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Register a new userSpatially Inhomogeneous Populations with Seed-banks: II. Clustering Regime
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We consider a spatial version of the classical Moran model with seed-banks where the constituent populations have finite sizes. Individuals live in colonies labelled by $mathbb{Z}^d$, $d geq 1$, playing the role of a geographic space, and change type via $resampling$ as long as they are $active$. Each colony contains a seed-bank into which individuals can enter to become $dormant$, suspending their resampling until they exit the seed-bank and become active again. Individuals resample not only from their own colony, but also from other colonies according to a symmetric random walk transition kernel. The latter is referred to as $migration$. The sizes of the active and the dormant populations depend on the colony and remain constant throughout the evolution. It was shown in den Hollander and Nandan (2021) that the spatial system is well-defined, has a unique equilibrium that depends on the initial density of types, and exhibits a dichotomy between $clustering$ (mono-type equilibrium) and $coexistence$ (multi-type equilibrium). This dichotomy is determined by a clustering criterion that is given in terms of the dual of the system, which consists of a system of $interacting$ coalescing random walks. In this paper we provide an alternative clustering criterion, given in terms of an auxiliary dual that is simpler than the original dual, and identify the range of parameters for which the criterion is met, which we refer to as the $clustering regime$. It turns out that if the sizes of the active populations are non-clumping, i.e., do not take arbitrarily large values in finite regions of the geographic space, and the relative strengths of the seed-banks in the different colonies are bounded, then clustering prevails if and only if the symmetrised migration kernel is recurrent.
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We consider a system of interacting Moran models with seed-banks. Individuals live in colonies and are subject to resampling and migration as long as they are $active$. Each colony has a seed-bank into which individuals can retreat to become $dormant$, suspending their resampling and migration until they become active again. The colonies are labelled by $mathbb{Z}^d$, $d geq 1$, playing the role of a $geographic, space$. The sizes of the active and the dormant population are $finite$ and depend on the $location$ of the colony. Migration is driven by a random walk transition kernel. Our goal is to study the equilibrium behaviour of the system as a function of the underlying model parameters. In the present paper we show that, under mild condition on the sizes of the active population, the system is well-defined and has a dual. The dual consists of a system of $interacting$ coalescing random walks in an $inhomogeneous$ environment that switch between active and dormant. We analyse the dichotomy of $coexistence$ (= multi-type equilibria) versus $clustering$ (= mono-type equilibria), and show that clustering occurs if and only if two random walks in the dual starting from arbitrary states eventually coalesce with probability one. The presence of the seed-bank $enhances, genetic, diversity$. In the dual this is reflected by the presence of time lapses during which the random walks are dormant and do not move.
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 compare the long term behaviour of `1-type Bienayme-Galton-Watson branching processes (describing populations consisting of `active individuals only) with that of a class of `2-type branching processes, describing populations consisting of `active and `dormant individuals. All processes are embedded in an environment changing randomly between `harsh and `healthy conditions, affecting the reproductive behaviour of the populations accordingly. For the 2-type branching processes, we consider several different switching regimes between active and dormant states. We also impose overall resource limitations which incorporate the potentially different `production costs of active and dormant offspring, leading to the notion of `fair comparison between different populations, and allow for a reproductive trade-off due to the maintenance of the dormancy trait. Our switching regimes include the case where switches from active to dormant states and vice versa happen randomly, irrespective of the state of the environment (`spontaneous switching), but also the case where switches are triggered by the environment (`responsive switching), as well as combined strategies. It turns out that there are rather natural scenarios under which either switching strategy can be super-critical, while the others, as well as complete absence of a seed bank, are strictly sub-critical, even under `fair comparison wrt. available resources. In such a case, we see a clear selective advantage of the super-critical strategy, which is retained even under the presence of a (potentially small) reproductive trade-off. [...]
Across the tree of life, populations have evolved the capacity to contend with suboptimal conditions by engaging in dormancy, whereby individuals enter a reversible state of reduced metabolic activity. The resulting seed banks are complex, storing information and imparting memory that gives rise to multi-scale structures and networks spanning collections of cells to entire ecosystems. We outline the fundamental attributes and emergent phenomena associated with dormancy and seed banks, with the vision for a unifying and mathematically based framework that can address problems in the life sciences, ranging from global change to cancer biology.
Newly-discovered superconductor UTe$_2$ is a strong contender for a topological spin-triplet state wherein a multi-component order parameter arises from two nearly-degenerate superconducting states. A key issue is whether both of these states intrinsically exist at ambient pressure. Through thermal expansion and calorimetry, we show that UTe$_2$ at ambient conditions exhibits two detectable transitions only in some samples, and the size of the thermal expansion jump at each transition varies when the measurement is performed in different regions of the sample. This result indicates that the two transitions arise from two spatially separated regions that are inhomogeneously mixed throughout the volume of the sample, each with a discrete superconducting transition temperature (T$_c$). Notably, samples with higher T$_c$ only show a single transition at ambient pressure. Above 0.3 GPa, however, two transitions are invariably observed in ac calorimetry. Our results not only point to a nearly vertical line in the pressure-temperature phase diagram but also provide a unified scenario for the sample dependence of UTe$_{2}$.
We investigate the behaviour of the genealogy of a Wright-Fisher population model under the influence of a strong seed-bank effect. More precisely, we consider a simple seed-bank age distribution with two atoms, leading to either classical or long genealogical jumps (the latter modeling the effect of seed-dormancy). We assume that the length of these long jumps scales like a power $N^beta$ of the original population size $N$, thus giving rise to a `strong seed-bank effect. For a certain range of $beta$, we prove that the ancestral process of a sample of $n$ individuals converges under a non-classical time-scaling to Kingmans $n-$coalescent. Further, for a wider range of parameters, we analyze the time to the most recent common ancestor of two individuals analytically and by simulation.
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