PAVARD Samuel

ANR Project MathKinD - Mathematics of Kinship Demography: new developments and application to Humans (2019 - 2023)

In coll. with. Sarah Cubaynes, Christophe Coste & Victor Ringet (in coll. with G. Pison and J-M Robine)

Researchers from the MathKinD project have developed a new method for linking genealogy to population dynamics. This work, at the crossroads between ecology and demography, has consequences on predicting the viability of species, monitoring their dynamics in time and space.

Population dynamics and family structures at the crossroads of ecology and evolution - Whatever their species, individuals are born, grow, reproduce, migrate and die. This is their life cycle. When all of the cycles of individuals in a population are considered, it is possible to assess whether a population is stable, increasing or decreasing over time. In other words, to predict its dynamics. At the same time, genealogy is determined by the same indicators of survival and reproduction, but focuses on the kinship ties between individuals. A question then has driven research for many years: as the continuous-time dynamics of populations and the genealogy of individuals by generation use common information, how can they be linked to each other? This is where the ANR MathKinD project comes in, co-directed by demographer Samuel Pavard and ecologist Sarah Cubaynes. The objective: to develop a new easy-to-use mathematical tool linking these two research objects and to apply it to human evolution and the ecology of various endangered species.

A major methodological advance - The first equations linking population dynamics and genealogy, and which constitute the method used until now, date from 1974 and calculate the probability that a relative (mother, grandmother, aunts, sisters and nieces) of a random individual at a given age is still alive. The interest of these complex equations is nevertheless limited. The model is unisex. Relationships beyond an individual's grandmothers and nieces are difficult to calculate. Finally, the model is only valid in a constant environment where everyone reproduces and survives in the same way. The primary objective of MathKinD is therefore to overcome these 45 years old limitations.

The challenge was nevertheless successfully met. A new mathematical model, developed by the ecologist and mathematician Christophe Coste, improves this founding work (Coste et al., Ecol. Letters, 2021). This method makes it possible to calculate, from a population projection matrix model, classically used in population demography and ecology, all the relatedness relationships of a population. But concretely, what can this tool be used for?

From humans to bears and wolves, predicting the evolutionary and ecological dynamics of social species - In humans, family models have shown how taking sociodemographic behavior between relatives into account is important in order to better understand the prevalence and evolution of diseases of aging (Pavard & Coste, Nat. Ecol. Evol., 2021). Indeed, mothers, fathers and grandparents help bring their children and grandchildren into adulthood. Thus, dying of cancer at age 60 can further reduce the number of living descendants carrying our genes. MathKinD has also made it possible to build models of family dynamics – mother and children – in polar bears and has considerably improved population projections for the conservation of this species. With regard to the wolf, MathKinD also showed how variations in coat color frequency result from complex dynamics between resistance to the distemper virus and optimal mating behavior between relatives.

And after? The researchers will also continue to simplify and improve their formula in order to democratize its uses. Finally, have you ever wondered if rodents, which have a relatively short lifespan, create the same social bonds with their parents as elephants, which have a much longer lifespan? The first works applying the MathKinD method to a wide variety of mammals will very soon answer this question and many others!

Who keeps children alive? is the title of a review from Rebecca Sear and Ruth Mace (2008, Evolution and Human Behavior). It is also a key question concerning the evolution of cooperative breeding and life-history traits in humans.

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© S. Pavard