Prof. Dr. Maite Wilke Berenguer
Profil
Forschungsthemen6
AA3-18 "Evolution Processes for Populations and Economic Agents"
Quelle ↗Förderer: DFG Exzellenzstrategie Cluster Zeitraum: 04/2024 - 12/2025 Projektleitung: Prof. Dr. Maite Wilke Berenguer
Deutsch-französisches Graduiertenkolleg: Statistisches Lernen für komplexe stochastische Prozesse/ Apprentissage statistique pour des processus stochastiques complexes
Quelle ↗Förderer: Deutsch-Französische Hochschule Zeitraum: 01/2025 - 12/2028 Projektleitung: Prof. Dr. Maite Wilke Berenguer
EXC 2046/1:TP EF4-7 The impact of dormancy on the evolutionary, ecological and pathogenic properties
Quelle ↗Förderer: DFG Exzellenzstrategie Cluster Zeitraum: 04/2021 - 03/2023 Projektleitung: Prof. Dr. Maite Wilke Berenguer
IGRK 2544: Stochastische Analysis in Interaktion
Quelle ↗Förderer: DFG Graduiertenkolleg Zeitraum: 04/2020 - 03/2029 Projektleitung: Prof. Dr. Peter Bank, Terry Lyons Ph.D.
SFB/TRR 388/1: „Ruhende Populationen in heterogenen Zufallsumgebungen” (TP A09)
Quelle ↗Förderer: DFG Sonderforschungsbereich Zeitraum: 10/2024 - 06/2028 Projektleitung: Prof. Dr. Maite Wilke Berenguer
SFB/TRR 388/1: „Statistik für Bevölkerungsmodelle mit stochastischen (partiellen) Verzögerungsdifferentialgleichungen“ (TP B07)
Quelle ↗Förderer: DFG Sonderforschungsbereich Zeitraum: 10/2024 - 06/2028 Projektleitung: Prof. Dr. Markus Reiß, Prof. Dr. Maite Wilke Berenguer
Mögliche Industrie-Partner10
Stand: 26.4.2026, 19:48:44 (Top-K=20, Min-Cosine=0.4)
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Publikationen25
Top 25 nach Zitationen — Quelle: OpenAlex (BAAI/bge-m3 embedded für Matching).
Nature Communications · 109 Zitationen · DOI
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.
The Annals of Applied Probability · 60 Zitationen · DOI
We identify a new natural coalescent structure, which we call the seed-bank coalescent, that describes the gene genealogy of populations under the influence of a strong seed-bank effect, where “dormant forms” of individuals (such as seeds or spores) may jump a significant number of generations before joining the “active” population. Mathematically, our seed-bank coalescent appears as scaling limit in a Wright–Fisher model with geometric seed-bank age structure if the average time of seed dormancy scales with the order of the total population size $N$. This extends earlier results of Kaj, Krone and Lascoux [J. Appl. Probab. 38 (2011) 285–300] who show that the genealogy of a Wright–Fisher model in the presence of a “weak” seed-bank effect is given by a suitably time-changed Kingman coalescent. The qualitatively new feature of the seed-bank coalescent is that ancestral lineages are independently blocked at a certain rate from taking part in coalescence events, thus strongly altering the predictions of classical coalescent models. In particular, the seed-bank coalescent “does not come down from infinity,” and the time to the most recent common ancestor of a sample of size $n$ grows like $\log\log n$. This is in line with the empirical observation that seed-banks drastically increase genetic variability in a population and indicates how they may serve as a buffer against other evolutionary forces such as genetic drift and selection.
Genetics · 37 Zitationen · DOI
We analyze patterns of genetic variability of populations in the presence of a large seedbank with the help of a new coalescent structure called the seedbank coalescent. This ancestral process appears naturally as a scaling limit of the genealogy of large populations that sustain seedbanks, if the seedbank size and individual dormancy times are of the same order as those of the active population. Mutations appear as Poisson processes on the active lineages and potentially at reduced rate also on the dormant lineages. The presence of "dormant" lineages leads to qualitatively altered times to the most recent common ancestor and nonclassical patterns of genetic diversity. To illustrate this we provide a Wright-Fisher model with a seedbank component and mutation, motivated from recent models of microbial dormancy, whose genealogy can be described by the seedbank coalescent. Based on our coalescent model, we derive recursions for the expectation and variance of the time to most recent common ancestor, number of segregating sites, pairwise differences, and singletons. Estimates (obtained by simulations) of the distributions of commonly employed distance statistics, in the presence and absence of a seedbank, are compared. The effect of a seedbank on the expected site-frequency spectrum is also investigated using simulations. Our results indicate that the presence of a large seedbank considerably alters the distribution of some distance statistics, as well as the site-frequency spectrum. Thus, one should be able to detect from genetic data the presence of a large seedbank in natural populations.
Ergodic Theory and Dynamical Systems · 36 Zitationen · DOI
We consider random dynamical systems generated by a special class of Volterra quadratic stochastic operators on the simplex $S^{m-1}$ . We prove that in contrast to the deterministic set-up the trajectories of the random dynamical system almost surely converge to one of the vertices of the simplex $S^{m-1}$ , implying the survival of only one species. We also show that the minimal random point attractor of the system equals the set of all vertices. The convergence proof relies on a martingale-type limit theorem, which we prove in the appendix.
Mathematical Biosciences · 31 Zitationen · DOI
Journal of Mathematical Biology · 14 Zitationen · DOI
arXiv (Cornell University) · 8 Zitationen · DOI
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.
Electronic Journal of Probability · 6 Zitationen · DOI
Consider a population evolving from year to year through three seasons: spring, summer and winter. Every spring starts with N dormant individuals waking up independently of each other according to a given distribution. Once an individual is awake, it starts reproducing at a constant rate. By the end of spring, all individuals are awake and continue reproducing independently as Yule processes during the whole summer. In the winter, N individuals chosen uniformly at random go to sleep until the next spring, and the other individuals die. We show that because an individual that wakes up unusually early can have a large number of surviving descendants, for some choices of model parameters the genealogy of the population will be described by a Λ-coalescent. In particular, the beta coalescent can describe the genealogy when the rate at which individuals wake up increases exponentially over time. We also characterize the set of all Λ-coalescents that can arise in this framework.
The Annals of Applied Probability · 5 Zitationen · DOI
We analyse a family of two-types Wright–Fisher models with selection in a random environment and skewed offspring distribution. We provide a calculable criterion to quantify the impact of different shapes of selection on the fate of the weakest allele, and thus compare them. The main mathematical tool is duality, which we prove to hold, also in presence of random environment (quenched and in some cases annealed), between the population’s allele frequencies and genealogy, both in the case of finite population size and in the scaling limit for large size. Duality also yields new insight on properties of branching-coalescing processes in random environment, such as their long-term behaviour.
Theoretical Population Biology · 4 Zitationen · DOI
In this paper, we investigate the consequences of dormancy in the 'rare mutation' and 'large population' regime of stochastic adaptive dynamics. Starting from an individual-based micro-model, we first derive the Polymorphic Evolution Sequence of the population, based on a previous work by Baar and Bovier (2018). After passing to a second 'small mutations' limit, we arrive at the Canonical Equation of Adaptive Dynamics, and state a corresponding criterion for evolutionary branching, extending a previous result of Champagnat and Méléard (2011). The criterion allows a quantitative and qualitative analysis of the effects of dormancy in the well-known model of Dieckmann and Doebeli (1999) for sympatric speciation. In fact, quite an intuitive picture emerges: Dormancy enlarges the parameter range for evolutionary branching, increases the carrying capacity and niche width of the post-branching sub-populations, and, depending on the model parameters, can either increase or decrease the 'speed of adaptation' of populations. Finally, dormancy increases diversity by increasing the genetic distance between subpopulations.
Electronic Journal of Probability · 3 Zitationen · DOI
We introduce a new Wright-Fisher type model for seed banks incorporating "simultaneous switching", which is motivated by recent work on microbial dormancy. We show that the simultaneous switching mechanism leads to a new jump-diffusion limit for the scaled frequency processes, extending the classical Wright-Fisher and seed bank diffusion limits. We further establish a new dual coalescent structure with multiple activation and deactivation events of lineages. While this seems reminiscent of multiple merger events in general exchangeable coalescents, it actually leads to an entirely new class of coalescent processes with unique qualitative and quantitative behaviour. To illustrate this, we provide a novel kind of condition for coming down from infinity for these coalescents using recent results of Griffiths.
arXiv (Cornell University) · 2 Zitationen · DOI
We analyse a family of two-types Wright-Fisher models with selection in a random environment and skewed offspring distribution. We provide a calculable criterion to quantify the impact of different shapes of selection on the fate of the weakest allele, and thus compare them. The main mathematical tool is duality, which we prove to hold, also in presence of random environment (quenched and in some cases annealed), between the population's allele frequencies and genealogy, both in the case of finite population size and in the scaling limit for large size. Duality also yields new insight on properties of branching-coalescing processes in random environment, such as their long term behaviour.
arXiv (Cornell University) · 2 Zitationen
We identify a new natural coalescent structure, the seed-bank coalescent, which describes the gene genealogy of populations under the influence of a strong seed-bank effect, where ‘dormant forms ’ of individuals (such as seeds or spores) may jump a significant number of generations before joining the ‘active ’ population. Mathematically, our seed-bank coalescent appears as scaling limit in a Wright-Fisher model with geometric seed-bank age structure if the average time of seed dormancy scales with the order of the total population size N. This extends earlier results of Kaj, Krone and Lascaux (2001) who show that the genealogy of a Wright-Fisher model in the presence of a ‘weak ’ seed-bank effect is given by a suitably time-changed Kingman coalescent. The qualitatively new feature of the seed-bank coalescent is that ancestral lineages are independently blocked at a certain rate from taking part in coalescence events, thus strongly altering the predictions of classical coalescent models. In particular, the seed-bank coalescent ‘does not come down from infinity’, and the time to the most recent common ancestor of a sample of size n grows like log log n, which is the order also observed for the Bolthausen-Sznitman coalescent. This is in line with the empirical ob-servation that seed-banks drastically increase genetic variability in a population and indicates how they may serve as a buffer against other evolutionary forces such as genetic drift and selection.
arXiv (Cornell University) · 1 Zitationen · DOI
In this paper, we investigate the consequences of dormancy in the `rare mutation' and `large population' regime of stochastic adaptive dynamics. Starting from an individual-based micro-model, we first derive the polymorphic evolution sequence of the population, based on previous work by Baar and Bovier (2018). After passing to a second `small mutations' limit, we arrive at the canonical equation of adaptive dynamics, and state a corresponding criterion for evolutionary branching, extending a previous result of Champagnat and Méléard (2011). The criterion allows a quantitative and qualitative analysis of the effects of dormancy in the well-known model of Dieckmann and Doebeli (1999) for sympatric speciation. In fact, a quite intuitive picture merges: Dormancy enlarges the parameter range for evolutionary branching, increases the carrying capacity and niche width of the post-branching sub-populations, and, depending on the model parameters, can either increase or decrease the `speed of adaptation' of populations. Finally, dormancy increases diversity by increasing the genetic distance between subpopulations.
arXiv (Cornell University) · 1 Zitationen · DOI
Consider a population evolving from year to year through three seasons:\nspring, summer and winter. Every spring starts with $N$ dormant individuals\nwaking up independently of each other according to a given distribution. Once\nan individual is awake, it starts reproducing at a constant rate. By the end of\nspring, all individuals are awake and continue reproducing independently as\nYule processes during the whole summer. In the winter, $N$ individuals chosen\nuniformly at random go to sleep until the next spring, and the other\nindividuals die. We show that because an individual that wakes up unusually\nearly can have a large number of surviving descendants, for some choices of\nmodel parameters the genealogy of the population will be described by a\n$\\Lambda$-coalescent. In particular, the beta coalescent can describe the\ngenealogy when the rate at which individuals wake up increases exponentially\nover time. We also characterize the set of all $\\Lambda$-coalescents that can\narise in this framework.\n
Discrete and Continuous Dynamical Systems - B · 1 Zitationen · DOI
Global random attractors and random point attractors for random dynamical systems have been studied for several decades. Here we introduce two intermediate concepts: Δ-Hausdorff-attractors are characterized by attracting all deterministic compact sets of Hausdorff dimension at most Δ, where Δ is a non-negative number, while cc-attractors attract all countable compact sets. We provide two examples showing that a given random dynamical system may have various different Δ-Hausdorff-attractors for different values of Δ. It seems that both concepts are new even in the context of deterministic dynamical systems.
arXiv (Cornell University) · 1 Zitationen · DOI
Global random attractors and random point attractors for random dynamical systems have been studied for several decades. Here we introduce two intermediate concepts: $Δ$-attractors are characterized by attracting all deterministic compact sets of Hausdorff dimension at most $Δ$, where $Δ$ is a non-negative number, while cc-attractors attract all countable compact sets. We provide two examples showing that a given random dynamical system may have various different $Δ$-attractors for different values of $Δ$. It seems that both concepts are new even in the context of deterministic dynamical systems.
arXiv (Cornell University) · 1 Zitationen
We investigate various aspects of the (biallelic) Wright-Fisher diffusion with seed bank, including moments, stationary distribution and reversibility, for which our main tool is duality. We also provide a complete boundary classification for this two-dimensional sde. Further, we show that the Wright-Fisher diffusion with seed bank can be reformulated as a one-dimensional stochastic delay differential equation, thus providing an elegant interpretation of the age structure in the seed bank. Finally, we investigate several scaling limits of the seed bank model and find a new coalescent-related ancestral process describing the genealogy in a `rare-resuscitation' regime over long timescales. Along the lines, we comment on the relation between the seed bank diffusion and the structured Wright-Fisher diffusion with two islands, which, despite their seeming similarity, exhibit remarkable qualitative differences.
arXiv (Cornell University) · 1 Zitationen · DOI
We investigate various aspects of the (biallelic) Wright-Fisher diffusion with seed bank in conjunction with and contrast to the two-island model analysed e.g. in Kermany, Zhou and Hickey, 2008, and Nath and Griffiths, 1993, including moments, stationary distribution and reversibility, for which our main tool is duality. Further, we show that the Wright-Fisher diffusion with seed bank can be reformulated as a one-dimensional stochastic delay differential equation, providing an elegant interpretation of the age structure in the seed bank also forward in time in the spirit of Kaj, Krone and Lascoux, 2001. We also provide a complete boundary classification for this two-dimensional SDE using martingale-based reasoning known as McKean's argument.
Electronic Journal of Probability · 1 Zitationen · DOI
We consider Lipschitz percolation in $d+1$ dimensions above planes tilted by an angle $γ$ along one or several coordinate axes. In particular, we are interested in the asymptotics of the critical probability as $d \to \infty$ as well as $γ\to π/4.$ Our principal results show that the convergence of the critical probability to 1 is polynomial as $d\to \infty$ and $γ\to π/4.$ In addition, we identify the correct order of this polynomial convergence and in $d=1$ we also obtain the correct prefactor.
bioRxiv (Cold Spring Harbor Laboratory) · 1 Zitationen · DOI
We analyse patterns of genetic variability of populations in the presence of a large seedbank with the help of a new coalescent structure called the seedbank coalescent. This ancestral process appears naturally as scaling limit of the genealogy of large populations that sustain seedbanks, if the seedbank size and individual dormancy times are of the same order as the active population. Mutations appear as Poisson processes on the active lineages, and potentially at reduced rate also on the dormant lineages. The presence of ‘dormant’ lineages leads to qualitatively altered times to the most recent common ancestor and non-classical patterns of genetic diversity. To illustrate this we provide a Wright-Fisher model with seedbank component and mutation, motivated from recent models of microbial dormancy, whose genealogy can be described by the seedbank coalescent. Based on our coalescent model, we derive recursions for the expectation and variance of the time to most recent common ancestor, number of segregating sites, pairwise differences, and singletons. Estimates (obtained by simulations) of the distributions of commonly employed distance statistics, in the presence and absence of a seedbank, are compared. The effect of a seedbank on the expected site-frequency spectrum is also investigated using simulations. Our results indicate that the presence of a large seedbank considerably alters the distribution of some distance statistics, as well as the site-frequency spectrum. Thus, one should be able to detect from genetic data the presence of a large seedbank in natural populations.
arXiv (Cornell University) · DOI
We introduce an individual-based model for structured populations undergoing demographic bottlenecks, i.e. drastic reductions in population size that last many generations and can have arbitrary shapes. We first show that the (non-Markovian) allele-frequency process converges to a Markovian diffusion process with jumps in a suitable relaxation of the Skorokhod J1 topology. Backward in time we find that genealogies of samples of individuals are described by multi-type $Ξ$-coalescents presenting multiple simultaneous mergers with simultaneous migrations. These coalescents are also moment-duals of the limiting jump diffusions. We then show through a numerical study that our model is flexible and can predict various shapes for the site frequency spectrum, consistent with real data, using a small number of interpretable parameters.
arXiv (Cornell University) · DOI
We consider two finite population Markov chain models, the two-island Wright-Fisher model with mutation, and the seed-bank model with mutation. Despite the relatively simple descriptions of the two processes, the the exact form of their stationary distributions is in general intractable. For each of the two models we provide two approximation theorems with explicit upper bounds on the distance between the stationary distributions of the finite population Markov chains, and either the stationary distribution of a two-island diffusion model, or the beta distribution. We show that the order of the bounds, and correspondingly the appropriate choice of approximation, depends upon the relative sizes of mutation and migration. In the case where migration and mutation are of the same order, the suitable approximation is the two-island diffusion model, and if migration dominates mutation, then the weighted average of both islands is well approximated by a beta random variable. Our results are derived from a new development of Stein's method for the stationary distribution of the two-island diffusion model for the weak migration results, and utilising the existing framework for Stein's method for the Dirichlet distribution.
Jahresbericht der Deutschen Mathematiker-Vereinigung · DOI
Journal of Mathematical Biology · DOI
We investigate scaling limits of the seed bank model when migration (to and from the seed bank) is 'slow' compared to reproduction. This is motivated by models for bacterial dormancy, where periods of dormancy can be orders of magnitude larger than reproductive times. Speeding up time, we encounter a separation of timescales phenomenon which leads to mathematically interesting observations, in particular providing a prototypical example where the scaling limit of a continuous diffusion will be a jump diffusion. For this situation, standard convergence results typically fail. While such a situation could in principle be attacked by the sophisticated analytical scheme of Kurtz (J Funct Anal 12:55-67, 1973), this will require significant technical efforts. Instead, in our situation, we are able to identify and explicitly characterise a well-defined limit via duality in a surprisingly non-technical way. Indeed, we show that moment duality is in a suitable sense stable under passage to the limit and allows a direct and intuitive identification of the limiting semi-group while at the same time providing a probabilistic interpretation of the model. We also obtain a general convergence strategy for continuous-time Markov chains in a separation of timescales regime, which is of independent interest.
Kooperationen7
Bestätigte Forscher↔Partner-Paare aus HU-FIS — Gold-Standard-Positive für das Matching.
SFB/TRR 388/1: „Ruhende Populationen in heterogenen Zufallsumgebungen” (TP A09)
university
SFB/TRR 388/1: „Ruhende Populationen in heterogenen Zufallsumgebungen” (TP A09)
university
IGRK 2544: Stochastische Analysis in Interaktion
university
Deutsch-französisches Graduiertenkolleg: Statistisches Lernen für komplexe stochastische Prozesse/ Apprentissage statistique pour des processus stochastiques complexes
university
Deutsch-französisches Graduiertenkolleg: Statistisches Lernen für komplexe stochastische Prozesse/ Apprentissage statistique pour des processus stochastiques complexes
university
Deutsch-französisches Graduiertenkolleg: Statistisches Lernen für komplexe stochastische Prozesse/ Apprentissage statistique pour des processus stochastiques complexes
university
IGRK 2544: Stochastische Analysis in Interaktion
other
Stammdaten
Identität, Organisation und Kontakt aus HU-FIS.
- Name
- Prof. Dr. Maite Wilke Berenguer
- Titel
- Prof. Dr.
- Fakultät
- Mathematisch-Naturwissenschaftliche Fakultät
- Institut
- Institut für Mathematik
- Arbeitsgruppe
- Interdisziplinäre Mathematik (J)
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- +49 30 2093-45499
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