A common task in experimental sciences is to fit mathematical models to real-world measurements to improve understanding of natural phenomenon (reverse-engineering or inverse modelling). When complex dynamical systems are considered, such as partial differential equations, this task may become challenging or ill-posed. In this work, a linear parabolic equation is considered as a model for protein transcription from MRNA. The objective is to estimate jointly the differential operator coefficients, namely the rates of diffusion and self-regulation, as well as a functional source. The recent Bayesian methodology for infinite dimensional inverse problems is applied, providing a unique posterior distribution on the parameter space continuous in the data. This posterior is then summarized using a Maximum a Posteriori estimator. Finally, the theoretical solution is illustrated using a state-of-the-art MCMC algorithm adapted to this non-Gaussian setting.

Models of evolution by natural selection often make the simplifying assumption that populations are infinitely large. In this infinite population limit, rare mutations that are selected against always go extinct, whereas in finite populations they can persist and even reach fixation. Nevertheless, for mutations of arbitrarily small phenotypic effect, it is widely believed that in sufficiently large populations, if selection opposes the invasion of rare mutants, then it also opposes their fixation. Here, we identify circumstances under which infinite-population models do or do not accurately predict evolutionary outcomes in large, finite populations. We show that there is no population size above which considering only invasion generally suffices: for any finite population size, there are situations in which selection opposes the invasion of mutations of arbitrarily small effect, but favours their fixation. This is not an unlikely limiting case; it can occur when fitness is a smooth function of the evolving trait, and when the selection process is biologically sensible. Nevertheless, there are circumstances under which opposition of invasion does imply opposition of fixation: in fact, for the [Formula: see text]-player snowdrift game (a common model of cooperation) we identify sufficient conditions under which selection against rare mutants of small effect precludes their fixation-in sufficiently large populations-for any selection process. We also find conditions under which-no matter how large the population-the trait that fixes depends on the selection process, which is important because any particular selection process is only an approximation of reality.

Honey bees make decisions regarding foraging and nest-site selection in groups ranging from hundreds to thousands of individuals. To effectively make these decisions, bees need to communicate within a spatially distributed group. However, the spatiotemporal dynamics of honey bee communication have been mostly overlooked in models of collective decisions, focusing primarily on mean field models of opinion dynamics. We analyze how the spatial properties of the nest or hive, and the movement of individuals with different belief states (uncommitted or committed) therein affect the rate of information transmission using spatially-extended models of collective decision-making within a hive. Honeybees waggle-dance to recruit conspecifics with an intensity that is a threshold nonlinear function of the waggler concentration. Our models range from treating the hive as a chain of discrete patches to a continuous line (long narrow hive). The combination of population-thresholded recruitment and compartmentalized populations generates tradeoffs between rapid information propagation with strong population dispersal and recruitment failures resulting from excessive population diffusion and also creates an effective colony-level signal-detection mechanism whereby recruitment to low quality objectives is blocked.

The method of administration of an effective drug treatment to eradicate viruses within a host is an important issue in studying viral dynamics. Overuse of a drug can lead to deleterious side effects, and overestimating the efficacy of a drug can result in failure to treat infection. In this study, we proposed a reaction-diffusion within-host virus model which incorporated information regarding spatial heterogeneity, drug treatment, and the intracellular delay to produce productively infected cells and viruses. We also calculated the basic reproduction number [Formula: see text] under the assumptions of spatial heterogeneity. We have shown that the infection-free periodic solution is globally asymptotically stable when [Formula: see text], whereas when [Formula: see text] there is an infected periodic solution and the infection is uniformly persistent. By conducting numerical simulations, we also revealed the effects of various parameters on the value of [Formula: see text]. First, we showed that the dependence of [Formula: see text] on the intracellular delay could be monotone or non-monotone, depending on the death rate of infected cells in the immature stage. Second, we found that the mobility of infected cells or virions could facilitate the virus clearance. Third, we found that the spatial fragmentation of the virus environment enhanced viral infection. Finally, we showed that the combination of spatial heterogeneity and different sets of diffusion rates resulted in complicated viral dynamic outcomes.

Spatially distributed populations with two sexes may face the problem that males and females concentrate in different parts of the habitat and mating and reproduction does not happen sufficiently often for the population to persist. For simplicity, to explore the impact of sex-dependent dispersal on population survival, we consider a discrete-time model for a semelparous population where individuals reproduce only once in their life-time, during a very short reproduction season. The dispersal of females and males is modeled by Feller kernels and the mating by a homogeneous pair formation function. The spectral radius of a homogeneous operator is established as basic reproduction number of the population, [Formula: see text]. If [Formula: see text], the extinction state is locally stable, and if [Formula: see text] the population shows various degrees of persistence that depend on the irreducibility properties of the dispersal kernels. Special cases exhibit how sex-biased dispersal affects the persistence of the population.

The goal of this article is to contribute towards the conceptual and quantitative understanding of the evolutionary benefits for (microbial) populations to maintain a seed bank consisting of dormant individuals when facing fluctuating environmental conditions. To this end, we discuss a class of '2-type' branching processes describing populations of individuals that may switch between 'active' and 'dormant' states in a random environment oscillating between a 'healthy' and a 'harsh' state. We incorporate different switching strategies and suggest a method of 'fair comparison' to incorporate potentially varying reproductive costs. We then use this concept to compare the fitness of the different strategies in terms of maximal Lyapunov exponents. This gives rise to a 'fitness map' depicting the environmental regimes where certain switching strategies are uniquely supercritical.

For classic Lotka-Volterra systems governing many interacting species, we establish an exclusion principle that rules out the existence of linearly asymptotically stable steady states in subcommunities of communities that admit a stable state which is internally D-stable. This type of stability is known to be ensured, e.g., by diagonal dominance or Volterra-Lyapunov stability conditions. By consequence, the number of stable steady states of this type is bounded by Sperner's lemma on anti-chains in a poset. The number of stable steady states can nevertheless be very large if there are many groups of species that strongly inhibit outsiders but have weak interactions among themselves. By examples we also show that in general it is possible for a stable community to contain a stable subcommunity consisting of a single species. Thus a recent empirical finding to the contrary, in a study of random competitive systems by Lischke and Löffler (Theor Popul Biol 115:24-34, 2017), does not hold without qualification.