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Register a new userHow the interplay of dormancy and selection affects the wave of advance of an advantageous gene
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In this paper we investigate the spread of advantageous genes in two variants of the F-KPP model with dormancy. The first variant, in which dormant individuals do not move in space and instead form localized seed banks, has recently been introduced in Blath, Hammer and Nie (2020). However, there, only a relatively crude upper bound for the critical speed of potential travelling wave solutions has been provided. The second model variant is new and describes a situation in which the dormant forms of individuals are subject to motion, while the active individuals remain spatially static instead. This can be motivated e.g. by spore dispersal of fungi, where the dormant spores are distributed by wind, water or insects, while the active fungi are locally fixed. For both models, we establish the existence of monotone travelling wave solutions, determine the corresponding critical wave-speed in terms of the model parameters, and characterize aspects of the asymptotic shape of the waves depending on the decay properties of the initial condition. Interestingly, the slow-down effect of dormancy on the speed of propagation of beneficial alleles is often more serious in model variant II (the spore model) than in variant I (the seed bank model), and this can be understood mathematically via probabilistic representations of solutions in terms of (two variants of) on/off branching Brownian motions. Our proofs make rather heavy use of probabilistic tools in the tradition of McKean (1975), Bramson (1978), Neveu (1987), Lalley and Sellke (1987), Champneys et al (1995) and others. However, the two-compartment nature of the model and the special forms of dormancy also pose obstacles to the classical formalism, giving rise to a variety of open research questions that we briefly discuss at the end of the paper.
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Our models for detecting the effect of adaptation on population genomic diversity are often predicated on a single newly arisen mutation sweeping rapidly to fixation. However, a population can also adapt to a new situation by multiple mutations of similar phenotypic effect that arise in parallel. These mutations can each quickly reach intermediate frequency, preventing any single one from rapidly sweeping to fixation globally (a soft sweep). Here we study models of parallel mutation in a geographically spread population adapting to a global selection pressure. The slow geographic spread of a selected allele can allow other selected alleles to arise and spread elsewhere in the species range. When these different selected alleles meet, their spread can slow dramatically, and so form a geographic patchwork which could be mistaken for a signal of local adaptation. This random spatial tessellation will dissipate over time due to mixing by migration, leaving a set of partial sweeps within the global population. We show that the spatial tessellation initially formed by mutational types is closely connected to Poisson process models of crystallization, which we extend. We find that the probability of parallel mutation and the spatial scale on which parallel mutation occurs is captured by a single characteristic length that reflects the expected distance a spreading allele travels before it encounters a different spreading allele. This characteristic length depends on the mutation rate, the dispersal parameter, the effective local density of individuals, and to a much lesser extent the strength of selection. We argue that even in widely dispersing species, such parallel geographic sweeps may be surprisingly common. Thus, we predict, as more data becomes available, many more examples of intra-species parallel adaptation will be uncovered.
We investigate the interplay between two fundamental mechanisms of microbial population dynamics and evolution called dormancy and horizontal gene transfer. The corresponding traits come in many guises and are ubiquitous in microbial communities, affecting their dynamics in important ways. Recently, they have each moved (separately) into the focus of stochastic individual-based modelling (Billiard et al. 2016, 2018; Champagnat, Meleard and Tran, 2021; Blath and Tobias 2020). Here, we examine their combined effects in a unified model. Indeed, we consider the (idealized) scenario of two sub-populations, respectively carrying trait 1 and trait 2, where trait 1 individuals are able to switch (under competitive pressure) into a dormant state, and trait 2 individuals are able to execute horizontal gene transfer, turning trait 1 individuals into trait 2 ones, at a rate depending on the frequency of individuals. In the large-population limit, we examine the fate of a single trait i individual (a mutant) arriving in a trait j resident population living in equilibrium, for $i,j=1,2,i eq j$. We provide a complete analysis of the invasion dynamics in all cases where the resident population is individually fit and the initial behaviour of the mutant population is non-critical. We identify parameter regimes for the invasion and fixation of the new trait, stable coexistence of the two traits, and founder control (where the initial resident always dominates, irrespective of its trait). The most striking result is that stable coexistence occurs in certain scenarios even if trait 2 (which benefits from transfer at the cost of trait 1) would be unfit when being merely on its own. In the case of founder control, the limiting dynamical system has an unstable coexistence equilibrium. In all cases, we observe the classical (up to 3) phases of invasion dynamics `a la Champagnat (2006).
It has been hypothesized that label smoothing can reduce overfitting and improve generalization, and current empirical evidence seems to corroborate these effects. However, there is a lack of mathematical understanding of when and why such empirical improvements occur. In this paper, as a step towards understanding why label smoothing is effective, we propose a theoretical framework to show how label smoothing provides in controlling the generalization loss. In particular, we show that this benefit can be precisely formulated and identified in the label noise setting, where the training is partially mislabeled. Our theory also predicts the existence of an optimal label smoothing point, a single value for the label smoothing hyperparameter that minimizes generalization loss. Extensive experiments are done to confirm the predictions of our theory. We believe that our findings will help both theoreticians and practitioners understand label smoothing, and better apply them to real-world datasets.
BACKGROUND: The uncoupling protein (UCP) genes belong to the superfamily of electron transport carriers of the mitochondrial inner membrane. Members of the uncoupling protein family are involved in thermogenesis and determining the functional evolution of UCP genes is important to understand the evolution of thermo-regulation in vertebrates. RESULTS: Sequence similarity searches of genome and scaffold data identified homologues of UCP in eutherians, teleosts and the first squamates uncoupling proteins. Phylogenetic analysis was used to characterize the family evolutionary history by identifying two duplications early in vertebrate evolution and two losses in the avian lineage (excluding duplications within a species, excluding the losses due to incompletely sequenced taxa and excluding the losses and duplications inferred through mismatch of species and gene trees). Estimates of synonymous and nonsynonymous substitution rates (dN/dS) and more complex branch and site models suggest that the duplication events were not associated with positive Darwinian selection and that the UCP is constrained by strong purifying selection except for a single site which has undergone positive Darwinian selection, demonstrating that the UCP gene family must be highly conserved. CONCLUSION: We present a phylogeny describing the evolutionary history of the UCP gene family and show that the genes have evolved through duplications followed by purifying selection except for a single site in the mitochondrial matrix between the 5th and 6th alpha-helices which has undergone positive selection.
In the present article, we investigate the effects of dormancy on an abstract population genetic level. We first provide a short review of seed bank models in population genetics, and the role of dormancy for the interplay of evolutionary forces in general, before we discuss two recent paradigmatic models, referring to spontaneous resp. simultaneous switching of individuals between the active and the dormant state. We show that both mechanisms give rise to non-trivial mathematical objects, namely the (continuous) seed bank diffusion and the seed bank diffusion with jumps, as well as their dual processes, the seed bank coalescent and the seed bank coalescent with simultaneous switching.
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