared risk SNPs were derived using cross-trait meta-analyses and Heritability Estimation from Summary Statistics. We explored the potential functional genes using summary-data-based Mendelian randomization (SMR). The expression profiles of the risk gene in tissues were further examined. We found a significantly positive genetic correlation between BMI and MS, and the causal association of BMI with MS was supported (β=0.22, P=8.03E-05). Cross-trait analysis yielded 39 shared risk SNPs, and the risk gene GGNBP2 was consistently identified in SMR. We observed tissue-specific level SNP heritability enrichment for BMI mainly in brain tissues for MS in immune-related tissues, and cell-type-specific level SNP heritability enrichment in 12 different immune cell types in brain, spleen, lung, and whole blood. The expressions of GGNBP2 were significantly altered in the tissues of patients with obesity or MS compared to those of control subjects. Our study indicates the genetic correlation and shared risk genes between obesity and MS. These findings provide insights into the potential mechanisms behind their comorbidity and the future development of therapeutics. This work was funded by the National Natural Science Foundation of China (82171698, 82170561, 81300279, and 81741067), the Program for High-level Foreign Expert Introduction of China (G2022030047L), the Natural Science Foundation for Distinguished Young Scholars of Guangdong Province (2021B1515020003), Natural Science Foundation of Guangdong Province (2022A1515012081), the Foreign Distinguished Teacher Program of Guangdong Science and Technology Department (KD0120220129), the Climbing Programme of Introduced Talents and High-level Hospital Construction Project of Guangdong Provincial People's Hospital (DFJH201803, KJ012019099, KJ012021143, and KY012021183), and in part by VA Clinical Merit and ASGE clinical research funds (FWL).

Genome-Wide Identification and Characterization of the TLP Gene Family in Phyllostachys edulis and Association with Witches' Broom Disease Resistance in Bamboo.

Thaumatin-like proteins (TLPs) are pathogenesis-related proteins with pivotal roles in plant defense mechanisms. In this study, various bioinformatics and RNA-seq methods were used to analyze the biotic and abiotic stress responses of the TLP family in Phyllostachys edulis. Overall, 81 TLP genes were identified in P. edulis; 166 TLPs from four plant species were divided into three groups and ten subclasses, with genetic covariance observed between these species. Subcellular localization in silico studies indicated that TLPs were primarily distributed in the extracellular. Analysis of the upstream sequences of TLPs demonstrated the presence of cis-acting elements related to disease defense, environmental stress, and hormonal responses. Multiple sequence alignment demonstrated that most TLPs possessed five conserved REDDD amino acid sequences with only a few amino acid residue differences. RNA-seq analysis of P. edulis responses to Aciculosporium take, the pathogenic fungus that causes witches' broom disease, showed that P. edulis TLPs (PeTLPs) were expressed in different organs, with the highest expression in buds. PeTLPs responded to both abscisic acid and salicylic acid stress. These PeTLP expression patterns were consistent with their gene and protein structures. Collectively, our findings provide a basis for further comprehensive analyses of the genes related to witches' broom in P. edulis.

Genetic risk shared across 24 chronic pain conditions: identification and characterization with genomic structural equation modeling.

Chronic pain conditions frequently co-occur, suggesting common risks and paths to prevention and treatment. Previous studies have reported genetic correlations among specific groups of pain conditions and reported genetic risk for within-individual multisite pain counts (≤7). Here, we identified genetic risk for multiple distinct pain disorders across individuals using 24 chronic pain conditions and genomic structural equation modeling (Genomic SEM). First, we ran individual genome-wide association studies (GWASs) on all 24 conditions in the UK Biobank ( N ≤ 436,000) and estimated their pairwise genetic correlations. Then we used these correlations to model their genetic factor structure in Genomic SEM, using both hypothesis- and data-driven exploratory approaches. A complementary network analysis enabled us to visualize these genetic relationships in an unstructured manner. Genomic SEM analysis revealed a general factor explaining most of the shared genetic variance across all pain conditions and a second, more specific factor explaining genetic covariance across musculoskeletal pain conditions. Network analysis revealed a large cluster of conditions and identified arthropathic, back, and neck pain as potential hubs for cross-condition chronic pain. Additionally, we ran GWASs on both factors extracted in Genomic SEM and annotated them functionally. Annotation identified pathways associated with organogenesis, metabolism, transcription, and DNA repair, with overrepresentation of strongly associated genes exclusively in brain tissues. Cross-reference with previous GWASs showed genetic overlap with cognition, mood, and brain structure. These results identify common genetic risks and suggest neurobiological and psychosocial mechanisms that should be targeted to prevent and treat cross-condition chronic pain.

Exact expressions and numerical evaluation of average evolvability measures for characterizing and comparing textbf{G} matrices

Theory predicts that the additive genetic covariance (textbf{G}) matrix determines a population’s short-term (in)ability to respond to directional selection—evolvability in the Hansen–Houle sense—which is typically quantified and compared via certain scalar indices called evolvability measures. Often, interest is in obtaining the averages of these measures across all possible selection gradients, but explicit formulae for most of these average measures have not been known. Previous authors relied either on approximations by the delta method, whose accuracy is generally unknown, or Monte Carlo evaluations (including the random skewers analysis), which necessarily involve random fluctuations. This study presents new, exact expressions for the average conditional evolvability, average autonomy, average respondability, average flexibility, average response difference, and average response correlation, utilizing their mathematical structures as ratios of quadratic forms. The new expressions are infinite series involving top-order zonal and invariant polynomials of matrix arguments, and can be numerically evaluated as their partial sums with, for some measures, known error bounds. Whenever these partial sums numerically converge within reasonable computational time and memory, they will replace the previous approximate methods. In addition, new expressions are derived for the average measures under a general normal distribution for the selection gradient, extending the applicability of these measures into a substantially broader class of selection regimes.

Kimma: flexible linear mixed effects modeling with kinship covariance for RNA-seq data.

The identification of differentially expressed genes (DEGs) from transcriptomic datasets is a major avenue of research across diverse disciplines. However, current bioinformatic tools do not support covariance matrices in DEG modeling. Here, we introduce kimma (Kinship In Mixed Model Analysis), an open-source R package for flexible linear mixed effects modeling including covariates, weights, random effects, covariance matrices, and fit metrics. In simulated datasets, kimma detects DEGs with similar specificity, sensitivity, and computational time as limma unpaired and dream paired models. Unlike other software, kimma supports covariance matrices as well as fit metrics like Akaike information criterion (AIC). Utilizing genetic kinship covariance, kimma revealed that kinship impacts model fit and DEG detection in a related cohort. Thus, kimma equals or outcompetes current DEG pipelines in sensitivity, computational time, and model complexity. Kimma is freely available on GitHub https://github.com/BIGslu/kimma with an instructional vignette at https://bigslu.github.io/kimma_vignette/kimma_vignette.html.

Strong selection is poorly aligned with genetic variation in Ipomoea hederacea: implications for divergence and constraint.

The multivariate evolution of populations is the result of the interactions between natural selection, drift, and the underlying genetic structure of the traits involved. Covariances among traits bias responses to selection, and the multivariate axis which describes the greatest genetic variation is expected to be aligned with patterns of divergence across populations. An exception to this expectation is when selection acts on trait combinations lacking genetic variance, which limits evolutionary change. Here we used a common garden field experiment of individuals from 57 populations of Ipomoea hederacea to characterize linear and nonlinear selection on 5 quantitative traits in the field. We then formally compare patterns of selection to previous estimates of within population genetic covariance structure (the G-matrix) and population divergence in these traits. We found that selection is poorly aligned with previous estimates of genetic covariance structure and population divergence. In addition, the trait combinations favored by selection were generally lacking genetic variation, possessing approximately 15%-30% as much genetic variation as the most variable combination of traits. Our results suggest that patterns of population divergence are likely the result of the interplay between adaptive responses, correlated responses, and selection favoring traits lacking genetic variation.

Morphology, evolution, and the whole organism imperative: Why evolutionary questions need multi-trait evolutionary quantitative genetics.

Since Washburn's New Physical Anthropology, researchers have sought to understand the complexities of morphological evolution among anatomical regions in human and non-human primates. Researchers continue, however, to preferentially use comparative and functional approaches to examine complex traits, but these methods cannot address questions about evolutionary process and often conflate function with fitness. Moreover, researchers also tend to examine anatomical elements in isolation, which implicitly assumes independent evolution among different body regions. In this paper, we argue that questions asked in primate evolution are best examined using multiple anatomical regions subjected to model-bound methods built from an understanding of evolutionary quantitative genetics. A nascent but expanding number of studies over the last two decades use this approach, examining morphological integration, evolvability, and selection modeling. To help readers learn how to use these methods, we review fundamentals of evolutionary processes within a quantitative genetic framework, explore the importance of neutral evolutionary theory, and explain the basics of evolutionary quantitative genetics, namely the calculation of evolutionary potential for multiple traits in response to selection. Leveraging these methods, we demonstrate their use to understand non-independence in possible evolutionary responses across the limbs, limb girdles, and basicranium of humans. Our results show that model-bound quantitative genetic methods can reveal unexpected genetic covariances among traits that create a novel but measurable understanding of evolutionary complexity among multiple traits. We advocate for evolutionary quantitative genetic methods to be a standard whenever appropriate to keep studies of primate morphological evolution relevant for the next seventy years and beyond.

Abstract 5761: Bayesian estimation of a semi-parametric recurrent event model with competing outcomes for personalized risk prediction among cancer survivors

Abstract Multiple primary cancer (MPC) is becoming more common in the general population, accounting for approximately 20% of incidence cases in the United States. Epidemiological studies indicate a strong dependence of the subsequent primary on the characteristics of the first primary. For example, there is evidence that individuals with a first primary breast cancer is more likely to develop a second primary lung cancer. These observations highlight the need to develop a statistical model that characterizes age-to-onset of cancers beyond the first primary, while accounting for the complex relationships between the cancer occurrences. Such a modeling framework was previously lacking. We hereby propose a Bayesian semiparametric framework, where the occurrences of each cancer type follow a non-homogeneous Poisson process. The time-varying intensity of this process is conditioned on genetic and demographic covariates, such as status of genetic mutation and sex, as well as on a patient’s cancer history, such as type and timing of the first primary, thus allowing our model to capture the heterogeneity in cancer risks across individuals. Since our model requires a dataset that is enriched with MPC cases, we utilize data collected from families affected with Li-Fraumeni Syndrome (LFS), which is a genetic disorder characterized by germline mutations in the tumor-suppressor gene TP53. People with LFS are at higher risks of certain cancer types, and many cancer survivors develop additional primary malignancy. We train and cross-validate our model on a patient cohort selected according to clinical LFS criteria at MD Anderson Cancer Center from year 2000 to 2015. The cohort consists of 11,186 individuals across 429 families, out of which 2,286 were diagnosed with at least one primary cancer and 335 were tested positive for germline mutations in TP53. Upon model training, we construct cancer-specific penetrance curves for the second primary cancer, which vary considerably among patients with different covariates and cancer history, thus highlighting the utility of our model for personalized risk prediction. Our penetrance estimates display good performance when being used to make cancer-specific predictions of the second primary among cancer survivors, achieving AUCs (Areas under the Receiver Operating Characteristic curves) of 0.91, 0.76 and 0.68 respectively for sarcoma, breast cancer, and all other cancers combined. While we apply our model to an LFS dataset, the statistical framework is general, and can be tailored to analyze any time-to-event datasets with suitably selected sets of covariates. Future applications include population-based characterization of specific cancer type combinations over time to impact public health policy making. Citation Format: Nam H. Nguyen, Elissa B. Dodd-Eaton, Seung Jun Shin, Jing Ning, Wenyi Wang. Bayesian estimation of a semi-parametric recurrent event model with competing outcomes for personalized risk prediction among cancer survivors. [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 5761.

General dimensions of human brain morphometry inferred from genome-wide association data.

Understanding the neurodegenerative mechanisms underlying cognitive decline in the general population may facilitate early detection of adverse health outcomes in late life. This study investigates genetic links between brain morphometry, ageing and cognitive ability. We develop Genomic Principal Components Analysis (Genomic PCA) to model general dimensions of brain-wide morphometry at the level of their underlying genetic architecture. Genomic PCA is applied to genome-wide association data for 83 brain-wide volumes (36,778 UK Biobank participants) and we extract genomic principal components (PCs) to capture global dimensions of genetic covariance across brain regions (unlike ancestral PCs that index genetic similarity between participants). Using linkage disequilibrium score regression, we estimate genetic overlap between those general brain dimensions and cognitive ageing. The first genetic PCs underlying the morphometric organisation of 83 brain-wide regions accounted for substantial genetic variance (R2 =40%) with the pattern of component loadings corresponding closely to those obtained from phenotypic analyses. Genetically more central regions to overall brain structure - specifically frontal and parietal volumes thought to be part of the central executive network - tended to be somewhat more susceptible towards age (r=-0.27). We demonstrate the moderate genetic overlap between the first PC underlying each of several structural brain networks and general cognitive ability (rg =0.17-0.21), which was not specific to a particular subset of the canonical networks examined. We provide a multivariate framework integrating covariance across multiple brain regions and the genome, revealing moderate shared genetic etiology between brain-wide morphometry and cognitive ageing.

An improved hyperparameter optimization framework for AutoML systems using evolutionary algorithms

For any machine learning model, finding the optimal hyperparameter setting has a direct and significant impact on the model’s performance. In this paper, we discuss different types of hyperparameter optimization techniques. We compare the performance of some of the hyperparameter optimization techniques on image classification datasets with the help of AutoML models. In particular, the paper studies Bayesian optimization in depth and proposes the use of genetic algorithm, differential evolution and covariance matrix adaptation—evolutionary strategy for acquisition function optimization. Moreover, we compare these variants of Bayesian optimization with conventional Bayesian optimization and observe that the use of covariance matrix adaptation—evolutionary strategy and differential evolution improves the performance of standard Bayesian optimization. We also notice that Bayesian optimization tends to perform poorly when genetic algorithm is used for acquisition function optimization.

Condition dependence and the paradox of missing plasticity costs.

Phenotypic plasticity plays a key role in adaptation to changing environments. However, plasticity is neither perfect nor ubiquitous, implying that fitness costs may limit the evolution of phenotypic plasticity in nature. The measurement of such costs of plasticity has proved elusive; decades of experiments show that fitness costs of plasticity are often weak or nonexistent. Here, we show that this paradox could potentially be explained by condition dependence. We develop two models differing in their assumptions about how condition dependence arises; both models show that variation in condition can readily mask costs of plasticity even when such costs are substantial. This can be shown simply in a model where plasticity itself evolves condition dependence, which would be expected if costly. Yet similar effects emerge from an alternative model where trait expression itself is condition-dependent. In this more complex model, the average condition in each environment and genetic covariance in condition across environments both determine when costs of plasticity can be revealed. Analogous to the paradox of missing trade-offs between life history traits, our models show that variation in condition can mask costs of plasticity even when costs exist, and suggest this conclusion may be robust to the details of how condition affects trait expression. Our models suggest that condition dependence can also account for the often-observed pattern of elevated plasticity costs inferred in stressful environments, the maintenance of genetic variance in plasticity, and provides insight into experimental and biological scenarios ideal for revealing a cost of phenotypic plasticity.

Quantitative genetics of breeding coloration in sand lizards; genic capture unlikely to maintain additive genetic variance

Sexual selection on fitness-determining traits should theoretically erode genetic variance and lead to low heritability. However, many sexually selected traits maintain significant phenotypic and additive genetic variance, with explanations for this “lek paradox” including genic capture due to condition-dependence, and breaks on directional selection due to environmental sources of variance including maternal effects. Here we investigate genetic and environmental sources of variance in the intrasexually selected green badge of the sand lizard (Lacerta agilis). The badge functions as a cue to male fighting ability in this species, and male–male interactions determine mate acquisition. Using animal models on a pedigree including three generations of males measured over an extensive 9-year field study, we partition phenotypic variance in both badge size and body condition into additive genetic, maternal, and permanent environmental effects experienced by an individual over its lifespan. Heritability of badge size was 0.33 with a significant estimate of underlying additive genetic variance. Body condition was strongly environmentally determined in this species and did not show either significant additive genetic variance or heritability. Neither badge size nor body condition was responsive to maternal effects. We propose that the lack of additive genetic variance and heritability of body condition makes it unlikely that genic capture mechanisms maintain additive genetic variance for badge size. That said, genic capture was originally proposed for male traits under female choice, not agonistic selection. If developmental pathways generating variance in body condition, and/or the covarying secondary sex trait, differ between inter- and intrasexual selection, or the rate at which their additive genetic variance or covariance is depleted, future work may show whether genic capture is largely restricted to intersexual selection processes.