Dynamic maximum entropy provides accurate approximation of structured population dynamics.

Realistic models of biological processes typically involve interacting components on multiple scales, driven by changing environment and inherent stochasticity. Such models are often analytically and numerically intractable. We revisit a dynamic maximum entropy method that combines a static maximum entropy with a quasi-stationary approximation.

Emerging algebraic growth trends in SARS-CoV-2 pandemic data.

We study the reported data from the SARS-CoV-2 pandemic outbreak in January-May 2020 in 119 countries. We observe that the time series of active cases in individual countries (the difference of the total number of confirmed infections and the sum of the total number of reported deaths and recovered cases) display a strong agreement with algebraic growth and at a later epidemic stage also with a combined algebraic growth with exponential decay. Our results are also formulated in terms of compartment-type mathematical models of epidemics.

Evolutionary Pathways for the Generation of New Self-Incompatibility Haplotypes in a Nonself-Recognition System.

Self-incompatibility (SI) is a genetically based recognition system that functions to prevent self-fertilization and mating among related plants. An enduring puzzle in SI is how the high diversity observed in nature arises and is maintained. Based on the underlying recognition mechanism, SI can be classified into two main groups: self-recognition (SR) and nonself-recognition (NSR).

Probabilistic models of individual and collective animal behavior.

Recent developments in automated tracking allow uninterrupted, high-resolution recording of animal trajectories, sometimes coupled with the identification of stereotyped changes of body pose or other behaviors of interest. Analysis and interpretation of such data represents a challenge: the timing of animal behaviors may be stochastic and modulated by kinematic variables, by the interaction with the environment or with the conspecifics within the animal group, and dependent on internal cognitive or behavioral state of the individual. Existing models for collective motion typically fail to incorporate the discrete, stochastic, and internal-state-dependent aspects of behavior, while models focusing on individual animal behavior typically ignore the spatial aspects of the problem.

A General Approximation for the Dynamics of Quantitative Traits.

Selection, mutation, and random drift affect the dynamics of allele frequencies and consequently of quantitative traits. While the macroscopic dynamics of quantitative traits can be measured, the underlying allele frequencies are typically unobserved. Can we understand how the macroscopic observables evolve without following these microscopic processes? This problem has been studied previously by analogy with statistical mechanics: the allele frequency distribution at each time point is approximated by the stationary form, which maximizes entropy.

Mathematical model of alternative mechanism of telomere length maintenance.

Biopolymer length regulation is a complex process that involves a large number of biological, chemical, and physical subprocesses acting simultaneously across multiple spatial and temporal scales. An illustrative example important for genomic stability is the length regulation of telomeres-nucleoprotein structures at the ends of linear chromosomes consisting of tandemly repeated DNA sequences and a specialized set of proteins. Maintenance of telomeres is often facilitated by the enzyme telomerase but, particularly in telomerase-free systems, the maintenance of chromosomal termini depends on alternative lengthening of telomeres (ALT) mechanisms mediated by recombination.