Populations and Evolution (q-bio.PE)

Abstract: Critical birth-death processes with $n$ distinct types are investigated. Each type $i$ cell divides independently $(i)\to(i)+(i)$ or mutates $(i)\to(i+1)$ at the same rate. The total number of cells grows exponentially as a Yule process until the maximal type $n$ cells appear, which cannot mutate but die at rate one. The last type makes the process critical and hence after the exponentially growing phase eventually all cells die with probability one. The process mimics the accumulation of mutations in a growing population where too many mutations are lethal. This has applications for understanding the mutational burden and so-called error catastrophe in cancer, bacteria, or virus. We present large-time asymptotic results for the general $n$-type critical birth-death process. We find that the mass function of the number of cells of type $k$ has algebraic and stationary tail $(\text{size})^{-1-\chi_k}$, with $\chi_k=2^{1-k}$, for $k=2,\dots,n$, in sharp contrast to the exponential tail of the first type. The same exponents describe the tail of the asymptotic survival probability $(\text{time})^{-\chi_n}$. We discuss the consequences and applications of the results for studying extinction due to mutational burden in biological populations.

Abstract: Pool sequencing is an efficient method for capturing genome-wide allele frequencies from multiple individuals, with broad applications such as studying adaptation in Evolve-and-Resequence experiments, monitoring of genetic diversity in wild populations, and genotype-to-phenotype mapping. Here, we present grenedalf, a command line tool written in C++ that implements common population genetic statistics such as $\theta$, Tajima's D, and FST for Pool sequencing. It is orders of magnitude faster than current tools, and is focused on providing usability and scalability, while also offering a plethora of input file formats and convenience options.

Abstract: With the development of network science, the Turing pattern has been proven to be formed in discrete media such as complex networks, opening up the possibility of exploring it as a generation mechanism in the context of biology, chemistry, and physics. Turing instability in the predator-prey system has been widely studied in recent years. We hope to use the predator-prey interaction relationship in biological populations to explain the influence of network topology on pattern formation. In this paper, we establish a predator-prey model with a weak Allee effect, analyze and verify the Turing instability conditions on the large ER (Erd\"{o}s-R\'{e}nyi) random network with the help of Turing stability theory and numerical experiments, and obtain the Turing instability region. The results show that the diffusion coefficient plays a decisive role in the generation of patterns, and it is interesting that the appropriate initial value will also bring beautiful patterns. When we analyze the model based on the network framework, we find that the average degree of the network has an important impact on the model, and different average degrees will lead to changes in the distribution pattern of the population.