Preventing Noise-Induced Extinction in Discrete Population Models

A problem of the analysis and prevention of noise-induced extinction in nonlinear population models is considered. For the solution of this problem, we suggest a general approach based on the stochastic sensitivity analysis. To prevent the noise-induced extinction, we construct feedback regulators which provide a low stochastic sensitivity and keep the system close to the safe equilibrium regime. For the demonstration of this approach, we apply our mathematical technique to the conceptual but quite representative Ricker-type models. A variant of the Ricker model with delay is studied along with the classic widely used one-dimensional system.

Recent advances in the study of fine-scale population structure in humans

Empowered by modern genotyping and large samples, population structure can be accurately described and quantified even when it only explains a fraction of a percent of total genetic variance. This is especially relevant and interesting for humans, where fine-scale population structure can both confound disease-mapping studies and reveal the history of migration and divergence that shaped our species’ diversity. Here we review notable recent advances in the detection, use, and understanding of population structure. Our work addresses multiple areas where substantial progress is being made: improved statistics and models for better capturing differentiation, admixture, and the spatial distribution of variation; computational speed-ups that allow methods to scale to modern data; and advances in haplotypic modeling that have wide ranging consequences for the analysis of population structure. We conclude by outlining four important open challenges: The limitations of discrete population models, uncertainty in individual origins, the incorporation of both fine-scale structure and ancient DNA in parametric models, and the development of efficient computational tools, particularly for haplotype-based methods.