Mathematical Models of Evolutionary Rescue

5 Jun 2023, 16:00 → 8 Jun 2023, 20:00 Europe/Berlin

IMPORTANT DATES

Registration deadline: 1 March, 2023

Symposium: 5-8 June, 2023

The symposium starts on June 5 at 5pm and ends on June 8 in the evening.

OVERVIEW

Evolution can rescue populations from extinction. In conservation this is desired, in medicine it is often not.

There has now been nearly 30 years of research under the banner of “evolutionary rescue”. A substantial proportion of this has been mathematical modelling. This theory has expanded from deterministic 1-locus and phenotypic models to incorporate complexities such as stochasticity, multiple loci, life-history, space, and interacting species.

The goal of this symposium is to bring together theoreticians working on a wide range of rescue models — from 1-locus to infinite-loci, from conservation to medicine — to synthesize what we already know and to identify key knowledge gaps.

In addition to invited and contributed talks and posters there will be “pitched discussions” on specific topics, designed to motivate and direct the future of evolutionary rescue theory.

INVITED SPEAKERS

Peter Czuppon (University of Münster)

Florence Débarre (Institute of Ecology and Environmental Sciences Paris)

Richard Gomulkiewicz (Washington State University)

Guillaume Martin (Institut des Sciences de l’Évolution de Montpellier)

Ophélie Ronce (Institut des Sciences de l’Évolution de Montpellier)

Lindi Wahl (Western University)

Masato Yamamichi (University of Queensland)

APPLICATION & REGISTRATION

Participants do not have to contribute a talk or poster. However, if you do not submit an abstract please briefly state your motivation for participating (max. 250 words) in the appropriate field. The number of participants is limited. Applicants will be notified about acceptance by March 8.

Registration is free. However, you need to pay for your own travel and accommodation. If you do not have sufficient funds to cover these expenses, please provide some information (including estimated gaps in funding) in the respective field upon registration. We may be able to subsidize travel in exceptional cases.

CONTACT

Please contact the organizers, Hildegard Uecker (uecker@evolbio.mpg.de) and Matthew Osmond (mm.osmond@utoronto.ca), if you have any questions.

Monday, 5 June

16:00 → 17:00 Check-In

17:00 → 18:00 Fingerfood & Drinks

18:00 → 19:00 Keynote: Plenary Talk by Robert Holt in memory of Richard Gomulkiewicz

18:00 Demographic and genetic constraints on adaptation to environmental change due to ecological interactions

If an environmental change is severe enough that local conditions are no longer within a species’ ecological persistence limits, populations must evolve in order to locally persist. Most species do not live in isolation and interactions with other species may help or hinder their ability to persist in a variety of ways. Previous studies have focused on the demographic effects of ecological interactions on adaption to environmental change. We extend this work by exploring the effects of genetic correlations between the traits involved in ecological interactions and those responding to abiotic environmental change. Using a multivariate quantitative genetic model, we show that genetic correlation can at times hinder adaptation and persistence following an environmental change, regardless of whether the ecological interaction is negative (e.g., predation) or positive (e.g., facilitation). Furthermore, we show that, given strong genetic correlations, increased facilitator density can actually decrease focal species persistence by slowing the rate of adaptation to abiotic change. Ecological facilitators can thus at times be evolutionary antagonists.

Speaker: Robert Holt (University of Florida)

Tuesday, 6 June

09:30 → 10:30 Keynote: Guillaume Martin

09:30 Evolutionary rescue on fitness landscapes

Random mutant data suggest that the genetic basis for changes in vital rates (survival, fecundity, birth and death rates) is typically very wide: most random mutations, everywhere in the genome, have an effect on these life history traits. However, most stochastic models of ER are only manageable with a narrow basis (one resistant genotype per ER
trajectory). I will present past and present work where we explore models where ER occurs with a wide large or arbitrary genetic basis, on fitness landscapes. In this approach, vital rates are determined by some underlying multivariate phenotype, with an environment specific optimum.
A change in environment induces a shift in the optimum for these rates, strong enough that the mean fitness is initially negative. I will use simple diffusion limits for stochastic population size in such models and show how we can take advantage of these diffusions to describe ER
analytically in this context.

Speaker: Guillaume Martin (Université Montpellier)

10:30 → 14:00 Posters

Please find the poster abstracts here, sort for posters: https://workshops.evolbio.mpg.de/event/82/contributions/

12:30 Lunch

14:00 → 15:00 Keynote: Keynote Peter Czuppon

14:00 Keynote Peter Czuppon

Models of evolutionary rescue are predominantly applied in two fields:
conservation biology, ecology and epidemiology. We are presenting two models using branching processes that cover these two fields of application.
First, we study the probability of adaptation and evolutionary rescue in a spatially structured environment. A common assumption of spatial models is that emigrating individuals are distributed uniformly among
patches. Empirical studies do not support this dispersal scheme, but instead often find non-uniform dispersal schemes like matching habitat choice, where individuals preferentially immigrate into patches they are best adapted to. Implementing non-random dispersal schemes into models of local adaptation or evolutionary rescue reveals substantial differences to the uniform dispersal scheme. In our model, patches
change their local environment from 'good' to 'bad' over time. The wild type has a negative growth rate in bad environments so that the population will go extinct if it fails to adapt. We find that the probability of evolutionary rescue depends on the interplay between demography and local fitness. When increasing the dispersal rate, the relative importance of demographic effects increases compared to the effect from adaptation to the local environment. In dispersal regions where demographic effects dominate, we find that matching habitat choice
reduces the probability of evolutionary rescue when compared to the uniform dispersal scheme, and vice versa for dispersal rates where the effect of local adaptation is dominant.
In our second model, we study the evolution of antibiotic resistance.
Experimental and theoretical studies have investigated the drug dose that minimizes the risk of resistance evolution over the course of treatment of an individual, showing that the minimizing dose will either be the highest or the lowest drug concentration possible to administer.
However, no analytical results exist that help decide between these two extremes. To address this gap, we develop a stochastic mathematical model of bacterial within-host dynamics under antibiotic treatment. We explore various scenarios of density regulation (bacterial density affects cell birth or death rates), and antibiotic modes of action (biostatic or biocidal). We derive analytical results for the survival probability of the resistant subpopulation until the end of treatment,
which is the probability of evolutionary rescue when viewed from the point of view of the bacterial colony. The analytical solution of the survival probability allows the derivation of conditions for the concentration that maximizes the risk of resistance evolution.

Speaker: Peter Czuppon (Universität Münster)

15:00 → 15:30 Talk: Léonard Dekens

15:00 Sharp habitat switches, tipping points and evolutionary rescue: the perilous path of a specialist species toward refugium

Over the last decades, numerous studies have begun documenting the impacts of climate deregulation on species ranges. Among them, specialists, which thrive under specific environmental conditions, typically in narrow geographic ranges, are widely recognised as one of the most threatened categories. Many might rely on both their potential to adapt and on the existence of an environmental refugium to reach to avoid extinction. It is thus crucial to understand the influence of environmental conditions on the unfolding process of adaptation. Here, I study the eco-evolutionary dynamics of a sexually reproducing specialist species in a two-patch quantitative genetic model with moving optima. Aligning with previous theoretical studies, I first derive the critical environmental speed beyond which the environment changes too fast for the species persistance. This quantity reflects how much the existence of a refugium can delay extinction. Moreover, my analysis provides key quantitative insights about the sharp dynamics that arise on the path towards this refugium. I show that after an initial increase of population size, there exists a lower critical environmental speed for which the species crosses a tipping point, resulting into an abrupt habitat switch. Besides, when selection for local adaptation is relatively strong, this habitat switch passes through an evolutionary “death valley”, from where a small portion of the population can get rescued by adapting fast enough to the local conditions of the refugium. This work highlights in particular how evolutionary rescue can occur from a small standing variation in sexually reproducing species and highly fragmented environments.

Speaker: Léonard Dekens (MAP5, University Paris-Cité)

15:30 → 16:00 Coffee Break

16:00 → 17:00 Talk: Ian Dewan, Remus Stana

16:00 Rescue of bacterial populations by plasmid-mediated heterozygosity

Bacterial plasmids and other extra-chromosomal DNA elements frequently carry genes that have important effects on the fitness of their hosts. Because plasmids often exist in the bacterial cell in multiple copies, different plasmid copies can carry distinct alleles, allowing for heterozygosity not possible for loci on haploid chromosomes. This plasmid-mediated heterozygosity may increase the fitness of bacterial cells in circumstances where there is an advantage to having multiple distinct alleles (heterozypgote advantage); for example, plasmid-mediated heterozygosity of antibiotic resistance alleles can produce multidrug resistance, in which a single bacterial strain is resistant to multiple antibiotics, a serious problem in the clinical context. However, plasmid-mediated heterozygosity is also subject to constant loss due to random segregation of plasmids on cell division: each division has some probability of producing a homozygous daughter cell. We present a model of the rescue of a bacterial population by the establishment of a novel (mutant) allele on a plasmid in a heterozygote advantage scenario. We derive the minimum threshold on the selective advantage of heterozygotes required to overcome segregative loss and make rescue possible; this threshold decreases with increasing copy number of the plasmid. We further show that the formation of cointegrates from the fusion of plasmids increases the probability of rescue, as distinct alleles on cointegrated plasmids are no longer subject to stochastic loss. These results contribute to understanding both the contribution of the evolution of plasmid-level traits, such as copy number, to bacterial evolution and the evolution of antibiotic resistance in complex selective environments.

Speaker: Ian Dewan (MPI for Evolutionary Biology)

16:30 Modelling the effect of aneuploidy on cancer evolution

A prime example of evolutionary rescue is the ability of cancer cells to survive treatment. Aneuploidy, the state of abnormal number of chromosomes in the cell, is hypothesized to increase fitness in the presence of anti-cancer drugs, e.g. due to incomplete pathways targeted by drugs. Aneuploidy is highly prevalent in tumours, and certain anti-cancer drugs attempt to combat cancer by increasing chromosomal instability. Here, we focus on the impact of aneuploidy on the fate of a population of cancer cells. We analysed an evolutionary model in which a population of cancer cells adapt to chemotherapy, focusing on the role of aneuploidy in the evolutionary rescue of the population. We use multi-type branching processes to analyse a two-step evolutionary rescue model, where aneuploidy has intermediate fitness between the sensitive wildtype and the resistant mutant. We estimated the probability that the cancer cell population will survive, how it is affected by the population size, the strength of selection imposed by the drug, and the rate of chromosome gain and validated our results using stochastic simulations. We observe that aneuploidy increases the probability of evolutionary rescue even when it is deleterious. We conclude that aneuploidy can play an important role in helping cancer cell populations escape the effects of treatment.

Speaker: Remus Stana (Tel Aviv University)

17:00 → 18:00 Discussion: Pitched Discussion: What even is rescue?

18:00 → 19:00 Dinner

19:00 → 20:00 Discussion: Discussion & Wrap-up of the day

Wednesday, 7 June

09:30 → 10:30 Keynote: Keynote Linda Wahl

09:30 Evolutionary Rescue on Genotypic Landscapes Induced by Fisher's Geometric Model

(work with Paulo R. A. Campos, Universidade Federal de Pernambuco, Brazil)

By defining a discrete set of available mutation vectors, the mapping from trait vector to fitness provided by Fisher's Geometric Model (FGM) has been previously extended to a mapping from genotype to fitness. We examine evolutionary rescue across this genotypic landscape. We first
provide a simple derivation of the distribution of fitness effects for a phenotype at a given distance from the optimum, and use this to approximate the probability of evolutionary rescue via de novo mutation. Confirming our theoretical predictions with simulation, we also explore how the probability of evolutionary rescue in the genotypic model varies with distance from the optimum, mean mutational effect size, and the dimensionality of trait space. Unsurprisingly, rescue probability is reduced when genotypes are limited to a discrete number
of available mutations. Unlike other complex features of these
landscapes, however, the probability of rescue increases monotonically with genome length, and approaches the behaviour of the classical FGM as genome length approaches infinity.

Speaker: Linda Wahl (Western University Canada)

10:30 → 11:00 Coffee Break

11:00 → 12:30 Talk: Talk Carla A. Villalobos, Teemu Kuosmanen, Vrinda Ravi Kumar

11:00 Synergistic epistasis among cancer drivers can rescue early tumors from the accumulation of deleterious passengers

Cancer cells evolve from a normal tissue due to the accumulation of pro-tumor mutations, called drivers, that coexist together with thousands of other somatic mutations that do not promote cancer growth, named passengers. However, the existence of drivers in normal tissues has been reported, suggesting that isolated drivers alone are not enough to trigger the development of malignant phenotypes. In addition, epistasis between drivers has been widely observed in several recent studies, indicating a potential role on cancer dynamics. Furthermore, a wide variety of epistasis networks, from star-like to dense clique motifs, has been inferred from experimental data across different cancer types. By combining computer simulations and mathematical modelling, this work investigates the impact of cooperative epistasis networks on cancer dynamics. We describe and fully characterize a phenomenon of epistasis-driven evolutionary rescue that allows for cancer progression in conditions in which the acquisition of drivers alone would be insufficient to compensate for the mutational burden imposed by slightly deleterious passenger mutations. Studying the probability of triggering such rescue and the time at which it occurs we discovered that they are dependent on the mutation rate, the strength of such epistasis and the topology of the network. Ultimately, this translates into more unpredictable behaviors of tumor progression than expected in the absence of epistasis and it could help explaining the presence of drivers in non-tumoral tissues.

Speaker: Carla Alejandre Villalobos (Centro de Astrobiología, Consejo Superior de Investigaciones Científicas, Spain)

11:30 Establishment threshold and the inference of establishment rates along a concentration gradient

Evolution of drug resistance is contingent on sufficient mutational supply as well as successful establishment of the initially rare resistant cells that are subject to stochastic extinction. Importantly, the potential for resistance evolution strongly depends on the drug concentration that not only directly affects the strength of selection, but also impacts the required mutational targets, probability of establishment as well as the mutational processes that generate genetic and phenotypic variability. Quantifying the risk of drug resistance along a concentration gradient thus represents a highly important but challenging task, because this requires factoring in the various complex dose-dependencies none of which are easily empirically investigable. In this contribution we present a fitting method which allows the inference of dose-dependent establishment rates from evolutionary rescue data and present theory which can then be used to compute optimal treatment strategies. We also refine the concept of establishment threshold and discuss its implications for resistance evolution. References: [1] Kuosmanen T, Cairns J, Noble R, Beerenwinkel N, Mononen T, et al. (2021) Drug-induced resistance evolution necessitates less aggressive treatment. PLOS Computational Biology 17(9): e1009418. https://doi.org/10.1371/journal.pcbi.1009418 [2] Kuosmanen, T., Särkkä, S., & Mustonen, V. (2022). Turnover shapes evolution of birth and death rates. bioRxiv, 2022.07.11.499527; https://doi.org/10.1101/2022.07.11.499527 [3] Kuosmanen, T., Minetto, A. & Mustonen, V. (2023). Theory and inference of mutant establishment, under preperation

Speaker: Teemu Kuosmanen (University of Helsinki)

12:00 Reproductive traits and development correlate with adaptation during and after after rescue

Rapid and widespread environmental change worldwide has raised concern about the ability of natural populations to rapidly adapt to novel conditions. Ancestral population phenotypes and population dynamics should predict successful evolutionary rescue (and adaptation) - but which specific phenotypic traits and demographic events matter? Might different founding traits and demographic events explain adaptation to different environments? To answer these questions, we experimentally evolved 10 distinct wild-collected populations of the generalist red flour beetle Tribolium castaneum. From each population, we founded three replicate laboratory lines, selecting for performance on two resources - wheat flour (optimal ancestral resource) and corn (highly suboptimal novel resource). We measured a range of fitness-related traits in the ancestral populations and collected census data every generation for 70 generations during and after evolutionary rescue (vs the control). We find that adaptation to corn versus persistence in wheat flour involves contrasting population dynamics that are correlated with distinct ancestral and demographic parameters. While competitive success under high density predict population performance in wheat flour, rapid development and high reproductive success predicts rescue and population performance in corn flour. Early dynamics also predict subsequent recovery in corn, suggesting that demographic processes are important during and after rescue. Studying the real-time adaptive evolution of these lines across different habitats have allowed us to test a range of hypotheses that have not been tested in a single experimental system. These results bring us closer to making predictions about the adaptive potential of wild populations during major changes in their natural environment.

Speaker: Vrinda Ravi Kumar (Czech Academy of Sciences )

12:30 → 13:30 Lunch

13:30 → 14:30 Discussion: Pitches Discussion: What are the key testable predictions of rescue theory?

16:00 → 16:30 Boat trip

16:30 → 18:00 Discussion: Group Discussions

18:00 → 19:00 Dinner

19:00 → 20:00 Discussion: Group Discussions

Thursday, 8 June

09:30 → 10:30 Keynote: Keynote Ophélie Ronce

09:30 Evolutionary rescue and life history evolution

Most populations are heterogeneous, containing individuals in different stages that have different tolerances to environmental changes and different contributions to the evolutionary and demographic future of the population. Several theoretical studies have examined how this heterogeneity makes the probability of evolutionary rescue dependent on the life cycle in structured populations. These studies revealed in particular a fundamental trade-off between the speed of evolution and the demographic robustness affecting evolutionary rescue in populations
with a slow or fast pace of life. In this presentation, I will focus on a different perspective on evolutionary rescue in structured
populations, not contrasting evolutionary rescue in populations with different initial life histories, but contrasting the effect of
evolution of different life history traits for evolutionary rescue in a
population with a given life cycle. I will first ask how the process of adaptation to a changing environment itself modifies the distribution of life histories in a population and how these changes in the life cycle feedback on the dynamics of evolutionary rescue. I will then revisit the concept of critical genetic variance allowing evolutionary rescue when
considering the joint evolution of several life history traits in a
structured population.

Speaker: Ophélie Ronce (Université Montpellier)

10:30 → 11:00 Coffee Break

11:00 → 11:30 Talk: Talk Jeremy Draghi

11:00 Shifts in generation time in maladapted populations set the pace of evolutionary rescue

Maladaptive changes in the environment can provoke an adaptive response, but also induce plastic changes in organisms. Here we derive a general model of the effects of maladaptation on vitals rates—recruitment and adult mortality—in order to explore plasticity in generation time in threatened populations. We find that generation time can shift considerably during the process of evolutionary rescue, accelerating or decelerating the pace of adaptation. These shifts can be predicted by comparing the mechanism of density-dependent population regulation to the effects of maladaptation—when these two forces have differing effects on demography, then generation time is subject to plasticity. These results will inform how we might make predictions about the likelihood of rescue that are specific to the ecology of each threatened species.

Speaker: Jeremy Draghi (Virginia Tech )

11:30 → 12:30 Discussion: Reporting back from previous day

12:30 → 13:30 Lunch

13:30 → 14:00 Discussion: Individual Discussions

14:00 → 15:00 Keynote: Masato Yamamichi

14:00 Evolutionary rescue with interspecific interactions

Classic studies on evolutionary rescue have considered single species dynamics, but no species exist in isolation in nature. By considering various interspecific interactions as well as coevolution, complex dynamics can emerge in evolutionary rescue. For example, rapid adaptive evolution of prey species can prevent predator extinction when there is a trade-off between defense and growth in the prey population (indirect
evolutionary rescue). This occurs because the initial reduction of the predator population drives adaptive evolution of less defended prey, which in turn increases predator population growth. To understand such unintuitive and complex dynamics, we employ mathematical models with
eco-evolutionary dynamics. This approach is also useful for community ecologists examining invasion growth rates to understand stable coexistence of competing species. Here I will discuss recent studies on evolutionary rescue with interspecific interactions, modern coexistence theory with rapid evolution, and future perspectives.

Speaker: Masato Yamamichi (The University of Queensland)

15:00 → 17:00 Talk: Talks Loïc Marrec, Dale Clement, Maria Orive

15:00 Evolutionary rescue in a fluctuating environment: periodic vs. quasi-periodic environmental changes

No environment is constant over time, and environmental fluctuations impact the outcome of evolutionary dynamics. Survival of a population not adapted to some environmental conditions is threatened unless, for example, a mutation rescues it, an eco-evolutionary process termed evolutionary rescue. We here investigate evolutionary rescue in an environment that fluctuates between a favorable state, in which the population grows, and a harsh state, in which the population declines. We develop a stochastic model that includes both population dynamics and genetics. We derive analytical predictions for the mean extinction time of a non-adapted population given that it is not rescued, the probability of rescue by a mutation, and the mean appearance time of a rescue mutant, which we validate using numerical simulations. We find that stochastic environmental fluctuations, resulting in quasi-periodic environmental changes, accelerate extinction and hinder evolutionary rescue compared to deterministic environmental fluctuations, resulting in periodic environmental changes. We demonstrate that high equilibrium population sizes and per capita growth rates maximize the chances of evolutionary rescue. We show that an imperfectly harsh environment, which does not fully prevent births but makes the death rate to birth rate ratio much greater than unity, has almost the same rescue probability as a perfectly harsh environment, which fully prevents births. Finally, we put our results in the context of antimicrobial resistance and conservation biology.

Speaker: Loïc Marrec

15:30 Coffee Break

16:00 Decomposing the effects of demographic, sex-ratio, and phenotypic stochasticity on extinction during evolutionary rescue

Uncertainty in the outcome of individual-level processes, such as death or reproduction, complicates the ability to predict population extinction; random chance may cause otherwise identical populations to experience different fates. Individual-level variability generates multiple population-level phenomena – such as demographic stochasticity, sex-ratio stochasticity, and phenotypic stochasticity – that have different effects on population dynamics and are often studied separately. I present a general framework for quantifying the importance of different forms of stochasticity to the predictability of population extinction. In the context of evolutionary rescue, I decompose the effects of demographic stochasticity, sex-ratio stochasticity, and genetic drift over time on the likelihood of rescue, time to recovery, and time to extinction. I find that phenotypic stochasticity contributes the most to the predictability of extinction early during rescue while the contributions of demographic stochasticity and sex-ratio stochasticity increase in importance as time goes on. I further find that phenotypic stochasticity is substantially more important for predicting time to recovery than for predicting time to extinction, while the opposite is true for demographic and sex-ratio stochasticity. The greater importance of phenotypic stochasticity to recovering populations reflects the fact that rapid evolution is required for successful recovery and hence faster-than-average evolution should lead to sooner-than-average recovery. Overall, these results present a nuanced picture of how stochasticity results in divergent population outcomes and illustrate how my framework for partitioning the effects of stochasticity may be used to derive novel insights into the dynamics of small populations and extinction.

Speaker: Dale Clement (Washington State University )

16:30 The effects of partial clonality on evolutionary rescue and the opportunity for spatial adaptation

Many ecologically important organisms (including perennial grasses that shape prairies and savannahs, reef-building corals, and many invasive and pathogenic species) have life histories that include stage structure and both sexual and asexual reproduction (partial clonality) Yet how partial clonality affect a populations ability to respond by phenotypic evolution to rapid environmental change is understudied. Our work shows that the effects of clonal reproduction on mean phenotype can be partitioned into two portions: one that is phenotype-dependent and one that is genotype-dependent. This partitioning is governed by the association between the non-additive genetic plus random environmental component of phenotype of clonal offspring and parents. Utilizing both deterministic models and stochastic, individual-based models, we show that increasing clonality allows populations to more effectively utilize standing genotypic and phenotypic variation and persist after a sudden shift in phenotypic optimum due to environmental change. This benefit of increased clonality greatly depends on the nature of the environmental change: increasing the probability of evolutionary rescue after a single step change, while decreasing population persistence under continuous, linear change requiring de novo variation. Increased clonality also expands the opportunity for spatial adaptation, and can reduce or even eliminate cases where dispersal between different habitats causes habitat loss (migrational meltdown).

Speaker: Maria Orive (University of Kansas )

17:00 → 18:00 Discussion: Pitched Discussion: Where should we take theory from here?

18:00 → 20:00 BBQ

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