Mathematics of Kinship Demography: new developments and application to Humans – MathKinD

The aim of the MathKinD project is twofold. Its first axis of research will provide a general mathematical method to infer kin distributions by stage/age/size, from any demographic model, by applying genealogical Markov chains methodology to Multitrait Population Projection Matrix (MPPM, Coste et al. 2017). This extraction would constitute a major breakthrough in population dynamics, ecology, population genetics and evolutionary demography. We will then test the robustness of these predictions with age-structured pedigree data (in the case of human populations). Furthermore we will explore, across species, whether kinship structure is itself structured by phylogeny using population projection matrices of hundreds of mammal species recently provided by available databases.

The second axis of MathKinD is to implement close-kin demographic interactions (as for instance bi-parental care, grandparental care or siblings’ cooperation/competition) into MPPMs. With these models in hand, we will be able to disentangle the socio-demographic forces at stake in the coevolution of sociality with the peculiar LHT of our species, under different biological, environmental and cultural scenarios. We will also examine the reciprocal changes in kinship and demography of past transitioning societies (e.g., Neolithic), as well as enhance the demographic forecasting of contemporary populations that, whilst differing in their kinship systems, are all affected (and sometimes threatened) by ever increasing environmental perturbations.

Over a three year and half period, this project will provide, from joint theoretical and empirical approaches, an array of tools and analysis that connect the demographic characteristics of populations with their kinship structure in several environmental contexts. Beyond the key implications for theoretical evolutionary ecology and demography, these results will prove essential for the conservation of endangered social species, as they allow for better predictions of the fate of social species in challenging environments. By its very nature, this project will also help better understand the forces at stake in the co-evolution of life history and sociality in general, and during the history of hominidae in particular thus yielding key results for primatology and biological anthropology.

To propose a general mathematical theory to extract the kin distribution of structured populations; second to test the robustness of these predictions in the case of human populations; third to explore whether kinship structure is itself structured by phylogenic proximities across species.

To implement close-kin relationships into models in order to improve our understanding of the relationship between close-kin social behaviors, population dynamics and evolution of life-history traits in humans.

NA

In social species, demographic processes (ie, growth, reproduction, migration, survival) are functions of cooperative/competitive interactions among individuals. In cooperative breeders for example, juveniles’ growth and survival depend on stage/age/size-structure transfers of resources from parents and from “helpers at the nest” siblings. In such species therefore, kinship interplay coevolves with life-history traits (LHT). Humans in particular have evolved a peculiar life-history in which age- and kin-structured social interactions play a major role: a protracted juvenile period, a short but intense and hazardous reproductive period for females, ending with a menopause, and an extended post-reproductive life. However, the main evolutionary drivers of this coevolution between age-structured demography and kin-structured interactions are mostly unknown.

This is because the field of evolutionary ecology is still lacking a general theory for the study of the dynamic interplay between kinship interactions, population dynamics and evolution of LHT. Whilst, the tenets of the Hamiltonian theory for the evolution of sociality (Hamilton, 1964) - an individual’s inclusive fitness is determined by the costs (weighted by kinship coefficients) and benefits of kin investments - are well known at the individual level, its implications at the population level are still largely understudied. This is in particular the case for the inherent feedback circuit between demography and sociality: the system of age/stage/size-structured demography and kin-structured behaviors determines the dynamics of the population, which, in turn, regulates the distribution of kinship coefficients and therefore the opportunities and magnitudes of cooperative behaviors.

By contrast with their importance, the mathematical tools required for the exploration of demographic-kinship systems are still in their infancy. While analytical structured-populations projection models incorporate increasingly complex environmental scenarios (e.g. spatial structure, environmental fluctuations, density-dependence) or population structuring (e.g. by genotype/phenotype or classes of heterogeneity), they are yet hardly incorporating kin-structure. Therefore researchers have had turn to agent-based models in order to incorporate kinship interactions, but the complexity of algorithmic computations makes reliability of such predictions uncertain.

The aim of the MathKinD project is twofold. Its first axis of research will provide a general mathematical method to infer kin distributions by stage/age/size, from any demographic model, by applying genealogical Markov chains methodology to Multitrait Population Projection Matrix (MPPM, Coste et al. 2017). This extraction would constitute a major breakthrough in population dynamics, ecology, population genetics and evolutionary demography. We will then test the robustness of these predictions with age-structured pedigree data (in the case of human populations). Furthermore we will explore, across species, whether kinship structure is itself structured by phylogeny using population projection matrices of hundreds of mammal species recently provided by available databases.

The second axis of MathKinD is to implement close-kin demographic interactions (as for instance bi-parental care, grandparental care or siblings’ cooperation/competition) into MPPMs. With these models in hand, we will be able to disentangle the socio-demographic forces at stake in the coevolution of sociality with the peculiar LHT of our species, under different biological, environmental and cultural scenarios. We will also examine the reciprocal changes in kinship and demography of past transitioning societies (e.g., Neolithic), as well as enhance the demographic forecasting of contemporary populations that, whilst differing in their kinship systems, are all affected (and sometimes threatened) by ever increasing environmental perturbations.