Ecological systems in an unsteady world

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Adaptation as a response to uctuations and changes

An ecosystem subject to uctuations or changes can respond in di erent ways. The two main categories of responses are demographic changes (changes in the absolute and relative abundance of di erent species), includings migration processes, and adaptation (changes in the traits/phenotypes of individuals and species) (Futuyma, 1998). We will focus here on the third mechanism, adaptation, and in particular on adaptive evolution (evolution driven by genetic changes and natural selection).

Definition of adaptation

Adaptation has a relatively broad meaning. The process of adaptation can in-volve di erent mechanisms as individual plasticity that is not heritable, or heri-table changes of the genome (Futuyma, 1998; Hendry, 2020). We will brie y de-scribe plasticity, before focusing on heritable changes that are the main focus of this manuscript.
Plasticity The term \plasticity » regroups processes through which environmen-tal conditions in uence the expression of phenotypic traits for a given genotype. It encompasses phenotypic plasticity, developmental plasticity, environmental in-duction, acclimation, epigenetics, induced defenses, maternal e ects, genotype-by-environment interaction, or also indirect genetic e ects (Hendry, 2020). Just to give a few examples, we can cite the phototaxis behavioral response of Daphnia to the presence of predators (Parejko & Dodson, 1991). This response to sh kairomones is shown to be a plastic response, that is greater for Daphnia that live in lakes with high levels of sh predation. Another example could be that of the morphological plasticity of some plants which develop leaves with smaller area and larger mass in response to an increase in temperature (Gratani, 2014).
Plasticity can be either adaptive as in the previous examples, or non-adaptive when the plasticity process results in a mean phenotypic response that is far from the favoured phenotypic optimum (Ghalambor et al., 2007). This distinction renders more complex the answer to the question of the selective advantage of plasticity and its contribution to adaptive evolution (Ghalambor et al., 2007).
Plasticity is often seen as a non-heritable response of individuals. It is worth to notice that actually, some plasticity processes as epigenetic (genetic changes that do not alter DNA sequences) can be heritable such as the survival of sh at high toxicity levels (hydrogen sul de{rich springs) due to a stable generational inheritance of certain DNA methylation (Kelley et al., 2021). Those heritable processes could fall under the scope of some of the present manuscript considerations (for Chapter 1 mostly).
Adaptive evolution The main focus of this manuscript remains that of adap-tation through heritable changes in the genome, which (may) results in changes in phenotype. Adaptive evolution involves the notion of tness. The tness of a given genotype is de ned as its contribution to the gene pool of the next generation (Wright, 1931). Gentotypes may di er in tness in many ways, e.g. viability, mat-ing success, fecundity (Orr, 2009). There are several ways to describe and measure tness (Endler, 2020). It is usually measured by quantities that are proportional to the mean number of viable, fertile progeny produced by a genotype/phenotype, as survival and reproductive success.
The curve or surface for individual tness versus individual trait values is called a tness landscape (idea derived by Wright in 1937 and widely used afterwards; Orr, 2005). This surface may present several local maximum. Adaptation will involve the walk up to the nearest tness peak (even if not the global optimum). However, adaptation might be a lot constrained by many factors so that most population have their phenotype in some distance from the nearest tness peak (Hendry, 2020).
This dynamical process involves four main evolutionary forces well described in most of the textbooks about evolution (Endler, 2020; Futuyma, 1998; Losos, 2017). Mutation brings new alleles to a population and participates to genetic variation. Migration creates gene ow between populations, brings new alleles into a population, enhancing genetic variation. Genetic drift randomly changes the frequency of an existing allele in a population (through stochastic death and mating). And selection provokes a di erential survival and/or reproduction of individuals, guiding which alleles are more probable to be maintained or to disappear. Natural selection is closely linked to the notion of tness, which can be seen as a within-generation measure of the process of natural selection. However, selection does not always imply \adaptation » in the sense of improved t between organism and environment (Orr, 2005).
Those four forces are known to interact with each other, what makes all the richness of this process, but also the di culties to grasp it in all its dimensions. To give just a few examples of such interactions: gene- ow may counteract selec-tion, bringing deleterious alleles and hampering local adaptation (Lenormand, 2002;
Burger, 2014), or being favorable for evolutionary rescue for instance (Tomasini & Peischl, 2020). It also interacts with drift, preventing the random loss of some al-leles into small populations (Lenormand, 2002; Blanquart et al., 2012). Similarly, the mutation-selection balance speci es the relative forces of mutation and selection in determining allele frequencies in a population (Crow et al., 1970; Lynch et al., 2016).
Even if mutation is the ultimate source of genetic variation and the fundamental aspect of several theory of evolution (Orr, 2005), it is not the only one. Adaptation can for instance also occur from standing genetic variation1. In any way, genetic variance is a prerequisite of adaptation. Such a genetic variation is actually found in nature, but the reason why is a fundamental question that has long been unresolved (Rice, 2004). Maynard-Smith highlighted that mutation should probably not be su cient (rate too low) for maintaining the observed genetic variation in nature. And indeed, other processes as recombination and immigration of new alleles also participate to genetic variation (Rice, 2004). Other mechanisms as habitat choice can help maintaining polymorphism, but is not always necessary depending on the joint e ects of density regulation and viability selection (Ravigne et al., 2004). In anyway, polymorphism maintenance requires in some way a frequency-dependent selection2 conferring an advantage to rare phenotypes or genotypes (Ravigne et al., 2004).

Manifestations of adaptation

Adaptation in a single population or species

A population subject to perturbation or changes in its environment can adapt to them. A lot of examples are reported in the literature, where some population or species are seen to adapt (here, to evolve, in the sense of the acquisition of heri-table traits) to new or uctuating conditions. Examples are as diverse as species evolutionary adaptation to urban environment (McDonnell & Hahs, 2015), to pes-ticides (Hawkins et al., 2019), to altitude for human (Rupert & Hochachka, 2001), to temperature for instance for bacteria (Bennett et al., 1992), or also to salinity (Ahmadi et al., 2016). In the case of environmental variability, evolution is generally expected to favor generalist species (see Wilson & Yoshimura, 1994, for a review), or bet-hedgers (Jansen & Stumpf, 2005). When considering heterogeneous environments, where several populations of the same species evolve in di erent environments, we can observe what is called local adaptation. A population is locally adapted when well locally suited compared to other individuals/populations of the same species (Rice, 2004; Hendry, 2020). Many examples exist as the local adaptation of disease vectors to temperature (Sternberg & Thomas, 2014), or of tropical plants to drought (Barton et al., 2020). Local adaptation implies in some way a trade-o , where a population well adapted to an environment will be mal- or less-adapted to another one (Levins, 1968). A popula-tion or species that would not be subject to any trade-o and would evolve without any biological constraints is called a Darwinian Demon (Leimar, 2002). Local adap-tation can be favored and protected by habitat choice (Johnson et al., 1996). On the contrary, local adaptation might be eventually slowed down or even prevented by gene ow between populations (Lenormand, 2002, but see for instance Walker et al., 2017). For instance, mosquitoes from Corsica did not develop a strong pesti-cide resistance as expected because of large gene ow from the mainland (Raymond & Marquine, 1994), what is called gene swamping (Lenormand, 2002).
Adaptation (and a fortiori local adaptation) might eventually result in evolu-tionary divergence and diversi cation, what participate in adaptive radiation and speciation (Losos, 2017). This can occur when selection maintains (stabilizing se-lection) or evolves (directional selection) phenotypic di erences among populations. Such an adaptive divergence in salt tolerance occurred for instance between coastal perennial and inland annual ecotypes of a yellow monkey- ower in the Western North America (Lowry et al., 2009).
Speciation can also occur in case of a disruptive selection, which increases the variance of a trait and progressively forms two groups. If their exists a reproductive isolation between the two groups, they will nally diverge to form two distinct species (adaptive radiation). Darwin’s Finches for instance are supposed to have di eren-tiated through disruptive selection and assortative mating (a kind of reproductive isolation) (Losos, 2017). There exist di erent types of reproductive isolation, either geographic (potential mates do not meet; referring here to the case of local adapta-tion), behavioral or sexual isolation, gametic incompatibilities, or hybrid inviability or sterility (Futuyma, 1998; Kirkpatrick & Ravigne, 2002).

Adaptation in an ensemble of populations within a community

Adaptive evolution is also found to a ect community assembly (Ricklefs, 1987; Vanoverbeke et al., 2016) as well as reorganization. Community adaptation refers to the reorganization and modi cation of the traits of the species that belong to the community, in response to a disturbance a ecting the species trait (loss or invasion) or the environment. For instance, bacterial communities adaptation examples are numerous, in part because of the rapid generation time and possibilities of evolution. They are shown to adapt to temperature (Pettersson & Baath, 2003), to nutrient limitation (Hoyos-Santillan et al., 2018). Fungi communities are also found to adapt to temperature (Barcenas-Moreno et al., 2009) or to soil copper for instance (Chu et al., 2010). At larger scales, there exist studies about adaptation in grasslands communities (van Moorsel et al., 2018) or even within trophic levels (Loeuille, 2010).
What distinguish a community from a population or species is precisely the presence of several species. Evolutionary change of one species is thus in uenced and constrained by the evolution of the other species, what is the notion of co-evolution (Losos, 2017; Hendry, 2020). The more species the more constraints, and some theoretical (Mazancourt et al., 2008) and experimental (terHorst et al., 2018; Scheuerl et al., 2020) studies have argued that biodiversity may leave much less room for adaptive evolution. However, other studies argued on the contrary that high functional diversity may promote species diversi cation due to increased competition (Jousset et al., 2016) in rich communities. The presence of strong co-evolutionary dynamics is suggested to increase the ongoing evolutionary potential because the adaptive peak for a population would be more mobile in a community (Garant et al., 2007). Ecological interactions are known to interplay with evolution, and are thus of great importance when considering adaptation to environmental changes, as the nowadays gradual shift in temperature (Akesson et al., 2021).
Ecological interactions are shown to be of great importance when considering adaptive evolution. For instance, (Akesson et al., 2021) highlighted that ecologi-cal and evolutionary processes both interplay in adaptation to gradual shift in the temperature.

How rapid is adaptation?

Evolution has long been considered as a slow process relatively to ecological time scales, and therefore has not been considered in concert with ecological studies and questions. However, evolution is now recognized to be relevant even on ecological timescales (Carroll et al., 2007; Ellner et al., 2011; Hendry, 2020; Hart et al., 2019). One famous example is the one of guppies. When moved from one predation en-vironment (high or low) to the other, they experience evolutionary changes (color, life history, behaviors) over only a few generations (Reznick et al., 1997). There are many other examples as the contemporary adaptation of fungi to fungicide (Walker et al., 2017), or of a kind of mosquitoes to variation in temperature (within 3 gen-erations, Foucault et al., 2018). The rate of phenotype change per trait, in cases reported as being rapid evolution cases, has been measured to be in average 1/4 (and up to 2/3) the rate of population change per generation (DeLong et al., 2016).
Some studies suggest that uctuating selection and associated periods of con-temporary evolution (i.e. rapid evolution) should probably be the norm rather than exception throughout the history of life (Carroll et al., 2007). Rapid evolution is moreover found to especially occur after extreme meteorological events (Grant et al., 2017) or in context of global variability such as the current anthropogenic changes in selection and population structure (Carroll et al., 2007). Besides, anthropogenic impacts induce a very particular type of variability at the world scale because it is rather homogeneous across many places. Thus, rapid adaptations that have ap-peared in some places can easily invade other places (Hufbauer et al., 2012).
Both ecological and evolutionary processes act in concert and for instance, con-temporary evolution implies that the maintenance of species diversity may be gov-erned by more than pure ecological processes (Hart et al., 2019). Diversity, in turns, is found to impact rapid evolution outcomes in grassland communities (van Moorsel et al., 2019). Species interaction as competitive population dynamics is also found to be modi ed by the evolution in response to inter-speci c competition (for instance in aquatic plant species over 10{15 generations, Hart et al., 2019).

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Tools for modeling adaptation

The classic Georges E.P. Box’s quote about modelling is not famous for nothing: \All models are wrong, but some are useful ». Models are useful to understand the mechanisms governing some processes, the interaction between parameters, the in-teraction between forces driving the system changes. They are useful to support, extend, revise or reject some of the narratives we mentally create to explain many kinds of phenomena (Otto & Rosales, 2020) whether for instance physical, biologi-cal, societal or nancial. Models require that we make assumptions at some levels in order to explore some aspects, forces and interactions acting at other levels. In the following, we will brie y expose some theoretical approaches used to study evo-lutionary dynamics.

Population genetics

In the early 20th century, Fisher, Wright and Haldane derived a model of evolution whose approach consisted in assigning a tness to each genotype, and then following the temporal changes in allele frequencies (Rice, 2004; Otto & Day, 2011). This approach works thanks to the relation that exists between genotypes and allele frequencies, and that comes from the Mendel’s laws of inheritance. The simplest { but strongly constrained { relations of this type are the well-known Hardy-Weinberg equations. Introducing the in uence of selection or mutation on allele frequencies into their model, the precursors of population genetics fused Darwin’s vision of gradual slight changes with Mendelenism.
Each genotype contributes to the next generation according to its tness and its frequency in the previous generation. Modeling changes in allele frequency (i.e. evolution) involves the use of various mathematical approaches dealing with prob-abilities (random sampling, Markov chains, random walk, diverse manipulation of probabilities, di usion theory, etc. ; see for instance Rice, 2004 for an general overview).
In the case of a large population (to the limit of an in nitely large population), we can neglect the stochastic e ects due to genetic drift. This allows to study the de-terministic variation of alleles frequencies under selection, mutation or migration, at one or two loci, and to study deviations from the Hardy-Weinberg equilibrium. With two loci, we can also study deviation from their independent frequency variation, what is called a linkage disequilibrium1 e ects (Losos, 2017). From one generation to the other, the change in allele frequencies is described using both the current allele frequencies and tness, along with mutation and migration rates when needed. This allows to study the equilibrium allele frequencies as resulting from a balance of two (or less often three) evolutionary forces. This is rather simple as we only consider deterministic mechanisms.
When the population size is not large enough, we cannot anymore ignore some stochastic changes in alleles frequencies as genetic drift. Stochastic changes are in general more di cult to model because we must consider at each point the prob-ability of all possible ways the system could change, and we cannot simply know exactly the next (deterministic) step it will go. This is why genetic drift has rst been studied at neutral loci. Drift has been considered using di erent approaches (Rice, 2004). For instance, Markov processes state that the probability to be in a given state only depends on the immediately preceding step, and not on the others. Another way involves Random walk which tells that the expected distance from the starting point goes as the square root of time. A third way considers the covariance between tness and the number of alleles present in the rst generation. This latter approach is a rst step to apprehend the joint e ects of selection and drift: to form the second generation, we randomly sample alleles in the rst generation, with a weight that depends on their tness (Rice, 2004).
To combine selection and drift in the same model, i.e. both deterministic and stochastic mechanisms, one of the most powerful method is di usion theory2, intro-duced to population genetic by Wright in 1945, and largely used since then (Kimura, 1983, in its neutral theory of evolution, Kimura, 1964; Gavrilets & Gibson, 2002). This method initially comes from Adolf Fick in 1855 who derived the particle di u-sion equation that represents the macroscopic behavior of many micro-particles in Brownian motion. The same equation has been widely used for di erent purposes in di erent elds, but still with the same rationale: studying the collective movement of particles in a medium caused by the random motion of each particle. The idea of this theory is that some processes act as a force, acting on the average position of the allele distribution (directional processes, e.g. selection, mutation, migration), while some other processes are spreading factors (non-directional processes, e.g. genetic drift). From those considerations, we can derive a Kolmogorov equation (Kimura, 1964). For this, we rst express the probability (p; t) of a given density population with allele frequency p at time t as a function of the probability that a popula-tion changes from allele frequency p to frequency p + in a given in nitesimal time interval. Then, expressing this probability of change as a function of the rate of directional changes M(p) and the variance in allele frequency due to non directional changes V (p), we end up with a Kolmogorov equation, for instance: @ (p; t) = @ (p; t)M(p) + 1 @2 (p; t)V (p)
Another form of this equation exists that explicitly takes into account the initial density population p0, and that will be useful to derive alleles xation probabilities for instance (Kimura, 1962). The di usion theory approach allows to consider various questions as how much or how small must be each of the evolutionary forces to gets strong or low e ects, what is the maintenance of genetic variation through the four evolutionary forces (Kimura & Crow, 1964), or also, what is the probability of mutant xation depending on its selection coe cient (Kimura, 1962; Gavrilets & Gibson, 2002).
This approach is elegant and useful. But of course, like any model, it comes with some assumptions. The di usion approximation needs the population to be large enough for two reasons. First, to be able to consider continuous changes in the variable of interest (that is often discrete by essence, e.g. number of alleles, individuals, etc.). Continuous changes will be more tractable than discrete ones with di erential equations. And second, to neglect high order terms (mutation and migration thus must be of the order of 1=2N so that lower terms can be neglected without removing the processes of interest ; Kimura, 1962). This is not realistic, but this di usion approach gives good approximations even under more biological realistic conditions (Rice, 2004).
This population genetic approach, by faithfully describing inheritance, can how-ever become very untractable with more than two loci, and many tness-related characters are known to be coded by several loci, possibly linked (Futuyma, 1998). The next modelling approach, which has some common points with the previous macroscopic description of microscopic things, will propose a way to overcome this issue.

Quantitative genetics, or dealing with continuous variation of char-acters

To deal with the previously mentioned limitations, other approaches have been pro-posed. Quantitative genetics (Falconer, 1996; Rice, 2004), which knew a boom in the 70’s and 80’s, takes phenotypes rather than genotypes as main focus. A phe-notypic trait may be controlled by a large number of loci whose exact description is neglected, as the whole e ect is captured by the phenotype value. It is R.A. Fisher in 1918 who rst proposed this vision, reconciling Mendelian and biometrical genetics. The latter indeed argued that single loci with large e ect governed by the Mendelian principles could not explain the inheritance of continuous traits (Visscher & Goddard, 2019).
Moreover, in quantitative genetics, the phenotypic trait is represented as a con-tinuous rather than a discrete variable. This description is particularly interesting for species traits that do not present sharply demarcated qualitative types (like dif-ferent colors), but rather a quantitative continuum as many traits if interest (like sizes, life-span, etc.). Despite this di erence, inheritance works the same for both qualitative or quantitative traits, and quantitative genetics is thereby an extension of Mendelian genetics, keeping its principle at its foundation. Indeed, the premises of quantitative genetics are (i) that genes are subject to Mendelian laws of transmis-sion, and may have any of the properties known from Mendelian genetics, and (ii) that the expression of the genotype in the phenotype is modi able by non-genetic causes. The genetic variance indeed comprises various genetic and non-genetic ef-fects as for instance mutations, recombination, epistasis1, mating success, or also, variations due to the environment. The phenotype is thus divided into two compo-nents: the genotype (set of genes possessed by the individual) and the environment (all non genetic circumstances that in uence the phenotypic value, or in other words, the environmental deviation from the genotypic value). Moreover, genotype and en-vironment can interact together, modifying the phenotype expected through the addition of genotypic and environmental e ects.
Phenotypes, genotypes and environment are represented as continuous variables (called the \phenotypic value », \genotypic value » and \environmental deviation »), and the population as the statistics (mean and variance usually) of the distribution of phenotypes.

Table of contents :

Introduction 
1 Ecological systems in an unsteady world
1.1 Biological systems and scales considered
1.2 Variability encountered
2 Adaptation as a response to uctuations and changes
2.1 Definition of adaptation
2.2 Manifestations of adaptation
2.3 Tools for modeling adaptation
3 Questions addressed in the thesis
1 How community adaptation impacts biodiversity-functioning relationships
1.1 Introduction
1.2 Material and methods
1.2.1 Ecological scenarios and traits
1.2.2 Random and co-adapted communities
1.2.3 Biodiversity-functioning relationships
1.3 Results
1.3.1 Biodiversity-Productivity
1.3.2 Species trait composition
1.3.3 Biodiversity-Stability
1.3.4 Biodiversity-Invasion
1.4 Discussion
2 Evolution of stress tolerance under a tolerance-fecundity trade-o 
2.1 Introduction
2.2 Model and Method
2.2.1 Model denition
2.2.2 Analysis
2.2.3 Specic denition and functions for numerical analyses
2.3 Results
2.3.1 Overview of model behavior through sensitivity analysis
2.3.2 Evolutionary equilibrium of stress tolerance x
2.3.3 The evolutionary stability
2.3.4 The relative coexistence surface for two species
2.3.5 Impact of the dose-response curve asymmetry
2.3.6 Evolutionary dynamics with more than one species
2.4 Discussion
3 Migration pulsedness alters patterns of allele xation and local adaptation in a mainland-island model 
3.1 Introduction
3.2 Methods
3.2.1 Mainland-island model
3.2.2 Mathematical analysis
3.2.3 Simulations
3.3 Results
3.3.1 A general criterion to predict the impact of migration pulsedness
3.3.2 Neutral alleles
3.3.3 Alleles under selection with co-dominance
3.3.4 Introducing dominant and recessive alleles
3.3.5 Mean tness and pulsedness load
3.3.6 The genomic signature of pulsedness
3.4 Discussion
Conclusions & Perspectives 
Appendix
A Supplementary information for Chapter 1
A.1 Modelling of the four ecological scenarios
A.1.1 Niche scenario
A.1.2 Body-size scenario
A.1.3 Life History Trade-o scenario
A.1.4 Trophic scenario: derivation of the Lotka-Volterra form
A.2 Parameter sets explored and those plotted in the main article gures
A.3 Algorithm of community formation
A.4 Metrics used to quantify diversity-functioning relationships
A.4.1 Productivity
A.4.2 Stability
A.4.3 Response to invasion
A.4.4 Metrics for trait composition
A.5 Magnitude of the dierence between random and co-adapted communities
A.6 Coecient of variation of the average interval between trait values
A.7 Results with a limit on possible trait change
B Supplementary information for Chapter 2
B.1 Equivalence between parameters
B.1.1 The fecundity steepness cs
B.1.2 The dose-response steepness s
B.2 Complements for the dose-response parameter choices
B.2.1 Symmetric versions
B.2.2 Asymmetric versions
B.3 Changes in x with the steepness of the fecundity and dose-response functions
B.4 Performance of the species at the evolutionary equilibrium
C Supplementary information for Chapter 3
C.1 Complements to the method
C.1.1 Time scale separation for the mathematical analysis
C.1.2 Gillespie algorithm for the simulations
C.1.3 Simulation time optimization
C.2 Selection values at transitions (gure 4 from the main article)
C.3 Finding sl1 and slopes of nl and n+ around it
C.3.1 Finding sl1 in frequency-independent selection case
C.3.2 Finding the slope of n+ around sl1 as a function of s
C.3.3 Finding the slope of nl, knowing the slope of n+
C.4 Eective migration rate from simulation
C.5 Mean number of migration events before xation
C.6 Simulations without time-scale separation and for dierent population sizes
C.6.1 Large m cases: the \mass » eect
C.6.2 Simulations for various m and N
C.7 Probability that a mainland allele gets xed, mean tness in the island and pulsedness load
C.7.1 Probability f1 that a mainland allele gets xed
C.7.2 Genetic load and pulsedness load
C.8 Likelihood and tting the continuous model on pulsed data
C.8.1 Methodology
C.8.2 The case of a migrant pool distribution centered on a negative value of s
C.8.3 Pulsedness load depending on the allelic distribution of the migrant pool
D Inferring migration pulsedness from a genomic dataset
D.1 Type of data needed
D.2 Model description
D.3 Comparison with stochastic simulations and Chapter 3’s mathematical model
D.4 Fit by a maximum likelihood method .

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