Detecting context dependence in the expression of life history trade-offs

Abstract

Life history trade-offs are one of the central tenets of evolutionary demography. Trade-offs, depicting negative covariances between individuals' life history traits, can arise from genetic constraints, or from a finite amount of resources that each individual has to allocate in a zero-sum game between somatic and reproductive functions. While theory predicts that trade-offs are ubiquitous, empirical studies have often failed to detect such negative covariances in wild populations. One way to improve the detection of trade-offs is by accounting for the environmental context, as trade-off expression may depend on environmental conditions. However, current methodologies usually search for fixed covariances between traits, thereby ignoring their context dependence. Here, we present a hierarchical multivariate 'covariance reaction norm' model, adapted from Martin (2023), to help detect context dependence in the expression of life-history trade-offs using demographic data. The method allows continuous variation in the phenotypic correlation between traits. We validate the model on simulated data for both intraindividual and intergenerational trade-offs. We then apply it to empirical datasets of yellow-bellied marmots (Marmota flaviventer) and Soay sheep (Ovis aries) as a proof-of-concept showing that new insights can be gained by applying our methodology, such as detecting trade-offs only in specific environments. We discuss its potential for application to many of the existing long-term demographic datasets and how it could improve our understanding of trade-off expression in particular, and life history theory in general.

Keywords: covariance reaction norm; demography; heterogeneity; life‐history; mixed effects; multivariate model; phenotypic correlation; trade‐off.

FIGURE 1

General relationships across correlations and repeatability ranges based on Equation 3 for a non‐repeated measures CRN (model of Equation 2), identifying the magnitude of correlation bias and the regions of sign bias. The bias is here defined as the difference between the observation‐level correlation and the among‐individual correlation, using the latter as a reference. Parameter spaces in grey represent the regions of sign bias, where the observation‐level correlation has a sign opposite to the among‐individual correlation. This highlights that the observation‐level correlation is mostly influenced by the among‐individual correlation for traits with high repeatability, while it is mostly influenced by the within‐individual correlation for traits with low repeatability.

FIGURE 2

Left panel: Estimated versus simulated observation‐level correlation between litter size and offspring mass as a function of climate, after accounting for the effect of climate on both traits. The regression line indicates the mean effect of climate on the correlation, while the shaded areas depict the 50% and 89% credible intervals predicted by the model. Each black dot represents the simulated observation‐level correlation between both traits in a given year depending on climate. Right panel: Estimated versus simulated intercepts and slopes for the offspring mass and litter size sub‐models. Dashed lines represent the value used to simulate the data, while the distributions and intervals represent the posterior distributions estimated by the model, alongside the median, 50% and 89% credible intervals. Litter size estimates are presented on the log scale.

FIGURE 3

Left panel: Estimated versus simulated observation‐level correlation between fecundity and growth as a function of climate, after accounting for the effect of climate on both traits. The regression line indicates the mean effect of climate on the correlation, while the shaded areas depict the 50% and 89% credible intervals predicted by the model. Each black dot represents the simulated observation‐level correlation between both traits in a given year depending on climate. Right panel: Estimated versus simulated intercepts and slopes for the growth and fecundity sub‐models. Dashed lines represent the value used to simulate the data, while the distributions and intervals represent the posterior distributions estimated by the model, alongside the median, 50%, 89% credible intervals. Fecundity estimates are presented on the log scale.

FIGURE 4

Observation‐level correlation between litter size and offspring mass in marmots as a function of the total amount of snow in the preceding winter at high and low temperature (top left panel) and the maximum daily June temperature of the year at high and low snow cover (top right panel). Estimated effects of standardised predictors (bottom panel) on offspring mass, fecundity, and the observation‐level correlation between both traits in marmots. The regression line indicates the median estimated effect, while the shaded areas depict the 50% and 89% credible intervals predicted by the model.

FIGURE 5

Observation‐level correlation between fecundity and mothers' mass in the following year in Soay sheep as a function of the winter NAO at high and low density (top left panel), and as a function of the population density at high and low winter NAO values (top right panel). Estimated effects (bottom panel) of standardised predictors on mother's mass in the following year, fecundity, and the observation‐level correlation between both traits in Soay sheep. The figure displays the posterior distributions estimated by the model, alongside the median, 50% and 89% credible intervals.