Nonparametric Estimation of Natural Selection on a Quantitative Trait Using Mark-Recapture Data

Abstract

Assessing natural selection on a phenotypic trait in wild populations is of primary importance for evolutionary ecologists. To cope with the imperfect detection of individuals inherent to monitoring in the wild, we develop a nonparametric method for evaluating the form of natural selection on a quantitative trait using mark-recapture data. Our approach uses penalized splines to achieve flexibility in exploring the form of natural selection by avoiding the need to specify an a priori parametric function. If needed, it can help in suggesting a new parametric model. We employ Markov chain Monte Carlo sampling in a Bayesian framework to estimate model parameters. We illustrate our approach using data for a wild population of sociable weavers (Philetairus socius) to investigate survival in relation to body mass. In agreement with previous parametric analyses, we found that lighter individuals showed a reduction in survival. However, the survival function was not symmetric, indicating that body mass might not be under stabilizing selection as suggested previously.

The temporal distribution of directional gradients under selection for an optimum

“…Several arguments, from basic functional considerations (Wright ; van Asch et al ) to standard properties of dynamical systems (Otto and Day ), and analyses of empirical rates of evolution across different timescales (Estes and Arnold ; Uyeda et al ), support the idea that many traits are under stabilizing selection for an optimum phenotype (see Charlesworth et al for a critical review of such arguments). Direct measurements of selection also commonly find fitness functions with an optimum phenotype (e.g., Schluter and Nychka ; Benkman and Miller ; Gimenez et al ; Garant et al ; Martin and Wainwright ). Although meta‐analyses did not find a prevalent role of negative over positive quadratic gradients in the literature (Kingsolver et al ; Kingsolver and Diamond ), positive curvature is also detected when the mean phenotype is far from an optimum, and does not necessarily imply disruptive selection (Schluter ).…”

Cormack–Jolly–Seber model with environmental covariates: A P‐spline approach

“…However, as more covariates enter the model, this requires additional smoothing parameters and thus the computation time will increase as a result of the curse of dimensionality. Individual covariates may also be considered in the CJS model (McDonald and Amstrup, ; Bonner and Schwarz, ; Gimenez et al, ) and modelled semi‐parametrically; however, information on each individual is not always readily available and the computation burden may worsen. We envisage the proposed P‐spline models as candidate competing models to be included in a set of models that may be compared using, say, the CVL criteria.…”

“…Recently, several semi‐parametric approaches under the CJS framework have been proposed to model nonlinear relationships between the survival probabilities and covariates. For example: Gimenez et al (, ) considered a Bayesian approach using truncated polynomial basis functions and penalized splines (Ruppert et al, ) on environmental covariates; Bonner et al () used a Bayesian free‐knot approach; and Viallefont () modelled survival probabilities as smooth functions of age. Here, we consider a frequentist approach and use generalized additive models (Hastie and Tibshirani, ; Marx and Eilers, ) to simultaneously model both the survival and capture probabilities as smooth functions of time‐dependent environmental covariates.…”

Morphological flexibility across an environmental gradient in the epiphytic orchid, Tolumnia variegata: complicating patterns of fitness

“…We evaluated the shape of the fitness function using the cubic spline approach (Schluter, 1988; GLMS software), which has been widely applied to a variety of systems (Herrera, 1983; Maad, 2000; Mendel, Botto‐Mahan & Kalin‐Arroyo, 2003; Gimenez et al ., 2006). This approach is not limited to the description of linear or quadratic functions, nor does it make a priori assumptions about the shape of the function (Schluter, 1988; Schluter & Nychka, 1994).…”