A modelling framework for the analysis of artificial-selection time series

Rouzic, Arnaud Le; Houle, David; Hansen, Thomas F.

doi:10.1017/s0016672311000024

Cited by 19 publications

(25 citation statements)

References 89 publications

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“…Plasticity in allometric relationships has been little studied, but two studies clearly show that static allometry varies in response to different environmental treatments . Similarly, a selection experiment on Drosophila wings in which selection was performed on the relative position of some veins showed erratic, but sometimes statistically significant, variation in static allometry (Fig. ).…”

Section: Is Static Allometry Evolvable?mentioning

confidence: 99%

Evolution of morphological allometry

Pélabon

Firmat

Bolstad

et al. 2014

Annals of the New York Academy of Sciences

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23Allometry refers to the power-law relationship that often occurs between body parts and total 24 body size. Whether measured during growth (ontogenetic allometry), among individuals at 25 similar developmental stage (static allometry) or among populations or species (evolutionary 26 allometry), allometric relationships are often surprisingly tight, and relatively invariant. 27Consequently, it has been suggested that allometry could constrain phenotypic evolution, that 28 is, force evolving species along fixed trajectories. Alternatively allometric relationship may 29 result from selection. Despite nearly a century of active research on allometry, distinguishing 30 between these two alternatives remains difficult partly due to the use of a broad sense 31 definition of allometry where the meaning of relative growth was lost. Focusing on the 32 original narrow-sense definition of allometry, we review evidence for and against the 33 "allometry as a constraint" hypothesis. Although the low evolvability of the static allometric 34 slopes observed in some studies suggests a possible constraining effect of this parameter on 35 phenotypic evolution, the nearly complete absence of knowledge about selection on allometry 36 prevents any firm conclusion. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 Introduction 42Allometry is the study of the relationship between body size and other organismal traits. 43Allometry is important because variation in a wide variety of morphological, physiological 44 and life history traits are highly correlated with organism size [1,2,3]. These relationships 45 generate intuitive hypotheses for understanding trait variation; for example, the fact that 46 humans are larger than mice can be used to explain why the basal metabolic rate of a human 47 is much higher than the basal metabolic rate of a mouse. In most cases, traits show a non-48 linear relationship with size that is accurately captured by a power relationship of the form z = 49, where the trait value is z, the organism size is x, and a and b are parameters of the 50 relationship. If b = 1, the relationship between the trait and size is linear, a condition referred 51 to as isometry. When b ≠ 1, the relationship is non-linear on the arithmetic scale. For 52 example, the basal metabolic rate in mammals scales with body mass with a coefficient b ≈ 53 0.71 [4]; as a result, for every unit increase in mass, a larger organism will have a smaller 54 increase in basal metabolic rate than a smaller organism. Consequently, humans have a basal 55 metabolic rate 5 to 10 times smaller than a mouse when corrected for body size. The ubiquity 56 of these power-law relationships has led biologists to refer to them as allometric relationships. 57Analyzed on log-transformed data these relationships become linear: log(z) = log(a) + 58 b×log(x), where log(a) and b re...

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Section: Is Static Allometry Evolvable?mentioning

confidence: 99%

Evolution of morphological allometry

Pélabon

Firmat

Bolstad

et al. 2014

Annals of the New York Academy of Sciences

Self Cite

223

230

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“…Including the effects of e.g., inbreeding, linkage disequilibrium, or canalization, is possible, but requires to numerically maximize the likelihood of complex models. This can be done with the software package for , described in Le Rouzic et al (2011). …”

Section: Multilinear Epistasismentioning

confidence: 99%

“…Nevertheless, useful approximations can still be derived by making realistic assumptions about the properties of genetic architectures. For instance, Le Rouzic et al (2011) proposed a model that can be simplified as:

μ_{t + 1} = μ_{t} + V_{A_{t}} β_{t}

V_{A_{t + 1}} = V_{A_{t}} + 2 β_{t} ε V_{A_{t}}^{2}

Equation (A5a) is the traditional breeder's equation, formulated as in Lande and Arnold (1983), where V A is the additive genetic variance, and β the selection gradient, i.e., the slope of the regression between phenotype and relative fitness. Equation (A5b) approximates the impact of directional epistasis on additive variance, summarized by the directionality coefficient ε.…”

Section: Two Locimentioning

confidence: 99%

Section: Two Locimentioning

confidence: 99%

“…This model requires 3 parameters: μ 0 , the initial phenotype, the initial additive variance V A 0 , and the epistatic parameter ε. Fitting the model by maximizing its likelihood for phenotype times series including means and variances provide convincing estimates of epistasis, especially when the data include bidirectional artificial selection (Le Rouzic et al, 2011). …”

Section: Two Locimentioning

confidence: 99%

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Estimating directional epistasis

Rouzic

2014

Front. Genet.

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Epistasis, i.e., the fact that gene effects depend on the genetic background, is a direct consequence of the complexity of genetic architectures. Despite this, most of the models used in evolutionary and quantitative genetics pay scant attention to genetic interactions. For instance, the traditional decomposition of genetic effects models epistasis as noise around the evolutionarily-relevant additive effects. Such an approach is only valid if it is assumed that there is no general pattern among interactions—a highly speculative scenario. Systematic interactions generate directional epistasis, which has major evolutionary consequences. In spite of its importance, directional epistasis is rarely measured or reported by quantitative geneticists, not only because its relevance is generally ignored, but also due to the lack of simple, operational, and accessible methods for its estimation. This paper describes conceptual and statistical tools that can be used to estimate directional epistasis from various kinds of data, including QTL mapping results, phenotype measurements in mutants, and artificial selection responses. As an illustration, I measured directional epistasis from a real-life example. I then discuss the interpretation of the estimates, showing how they can be used to draw meaningful biological inferences.

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Making quantitative morphological variation from basic developmental processes: Where are we? The case of the Drosophila wing

Matamoro‐Vidal

Salazar‐Ciudad

Houle

2015

Developmental Dynamics

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One of the aims of evolutionary developmental biology is to discover the developmental origins of morphological variation. The discipline has mainly focused on qualitative morphological differences (e.g., presence or absence of a structure) between species. Studies addressing subtle, quantitative variation are less common. The Drosophila wing is a model for the study of development and evolution, making it suitable to investigate the developmental mechanisms underlying the subtle quantitative morphological variation observed in nature. Previous reviews have focused on the processes involved in wing differentiation, patterning and growth. Here, we investigate what is known about how the wing achieves its final shape, and what variation in development is capable of generating the variation in wing shape observed in nature. Three major developmental stages need to be considered: larval development, pupariation, and pupal development. The major cellular processes involved in the determination of tissue size and shape are cell proliferation, cell death, oriented cell division and oriented cell intercalation. We review how variation in temporal and spatial distribution of growth and transcription factors affects these cellular mechanisms, which in turn affects wing shape. We then discuss which aspects of the wing morphological variation are predictable on the basis of these mechanisms.

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A modelling framework for the analysis of artificial-selection time series

Cited by 19 publications

References 89 publications

Evolution of morphological allometry

Evolution of morphological allometry

Estimating directional epistasis

Making quantitative morphological variation from basic developmental processes: Where are we? The case of the Drosophila wing

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