A branching process, its application in biology: influence of demographic parameters on the social structure in mammal groups

ETAS Space–Time Modeling of Chile Triggered Seismicity Using Covariates: Some Preliminary Results

Chilean seismic activity is one of the strongest in the world. As already shown in previous papers, seismic activity can be usefully described by a space–time branching process, such as the ETAS (Epidemic Type Aftershock Sequences) model, which is a semiparametric model with a large time-scale component for the background seismicity and a small time-scale component for the triggered seismicity. The use of covariates can improve the description of triggered seismicity in the ETAS model, so in this paper, we study the Chilean seismicity separately for the North and South area, using some GPS-related data observed together with ordinary catalog data. Our results show evidence that the use of some covariates can improve the fitting of the ETAS model.

Including covariates in a space-time point process with application to seismicity

The paper proposes a spatio-temporal process that improves the assessment of events in space and time, considering a contagion model (branching process) within a regression-like framework to take covariates into account. The proposed approach develops the forward likelihood for prediction method for estimating the ETAS model, including covariates in the model specification of the epidemic component. A simulation study is carried out for analysing the misspecification model effect under several scenarios. Also an application to the Italian seismic catalogue is reported, together with the reference to the developed R package.

Birth-death branching models. Application to African elephant populations

Branching models have a long history of biological applications, particularly in population dynamics. In this work, our interest is the development of mathematical models to describe the demographic dynamics of socially structured animal populations, focusing our attention on lineages, usually matrilines, as the basic structure in the population. Significant efforts have been made to develop models based on the assumption that all individuals behave identically with respect to reproduction. However, the reproduction phase has a large random component that involves not only demographic but also environmental factors that change across range distribution of species. In the present work, we introduce new classes of birth-death branching models which take such factors into account. We assume that both, the offspring probability distribution and the death probabilities may be different in each generation, changing either predictably or unpredictably in relation to habitat features. We consider the genealogical tree generated by observation of the process until a pre-set generation. We determine the probability distributions of the random variables representing the number of dead or living individuals having at least one ancestor alive, living individuals whose ancestors are all dead, and dead individuals whose ancestors are all dead, explicitly obtaining their principal moments. Also, we derive the probability distributions corresponding to the partial and total numbers of such biological variables, obtaining in particular the distribution of the total number of matriarchs in the genealogical tree. We apply the proposed models to describe the demographic dynamics of African elephant populations living in different habitats.

Bisexual branching processes to model extinction conditions for Y-linked genes

In a two-sex monogamic population, the evolution of the number of carriers of the two alleles of a Y-linked gene is considered. To this end, a multitype bisexual branching model is presented in which it is assumed that the gene has no influence on the mating process. It is deduced from this model that the average numbers of female and male descendants per mating unit constitute the key to determining the extinction or survival of each allele. Moreover, the destiny of each allele in the population is found not to depend on the behavior of the other.

A genetic analysis of group movement in an isolated population of tree-roosting bats

Group fission is an important dispersal mechanism for philopatric adults. In Cypress Hills Interprovincial Park, Saskatchewan, tree-roosting big brown bats (Eptesicus fuscus) exhibit fission-fusion roosting behaviour. During 2004-2007, the majority of females previously resident to roosting area 1 (RA1) moved to a new roosting area (RA4). We examined how genetic relationships, inferred from data for microsatellite loci and mitochondrial DNA, influenced new roost area (RA) selection during 2006 when colony members were split between the RAs. We found that females who moved to RA4 had higher average relatedness than those that remained in RA1. We found that nearly all females belonging to matrilines with high average relatedness moved to RA4 while females from matrilines with low average relatedness were split between the two RAs. These results suggest that closely related maternal kin preferentially move to new RAs. However, daily roosting preferences within a RA are not based on genetic relationships probably because daily roosting associations between kin and non-kin are used to ensure adequate roost group size. Studying the effects of kinship on the fission and movements of groups not only enhances our understanding of social behaviour and population genetics but also informs conservation decisions.