Des différences, pourquoi? Transmission, maintenance and effects of phenotypic variance.

Despite the observed distribution of variable individual phenotypes, survival and reproductive performance in wild populations, models of population dynamics often focus on mean demographic rates. Populations are constituted by individuals with different phenotypes and thus different performances. However, many models of population dynamics provide no understanding of the influence of this phenotypic variation on population dynamics. In this paper, we investigate how the relationships between demographic rates and phenotype distribution influence the transmission and the upholding of phenotypic variation, and population dynamics. We used integral projection models to measure associations between differences of phenotypic trait (size or mass) among individuals and demographic rates, growth and inheritance, and then quantify the influence of phenotypic variation on population dynamics. We build an analytical and general model resulting from simplifications assuming small phenotypic variance. We illustrate our model with two case studies: a short- and a long-lived life history. Population growth rate r is determined by a Lotka style equation in which survival and fertility are averaged over a phenotypic distribution that changes with age. Here, we further decomposed r to show how much it is affected by shifts in phenotypic average as well as variance. We derived the elasticities of r to the first and second derivative of each demographic rate. In particular, we show that the nonlinearity of change in selective pressure with phenotype matters more to population dynamics than the strength of this selection. In other words, the variance of a given trait will be most important when the strength of selection increases (or decreases) nonlinearly with that trait. Inheritance shapes the distribution of newborn phenotypes. Even if newborns have a fixed average phenotype, the variance among newborns increases with phenotypic variance among mothers, strength of inheritance and developmental variation. We explain how the components of inheritance can influence phenotypic variance and thus the demographic rates and population dynamics. In particular, when mothers of different ages produce offspring of different mean phenotype, the inheritance function can have a large influence on both the mean and variance of the trait at different ages and thus on the population growth rate. We provide new tools to understand how phenotypic variation influences population dynamics and discuss in which life histories we expect this influence to be large. For instance, in our short-lived life history, individual variability has larger effect than in our long-lived life history. We conclude by indicating future directions of analysis.