Drivers of diversification in individual life courses

Abstract

Heterogeneity in life courses among individuals of a population influences the speed of adaptive evolutionary processes, but it is less clear how biotic and abiotic environmental fluctuations influence such heterogeneity. We investigate principal drivers of variability in sequence of stages during an individual's life in a stage-structured population. We quantify heterogeneity by measuring population entropy, which computes the rate of diversification of individual life courses of a Markov chain. Using individual data of a primate population, we show that density regulates the stage composition of the population, but its entropy and the generating moments of heterogeneity are independent of density. This lack of influence of density on heterogeneity is neither due to low year-to-year variation in entropy nor due to differences in survival among stages, but due to differences in stage transitions. Our analysis thus shows that well-known classical ecological selective forces, such as density regulation, are not linked to potential selective forces governing heterogeneity through underlying stage dynamics. Despite evolution acting heavily on individual variability in fitness components, our understanding is poor whether observed heterogeneity is adaptive and how it evolves and is maintained. Our analysis illustrates how entropy represents a more integrated measure of diversity compared to the population structural composition, giving us new insights about the underlying drivers of individual heterogeneity within populations and potential evolutionary mechanisms.

Drivers of Diversification in Individual Life Courses

“…The scaled entropy we computed for the 3 × 3 mean submatrix P across all years (table 4, boldface area) equals H = 0:71. Annual P and R matrices are deposited in the Dryad Digital Repository: http://dx.doi.org/10.5061/dryad.p2c6r (Hernández-Pacheco and Steiner 2017). If we estimate entropy for each period, the annual entropy $H_{{\mathrm{normalR}}_t}$ varied between 0.54 and 0.80, but there was no trend across periods (1973–2013; fig.…”

“…4). Data on annual number of adults is deposited in the Dryad Digital Repository: http://dx.doi.org/10.5061/dryad.p2c6r (Hernández-Pacheco and Steiner 2017). Similarly, density at birth did not influence the observed changes in $H_{{\mathrm{normalR}}_c}$ (tables 5, 6), and we did not find a correlation between $H_{{\mathrm{normalR}}_t}$ and $H_{{\mathrm{normalR}}_c}$ (cohort effects; app.…”

“…Annual censuses are based on daily census data of 3,909 females. Demographic data of female rhesus macaques is deposited in the Dryad Digital Repository: http://dx.doi.org/10.5061/dryad.p2c6r (Hernández-Pacheco and Steiner 2017). We used a birth-pulse model employing postbreeding censuses including female data only and discrete-time, stage-structured matrix models with annual intervals (periods; Caswell 2001).…”

Drivers of diversity in individual life courses: Sensitivity of the population entropy of a Markov chain

“…Note, that we can generate population stage frequencies with very different underlying individual trajectories. For instance, heterogeneous trajectories with individuals frequently changing among stages can lead to very similar population level frequencies as can a few trajectories with low level of dynamics (Hernandez-Pacheco and Steiner, 2017). Therefore the population stage frequencies, which are also the focus of population genetics and quantitative genetics, does not reveal underlying individual level stage dynamics.…”

“…Our contributions are an exact result for the sensitivity of the entropy of an ergodic chain and absorbing Markov chains. Comparing the sensitivities between the two types of markov chains (ergodic and absorbing) from the same system can then be used to evaluate the contribution of survival differences among individuals on the diversity of stage trajectories (Hernandez-Pacheco and Steiner, 2017).…”