scholarly journals Analogues of the fundamental and secondary theorems of selection, assuming a log-normal distribution of expected fitness

2019 ◽  
Vol 110 (4) ◽  
pp. 396-402 ◽  
Author(s):  
Michael B Morrissey ◽  
Timothée Bonnet
Keyword(s):  
Additive Genetic Variance ◽  
Natural Populations ◽  
Relative Fitness ◽  
Empirical Estimation ◽  
Genetic Covariance ◽  
Quantitative Genetic ◽  
Log Normal ◽  
Methodological Considerations ◽  
Fundamental Theorems ◽  
Log Normal Distribution

Abstract It is increasingly common for studies of evolution in natural populations to infer the quantitative genetic basis of fitness (e.g., the additive genetic variance for relative fitness), and of relationships between traits and fitness (e.g., the additive genetic covariance of traits with relative fitness). There is a certain amount of tension between the theory that justifies estimating these quantities, and methodological considerations relevant to their empirical estimation. In particular, the additive genetic variances and covariances involving relative fitness are justified by the fundamental and secondary theorems of selection, which pertain to relative fitness on the scale that it is expressed. However, naturally-occurring fitness distributions lend themselves to analysis with generalized linear mixed models (GLMMs), which conduct analysis on a different scale, typically on the scale of the logarithm of expected values, from which fitness is expressed. This note presents relations between evolutionary change in traits, and the rate of adaptation in fitness, and log quantitative genetic parameters of fitness, potentially reducing the discord between theoretical and methodological considerations to the operationalization of the secondary and fundamental theorems of selection.

scholarly journals The ‘algebra of evolution’: the Robertson–Price identity and viability selection for body mass in a wild bird population

2020 ◽  
Vol 375 (1797) ◽  
pp. 20190359 ◽  
Author(s):  
G. K. Hajduk ◽  
C. A. Walling ◽  
A. Cockburn ◽  
L. E. B. Kruuk
Keyword(s):  
Phenotypic Diversity ◽  
Additive Genetic Variance ◽  
Natural Populations ◽  
Phenotypic Selection ◽  
Relative Fitness ◽  
Price Equation ◽  
Genetic Covariance ◽  
Selection Gradient ◽  
Viability Selection ◽  
Temporal Correlations

By the Robertson–Price identity, the change in a quantitative trait owing to selection, is equal to the trait's covariance with relative fitness. In this study, we applied the identity to long-term data on superb fairy-wrens Malurus cyaneus , to estimate phenotypic and genetic change owing to juvenile viability selection. Mortality in the four-week period between fledging and independence was 40%, and heavier nestlings were more likely to survive, but why? There was additive genetic variance for both nestling mass and survival, and a positive phenotypic covariance between the traits, but no evidence of additive genetic covariance. Comparing standardized gradients, the phenotypic selection gradient was positive, β P = 0.108 (0.036, 0.187 95% CI), whereas the genetic gradient was not different from zero, β A = −0.025 (−0.19, 0.107 95% CI). This suggests that factors other than nestling mass were the cause of variation in survival. In particular, there were temporal correlations between mass and survival both within and between years. We suggest that use of the Price equation to describe cross-generational change in the wild may be challenging, but a more modest aim of estimating its first term, the Robertson–Price identity, to assess within-generation change can provide valuable insights into the processes shaping phenotypic diversity in natural populations. This article is part of the theme issue ‘Fifty years of the Price equation’.

scholarly journals Estimation of Genetic Variance in Fitness, and Inference of Adaptation, When Fitness Follows a Log-Normal Distribution

2019 ◽  
Vol 110 (4) ◽  
pp. 383-395 ◽  
Author(s):  
Timothée Bonnet ◽  
Michael B Morrissey ◽  
Loeske E B Kruuk
Keyword(s):  
Natural Selection ◽  
Animal Models ◽  
Normal Distribution ◽  
Genetic Variance ◽  
Additive Genetic Variance ◽  
Relative Fitness ◽  
Parameter Estimates ◽  
Log Normal ◽  
Change In Mean ◽  
Log Normal Distribution

AbstractAdditive genetic variance in relative fitness (σA2(w)) is arguably the most important evolutionary parameter in a population because, by Fisher’s fundamental theorem of natural selection (FTNS; Fisher RA. 1930. The genetical theory of natural selection. 1st ed. Oxford: Clarendon Press), it represents the rate of adaptive evolution. However, to date, there are few estimates of σA2(w) in natural populations. Moreover, most of the available estimates rely on Gaussian assumptions inappropriate for fitness data, with unclear consequences. “Generalized linear animal models” (GLAMs) tend to be more appropriate for fitness data, but they estimate parameters on a transformed (“latent”) scale that is not directly interpretable for inferences on the data scale. Here we exploit the latest theoretical developments to clarify how best to estimate quantitative genetic parameters for fitness. Specifically, we use computer simulations to confirm a recently developed analog of the FTNS in the case when expected fitness follows a log-normal distribution. In this situation, the additive genetic variance in absolute fitness on the latent log-scale (σA2(l)) equals (σA2(w)) on the data scale, which is the rate of adaptation within a generation. However, due to inheritance distortion, the change in mean relative fitness between generations exceeds σA2(l) and equals (exp⁡(σA2(l))−1). We illustrate why the heritability of fitness is generally low and is not a good measure of the rate of adaptation. Finally, we explore how well the relevant parameters can be estimated by animal models, comparing Gaussian models with Poisson GLAMs. Our results illustrate 1) the correspondence between quantitative genetics and population dynamics encapsulated in the FTNS and its log-normal-analog and 2) the appropriate interpretation of GLAM parameter estimates.

scholarly journals Genetic variance in fitness and its cross-sex covariance predict adaptation during experimental evolution

2020 ◽  
Author(s):  
Eva L. Koch ◽  
Sonja H. Sbilordo ◽  
Frédéric Guillaume
Keyword(s):  
Experimental Evolution ◽  
Genetic Variance ◽  
Environmental Changes ◽  
Additive Genetic Variance ◽  
Relative Fitness ◽  
Male Fitness ◽  
Adaptive Potential ◽  
Genetic Covariance ◽  
Flour Beetles ◽  
Single Stress

AbstractIn presence of rapid environmental changes, it is of particular importance to assess the adaptive potential of populations, which is mostly determined by the additive genetic variation (VA) in fitness. In this study we used Tribolium castaneum (red flour beetles) to investigate its adaptive potential in three new environmental conditions (Dry, Hot, Hot-Dry). We tested for potential constraints that might limit adaptation, including negative genetic covariance between female and male fitness. Based on VA estimates for fitness, we expected the highest relative fitness increase in the most stressful condition Hot-Dry and similar increases in single stress conditions Dry and Hot. High adaptive potential in females in Hot was reduced by a negative covariance with male fitness. We tested adaptation to the three conditions after 20 generations of experimental evolution and found that observed adaptation mainly matched our predictions. Given that body size is commonly used as a proxy for fitness, we also tested how this trait and its genetic variance (including non-additive genetic variance) were impacted by environmental stress. In both traits, variances were sex and condition dependent, but they differed in their variance composition, cross-sex and cross-environment genetic covariances, as well as in the environmental impact on VA.

Age and Size at Maturity

2001 ◽  
Author(s):  
Derek A. Roff
Keyword(s):  
Artificial Selection ◽  
Additive Genetic Variance ◽  
Natural Populations ◽  
The Arctic ◽  
Size At Maturity ◽  
Age At Maturity ◽  
Large Size ◽  
Quantitative Genetic ◽  
Trade Offs ◽  
The Many

Age and size at maturity have been an object of interest to humans since the domestication of animals and plants, for one of the objectives of domestication was to produce an organism that grew fast and matured early at a large size. Selection was also practiced to produce animals that could be used for such purposes as hunting and portaging, and to produce products for pleasure alone, as seen in the many ornamental varieties of dogs, cats, goldfish, pigeons, and plants. All of these instances demonstrate that age and size at maturity are traits that are relatively easily molded by artificial selection and, by extension, natural selection. Historically, artificial selection experiments were concerned not with the evolution of age and size at maturity in natural populations but with the production of economically more valuable plants and animals. Recently, there has been a substantial increase in the quantitative genetic analysis of nondomesticated organisms, which has shown that, with respect to morphological traits such as adult size, there is typically abundant additive genetic variance, with heritabilities averaging approximately 0.4 (reviewed in Roff 1997). Life history traits, such as the age at maturity, show, on average, lower heritabilities (approx. 0.26) but still enough for rapid evolutionary change. Quantitative genetic analyses have shown that age and size at maturity can evolve, but the most significant advances in our understanding of the factors favoring particular age at maturity/body size combinations are due to mathematical models predicated upon the assumption that selection maximizes some fitness measure such as the rate of increase, r. In a paper entitled “Adaptive Significance of Large Size and Long Life of the Chaetognath Sagitta elegans in the Arctic,” McLaren (1966) produced a seminal analysis in which he incorporated all the important elements that have appeared in subsequent analyses of the evolution of age and size at maturity. Specifically, McLaren attempted to take into account the trade-offs produced by increased fecundity being bought at the expense of delayed maturity and increased mortality. In this chapter, I shall primarily consider analyses that have followed in McLaren’s footsteps.

scholarly journals A Universal Model for the Log-Normal Distribution of Elasticity in Polymeric Gels and Its Relevance to Mechanical Signature of Biological Tissues

Biology ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 64
Author(s):  
Arnaud Millet
Keyword(s):  
Elastic Modulus ◽  
Normal Distribution ◽  
Biological Tissues ◽  
Force Microscopy ◽  
Polymeric Gels ◽  
Atomic Force ◽  
Clear Explanation ◽  
Log Normal ◽  
Log Normal Distribution

The mechanosensitivity of cells has recently been identified as a process that could greatly influence a cell’s fate. To understand the interaction between cells and their surrounding extracellular matrix, the characterization of the mechanical properties of natural polymeric gels is needed. Atomic force microscopy (AFM) is one of the leading tools used to characterize mechanically biological tissues. It appears that the elasticity (elastic modulus) values obtained by AFM presents a log-normal distribution. Despite its ubiquity, the log-normal distribution concerning the elastic modulus of biological tissues does not have a clear explanation. In this paper, we propose a physical mechanism based on the weak universality of critical exponents in the percolation process leading to gelation. Following this, we discuss the relevance of this model for mechanical signatures of biological tissues.

scholarly journals The limits of normal approximation for adult height

2021 ◽  
Author(s):  
Sergei A. Slavskii ◽  
Ivan A. Kuznetsov ◽  
Tatiana I. Shashkova ◽  
Georgii A. Bazykin ◽  
Tatiana I. Axenovich ◽  
...  
Keyword(s):  
Complex Traits ◽  
Adult Height ◽  
Normal Approximation ◽  
Classical Model ◽  
Model Complexity ◽  
Test Case ◽  
Genetic Studies ◽  
Quantitative Genetic ◽  
Profound Influence ◽  
Log Normal

AbstractAdult height inspired the first biometrical and quantitative genetic studies and is a test-case trait for understanding heritability. The studies of height led to formulation of the classical polygenic model, that has a profound influence on the way we view and analyse complex traits. An essential part of the classical model is an assumption of additivity of effects and normality of the distribution of the residuals. However, it may be expected that the normal approximation will become insufficient in bigger studies. Here, we demonstrate that when the height of hundreds of thousands of individuals is analysed, the model complexity needs to be increased to include non-additive interactions between sex, environment and genes. Alternatively, the use of log-normal approximation allowed us to still use the additive effects model. These findings are important for future genetic and methodologic studies that make use of adult height as an exemplar trait.

scholarly journals Extreme geomagnetic activities: a statistical study

2020 ◽  
Vol 72 (1) ◽  
Author(s):  
Ryuho Kataoka
Keyword(s):  
Magnetic Storms ◽  
Magnetic Observatory ◽  
Statistical Distributions ◽  
Limited Data ◽  
Data Set ◽  
Sudden Commencements ◽  
The One ◽  
Log Normal ◽  
Geomagnetic Activities ◽  
Log Normal Distribution

Abstract Statistical distributions are investigated for magnetic storms, sudden commencements (SCs), and substorms to identify the possible amplitude of the one in 100-year and 1000-year events from a limited data set of less than 100 years. The lists of magnetic storms and SCs are provided from Kakioka Magnetic Observatory, while the lists of substorms are obtained from SuperMAG. It is found that majorities of events essentially follow the log-normal distribution, as expected from the random output from a complex system. However, it is uncertain that large-amplitude events follow the same log-normal distributions, and rather follow the power-law distributions. Based on the statistical distributions, the probable amplitudes of the 100-year (1000-year) events can be estimated for magnetic storms, SCs, and substorms as approximately 750 nT (1100 nT), 230 nT (450 nT), and 5000 nT (6200 nT), respectively. The possible origin to cause the statistical distributions is also discussed, consulting the other space weather phenomena such as solar flares, coronal mass ejections, and solar energetic particles.

scholarly journals Heritability of DNA methylation in threespine stickleback (Gasterosteus aculeatus)

Genetics ◽  
2021 ◽  
Vol 217 (1) ◽  
Author(s):  
Juntao Hu ◽  
Sara J S Wuitchik ◽  
Tegan N Barry ◽  
Heather A Jamniczky ◽  
Sean M Rogers ◽  
...  
Keyword(s):  
Dna Methylation ◽  
Genetic Architecture ◽  
Gasterosteus Aculeatus ◽  
Additive Genetic Variance ◽  
Natural Populations ◽  
Threespine Stickleback ◽  
Phenotypic Change ◽  
Cpg Sites ◽  
Cis And Trans ◽  
Methylation Variation

Abstract Epigenetic mechanisms underlying phenotypic change are hypothesized to contribute to population persistence and adaptation in the face of environmental change. To date, few studies have explored the heritability of intergenerationally stable methylation levels in natural populations, and little is known about the relative contribution of cis- and trans-regulatory changes to methylation variation. Here, we explore the heritability of DNA methylation, and conduct methylation quantitative trait loci (meQTLs) analysis to investigate the genetic architecture underlying methylation variation between marine and freshwater ecotypes of threespine stickleback (Gasterosteus aculeatus). We quantitatively measured genome-wide DNA methylation in fin tissue using reduced representation bisulfite sequencing of F1 and F2 crosses, and their marine and freshwater source populations. We identified cytosines (CpG sites) that exhibited stable methylation levels across generations. We found that additive genetic variance explained an average of 24–35% of the methylation variance, with a number of CpG sites possibly autonomous from genetic control. We also detected both cis- and trans-meQTLs, with only trans-meQTLs overlapping with previously identified genomic regions of high differentiation between marine and freshwater ecotypes. Finally, we identified the genetic architecture underlying two key CpG sites that were differentially methylated between ecotypes. These findings demonstrate a potential role for DNA methylation in facilitating adaptation to divergent environments and improve our understanding of the heritable basis of population epigenomic variation.

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