individuals promoting the persistence and spread of altruistic phenotypes (Hochberg et al., 2008; Koella, 2000; Le Galliard et al., 2005; Mullon et al., 2018; Purcell et al., 2012). Empirical evidence on the evolution of reduced virulence (Boots and Mealor, 2007), the evolution of altruism (Harcombe, 2010), and the evolution of restraint predation (Kerr et al., 2006) also supports the crucial role of the spatial structure.

With respect to altruism, spatial structure can allow mutualists to overcome non-mutualists (Akçay, 2017; Yamamura et al., 2004), and this can involve the evolution of dispersal (Mack, 2012). However, this may not be sufficient to account for the transition from parasitism to mutualism, since parasitic symbionts should discourage hosts from initiating the transition, whereas non-mutualists have a weaker impact (Mack, 2012; Yamamura et al., 2004). Moreover, in previous attempts, mutualistic efforts were initially polymorphic but were not subject to mutations (Mack, 2012). In that case, mutualistic clusters cannot be invaded from inside through parasitic mutations, which favours mutualism. The present work therefore constitutes, to our knowledge, the first spatially explicit eco-evolutionary model where the mutualistic efforts and dispersal abilities of hosts and symbionts coevolve, beginning from a fully parasitic interaction. If some hosts and symbionts simultaneously become mutualists and start dispersing locally, this may lead to the formation of mutualistic host/symbiont clusters producing more offspring than parasitic host/symbiont pairs, thereby initiating the transition. Meanwhile, parasitic symbionts should continue dispersing globally to invade such clusters, which could homogenize the spatial structure and compromise the transition. Therefore, it is unclear whether mutualists will invade, whether mutualists will replace parasites, or whether both strategies will coexist, as is often the case in nature (e.g., (Borges, 2015; Després and Jaeger, 1999)).

The concept of major transitions also implies that the host and the symbiont become dependent upon each other (Szathmáry, 2015; Szathmáry and Smith, 1995), with each partner needing the other to perform essential functions. Dependence is often accompanied by gene loss and gene exchange, rendering the transition irreversible (Estrela et al., 2016). For instance, aphids and their intracellular bacterial symbiont *Buchnera aphidicola* are irreversibly mutually dependent since the symbiont provides essential amino acids to its host (Akman Gündüz and Douglas, 2009; Bennett and Moran, 2015). However, most mutualistic interactions do not exhibit such physiological or reproductive dependencies (e.g., plant-ants or legume-rhizobium mutualisms), and several reverse pathways are often possible from mutualism to parasitism (Sachs and Simms, 2006; Week and Nuismer, 2021; Werner et al., 2018). Since the present work focuses on eco-evolutionary dynamics, we will not consider any physiological or developmental dependency or irreversibility and will instead assume that hosts are always able to produce offspring when alone. Nevertheless, the number of offspring produced by the hosts can depend on the mutualistic efforts of both species as well as on the population densities, which are expected to change during the transition. Under these altered ecological conditions, isolated hosts may exhibit a negative population growth rate, although they are physiologically able to produce offspring. This is hereafter called "ecological dependence".

To sum up, we tackle the following issues:

* **Main question:** Can the transition from parasitism to mutualism occur when mutualistic effort coevolves with local dispersal in the absence of vertical transmission and partner control?

* **Q1:** How do mutualistic clusters arise during the first steps of the transition? Is their formation necessary for the transition?
* **Q2:** By maintaining global dispersal, can non-mutualistic hosts and parasitic symbionts coexist with mutualists?

* **Q3:** Do mutualistic hosts become ecologically dependent on their symbiont

To investigate these questions, we built an agent-based model using a two-dimensional space lattice that supports an autonomous host and a host-dependent symbiont. Hosts compete for space and other resources, while symbionts compete for available hosts. This situation occurs in many biological systems, such as plant-ant, plant-fungi, or plant-seed eating pollinator. To model the transition from parasitism, the symbiont is initially detrimental to the host, and the host provides it the minimal energy possible, without any spontaneous mutualistic effort, as would be the case after an antagonistic evolutionary arms race. Moreover, the host-parasite system is ecologically viable even in the absence of any mutualistic agent in the landscape. At first, both species disperse globally; this situation corresponds to the most disadvantageous conditions for the emergence of mutualism. Through continuous mutations, mutualistic and locally dispersing symbionts and hosts can appear, establish and eventually change the population dynamics, triggering feedback on their own evolutionary dynamics. In addition to these general hypotheses, no assumptions specific to a particular biological system were required.

### III.2.3 Model description

**Main rules** Our model considers two types of agents, hosts and symbionts, living on the same two-dimensional space lattice. The interaction between the two species occurs when they share the same cell. Each cell can assume three states: i) empty, ii) occupied by a solitary host (only one host is allowed per cell), iii) occupied by a host-symbiont couple, (only one symbiont is allowed per host). Each individual brings two traits, the mutualistic interaction trait ($\alpha$) and the dispersal trait ($\epsilon$). Both influence fecundity.

At every time point, agents undergo each following steps (see appendix III.2.7 and Figure III.10 for more details and schematic representation of the life cycle):

* The host and symbiont die with fixed probability $m$.

* They produce offspring, possibly with different traits from them due to mutations. The fecundity of the parents depends on their traits and on their interactions with their possibly cell-sharing partner.

* The offspring are dispersed according to the parents' dispersal traits $\epsilon$.

* The host offspring may establish only in empty cells, while the symbiont offspring can only establish in cells already occupied by a solitary host. If several individuals come to implant in the same cell, a uniform lottery determines which one will implant, while the others die.

**Fecundity rate and mutualism/parasitism** The fecundity rate $f$ of an agent depends on its mutualistic interaction trait $\alpha$ as well as the trait of its cell-sharing partner. This continuous trait, ranging between 0 and 1, determines the intensity of the agent investment in the mutualistic relationship. We assume a positive interaction trait dependence between agents. A mutualistic agent tends to increase the fecundity of its cell-sharing partner. On the other hand, a mutualistic agent has an intrinsic cost, reducing its fecundity. Thus, the effective agent fecundity results from the gain induced by the mutualistic behaviour of its partner weighted by its own intrinsic cost of mutualism (for mathematical details see appendix
### III.2.7).

In addition, the cost of mutualism is a developmental characteristic that applies regardless of the actual interaction. Thus, a solitary mutualistic host always pays the cost of mutualism. Therefore, we consider "strong mutualism", where no direct feedback occurs for mutualists and mutualism always has a cost.

The hosts are autonomous, i.e., their fecundity is nonzero when they are alone in their cell without a symbiont. In addition, while hosts are always beneficial to symbionts, because they are necessary for their establishment, symbionts can be parasitic to hosts. Indeed, we assume that the presence of a symbiont induces a cost for the host. Thus, if the symbiont invests insufficiently in the mutualistic interaction, it does not compensate for this cost, and the host has reduced fecundity than if it was alone; the symbiont is parasitic to the host. The symbiont becomes mutualistic when it sufficiently invests in the mutualistic interaction so that the host has a higher fecundity than if it was alone. In our model, a symbiont is parasitic if $\alpha < 0.475$ and mutualistic if $\alpha > 0.475$ (see Figure III.4).

We note interaction traits of the host and the symbiont $\alpha_h$ and $\alpha_s$, respectively. The fecundity rate ranges between a positive low value that depends on the agent type and a maximum rate of 8 corresponding to the maximum number of direct neighbours in a 2D space (Figure III.4).

<figure><img src="image_31.png" /><figcaption>Figure III.4 – Fecundity rates of hosts and symbionts according to the interaction trait of their partners (dashed lines). Plain line: fecundity of a solitary host. The dashed-dotted red line corresponds to the threshold $\alpha_s^*$ between the parasitic symbiont (solitary host fecundity higher than the fecundity of a host associated with a symbiont of trait $\alpha_s < \alpha_s^*$) and mutualistic symbiont (solitary host fecundity lower than fecundity of a host associated with a symbiont of trait $\alpha_s < \alpha_s^*$).</figcaption></figure>

**Mutation** Offspring inherit traits from their parents with variability due to mutations. The effects of mutations on each trait are independent, and can be either beneficial or detrimental. We describe these effects using an exponential distribution that allows for rare mutations with large effects. We set a maximum mutation distance $d$; if a distance from the exponential distribution is greater than $d$, the mutation is cancelled. Similarly, a mutation is cancelled if it
implies that the trait exceeds the limits of its domain [0, 1].

**Dispersal** The parents are sessile, whereas their descendants are dispersed. The individuals can invest in two modes of dispersal, a local dispersal considering the 8 neighbouring cells of the parent's cell and a global dispersal corresponding to a uniform dispersal across the entire space.

Their dispersal trait $\epsilon$ provides the proportion of offspring globally dispersed uniformly in the space. The remaining proportion $1 - \epsilon$ is locally dispersed uniformly in the cells around the parent. Similar dispersal was used in Kéfi et al. (2007, 2008).

Global dispersal implies an additional cost that reduces the number of offspring. Therefore, effective fecundity $f_e$ is equal to the fecundity rate $f$ reduced by a cost that is linearly proportional to the investment in global dispersal: $f_e = f(1 - d\epsilon)$, with $d$ a coefficient to modulate cost intensity.

**Competition** The host is subject to intraspecific density-dependent competition, which influences the establishment success of the offspring. The establishment probability $P_I$ decrease with the host density $\rho_h$ as follows:

$$P_I = 1 - (\rho_h)^{\gamma_C} \qquad (III.1)$$

where $\rho_h$ is the proportion of cells occupied by hosts and $\gamma_C$ is the competition strength. The competition is strong when $\gamma_C < 1$ (sub-linear function), while it is weak when $\gamma_C \ge 1$ (super-linear function).

**Parasitic system and transition** To tackle the issue of transition to mutualism, we assume that the system is viable without mutualism. More precisely, we chose parameters such that the extinction probability of a population with parasitic global dispersers (minimal interaction traits, $\alpha_s = \alpha_h = 0$ and dispersal trait $\epsilon = 1$) was less than 1 in the absence of mutation. Moreover, this parasitic population without evolution stabilizes around a demographic equilibrium called the "parasitic system". From our perspective, this situation is the worst-case scenario because interactions are parasitic and dispersal cost is maximal. However, under evolution, mutations generate diversity, and mutualistic symbionts can appear. Starting from the parasitic system, mutations lead to the presence of approximately 2% of mutualistic symbionts in the population. They are not selected but simply result from the phenotypic variability induced by mutations. Then, the system can either remain in this state, or a transition to mutualism can occur. The transition is characterized by a significant increase of the percentage of mutualistic symbionts above the percentage generated by simple phenotypic variability. In our following work, we assume that transition occurs when the percentage of mutualistic symbionts rises above the threshold of 10%.

### III.2.4 Results

In the following results, the maximum cost of mutualism is 30%, and the other parameters are set to satisfy the viability of the parasitic system (see Table III.1 in appendix III.2.7).
The transition from parasitism to mutualism under restrictive conditions

Our first objective was to investigate whether in the absence of dispersal cost, the transition to mutualism is possible starting from the viable parasitic system without dispersal cost. It represents the most difficult condition for the transition to mutualism. From our simulations, we can compute the transition time when the percentage of mutualistic symbionts rises above 10%, which is our transition threshold.

Without dispersal cost, the transition is more likely to occur under strong competition than weak competition (see the probability of transition in Figure III.5a)). Moreover, when the transition succeeds, it occurs more rapidly under strong competition (median transition time around 7.10⁴) than under weak competition (median transition time around 2.5.10⁴). However, with a large dispersal cost ($d = 0.45$), the transition occurs systematically (the probability of transition is 1) and quickly (the median transition time is divided by a hundred 7.10²), regardless of whether the competition is weak or strong (see Figure III.5a).

The transition is characterised not only by an increase in mutualistic symbionts but also by an increase in host and parasitic symbiont densities (see Figure III.5b and c). During the transition, we also observe an increase in the mean interaction trait of mutualistic symbionts toward 1 (see curve colour in Figure III.5c). Thus, the transition is initiated by weakly mutualistic symbionts, which then rapidly increase their mutualistic interaction. In contrast, the increase in the average host interaction trait is delayed in response to the symbionts' transition (see curve colour in Figure III.5b). Moreover, the transition does not occur at the expense of parasitic symbionts. The latter benefits from the increase in host density created by the mutualistic symbionts. As a result, their density increases so that the parasitic symbionts remain dominant (Figure III.5c).

Note that if the cost of mutualism is sufficiently low (e.g., a maximum cost of only 10% instead of the 30% of the previous results), the transition to mutualism occurs even in the absence of host competition (details not shown).

The evolutionary branching resulting from the transition is accompanied by coevolution with the dispersal trait (see Figure III.6a). As a result, we obtain two classes of symbionts: parasitic global dispersers ($\alpha_s \ll 1$ and $\epsilon \sim 1$) and mutualistic local dispersers ($\alpha_s \sim 1$ and $\epsilon \ll 1$). Conversely, the host trait distribution is more aggregated, and coevolution with the dispersal trait leads to a negative correlation between global dispersal and mutualism intensity (Figure III.6b, $R^2=0.102$, p-value=0). Moreover, we observe that very few hosts exhibit a weak interaction trait ($\alpha_h < 0.2$). The low density of very weak mutualistic hosts results from the apparent competition between hosts due to a high density of symbionts. In this situation, a host is frequently associated with a symbiont. Strong mutualistic hosts will benefit more from parasitic symbionts than weak mutualistic hosts. Indeed, a parasitic symbiont will benefit from a strong mutualistic host by increasing its number of offspring, which eventually reduces the host density and thus host competition.

To investigate whether the transition to mutualism is associated with the emergence of a spatial structure, we measured an index of assortment (see appendix III.2.7 for details). A positive index indicates that on average, individuals with similar phenotypes are closer than individuals with different phenotypes when compared to a random spatial distribution of the individuals in the space (Figure III.7a). The intraspecific assortment quantifies the similarity of agents in a local neighbourhood (8 cells), and the interspecific assortment quantifies the similarity between host and symbiont in the same cell.

Positive assortment indices demonstrate that the agents are locally similar and that hosts and symbionts in the same location also have the same interaction behaviour. As a result, we show
that the transition to mutualism occurs along with the emergence of a spatial structure (see clusters of hosts and mutualistic symbionts Figure III.7b and c). The intraspecific spatial structure is stronger than the interspecific structure. This is not surprising since the formation of the intraspecific spatial structure simply requires that a sufficient proportion of the dispersal is local. However, for an interspecific spatial structure to emerge, a phenotype must have a sufficiently local dispersal, and it must interact with a similar phenotype that also exhibits a local dispersal.

**Effect of competition** We have shown that competition between hosts promotes the transition to mutualism. We next investigated its quantitative effect on the percentage of mutualistic symbionts. The following results were obtained using a large dispersal cost ($d = 0.45$) to reduce the mean time of transition and thus save computational time. We also discuss the effect of dispersal cost in the next section.

Competition strength increases the percentage of mutualistic symbionts after the transition when competition is global over the landscape, i.e., hosts compete with all the hosts in the landscape (Figure III.8a). However, when competition is more local, individuals compete only with their neighbours (see appendix III.2.7 and Figure III.11 for details), and the percentage of mutualistic symbionts decreases drastically (Figure III.8b). When the competition is too local, the average percentage of mutualistic symbionts eventually drops below the transition threshold, and no transition occurs.

Finally, we showed that mutualism persists only because of strong competition. Indeed, if we reduce the competition after a transition to mutualism, we observe that the population evolves towards the parasitic system (see Figure III.8c and Figure III.12 in the appendix for more details).

Another way to reduce density-dependent competition is to reduce the density of the host. In this case, we show that mutualism still persists (Figure III.13a in appendix). Thus, temporal perturbations in host density tend to enhance the proportion of mutualism. Indeed, the perturbation itself does not change the proportion of mutualistic symbionts because the different symbionts are fairly evenly distributed throughout the space. Then, the space vacated by the perturbation is recolonised mostly by parasitic symbionts due to their more global dispersal (Figure III.13b). However, due to the relaxation of global competition, the probability of host establishment is better, and the mutualistic clusters outside the perturbation zone gain in size, which explains why the proportion of mutualistic symbionts increases slightly despite the recolonization of the centre by parasites. In the end, once recolonization is complete, the system returns to an equilibrium state close to before the perturbation. In terms of trait distribution, the new state is similar to the previous state before the perturbation (details not shown).

The same experiment but with a perturbation that causes the death of 50% of uniformly occupied cells leads to the same results.

**Mortality and dispersal cost can induce host dependency in emerging mutualistic systems.** Competition is a major process leading to mutualism. However, mortality and dispersal cost also play important roles in shaping the mutualistic system. Thus, for the results below, the competition is both strong and global.

We demonstrated that dispersal cost and mortality promote mutualism (Figure III.9). Although the mutualistic system emerges in a wide range of parameters where the parasitic system is viable, the transition is more likely to occur when the system is close to extinction. We demonstrated that the transition is less likely to occur when the dispersal cost is low.
In particular, for the parameter pair in the area indicated by the grey star, we have shown previously that the probability of transition is very low around 0.086 (see Figure III.5). In addition, we show that the transition is unlikely to occur if the mortality is too low, which tends to demonstrate that the time of emergence increases if the mortality decreases. The dispersal cost also modifies the characteristics of the system by reducing the average dispersal trait of both species (Figure III.14 and Table III.2 in the appendix). This reduction is associated with more pronounced branching of the symbiont due to the increase in the percentage of mutualistic symbionts. We observed that even in response to a strong dispersal cost, the mean dispersal trait of parasitic symbionts is higher than the mean dispersal trait of mutualistic symbionts.

Under favourable conditions leading to the transition to mutualism, the population of mutualistic hosts always persists in the absence of the population of mutualistic symbionts. Therefore, in our model, the transition to mutualism does not exhibit an absolute dependency between host and symbiont populations. However, *ecological dependency* may occur. The transition to mutualism cooccurs with an increase in host density and thus an increase in intraspecific competition. If this increase in competition is sustainable only in the presence of mutualistic symbionts, we say that the hosts are *ecologically dependent* on the symbionts. To test this dependence, we measured the global competition between hosts in a population at equilibrium after a transition to mutualism. Then, we used this competition as a fixed non-density-dependent competition to test whether a host population with all individuals having the same trait as the mean trait of a population at equilibrium can survive in the absence of mutualistic symbionts and mutation. We show that this dependency occurs when the system evolves toward a mutualistic system in which the percentage of mutualistic symbionts is sufficiently large (Figure III.9 hatched area).

### III.2.5 Discussion

**The mechanism underlying the transition to mutualism.** In relation to our primary question, our results indicate that the transition from parasitism to mutualism occurs when mutualistic efforts coevolve with dispersal, despite the absence of vertical transmission or partner control. Before the transition, the host performs better when alone; therefore, it has no interest in increasing its mutualistic effort; in fact, it is selected to keep it as low as possible. In contrast, the symbiont population is limited by the number of available hosts, which increases when the symbiont becomes mutualistic. If by chance mutations produce a mutualistic symbiont dispersing locally and interacting with a host dispersing locally as well, its offspring will benefit from the increased density of hosts in their neighbourhood and will form a mutualistic cluster (question Q1, Figure III.7c). The cluster will be rapidly invaded by parasitic symbionts dispersing globally, which can lead to its extinction if competition between hosts is weak. Under such conditions, the transition to mutualism rarely occurs (Figure III.5a), and when it does, the percentage of mutualistic symbionts remains low (Figure III.8a). Conversely, when hosts strongly compete for resources, the ecological conditions change dramatically. The formation of mutualistic clusters (Figure III.7a) increases population densities (Figures III.5b and III.5c), which enhances competition between hosts. Areas dominated by parasitic host/symbiont pairs were initially viable, but their population growth rate became negative following the increase in competition. This creates empty space that can be colonized by mutualists, which still disperse globally from time to time. Therefore, contrary to our expectation, the transition is not directly caused by the higher fecundity of mutualistic clusters but only indirectly by the increase in host competition. However, this only occurs when competition between hosts
is partly global (Figure III.8b); if it is purely local, mutualistic clusters cannot influence the viability of parasitic regions. Although areas dominated by parasitic host/symbiont pairs become unsuitable, parasitic symbionts can still invade mutualistic clusters and overcome them. This results in a dynamic equilibrium between mutualism and parasitism (question Q2, Figure III.5c). Coevolution with dispersal results in a negative correlation between mutualism intensity and global dispersal (80% of mutualists disperses locally, Figure III.6), which mirrors the link between altruistic behaviour and local dispersal (Hochberg et al., 2008; Koella, 2000; Le Galliard et al., 2005; Mullon et al., 2018; Purcell et al., 2012). Empirical work has shown that the outcome of interactions between hosts and symbionts depends not only on the traits of the protagonists, but also on the ecological conditions (Bronstein, 1994). For instance, plants take advantage of seed-eating pollinators in the absence of alternative pollinators but not in their presence (Thompson and Cunningham, 2002). Mycorrhizae are beneficial for plants when soil resources are scarce while they are detrimental when resources are abundant (Johnson et al., 1997). In the above cases, the outcome of the interaction depends on both biotic and abiotic factors that are external to the host-symbiont system. Our model showed that the association with symbionts remains parasitic when host competition is low, while it evolves towards mutualism when host competition increases. In that case, the outcome of the interaction depends on intrinsic features of the interactions that are constructed by the eco-evolutionary dynamics of the system, as the emergence of mutualists increases host density.

The transition needs some time to occur because several obstacles must be overcome (si-
multaneity of the mutations, demographic stochasticity, susceptibility to invasions by parasites)
before the mutualists are numerous enough to induce the shift in host competition. For this
reason, the dispersal cost was introduced to speed up the transition (Figure III.5a) without
affecting the overall behaviour of the model. Dispersal cost induces a selection pressure at the
individual level in favour of local dispersal, which increases the likelihood of the formation of
mutualistic clusters.

In addition to dispersal cost, mortality enhances the probability of transition. Mortality pushes the parasitic system towards its viability boundary and promotes the eco-evolutionary feedback loop involving host competition. The facilitation of mutualistic symbiosis in harsh environmental conditions has already been observed theoretically and empirically (Callaway et al., 2002; Maestre et al., 2003; Travis et al., 2006). However, explaining mutualistic behaviour it is not always a significant process (Werner et al., 2015). Moreover, in the context of altruism, an inverse relationship is observed (Taylor and Irwin, 2000).

**The role of quasi-vertical transmission** Although mutualistic symbionts are environmentally acquired, their local dispersal, together with mutualistic hosts, produces a similar effect as vertical transmission (as for mycorrhizae, (Wilkinson, 1997)), which we term "quasi-vertical" transmission. However, local dispersal (even 100%) is not equivalent to vertical transmission because host and symbiont offspring can disperse to any of the 8 neighbouring cells. Vertical transmission due to specific reproductive and physiological adaptations would have produced transitions to mutualism more easily. Moreover, the colonization of empty space by a mutualistic pair requires the simultaneous long-distance dispersal of both species, whereas in the case of vertical transmission, this always occurs. In addition, the need to colonize empty space constitutes an important selection pressure, which partly counteracts the necessity of quasi-vertical transmission. Indeed, mutualistic phenotypes retain their ability to disperse globally (~ 20% for symbionts and ~ 40% for hosts, Figure III.6), which cannot be due to mutations alone. Colonization ability comes along with the avoidance of local overpopulation
generated by mutualism. Similarly, although the evolution of altruism is favoured by kin selection (itself induced by local dispersal (Hamilton, 1964b)), it can also be limited by kin competition (Akdeniz and Van Veelen, 2020; Alizon and Taylor, 2008; Wilson et al., 1992).

A mixed strategy combining both dispersal modes takes advantage of kin selection and simultaneously maintains the opportunity to escape kin competition. Figure III.8b shows that purely local competition between hosts prevents the transition to mutualism because kin competition overcomes kin selection in that case with respect to the evolution of cooperation (Akdeniz and Van Veelen, 2020). In nature, global competition between hosts may arise when plants compete for water present in the same groundwater, while competition for light is more local. Thus, the evolution of mutualism may depend on the dominant form of competition for resources between hosts.

**The interplay between three levels of organization** The mechanism by which parasitic symbionts and hosts can invade mutualistic clusters is a two-species version of the tragedy of the commons (Feeny et al., 1990; Garrett, 1968; Hardin, 1998), which can be bypassed by local dispersal in the case of altruism (Mitteldorf and Wilson, 2000) as well as in the present case. Indeed, there is no transition to mutualism when dispersal is primarily global ($ε > 0.55$), mutualists and parasites coexist for mixed dispersal strategy ($0.55 < ε > 0.1$), and mutualists almost outcompete parasites when dispersal is mainly local ($ε < 0.1$, details not shown). In the context of altruism, the resolution of the tragedy of the commons involves two levels of organization, the individual-level favouring cheaters and the group-level favoring altruism (Van Baalen and Rand, 1998). In the context of mutualism, parasites are selected at the individual level and mutualists at the host/symbiont pair level, resembling the tit-for-tat strategy where cooperators are selected at the pair level. However, this is not the end of the story because in the absence of dispersal cost, mutualism rarely invades when host competition is weak (Figure III.5a), despite the occasional formation of mutualistic pairs. For the transition to occur, competition between hosts at the global scale is necessary (Figure III.8b), which constitutes a third level of organization involved in the coevolutionary process.

**Host dependency and irreversibility of the transition** Major transitions in evolution are characterized by the irreversibility and the interdependence between the agents (Estrela et al., 2016; Szathmáry and Smith, 1995). Our model does not include any physiological dependence of the host on its symbiont or any loss of functions in the host due to gene transfers, assuming that this generally occurs during later stages of the evolution of mutualism. Instead, we have defined dependence from a population dynamics perspective: the host is "ecologically dependent" when its population growth rate is negative in the absence of its symbiont, even though it can produce offspring (question Q3). We found that mutualistic hosts deprived of their symbiont exhibit a negative growth rate when the host density after the transition to mutualism becomes sufficiently large (Figure III.9). In our model, this ecological dependency resulted from the density-dependent competition between hosts and the assumption that mutualism is costly for the host, even when its symbiont is absent (e.g., the unconditional production of extrafloral nectaries (Bronstein, 1998)). However, this dependency is not absolute. Indeed, once the density becomes sufficiently low, the mutualistic hosts alone are viable. The dependency may become absolute for a sufficiently high cost of mutualism, but in these conditions, the transition to mutualism will not occur.

If host competition strength decreases permanently, e.g., following the continuous supply of extra resources, the reverse transition back to parasitism occurs (Figure III.8c). This reversion
occurs because host dependency relies on the ecological conditions that change when the host
competition strength is modified. However, if host competition decreases punctually, e.g.,
following a perturbation of a fraction of the landscape, mutualism persists (Figure III.13)
because mutualistic clusters take advantage of the reduction of global host competition to
colonize free cells around them. This leads to an increase in host competition; in that case,
mutualism can restore the ecological conditions, allowing its own persistence, as in a niche
construction process (Laland et al., 2016; Lewontin, 1982, 1983; Odling-Smee et al., 2003).
Niche construction is generally understood as the improvement of abiotic conditions. In
the context of mutualism, it is due to the improvement of host densities, which induces an
increase in host competition. This also occurs at the beginning of the transition, when the
first mutualistic clusters trigger an increase in global host density.

**Conclusion** In the present paper, we aim to understand the mechanisms promoting the transition from parasitism to mutualism. To tackle this issue, we develop an agent based model on a lattice. In our general model, we only assume that the mutualistic interactions influence the fecundity of both partners and that hosts face density-dependent competition. In addition, we ensure that the antagonistic system is stable in absence of mutations. We show that in the absence of vertical transmission or partner control mechanisms, the coevolution between mutualistic effort and local dispersal can trigger the transition from parasitism to mutualism, provided that intraspecific competition between host is sufficiently global and that either dispersal cost or competition strength is large enough.

Unexpectedly, we found that mutualistic clusters invade the antagonistic system thanks to
their ability to increase the population densities of both partners, thereby triggering global
competition between hosts and rendering regions dominated by parasitic host/symbiont pairs
unsuitable. In contrast, the higher fecundity of mutualists is not advantageous enough to
compensate for the ability of parasites to invade mutualistic clusters. Thus, our results
suggest that the eco-evolutionary feedback involving competition between hosts might promote
the transition from parasitism to mutualism in a wide range of biological systems, such as
plant-fungi, plant-ant and plant-seed-eating pollinator interactions.
<figure><img src="image_32.png" /><figcaption>Figure III.5 – a) Transition time as a function of competition strength $\gamma_C$ and dispersal cost $d$. Boxplots representing the transition time when the percentage of mutualistic symbionts increases above 10% when starting from the parasitic system. We ran 1000 replicates per parameter pair with a maximum projection time of $10^5$. The probability of transition corresponds to the frequency of transition over the 1000 simulations. In panels b) and c), coloured plain curves represent the host and symbiont densities over time averaged over 100 simulations under strong competition $\gamma_C = 0.2$ and no dispersal cost $d = 0$. The time series are adjusted so that all simulations have a transition time $t = 2000$. The colour gradient corresponds to the mean interaction trait $\alpha$, and shaded regions correspond to the standard deviation for densities. In panel c), the purple dotted line and the right y-axis show the relative density of mutualistic symbionts, and the black line indicates the 10% transition threshold.</figcaption></figure>
<figure><img src="image_33.png" /><figcaption>Figure III.6 – Distribution after transition to mutualism in traits domain (ϵ, α) of symbionts (panel a) and hosts (panel b). Plain red line (panel b) shows the linear regression between host traits (R²=0.102, p-value=0). Distributions corresponds to 100 simulations with strong competition γc = 0.2 and no dispersal cost d = 0.</figcaption></figure>
<figure><img src="image_34.png" /><figcaption>Figure III.7 – a) Spatial structures are described by the assortment index measuring the intraspecific assortment between hosts (plain line), the intraspecific assortment between symbionts (dashed line) and the interspecific assortment between hosts and symbionts (dash-dot line). Results are averaged over 100 simulations with strong competition $\gamma_C = 0.2$ and no dispersal cost $d = 0$. The time series are adjusted so that all simulations have a transition time $t = 2000$ (red dotted line). Grey areas show the standard deviation. b)-c) Snapshots of a region of 40x40 cells before (panel b) and after (panel c) the transition to mutualism. Coloured cells represent host alone (green), host with parasitic symbiont (blue), host with mutualistic symbiont (red), empty (black).</figcaption></figure>
<figure><img src="image_35.png" /><figcaption>Figure III.8 – The role of host competition in the transition to mutualism. a) The effect of the competition intensity (defined by the competition shape parameter $\gamma_C$) on the transition to mutualism (global competition). b) The effect of the spatial scale of the competition (strong competition $\gamma_C = 0.2$). c) The effect of competition on the transition and on the maintenance of mutualism (simulation without dispersal cost). Panels a and b show the results averaged over 50 simulations with a maximum projection time of $10^4$ steps, and grey areas give the standard deviation. The red dotted line is the threshold of 10% of mutualistic symbionts above which transition to mutualism occurs.</figcaption></figure>
<figure><img src="image_36.png" /><figcaption>Figure III.9 – The percentage of mutualistic symbionts when there is transition to mutualism as a function of intrinsic mortality and dispersal cost. We performed 50 simulations per parameter with strong global competition $\gamma_C = 0.2$. The percentages are averaged over the simulations that lead to transition, if any occur. The white cells correspond to the nonviability domain for the system with evolution, and above the black dotted line, the parasitic system is not viable. The dark grey area corresponds to no transition for all simulations. The evolution of host ecological dependency occurs in the hatched area. Ecological dependency means that the average host from a population where mutualism has emerged cannot survive the competition experienced by that population (i.e. the ecological conditions) if the mutualistic symbionts are removed. The grey star corresponds to the restrictive conditions of Figure III.6; note that under these conditions, a transition is possible but rare (probability of transition is 0.086), so with only 50 simulations per parameter no transition occurs here.</figcaption></figure>
**III.2.6 Acknowledgements**

We are grateful to Jean-François Arnoldi, Cédric Gaucherel and Sébastien Lion for their thoughtful comments and discussion on this work.
### III.2.7 Appendix

#### Mathematical and numerical details of the model

We present here the mathematical underpinnings of the model as well as some details of the numerical computation.

**Algorithm** Our model follows the cycle presented in Figure III.10:

* Host and symbiont die with fixed probability $m \in (0, 1)$.

* They produce offspring, possibly with different traits from them due to mutation. The fecundity of the parents depends on their two traits $(\alpha, \epsilon) \in [0, 1]^2$ and on their interactions with their possibly cell-sharing partner.

* The offspring are dispersed according to the parents' dispersal traits $\epsilon$.

* The offspring of the hosts may establish only in empty cells, while the offspring of the symbionts can only establish in cells already occupied by a solitary host. If several individuals arrive in the same cell, a lottery determines which one will establish, while the others die.

In our numerical computations, mutations occurred only after the descendant was successfully established in a cell. This procedure saves computational time and did not influence our results because offspring dispersal and establishment do not depend on their traits but only on their parent traits. Furthermore, the mortality process was applied to both types of agents simultaneously, while the reproduction and dispersal processes were applied consecutively to the hosts and then to the symbionts. We confirmed that the order of the algorithm did not qualitatively affect our results.

**Fecundity rate** The fecundity rate $f$ of an agent depends on its mutualistic interaction trait $\alpha$ as well as the interaction trait of its cell-sharing partner. This continuous trait ranging between 0 and 1 determines the intensity of the agent investment in the mutualistic relationship.

We assumed a positive interaction trait dependence between agents. A mutualistic agent tends to increase the fecundity of its cell-sharing partner. The interaction fecundity $f_I^i(\alpha_j)$ of an individual of type $i \in \{h, s\}$, ($h$ = host, $s$ = symbiont) interacting with an individual of type $j \in \{s, h\}$ with trait $\alpha_j$ was defined by

$$ 
\begin{gathered}
f_I^h(\alpha_s) = f_{I,min}^h(1 + c_f^h f_{I,min}^h \alpha_s^{\gamma_f}) \\
f_I^s(\alpha_h) = f_{I,min}^s(1 + c_f^s f_{I,min}^s \alpha_h) \\
\text{with } c_f^h = \frac{f_{I,max} - f_{I,min}^h}{f_{I,min}^h} \quad \text{and} \quad c_f^s = \frac{f_{I,max} - f_{I,min}^s}{f_{I,min}^s}
\end{gathered}
\qquad (III.2) 
$$

The coefficient $\gamma_f$ allows us to set the influence of trait $\alpha_s$ on fecundity. Using a coefficient $\gamma_f < 1$, we create a convex function allowing a transition from parasitism to mutualism for a central value of the symbiont interaction trait. However, note that modifying the shape of this fecundity curve (from concave to convex via linear) does not qualitatively change our results.

On the other hand, a mutualistic agent has an intrinsic cost reducing its fecundity. The mutualism cost $c_m(\alpha_i)$ of an individual of type $i \in \{h, s\}$ ($h$ = host, $s$ = symbiont) ranges
<figure><img src="image_37.png" /><figcaption>Figure III.10 – Diagram of the numerical algorithm. The host population (H) and the symbiont population (S) undergo intrinsic mortality, then reproduction, dispersal, establishment, and finally mutation. The mortality step is simultaneous for the host and the symbiont, while the other steps occur first for the host and then for the symbiont.</figcaption></figure>

between 0 and 1, and it increases with interaction trait $\alpha_i$ of the agent. It is defined by

$$c_m^i(\alpha_i) = 1 - c\alpha_i \qquad (III.3)$$

where c is the maximal cost of mutualism.

Thus, for the host as for the symbiont, the fecundity $f_i$ of an individual i interacting with an individual j is the product of the interaction fecundity $f_I(\alpha_j)$ defined by (III.2) and the cost of mutualism $c_m(\alpha_i)$ defined by (III.3).

$$ \begin{aligned} f_h &= c_m^h(\alpha_h)f_I^h(\alpha_s) \\ f_s &= c_m^s(\alpha_s)f_I^s(\alpha_h) \end{aligned} \qquad (III.4) $$

When a host agent is alone in a cell, its fecundity is defined by its intrinsic host fecundity
$f_a^{max}$ weighted by its mutualism cost $c_m(\alpha_h)$: Fecundity of the solitary host:

$$f_a = c_m^h(\alpha_h) f_{max}^a. \qquad (III.5)$$

Fecundity still depends on the interaction trait of the host but we replace the interaction fecundity $f_I^h(\alpha_s)$ with an intrinsic fecundity $f_{max}^a$. We therefore consider that the cost of mutualism is a developmental cost that is paid regardless of whether the interaction is realized. It can therefore be said that the mutualism modelled here is a "strong mutualism" in the sense that there is no direct return on investment for the partner with a mutualist effect, and the cost of mutualist behaviour is always paid.

The fecundity rates produced by our process were rarely integers, yet the number of offspring in our model can only be represented by an integer. Thus, in the numerical algorithm, the fecundity was rounded down to the lower integer, and then the decimal part is used as a parameter of a Bernoulli trial to determine whether a descendant was added.

**Mutualism/parasitism threshold** In our model, the presence of a host always produced a net benefit for the symbiont. However, the presence of the symbiont might be detrimental for the host. Indeed, the fecundity of a host $h$ interacting with a symbiont $s$ is $f_I(\alpha_s)c_m(\alpha_h)$, while the fecundity of the same host $h$ without a symbiont is $f_a^{max}c_m(\alpha_h)$. Thus, the host has net benefit only if its fecundity in association with a symbiont is larger than its fecundity alone. Therefore, mutualism only occurs when $f_I(\alpha_s) > f_a^{max}$. Otherwise, the interaction is parasitic. This criterion does not depend on the host mutualism trait $\alpha_h$ because the hosts always pay the same mutualism cost. Thus, we can define the mutualism/parasitism threshold $\alpha_s^*$ such that $f_I(\alpha_s^*) = f_a^{max}$; thus, we obtain

$$\alpha_s^* = \left( \frac{f_{max}^a - f_{I,min}^h}{c_f^h f_{I,min}^h} \right)^{1/\gamma_f} \approx 0.475 \qquad (III.6)$$

with the parameters set in Table III.1.

**Competition** To test the effect of the spatial scale of the competition, we introduced a scale parameter $c_s \in [0, 1]$ that weighs the effect of local $\rho_h^{local}$ and global $\rho_h^{global}$ host density on the competition. The establishment probability thus satisfies

$$P_I = 1 - ((1 - c_s)\rho_h^{local} + c_s \rho_h^{global})^{\gamma_C} \qquad (III.7)$$

The local host density $\rho_h^{local}$ corresponds to the host density in the 8 neighbouring cells surrounding the implantation cell of the host, while the global density $\rho_h^{global}$ corresponds to the host density all over the landscape (see Figure III.11 for a schematic representation).

These competition scales may have various ecological explanations. For instance, plants sharing the same water table face global competition for this resource. Conversely, the competition for light between plants is an example of local competition. Thus, our competition scale model allows us to describe the competition for several different resources that may appear at different scales. Following our previous examples, if the water supply represents 90% of the competition and light supply represents only 10%, then the competition scale $c_s$ is $c_s = 0.9$ (90% global competition and 10% local competition).
<figure><img src="image_38.png" /></figure>

Figure III.11 – Local and global host densities influence the probability of establishment in the focus cell (pink filled square). The global density corresponds to the host density in the whole 36-cell landscape. The local density corresponds to the density in the eight cells vicinity around the focus cell.

**Assortment index** To compute the assortment index, we measured the similarity between spatially neighbouring phenotypes for the space resulting from the transition to mutualism and for a space containing the same phenotypes but whose distribution in space was randomised. The assortment index corresponds to the difference between the measurement made on the space resulting from the transition to mutualism and the measurement on the randomly rearranged space. If the index shifts positively (resp. negatively) from zero, it means that similar phenotypes are closer (resp. more distant) than different phenotypes compared to random spatial distribution. This methodology is similar to that used in Pepper and Smuts (2002) and Pepper (2007).

In practice, for the intraspecific assortment index, we utilized the following algorithm for each species: i) for each occupied cell by the target species, we measured the difference between the interaction trait present in the cell and the average of the interaction traits present in the neighbouring cells (a maximum of 8 neighbours can be present), and then we averaged these measurements to obtain an average similarity $S$ at the scale of the whole space; ii) this operation was repeated on 1000 spaces containing the same interaction traits but randomly redistributed between the occupied cells to obtain the average similarity corresponding to a random spatial distribution $S_r$; iii) finally, the assortment index corresponds to $S - S_r$.

For the interspecific assortment index, the first step was different: i) for each cell occupied by a host-symbiont pair, we measured the difference between their interaction traits, and then we averaged all of these measurements to obtain an average similarity $S$. Steps ii and iii follow the same methods as described above.

## Competition strength, perturbation and mutualism persistence

**Competition strength determines mutualism persistence** In the main text, we show that competition is essential for the transition to mutualism, but it is also important for its persistence, as shown here. In this section, we explored the effect of a sudden variation in competition strength $\gamma_C$ on the persistence of mutualism. We started with a strong competition $\gamma_C = 0.2$. As expected from our previous results, a transition to mutualism occurred (see
<table><caption>Table III.1 – Fixed parameters used for results unless otherwise specified.</caption><thead><tr><th>Parameters</th><th>Values</th></tr></thead><tbody><tr><td>mortality <i>m</i></td><td>0.06</td></tr><tr><td>mutualism cost <i>c</i></td><td>0.3</td></tr><tr><td>upper limit of host and symbiont interaction fecundity <i>f</i><sub>I,max</sub></td><td>8</td></tr><tr><td>lower limit of host interaction fecundity <i>f</i><sub>I,min</sub><sup>h</sup></td><td>0.1</td></tr><tr><td>lower limit of symbiont interaction fecundity <i>f</i><sub>I,min</sub><sup>s</sup></td><td>2.5</td></tr><tr><td>upper limit of solitary host fecundity <i>f</i><sub>max</sub><sup>sh</sup></td><td>0.5</td></tr><tr><td>shape coefficient of the host interaction fecundity <i>γ</i><sub>f</sub></td><td>4</td></tr><tr><td>maximum mutation distance <i>d</i></td><td>0.5</td></tr></tbody></table>

Figure III.12a), c) and d)). Then, around $t = 10^4$, we suddenly switched the competition strength to $\gamma_C = 2$, corresponding to weak competition. We observed regression of mutualism due to the proportion of mutualistic symbionts decreasing from 20% to less than 5% (see Figure III.12a) and e)). We observed that the regression of mutualism due to a weakening of the competition corresponded with an increase in host and symbiont densities. This increase is due to the reduction of competition, which determines densities more than the presence or absence of mutualism does.

<figure><img src="image_39.png" /><figcaption>Figure III.12 – The transition to mutualism and collapse of mutualism depending on competition. a) Host and symbiont average interaction traits and the percentage of mutualistic symbionts over time. b) Host and symbiont abundance. There is high competition from time = 0 to time = 10000 and weak competition from time = 10001 to the end. c) Dispersal and interaction traits domain before the transition to mutualism. d) Dispersal and interaction traits domain during mutualism persistence. e) Dispersal and interaction traits domain after mutualism collapse.</figcaption></figure>

**Density perturbation does not affect mutualism persistence**

Next, we tested how mutualism responds to a decrease in competition due to eradication of hosts and symbionts
### III.2 Article: Mutualists construct the ecological conditions that trigger the transition from parasitism

in a large homogeneous region of space (Figure III.13). While previously we demonstrated that mutualism regresses when competition is set to be weak, we show here that mutualism persists in the face of decreased competition due to decreased host density.

<figure><img src="image_40.png" /></figure>

Figure III.13 – Maintenance of mutualism in the face of a reduction in competition caused by a perturbation creating a large square of free cells. a) The proportion of mutualist symbionts, showing from *t*0 to *t*10000 the transition to mutualism and the eco-evolutionary equilibrium, then until *t*20000 the response following the perturbation. b) Snapshot at several times: *t* − 1 is the eco-evolutionary equilibrium with mutualism just before the perturbation, then at *t*0 the perturbation, and then *t* + 5, *t* + 10, *t* + 100 and *t* + 10000 after the perturbation. In black, the free cells; in green, the hosts alone; in blue, the couples with parasitic symbionts; and in red, the couples with mutualist symbionts.
Mortality and dispersal cost can induce host dependency in emerging mu-
tualistic systems.

In the main text, we focused on the effect of mortality and dispersal cost on the transition to mutualism and host dependency. Here, we present in more detail the effect of dispersal cost on the distribution of hosts and symbionts in trait space for three values of dispersal cost and fixed mortality rate (Figure III.14). In addition, the table III.2 shows the features of the clusters in the trait distribution.

We demonstrated that the dispersal cost favours the transition to mutualism. Moreover, even when the cost was high, the features of the clusters revealed that parasitic symbionts maintained a more global dispersal than mutualistic symbionts.

<figure><img src="image_41.png" /><figcaption>Figure III.14 – Joint distribution of the host (green), the parasitic symbiont (blue) and the mutualistic symbiont (red) populations in the traits domain for mortality *m* = 0.03 and an increasing dispersal cost *d* ∈ {0, 0.3, 0.75}. The ellipses correspond to the standard deviation. The 48 runs averaged in Figure III.9 are plotted together.</figcaption></figure>
<table><caption>Table III.2 – Features of the clusters in the traits domain</caption><thead><tr><th>dispersal cost</th><th>species</th><th>mean<br>interaction trait</th><th>mean<br>dispersal trait</th></tr></thead><tbody><tr><td rowspan="3">d = 0</td><td>hosts</td><td>0.074</td><td>0.81</td></tr><tr><td>parasitic symbionts</td><td>0.06</td><td>0.82</td></tr><tr><td>mutualistic symbionts</td><td>* (density &lt; 2%)</td><td>* (density &lt; 2%)</td></tr><tr><td rowspan="3">d = 0.3</td><td>hosts</td><td>0.45</td><td>0.35</td></tr><tr><td>parasitic symbionts</td><td>0.07</td><td>0.39</td></tr><tr><td>mutualistic symbionts</td><td>0.88</td><td>0.17</td></tr><tr><td rowspan="3">d = 0.75</td><td>hosts</td><td>0.36</td><td>0.19</td></tr><tr><td>parasitic symbionts</td><td>0.08</td><td>0.18</td></tr><tr><td>mutualistic symbionts</td><td>0.84</td><td>0.10</td></tr></tbody></table>
# CHAPITRE IV

## CAUSALITÉ RÉCIPROQUE ENTRE INDIVIDUS, NIVEAUX TROPHIQUES ET COMMUNAUTÉ

### IV.1 Introduction et synthèse des résultats

Dans ce dernier chapitre nous explorons la causalité réciproque entre dynamique écologique et évolutive à travers un modèle de communauté ressources-consommateurs dans lequel plusieurs traits évoluent. Le trait déterminant les stratégies d'acquisition des ressources (Adaptive Foraging, noté AF) par les consommateurs est notamment pris en compte. Dans ce contexte, la causalité réciproque écologie-évolution se matérialise par les effets que l'évolution de l'AF chez les consommateurs peut avoir sur les propriétés de la communauté (diversité, productivité, biomasse, stabilité), propriétés qui à leur tour influencent les dynamiques évolutives des ressources et des consommateurs.

Cet intérêt pour les propriétés de la communauté fait écho au programme de recherche "Biodiversity and Ecosystem Functioning" (BEF) qui cherche à conceptualiser les relations entre les différentes propriétés des écosystèmes, notamment les relations entre la diversité et la biomasse, la productivité et la stabilité (Hector et al., 1999; Loreau and De Mazancourt, 2013; Loreau et al., 2002; Tilman et al., 2014). Ce cadre BEF considère la relation diversité-stabilité comme généralement positive grâce à un effet "d'assurance". En effet, plus la diversité est grande plus il y a de chances que parmi les espèces constitutives de l'écosystème certaines soient résistantes et continuent d'assurer les fonctions de l'écosystème face à une perturbation. Cette relation positive a été en particulier explorée expérimentalement (Tilman and Downing, 1994; Tilman et al., 1997, 2006) et théoriquement (Loreau, 2010b; Loreau and De Mazancourt, 2013; Wang et al., 2021).

Cependant, la corrélation positive de la relation diversité-stabilité (ou sa notation équivalente complexité-stabilité) n'est pas universellement reconnue et fait toujours l'objet de débats et controverses (voir la méta-analyse de (Landi et al., 2018)). Les résultats non concordants obtenus ont été attribués à de multiples facteurs, comme la diversité des modèles utilisés ou encore le caractère flou inhérent à la notion de stabilité (Nikisianis and Stamou, 2016). La stabilité peut en effet être définie par des propriétés à l'échelle de l'écosystème (travaux propres au cadre BEF), mais également en se fondant sur des métriques centrées sur les extinctions d'espèces (Chen and Cohen, 2001; May, 1973). Ainsi, alors que des extinctions d'espèces ne vont pas forcément influencer les métriques de stabilité dans le cadre BEF grâce à l'effet d'assurance, elles vont générer de l'instabilité dans d'autres contextes.

Cependant, la prise en compte de l'AF - c'est-à-dire la capacité pour les consommateurs de
choisir activement comment ils dispensent leurs efforts de consommation entre les différentes ressources disponibles - dans des modèles où la mesure du nombre d'extinctions suggérerait une relation complexité-stabilité négative, inverse la nature de la relation qui devient positive (Beckerman et al., 2010; Heckmann et al., 2012; Kondoh, 2003a, 2006, 2010). L'AF intègre dans ce cas le fait que les consommateurs se détournent des espèces dont les densités deviennent très faibles, prévenant ainsi l'extinction de ces espèces. L'AF peut donc jouer un rôle important dans les propriétés des écosystèmes, au-delà des spécificités liés à la structure des modèles et des méthodes de mesure de la stabilité.

Or, la plupart des travaux du cadre BEF n'intègrent pas ce processus d'AF, et ceux cités précédemment comportent des faiblesses qui nous semblent importantes. En effet, les modèles utilisés ne considèrent pas la dynamique évolutive ni des traits déterminant les interactions entre les individus, ni de l'AF lui-même qui est simplement considéré comme étant présent et fixe chez toutes les espèces. Pour dépasser ces limites, nous proposons d'inclure l'évolution de l'AF par sélection naturelle. Ceci pourrait éventuellement conduire à la disparition de ce trait, notamment à cause des coûts entraînés, qu'ils soient métaboliques ou en temps de recherche des proies préférées ; ce qui ne peut pas se produire dans les modèles pré-cités. De plus, ces modèles écologiques déterminent a priori le nombre d'espèces et la connectivité du réseau généré (méthode en modèle de niche (Williams and Martinez, 2000)) et ne peuvent donc accéder à la relation entre AF et complexité (diversité). En fait, ces travaux proposent une relation complexité-stabilité positive en présence de l'AF, mais si on imagine une relation négative entre l'AF et la complexité alors la relation globale devient incertaine. Si l'AF réduit la complexité, et donc la stabilité, alors la conclusion devient l'inverse de celle proposée lorsque la complexité est fixée a priori, c'est-à-dire une déstabilisation des réseaux par l'AF.

Nous proposons ici de pallier ces faiblesses grâce à un modèle éco-évolutif ressources-consommateurs permettant d'explorer les interactions et causalités réciproques, au sein de la triade AF-diversité-stabilité. Dans ce modèle les ressources et les consommateurs ont la possibilité de se diversifier selon un trait de niche. Le trait de niche des ressources détermine leur capacité de charge, et peut prendre une valeur optimale. La compétition avec les autres ressources est également prise en compte selon le scénario suivant : plus des ressources ont des traits de niche similaires plus elles entrent en compétition entre elles. Le trait de niche des consommateurs détermine leur adaptation à l'exploitation des ressources. Plus un consommateur a un trait de niche similaire à celui d'une ressource, plus il est physiologiquement capable d'exploiter efficacement cette ressource. De plus, les consommateurs sont caractérisés par un second trait déterminant la manière dont ils organisent leur temps d'exploitation des différentes ressources. Ce trait définit le compromis entre un comportement d'AF et un comportement aléatoire (défini par une exploitation des ressources proportionnellement à leurs densités). Ainsi, notre modèle considère une dynamique évolutive de l'AF, ce qui nous évite de tirer des conclusions sur l'effet de l'AF dans des conditions où il n'évoluerait pas. Ainsi, l'AF influence la communauté (diversité, biomasse, productivité, stabilité) à condition qu'il ait pu évoluer par sélection naturelle dans cette communauté. Notre modèle permet également d'empêcher l'évolution de l'AF (en ne considérant pas de mutation), ce qui permet de comparer les propriétés d'une communauté selon que l'AF soit libre d'évoluer ou qu'il soit bloqué. De plus, notre modèle permet l'émergence de communauté, c'est-à-dire que nous ne définissons pas a priori le nombre d'espèces et la connectivité. Ces propriétés émergent de l'histoire évolutive de la communauté. Plus précisément, les conditions initiales fixent une seule ressource et un seul consommateur, ensuite la dynamique éco-évolutif permet la diversification de chaque niveau trophique par la mutation des traits de niche. Ainsi, l'évolution de l'AF peut avoir un effet sur la diversité de la communauté qui a son tour peut avoir un effet sur les pressions de
sélection en faveur ou au détriment de l'AF formant une causalité réciproque.

La plupart des modèles s'intéressant au cadre BEF et la relation diversité-stabilité sont des modèles écologiques, sans évolution. De ce fait, ils explorent les interactions des parties (les individus, ou les espèces) vers le tout qui est l'écosystème. Avec un modèle éco-évolutif nous explorons les interactions des parties sur le tout mais également les interactions inverses, du tout vers les parties, l'ensemble formant une causalité réciproque. Nous répondons ainsi aux incitations à développer une approche éco-évolutive du programme BEF (Fussmann et al., 2007; Thuiller et al., 2013).

Nos résultats montrent que la triade AF-diversité-stabilité est étroitement inter-connectée
à travers une causalité réciproque entre écologie et évolution (Figure IV.1). Un premier
résultat concerne l'évolution non systématique de l'AF, ce qui questionne son rôle dans la
relation diversité-stabilité lorsque les conditions ne permettent pas son évolution. Nous mon-
trons entre autre que l'évolution de l'AF dépend des interactions entre les consommateurs
(notamment la compétition), ainsi que des caractéristiques de la communauté de ressources
(notamment sa diversité). Par exemple, lorsque les conditions permettent une grande diver-
sification des ressources, l'évolution de l'AF est favorisée. Effectivement, l'exploitation des
ressources éloignées de l'optimum de niche et à faibles densités imposent un choix actif par les
consommateurs d'aller exploiter ces ressources.

Nous montrons également que l'AF a un effet positif sur la diversité. En effet, les consom-
mateurs ont besoin de l'AF pour exploiter les ressources éloignées de l'optimum de niche.
Ainsi, ces consommateurs chez lesquels l'AF évolue vont exploiter ces ressources et exercer
une pression évolutive qui va les forcer à s'éloigner d'autant plus de l'optimum de niche. Il se
crée un équivalent de la "course à l'armement" dans laquelle d'une part les ressources sont
sélectionnées pour avoir un trait de niche de plus en plus éloigné de l'optimum et d'autre
part les consommateurs doivent accroître leur efficacité dans l'exploitation de ces ressources
et sont sélectionnés en conséquence en faveur de l'AF. Le modèle admet une limite à cette
course puisque la niche a une taille limitée au-delà de laquelle les ressources ne peuvent plus se
développer. Donc la diversification des ressources, quand les conditions le permettent, entraîne
l'évolution de l'AF, qui elle-même stimule la diversification des ressources de sorte qu'au final
l'AF augmente la diversité qui renforce l'AF selon une causalité réciproque. Lié à cet effet sur
la diversité, l'évolution de l'AF augmente aussi la complémentarité entre les consommateurs,
mesurée par l'inverse du chevauchement de leur régime alimentaire. Effectivement lorsque les
consommateurs ont un comportement d'exploitation des ressources aléatoire, ils consomment
les ressources proportionnellement à leurs densités. Ainsi, tous les consommateurs passent
la même durée à exploiter chaque ressource, et la différence entre leurs régimes alimentaires
provient de leurs différences d'efficacité sur chacune. Avec l'AF non seulement les consom-
mateurs choisissent activement l'organisation de leur temps mais en plus ils augmentent la
diversité des ressources ce qui offre plus de choix à la constitution de régimes différents.

L'AF a également un effet sur la biomasse. Elle augmente la biomasse des consommateurs au
détriment de la biomasse des ressources. Elle a aussi un effet non linéaire sur la productivité.
Par ailleurs, nous observons une forte corrélation entre la variabilité des propriétés de la
communauté et l'augmentation de l'AF moyen dans la communauté. Lorsque l'AF devient
fort dans la communauté, la productivité peut aussi bien être plus forte que plus faible par
rapport à celle d'une communauté caractérisée par les mêmes conditions mais pour laquelle
l'AF est inhibée.

En outre, l'effet de l'AF sur la stabilité dépend de la perturbation subie. Nous avons considéré trois types de perturbation : une augmentation graduelle de la mortalité des consommateurs, un déplacement de l'optimum de niche à une vitesse croissante et un déplacement brutal de
l'optimum de niche à une distance croissante. Pour ces trois perturbations nous augmentons graduellement leur intensité jusqu'à extinction du niveau trophique des consommateurs. La mesure de stabilité se fait à partir de l'intensité maximale de la perturbation qu'une communauté peut supporter. Face à l'augmentation de la mortalité l'AF n'a pas d'effet notable, c'est-à-dire que les deux communautés réagissent de façon similaire : celle où l'AF a évolué et celle partageant les mêmes conditions mais sans évolution de l'AF (pas de mutation du trait). Le point important est cependant la régression de l'AF avec l'accroissement de la perturbation, lorsque ce dernier a la possibilité d'évoluer, de sorte que face à la perturbation maximale supportable, les deux communautés - avec et sans évolution de l'AF - sont pratiquement similaires car l'AF a pleinement régressé là où il avait évolué. Nous soulignons ici qu'avec une approche écologique où l'AF n'aurait pas de dynamique évolutive le résultat serait différent et conclurait à un effet négatif de l'AF car celui-ci n'aurait pas pu régressé. C'est grâce à sa capacité d'évolution, et en l'occurrence de régression, que l'AF n'a pas d'effet sur la stabilité face à cette perturbation.

Face à la deuxième perturbation pour laquelle l'optimum de niche dérive à une vitesse croissante l'AF a un effet négatif sur la stabilité. À cause du déplacement de la niche, la communauté de ressources est contrainte de suivre l'optimum de niche entraînant une diminution de la diversité, de sorte que l'AF est défavorable pour les consommateurs. L'AF régresse avec l'augmentation de la perturbation mais il ne régresse pas assez vite et finalement a un effet négatif sur la stabilité de la communauté.

Pour la dernière perturbation, consistant également en un déplacement de l'optimum de niche mais cette fois-ci par un "saut" brutal de plus en plus distant, l'AF a un effet positif sur la stabilité. De manière inattendue, l'effet est direct et indirect au travers de l'effet sur la diversité. En transposant la diversité de la communauté avec évolution de l'AF à la communauté sans AF, cette dernière a une stabilité équivalente à la communauté avec AF. Autrement dit, l'effet positif de l'AF s'explique en premier lieu par son effet positif sur la diversité. En fait, la plus grande diversification de la communauté permet une plus grande proximité des ressources et des consommateurs (dans l'espace des traits de niche) par rapport à l'optimum de niche après perturbation, et ainsi de supporter un saut de l'optimum de niche à une distance supérieure par rapport à une diversification moindre. Cependant, en effectuant la manipulation inverse, c'est-à-dire en attribuant la faible diversité de la communauté sans AF à la communauté avec AF, cette dernière atteint une stabilité intermédiaire entre les deux communautés. L'AF a donc également un effet positif direct, indépendant de la diversité, face à cette perturbation.
<figure><img src="image_42.png" /><figcaption>Figure IV.1 – Synthèse des interactions multiples, et causalités réciproques, liées au couplage entre l’évolution de l’AF et la dynamique écologique entre ressources et consommateurs. Nous renvoyons le lecteur vers le corps de texte pour les détails.</figcaption></figure>
## IV.2 Article : The evolution of adaptive foraging mitigates the biodiversity-ecosystem functioning relationships

Léo Ledru<fnref n="1" />, Jimmy Garnier<fnref n="2" />, Océane Guillot<fnref n="1" />, Camille Noûs<fnref n="3" />, Sébastien Ibanez<fnref n="1" />

### IV.2.1 Abstract

Diversity among ecosystems generally enhances their productivity, stability and more generally their functioning. This positive relationship between biodiversity and ecosystem functioning (BEF) may result from various mechanisms such as interspecific complementarity or the greater use of limiting resources through Adaptive Foraging (AF). However, those mechanisms may be absent in some ecosystem or they can evolve by natural selection under environmental disturbance. In this paper, we first investigate under which conditions the AF behavior evolves within ecosystems. Furthermore, we aim to disentangle the impacts of AF on diversity and stability of ecosystems under environmental disturbances. To tackle those issues, we develop an eco-evolutionary model of resource-consumer community. Resources and consumers can diversify within a niche and consumers can modify their foraging strategy from random foraging to adaptive foraging. We first show that AF emerges by natural selection only when the environment allows for high resource diversity. When the AF evolves, we show that it promotes diversity among all trophic levels. However, it has a mixed effect on biomass and productivity. Although it enhances consumer biomass, it reduces resources biomass. And a strong AF behavior reduces productivity while a moderate AF increases it. Finally, we show that the nature of the disturbance modifies the effect of AF on stability. Under sudden environmental disturbances, the evolution of AF directly enhances stability or indirectly through its positive effect on diversity. However, under gradual changes, the AF has detrimental effects on stability and it is not stable because it disappears among the community as the intensity of change increases.

**Keywords:** biodiversity ecosystem functioning, stability-diversity relationship, adaptive foraging, eco-evolutionary dynamics

Author contributions: SI, JG and LL originally formulated the project; SI, JG and LL developed the model; LL and OG performed the numerical analyses; all authors participated in writing the manuscript

### IV.2.2 Introduction

In a context of global change and biodiversity loss, knowledge of ecosystem properties and their relationship with biodiversity is a major issue, particularly the relationship between biodiversity and ecosystem stability. It is in this context that the "Biodiversity Ecosystem Functioning" (BEF) research program has been deployed to describe the interactions between biodiversity and ecosystem properties (Hector et al., 1999; Loreau, 2010a; Loreau and De Mazancourt,

<footnote n="1">¹Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, LECA, 38000 Grenoble, France</footnote>

<footnote n="2">²CNRS, Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, LAMA, 73000 Chambery, France</footnote>

<footnote n="3">³Laboratory Cogitamus</footnote>
2013; Loreau et al., 2002; Tilman et al., 2014).

The BEF framework proposes that diversity and stability are positively related, i.e. greater diversity leads to greater stability. Indeed, the insurance hypothesis, or portfolio effect, suggests that when an ecosystem faces a disturbance, a high diversity of species ensures a greater chance that some of them will be resistant to this disturbance and will continue to ensure the ecosystem's functions (Figge, 2004; Tilman, 1996). Conversely, when diversity is poor, it is enough for the disturbance to affect the few species present for the whole ecosystem to be strongly impacted.

Prior to the BEF framework, the relationship between diversity and stability was already the source of considerable debate. In particular, (May, 1973, 1972) proposed a negative relationship based on a modelling approach, whereas the classic studies were rather in favour of a positive relationship (Elton, 1958; MacArthur, 1955). Ever since, many studies have focused on the diversity-stability relationship with contrasting results, see (Landi et al., 2018) for a review. Besides, the relationship with diversity, the food web stability has been widely explored. In particular, many studies have focused on the disturbance propagation along a food web (Dunne et al., 2002; Eklöf and Ebenman, 2006; Sole and Montoya, 2001). Indeed, if within a food web a species sees all the species it consumes disappear, then it will also disappear, which constitutes a secondary extinction.

However, these works generally use fixed interaction food webs, i.e. the interactions are defined at the generation of the food web and do not change afterwards, according to the niche model method (Williams and Martinez, 2000). This lack of possible variability in the system prevents any adaptation in the system, which is a strong assumption. Indeed, it is thus considered that if a species sees its resources or its prey disappear, then it will also disappear without being able to redirect its interactions towards other species. However, it is clear in behavioral ecology that a large diversity of species show adaptive foraging (AF) abilities, i.e., an active adjustment of their foraging efforts to the various resources available (Dill, 1983; Owen-Smith, 2008). In a food web model this means the ability of species to actively modulate the intensity of their interactions with other species.

Indeed, many studies highlight the importance of AF in the relationship between diversity and stability Beckerman et al. (2010); Heckmann et al. (2012); Kondoh (2003a,b); Mougi (2016); Uchida and Drossel (2007). Using the robustness (number of species extinction) as a measure of stability, they show a positive effect of diversity on stability once AF is present. The same type of ecological models admit a negative relationship between stability and diversity in the absence of AF (Chen and Cohen, 2001; May, 1973). Thus, AF has an effect on stability. However, those works do not allow to explore possible effects of AF on diversity, because in those models diversity is defined a priori. Since there is a relationship between diversity and stability, it seems that not taking into account the possible role of AF on diversity could bias the results. For example, one can imagine that if AF has a negative effect on diversity, and the diversity-stability relationship is positive, then one could conclude that AF has a negative effect on stability, which is the opposite of what is established by Beckerman et al. (2010); Heckmann et al. (2012); Kondoh (2003a,b); Uchida and Drossel (2007).

A way to disentangle this issue is to use eco-evolutionary models which capture the food web properties, including diversity, emerging from species interactions and evolution processes (Allhoff et al., 2015; Aubree et al., 2020; Girardot et al., 2020; Loeuille and Loreau, 2005). However, only few of those studies take into account adaptive foraging (Drossel et al., 2001; Guill and Drossel, 2008).

In addition, up to our knowledge no ecological or eco-evolutionary models on food web allows AF to evolves. In those studies, AF is fixed in the sense that there are no evolutionary dynamics
of this trait. Those studies implicitly assume that AF is an evolutionary advantageous and stable strategy. However, AF implies actively searching and selecting resources, at the expense of time and energy. Thus, it is not certain that AF evolves systematically by natural selection under all conditions.

Therefore, these considerations call for re-exploring the relationships between diversity and stability in an eco-evolutionary context where AF has a true evolutionary dynamics and diversity is an emergent property of the eco-evolutionary dynamics. This need to include eco-evolutionary dynamics in the development of the BEF framework has already been advocated (Fussmann et al., 2007; Loreau, 2010b; Thuiller et al., 2013). Indeed, primarily to question the relationship between diversity and ecosystem properties one can ask how diversity emerges and what feedbacks may exist between diversity and other properties when evolution is taken into account. Indeed, evolution can be fast enough to share a time scale close to that of ecological dynamics, so that feedbacks exist between evolutionary and ecological dynamics (Hairston Jr et al., 2005; Thompson, 1998). Thus, we propose an eco-evolutionary context where the evolutionary and ecological dynamics interact in order to understand the links within the AF-diversity-stability triangle. In particular, we seek to answer the following questions (Figure IV.2):

* To what extent is AF evolutionary adaptive ?

* When AF evolves, what are its effects on the emergent properties of the community: biomass, productivity and diversity ?

* What is the effect of AF on stability ? Furthermore, after exploring its effect on diversity, is its effect on stability direct or indirect (i.e. through diversity)?

<figure><img src="image_43.png" /><figcaption>Figure IV.2 – The main interactions explored by the study. We question the evolution of AF through natural selection, and then its effect on community diversity and stability. We distinguish whether the effect of AF on stability is directly related to AF or whether it is related to the effect of AF on diversity.</figcaption></figure>
IV.2.3 Model and methods

Consumer-resource model

We focus on a system consisting of resources and consumers characterised by a niche trait and foraging strategies characterized by a foraging trait. Resources can diversify in the ecological niche thanks to mutation, natural selection and competition. Consumers need resources to survive in the ecological niche. Their consumption depends on their niche trait as well as their foraging strategy ranging from random foraging to adaptive foraging. Our deterministic model describe the evolution in time and trait space of the resources density (r), the consumer density (c) and the foraging strategy (φ) of the consumers under mutations, selection and interactions. We write:

$$
\partial_t r = r \left( g \left( 1 - \frac{r_{eff}}{K(y)} \right) - \overbrace{F_r[r, c, \phi]}^{\text{resource consumption}} \right) + \overbrace{M_y(r)}^{\text{niche trait mutations}} \quad (\text{IV.1})
$$

$$
\partial_t c = c \left( \underbrace{F_c[r, \phi]}_{\text{resource absorption}} - \underbrace{(d + I \rho_c(t))}_{\text{maintenance cost competition}} \right) + \underbrace{M_x(c)}_{\text{niche trait mutations}} + \underbrace{M_z(c)}_{\text{AF trait mutations}} \quad (\text{IV.2})
$$

The components of the model and the foraging strategy model for φ are described below.

**Resource-consumer interactions and niche traits.** In the absence of consumers, resources grow logistically depending on their niche trait *y* which defines their carrying capacity *K*(*y*). We fix the centre of niche at *y*₀ = 0, the optimal trait where the carrying capacity is maximal *K*₀. The carrying capacity follows a Normal distribution of variance *σ*ₖ which describes the niche width (see Figure IV.3a). Inside the niche, the resources face competition with resources in their trait neighbourhood *r*ₐₗ(*t*, *y*) = ∫ *C*(|*y* − *y*′|)*r*(*t*, *y*′)d*y*′ (Dieckmann and Doebeli, 1999). The competition strength *C*(|*y* − *y*′|) between two resources of trait *y* and *y*′ only depends on the distance between their niche traits |*y* − *y*′|. The competition kernel *C* is a centered Normal distribution with variance *σ*ₚ characterizing the average neighbourhood around each trait (see Figure IV.3b).

In the presence of consumers, resources are exploited at a rate $F_r(r, c, \phi)$ while consumers
density increases thanks to the resource absorption $F_c(r, \phi)$. The interactions between resource
of trait $y$ and consumer of trait $x$ also depend on the resource-consumer affinity described by
the interaction kernel $\Delta(x, y)$. The interaction strength only depends on the distance between
traits and it follows a centered normal distribution of variance $\sigma$ describing the generalist
degree of consumers (see Figure IV.3c). We choose a Holling type II functionnal response to
describe those interactions. We write

$$
F_r[r, c, \phi](t, x, y) = \iint \frac{b\phi(t, x, y, z)\Delta(x, y)c(t, x)}{1 + s(z)b \int \phi(t, x, y, z)\Delta(x, y)r(t, y)dy} dxdz \quad (\text{IV.3})
$$

$$
F_c[r, \phi](t, x, y, z) = \alpha \int \frac{b\phi(t, x, y, z)\Delta(x, y)r(t, y)}{1 + s(z)b \int \phi(t, x, y, z)\Delta(x, y)r(t, y)dy} dy \quad (\text{IV.4})
$$

where $\alpha$ is the conversion coefficient, $b$ the extraction coefficient and $s(z)$ the searching time
which depends on the foraging trait $z$ as explained below.

Moreover, consumer density decreases due to mortality *d* and the competition between all
consumers at a rate *Iρ*<sub>c</sub> where ρ<sub>c</sub>(*t*) = ∬ *c*(*t*, *x*, *z*)dxdz is the total consumer biomass.
<figure><img src="image_44.png" /><figcaption>Figure IV.3 – a) Carrying capacity $K(y)$ of resources for various niche width $\sigma_K = \{0.5, 1, 2\}$. The niche centre fixed at $y_0 = 0$ corresponds to the maximal carrying capacity. b) Competition kernel $K_C$ for various neighbourhood sizes $\sigma_C = \{0.5, 1, 2\}$ between a focal resource $y' = 1$ and all resources according to their niche trait $y$. c) Interactions kernel for various generalist degree $\sigma = \{0.5, 1, 2\}$ between a focal consumer $x = 1$ and all resources according to their niche trait $y$. d) Searching time according to the foraging trait $z$. For panels a-c, the values of -5 and 5 as niche trait limits are arbitrary. The choice of negative and positive values on either side of the niche centre is for clarity.</figcaption></figure>

**Foraging strategies and adaptive foraging trait** The interaction between consumers and resources not only depends on the match between their niche traits but also on the way consumers distribute their foraging efforts. Since consumers have a finite time available for resources acquisition, they share this time between the different resources available. Consumers can choose different strategies to organize their foraging efforts $\phi(t)$: i) Random Foraging ($\phi_{RF}$)), the consumer randomly forages its environment without selecting resources or ii) Adaptive Foraging ($\phi_{AF}$), the consumer uses adaptive foraging by actively searching for the resources maximizing its energy gain. The consumer foraging strategy depends on its foraging trait $z \in [0, 1]$ which corresponds to the proportion of its foraging time spent using AF strategy. Thus, the resulting consumer efforts are

$$ \phi = z\phi_{AF} + (1-z)\phi_{RF}. $$

The RF effort $\phi_{RF}$ is directly proportional to the resource density

$$ \phi_{RF}(t, x, y) = \frac{r(t, y)}{\int r(t, y')dy'} \qquad (IV.5) $$

While the AF effort $\phi_{AF}$ evolves over time according to the following dynamics

$$ \partial_t \phi_{AF}(t, x, y, z) = l_{\phi} c(t, x, z) \left( \begin{aligned} & \int r(t, y) \phi_{AF}(t, x, y', z) [u(t, x, y, z) - u(t, x, y', z)]_+ dy' \\ & - \int r(t, y') \phi_{AF}(t, x, y, z) [u(t, x, y', z) - u(t, x, y, z)]_+ dy' \end{aligned} \right) \qquad (IV.6) $$
where $u(t, x, y, z)$ represents the potential gain of a consumer of trait $(y, z)$ on a resource of trait $x$, i.e. if the foraging efforts are only on this resource:

$$u(t, x, y, z) = \frac{b\Delta(x, y)r(t, y)}{1 + s(z)b \int \phi(t, x, y, z)\Delta(x, y)r(t, y)dy} \quad (IV.7)$$

The AF dynamics assumes that a consumer is able to compare the gains received from exploiting resource $y$ with the gains received from other resources $y'$ according to the effort it puts into each resource. For instance, if the potential gain $u$ is greater on resource $y$ than on resource $y'$, the consumer increases its foraging effort on resource $y$. Moreover, the increase is weighted by the density of resource $y$ and the effort it has put on resource $y'$ up to now. The more effort the consumer puts into a resource that is not optimal, the faster it will adjust its effort to the better resource.

However, we consider that the comparison between resources takes time for the consumer, so the adjustment of its efforts is not instantaneous. The parameter $l_{\phi}$ describes the speed at which it adapts its effort.

Moreover, the adaptive foraging induces an increase on the searching time, $s(z) = s_{min} + z(s_{max} - s_{min})$, because the consumer has to search for the targeted resources (Figure IV.3d).

**Mutation of traits and diffusion** In our model, we assume that the ecological and evolutionary dynamics occurs at the same time scale. Thus, the niche traits and the foraging traits evolves due to mutations. Unlike the adaptive dynamic framework where a mutant phenotype is introduced only if its invasive fitness is positive (Geritz et al., 1998), we constantly introduce mutants through niche trait diffusion $M_y(r)$ and $M_x(c)$ as well as AF trait diffusion $M_z(c)$ when AF evolves

$$M_x(c)(t, x, z) = \frac{U\sigma_m^2}{2}\partial_x^2 c(t, x, z), \quad M_y(r)(t, y) = \frac{U\sigma_m^2}{2}\partial_y^2 r(t, y) \quad \text{and} \quad M_z(c)(t, x, z) = \frac{U\sigma_m^2}{2}\partial_z^2 c(t, x, z)$$

where $U$ is the frequency of mutation and $\sigma_m^2$ is the mean effect of a mutation. The ecological dynamics selects for the mutants that persist. Thus, we assume that foraging traits and niche traits evolve separately, there are only additive effects of mutations, no epistasis.

## Numerical analysis of the model

**Community emergence** The eco-evolutionary dynamics of the model allows for the diversification of resources and consumers, thanks to mutation, until a community emerges (Figure IV.4a). In the initial condition, we consider a single resource placed in the centre of the niche $(y = y_0)$ and a consumer at the same position $(x = y)$. Since one of the objectives is to evaluate whether adaptive foraging can evolve by natural selection, the initial consumer has a purely random foraging strategy $(z = 0)$.

Note that although we consider continuous traits, the numerical analysis requires them to be discretised. Therefore, community emergence takes as input parameter the maximum number of niche trait values and foraging trait values. Typically the numerical simulations are performed with 31 values of niche trait and 11 values of foraging trait.

**Community proxies** To assess the effect of adaptive foraging on the community we measure community-level proxies: biomass, productivity and diversity. Biomass proxies are the total biomass of resources and the total biomass of consumers. For diversity we use functional diversity indices: the functional dispersion FDis (Laliberté and Legendre, 2010) and the functional regularity FRO (Mouillot et al., 2005). The productivity is measured as the
<figure><img src="image_45.png" /><figcaption>Figure IV.4 – a) Eco-evolutionary dynamics of a resource-consumer community starting from an initial condition with a resource and a consumer at the niche centre, and a purely random foraging strategy. Resource density ($r(t, y)$ (top panel), consumer densities according to niche trait $\int c(t, x, z)dz$ (centre panel) and foraging trait $\int c(t, x, z)dx$ (bottom panel). b) General structure of the study. 1) To what extent adaptive foraging can evolve through natural selection, 2) what are the effects of the evolution of adaptive foraging on community biomass, diversity and productivity and 3) what is the effect of the evolution of adaptive foraging on stability.</figcaption></figure>

total flow of biomass from resources to consumers.

**Overall scheme** Our numerical analysis is threefold (Figure IV.4b). First, we test how adaptive foraging can be adaptive from the perspective of natural selection. We generate 5000 communities associated to different set of parameters ($\sigma, \sigma_K, s_{max}, d, I, g$) and then we perform a global sensitivity analysis by Partial Rank Correlation Coefficients (PRCC, Saltelli et al. (2004)) on this sample. We focus on the mean value of the foraging trait in the community $\bar{z}$ defined as

$$ \bar{z}(t) = \iint z \frac{c(t, x, z)dxdz}{\iint c(t, x', z')dx'dz'} \quad (IV.8) $$
In this way, we highlight the influence of each parameter on the evolution of adaptive foraging, and thus the conditions that allow or prevent its evolution. Secondly, we choose 500 parameters values leading to persistence of resource-consumer community but with various mean trait foraging in the community. We compare those emerged communities with a community resulting from our model without foraging evolution ($M_z(c)$ is set to 0 in (IV.1) and the fixed foraging trait in the community is $z = \bar{z}$, the mean trait of the compared community). We then compare proxies of the communities to measure the effect of adaptive foraging evolution. The final step is to assess the effect of the evolution of adaptive foraging on the stability of the community. We use a single set of parameters to ensure the evolution of strong adaptive foraging (mean foraging trait $\bar{z} \approx 0.9$) and compare the responses to perturbations between the community with adaptive foraging evolution and the community with inhibited evolution.

**Adaptation to changing environment** Because of the eco-evolutionary dynamics induced by our model, we cannot use classical stability metrics of ecological studies (Domínguez-García et al., 2019). For instance, the robustness metric is based on the number of species that disappear after a disturbance (Kondoh, 2006, 2010). This metric is not suitable for our model because evolution can produce a constant turnover of species and can quickly replace a species that would become extinct. To maintain our community point of view, we investigate three type of perturbations: a) gradually increasing consumer mortality, c) brutally changing niche centre and b) gradually moving niche centre at constant speed. For each perturbation, we measure the critical perturbation intensity leading to extinction of consumers.

In the first perturbation, we measure the maximal mortality rate *d* the community can withstand (Figure IV.5a).

In the second, we induce a shift of the niche centre $y_0$ at constant speed $c > 0$, $y_0(t) = ct$. We measure the critical speed above which the community cannot keep pace with the niche shift (Figure IV.5b).

The last perturbation is an abrupt displacement of the niche centre from $y_0$ to $y_0 + \delta$, $\delta > 0$. We measure the maximal jump size of the niche centre above which community cannot adapt (Figure IV.5c).

## IV.2.4 Results

### How adaptive is adaptive foraging

To investigate under which conditions adaptive foraging (AF) is evolutionary adaptive we conduct a PRCC analysis on the six main parameters influencing the evolution of AF (Figure IV.6a). If the PRCC is positive, the parameter tends to promote AF, while it tends to inhibit AF for negative PRCC.

We show that all six parameters can play a significant role in the evolution of adaptive foraging (Figure IV.6a), so that depending on the conditions AF will not necessarily evolve. Thus, the conditions inhibiting the evolution of AF are: intrinsically specialised consumers (small $\sigma$), a narrow niche (small $\sigma_K$), a strong searching time trade-off (large $s_{max}$), a low intrinsic consumers mortality *d*, low inter-consumer competition (small *I*) and low resource growth (small *g*).

The effect of the intensity of the trade-off is rather obvious, but the effects of the other parameters require a little more thought. For instance, the promotion of AF when consumers are intrinsically generalists (large $\sigma$) is not intuitive. However, when consumers are intrinsically
<figure><img src="image_46.png" /><figcaption>Figure IV.5 – Schematic representation of the three perturbations: a) Gradually increasing mortality perturbation consists of successively increasing the mortality of consumers until all consumers are extinct. b) Niche-speed perturbation consists of a progressive displacement of the niche. The speed is gradually increased until all consumers are extinct. c) The niche-jump perturbation consists of an instantaneous displacement of the niche centre to a certain range. The range of the jump is gradually increased until the consumers are extinct.</figcaption></figure>

generalists they have a high capacity to extract all resources, so if they simply focus on resource abundance they will quickly over-exploit the most abundant resources. Thus, when consumers have an intrinsic generalist capacity they actually benefit more from being each specialised on a few resources through AF.

The effect of the size of the niche could be anticipated, as when the niche is narrow (small $σ_K$) there is little diversity with only a few resources and a few consumers, all with close niche traits. Thus, there is no interest in considering the match between the niche traits of resources and consumers, therefore the AF is detrimental.

Regarding the mortality of consumers ($d$), as well as their competition, it is possible to conclude that the more difficult the conditions are for consumers, the more the AF is favoured. In general, it can be assumed that when conditions are difficult consumers can no longer simply exploit resources in proportion to their abundance (but see further that this is no longer true when conditions reach the limits of viability).

Finally, when resources grow rapidly (large $g$), those that are far from the niche centre become interesting to exploit for adapted consumers. These consumers then use AF to exploit these resources (see Figure IV.6b). Indeed, since the densities of these resources are lower than those of resources close to the niche centre, AF is essential in order to focus foraging efforts on them.
<figure><img src="image_47.png" /></figure>

Figure IV.6 – a) PRCC analysis on the mean foraging trait of the community for the six main parameters: σ, σ<sub>K</sub>, s<sub>max</sub>, d, I and g. The proxy targeted by the analysis is the evolution of adaptive foraging, expressed by the average value of the foraging trait at the community level. b) Example of a community with a diversity of foraging trait values. The red arrow indicates the propensity of consumers to adopt a foraging strategy with higher proportion of adaptive foraging when they are far from the niche centre.

Moreover, not all consumers in a community have the same adaptive foraging intensity (Figure IV.6b). In fact, the position of consumers in the niche determines their foraging strategy. Consumers furthest from the niche centre use AF while consumers in the centre of the niche have a more random foraging strategy, and therefore focus on the most abundant resources in the niche centre.

Effect of adaptive foraging on community

First, we show that in general the evolution of AF is accompanied by a gain in consumers biomass on average, at the expense of a decrease in resources biomass (Figure IV.7a). By measuring the niche overlap between consumers we show that the gain in biomass of consumers is explained by a complementarity effect (Figure IV.12). Indeed, the presence of adaptive foraging in the community decreases the niche overlap between consumers (Figure IV.12a), i.e. consumers use resources differently, thus increasing the complementarity between them. Moreover, the diversity of foraging strategies, i.e. different values of foraging trait, increases complementarity even more (Figure IV.12b).

However, some communities where AF evolves have lower consumer biomass than communities
where AF is inhibited. Indeed, the variability of biomass increases with the mean foraging
trait of the community.

Secondly, AF has a positive effect on consumer and resource diversities, both on functional dispersion (Figure IV.7b) and functional regularity (Figure IV.13). Although the variability of diversity increases with mean foraging trait, the difference of communities without AF is
<figure><img src="image_48.png" /><figcaption>Figure IV.7 – Difference in the three proxies (biomass, diversity, productivity) between communities where the evolution of AF is allowed by the diffusion of the foraging trait and communities where the evolution of AF is inhibited. a) Difference in biomass. b) Difference in functional dispersion. c) Difference in productivity. For all panels, differences are made from 500 pairs of communities that emerged with 500 different parameter sets. The dotted lines represent the mean and the areas the standard deviation</figcaption></figure>

almost always positive with rare exceptions. Thanks to AF, consumers have the ability to impose a superior consumption pressure on resources that are far from the centre of the niche than consumers without AF. This consumption pressure leads to an eco-evolutionary dynamics comparable to an arms race where resources have a selection pressure to grow towards the limits of the niche to escape the consumers. Moreover, the consumption of resources that are far from the niche centre reduces the competition between them, which allows the growth of resources even further from the centre.

Finally, the relationship with productivity (i.e the flow of biomass from resources to consumers) seems more complex because non-linear (Figure IV.7c). Thus, when the community with AF evolution has a rather low mean foraging trait, although higher than 0, there is a consequent productivity gain compared to the community without AF. However, above a mean foraging trait of about 0.4, the increase in AF within communities results in a productivity gain that becomes smaller, until it is slightly negative on average for mean foraging trait close to 1. Interestingly, with strong AF there is an increase of variability of productivity. Thus, although the negative effect on average, among the communities with strong AF some have a great gain in productivity and others a great deficit.
Relationship between diversity, adaptive foraging and stability

Now, we aim to understand the effect of AF on the stability of community. Since Stability and diversity are often linked, we aim to disentangle the direct effect of AF on stability from its indirect effect through diversity.

<figure><img src="image_49.png" /></figure>

Figure IV.8 – Communities with and without AF evolves similarly under consumer mortality increase. a) Responses of both communities (with and without the AF evolution) expressed as the coefficient of variation of consumer biomass. A negative coefficient of variation indicates a decrease in biomass, the threshold value of –1 corresponds to an extinction of all consumers. The coloured gradient indicates the mean foraging trait inside the community. b) Response of the monospecific community according to the value of the single foraging trait allowed. In this case the evolution of the foraging trait is inhibited.

Regression of AF prevents the direct negative effect of AF on the stability of community facing mortality increase

By applying the perturbation of increasing mortality until consumers extinction we show that the community with AF evolution reacts similarly to the community without AF evolution. Both communities lose their consumers at close mortality values (Figure IV.8a). After each increase in consumers mortality the two communities reach a new equilibrium with a lower and lower consumers biomass. Thus the coefficient of variation of the biomass follows a monotonic decrease until it reaches the limit value of –1 corresponding to a zero consumers biomass. Moreover, under this mortality perturbation, consumers in the community with AF evolution gradually reduce their foraging trait.

However, by examining the response of monospecific communities in terms of foraging trait and without evolution, we show that the greater the foraging trait of consumers the smaller the maximum mortality they can sustain (Figure IV.8b). When the mortality increases the consumers cannot persist far from the niche centre where resources have a low growth rate. This leaves only consumers close to the niche centre, where it is better to have a random foraging strategy. Thus, when consumers are forced to do AF in a niche centre they pay the trade-off due to AF while having no gain from AF and eventually the maximum mortality they can sustain is lower than consumers not using AF. Hence, we show a direct negative effect of
## AF.

In fact, this negative effect explains why under a critical increase of mortality the community with AF evolution is very similar to the community without AF evolution. As mortality increases, consumers gradually reduce their adaptive foraging until an average foraging trait close to 0 (Figure IV.8a, color gradient). Thus, AF has a direct negative effect on community stability in the face of increase mortality, but with AF evolution the negative effect only causes AF regression and community stability with evolution is not impacted.

<figure><img src="image_50.png" /><figcaption>Figure IV.9 – Results of the niche-speed perturbation. a) Responses of both communities (with and without the AF evolution) expressed as the coefficient of variation of consumer biomass. A negative coefficient of variation indicates a decrease in biomass, the threshold value of -1 corresponds to an extinction of all consumers. The coloured gradient indicates the value of the average foraging trait at the community level. b) Response of the monospecific community according to the value of the single foraging trait allowed. In this case the evolution of the foraging trait is inhibited.</figcaption></figure>

## AF enhances lag load under shifting niche

We then investigate the impact of resource niche perturbations on the community stability. We start with a niche shifting its centre at a constant speed.

We show that the community with AF evolution suffers the disappearance of its consumers for a maximum speed of niche displacement lower than the maximum speed sustainable by the community without AF evolution (Figure IV.9a). In fact, we see that with the increase in the speed of niche displacement, i.e. the intensity of the perturbation, the AF regresses in the community with evolution. While in the initial community the average foraging trait is about 0.9, at the first perturbation intensity it drops to 0.4. And at the maximum perturbation that the community can sustain the average foraging trait is about 0.05. Thus, although the AF is detrimental face of this perturbation, its evolution allows its regression. However, when the speed of niche displacement is too fast, consumers do not have time to evolve towards a reduction in AF and become extinct. This is why the community with AF evolution, and initially a strong AF, does not withstand as much perturbation as the community without AF can.

By testing the response of monospecific communities, we validate the direct negative effect of
AF on the stability of the community in the face of this disturbance (Figure IV.9b). When the niche shifts, the diversity of resources is reduced and only those resources that follow the shift of the niche centre have abundances that are attractive to consumers. A random foraging strategy will mostly exploit these resources and there is no possible advantage to increase foraging effort on other resources since their abundances are too low. Thus, the use of AF by consumers does not bring any advantage in the exploitation of resources, and on the contrary consumers pay the trade-off of searching time.

a

<table><thead><tr><td>Community type</td><td>Maximum sustainable niche-jump</td></tr></thead><tbody><tr><td>Community B :<br>without adaptive foraging evolution</td><td>8</td></tr><tr><td>Community A :<br>with adaptive foraging evolution</td><td>10</td></tr><tr><td>With adaptive foraging evolution<br>but with diversity of community B</td><td>9</td></tr><tr><td>Without adaptive foraging evolution<br>but with diversity of community A</td><td>10</td></tr></tbody></table>

<figure><img src="image_51.png" /></figure>

Figure IV.10 – Results of the niche-jump perturbation. a) Responses of four types of community: the two classic communities (with and without AF evolution) named A and B, and two other communities corresponding to the classical communities but whose diversity has been exchanged. b) Response of the monospecific community according to the value of the single foraging trait allowed. In this case the evolution of the foraging trait is inhibited.

## Direct and indirect stability enhancement by AF under niche-jump perturbation

The second perturbation of the niche is the niche-jump, i.e. sudden shift of the niche centre to a certain distance from the initial centre. Following a niche-jump if the community persists it will rebuilt a similar community around the new niche centre and reach an equilibrium similar to the one before the perturbation. Thus it is impossible to use the coefficient of variation of biomass as a proxy for the response to the perturbation. We only look at the maximum magnitude of the niche-jump that the community can sustain as a proxy for stability.

We show that the community with AF evolution can manage a larger maximum niche-jump than the community without AF evolution (Figure IV.10a, first and second rows). This effect suggest that a greater diversity leads to greater stability through a selection effect. We test the effect of diversity by applying the diversity of the community without AF evolution to the community with AF evolution, i.e. a decrease in diversity. The maximum niche-jump sustained by this community falls between the two values of the previous community (Figure IV.10a, third row). This means that there is a positive effect of diversity, which is lost by reducing diversity, but also a positive effect directly related to the use of AF by consumers. Conversely, by applying the diversity of the community with AF evolution to the community without AF evolution, the maximum sustainable perturbation is the same as that supported
by the community with AF evolution (Figure IV.10a, last row). Thus, diversity in itself is
sufficient to sustain this disturbance without the help of AF.

By testing the response of monospecific communities in terms of foraging trait, we find the positive effect of adaptive foraging on stability in the face of niche-jump perturbation (Figure IV.10b). Moreover, we see that when consumers make little use of adaptive foraging, the maximum sustainable perturbation corresponds to an intermediate value. We know that AF has a positive effect on diversity (Figure IV.7b), so the monospecific community with low AF has an intermediate diversity compared to diversity without AF and diversity with high AF, and therefore an intermediate stability.

IV.2.5 Discussion

<figure><img src="image_52.png" /><figcaption>Figure IV.11 – Caption</figcaption></figure>

The present work explores the threefold interactions between Adaptive Foraging, diversity and stability in an eco-evolutionary context (Figure IV.11). We show that AF is an important process within the BEF framework because its evolution have direct and indirect effects on both diversity and stability of communities composed of primary producers and consumers.

**Evolution of adaptive foraging**

Previous models exploring the effect of AF on community characteristics assumed that AF was a fixed trait of equal intensity for all consumers (Beckerman et al., 2010; Heckmann et al., 2012; Kondoh, 2003a,b; Uchida and Drossel, 2007). However, its intensity may vary between consumers and this behavior may be absent in some ecological contexts. In our study, we first investigate under which conditions the AF can emerge. We show that AF does not evolve systematically by natural selection. In stressed ecosystems where the diversification of primary producers is constrained by a narrow niche, the evolution of AF is limited, due to the low diversity of resources. Furthermore, when the cost of AF is too large compared to the size of the niche (for instance small $\sigma_K$ and high $s_{max}$), the AF does not emerge (see Figure IV.6a for a full representation of the unsuitable condition for the AF to emerge). In those unfavorable cases, consumers diversify according to their niche trait but all maintain a minimal foraging trait corresponding to random foraging.

Moreover, even under ecological conditions for which AF can evolve, this does not occur with
the same intensity for all consumers. Consumers adapted to resources that are far away from
the niche optimum are selected for strong AF, because their resources occur at low density.
Conversely, consumers adapted to abundant resources growing at the center of the niche do
not need to be choosy, since by feeding randomly they often encounter their optimal resource.
Thus, evolution does not simply lead to either the presence or the absence of AF at the
community level, but to a diversity of strategies among the community. The foraging strategy
truly depends on the position of consumers in the niche.

Effects of adaptive foraging on biomass, productivity and diversity of community

The evolution of AF, measured by the mean foraging trait across consumers, has several effects on community properties in comparison with communities emerging in the same conditions except that consumers cannot become choosy. The evolution of AF increases the biomass of consumers and decreases the biomass of resources (Figure IV.7a). Indeed, AF induces a reduction of the niche overlap between consumers (Figure IV.12). In other words, it promotes interspecific complementarity. With AF, consumers have more diversified diets and therefore use more resources. Its effect on productivity is non-linear (Figure IV.7c). When AF intensity is from low to moderate, community productivity increases, whereas intense AF induces on average a slight decrease in productivity. In fact, it seems that when the AF becomes too strong, the gain in biomass of the consumers is too much at the expense of the biomass of the resources. Thus the productivity corresponding to the flow of the resources to the consumers, is reduced. Finally, the evolution of AF also enhances the functional diversity of both consumers and resources (Figure IV.7b). Indeed, this positive effect of AF is due to an eco-evolutionary loop between resources and consumers that resembles the Red Queen hypothesis (Van Valen, 1973). In the absence of AF, the resources standing far away from the niche centre are subject to a small consumption pressure, because the consumers cannot specialize on them. These resources exert interspecific competition in the vicinity of their niche, which prevents the emergence of other resources further away from the niche centre. In contrast when AF evolves consumers can consume these resources more heavily, reducing their density. Thus, it decreases competition among resources allowing for the emergence of new resources among the niche. therefore, resource diversity increases. The evolution of new resource species triggers the diversification of consumers which are also further away from the niche centre, and so on. This process stops when the limits of the exploitable niche are reached by the resources.

Moreover, the evolution of AF in the first place occurs when the diversity of resources is high enough, which occurs in relatively unstressed environments (large resource niche width, σ<sub>K</sub>). Causation is therefore circular: AF both promotes and is promoted by resource diversity. However, the evolution of AF increases the variability of each of these community properties, which may blur the overall trends. When AF does not evolve the emerging communities have similar properties across simulations. However, when AF emerges, the resulting communities can show contrasting biodiversity and productivity characteristics, even if the mean foraging trait among consumers are similar. Beside some rare exceptions, AF always increases diversity. However, the gain of diversity can vary a lot, from a slight increase to a doubling increase (Figure IV.7b). However, the impact of AF on biomass and productivity is more complex. Although biomass and productivity are often positively correlated (Balvanera et al., 2006; Cardinale et al., 2006; Loreau, 2010b; Tilman, 1996; Tilman et al., 1997), the evolution of AF can mitigate this relationship.
## Community stability

Previous theoretical studies have reported a positive effect of AF on community stability (Beckerman et al., 2010; Heckmann et al., 2012; Kondoh, 2003a,b; Uchida and Drossel, 2007), based on ecological niche-model and measures of food web robustness. In parallel, several experiments (Schläpfer and Schmid, 1999; Tilman, 1996; Tilman and Downing, 1994; Tilman et al., 1996) and models (May, 1973; Thibaut and Connolly, 2013; Van Altena et al., 2016; Yodzis, 1981) have established a causal relationship between diversity and stability. Given the bidirectional relationship between AF and diversity, the effect of AF on community stability may therefore be direct, indirect, or both. This question can be tackled by the present work because, contrary to previous studies, diversity was not fixed but instead emerged during the eco-evolutionary dynamics.

We show that, after a sudden environmental change (niche-jump perturbation), communities with AF were more stable (Figure IV.10a). AF increases diversity of both producers and consumers, in particular it favors the emergence of species standing far away from the niche center. In a sense, those extreme species were already adapted to the niche jump perturbation and therefore persisted, unlike the central species. The positive effect of diversity on stability was therefore due to a selection effect (Loreau and Hector, 2001), since the higher diversity triggered by AF allows for "selection" of perturbation-resistant species. We also found that AF increased the complementarity between species (Figure IV.12), since it reduced their niche overlap, but this had no effect on stability at least with respect to the different perturbations tested.

We also show that there is a positive direct effect of AF in the face of this pressure, although weaker than the indirect effect through diversity. This effect is certainly explained by the delay in the evolution of consumers towards the new niche optimum compared to resources. After the abrupt change in environment, resources evolve towards the new optimum so that resources with high densities are quickly distanced from consumers in trait space. Consumers with a random foraging strategy continue to exploit these resources even though they are no longer sufficiently adapted to them. On the contrary, thanks to AF, consumers can focus on resources to which they are better adapted despite their lower densities. Because of its positive effect, and the punctual nature of the disturbance, the AF is not affected by the disturbance, and when the community shifts on the new niche optimum it is similar to before the disturbance. In contrast, in the cases of ecosystem disturbance or constant environmental change, AF had a negative direct effect on stability. This occurred because AF is costly; choosy consumers went extinct prematurely in comparison to random consumers. This time, diversity had no effect on stability, which precluded any indirect positive effect of AF. This non-effect of diversity is due to the gradual and persistent nature of these disturbances that destroy diversity, thereby depriving it of a possible positive effect. Finally, the evolution of AF was hampered by these two ecosystem pressures (Figure IV.11), intense disturbances even led to its complete disappearance. In the case of mortality increase AF regressed quickly, so that its potential negative effects were not perceived. A purely ecological model without evolution would have found a negative effect of AF on stability, missing the fact that AF can regress during the course of the ecosystem pressures. The same process was at work with the niche-speed pressure but the regression of AF was not fast enough, so that the direct negative effect of AF was apparent for intense pressures.

**Conclusion** In communities harboring primary producers and their consumers, diversity and ecosystem properties such as biomass, productivity and stability are often positively related (Schläpfer and Schmid, 1999; Tilman, 1996; Tilman and Downing, 1994; Tilman et al., 1996). This can be explained by a complementarity effect between species when they are
diverse, which also increases the chances of resisting a disturbance since some species will probably be insensitive to it (Griffin et al., 2009; Loreau and Hector, 2001; Poisot et al., 2013; Vanelslander et al., 2009). Greater diversity also increases the probability of having a few species that perform well under certain conditions, this is the selection effect (Loreau and Hector, 2001). However, since consumers often modify their foraging activities in function of the abundance distribution of the resources (Bergman et al., 2001; Hassell and Southwood, 1978; Whiten et al., 1991), theory should incorporate the evolution of adaptive foraging (AF) to the evolutionary diversification of producer-consumers communities.

We show that the emergence of diversity can be favored by the evolution of AF, and reciprocally that diversity can promote AF evolution. In the case of sudden environmental change, this bidirectional process between AF and diversity enhances community stability through the selection of species at the edge of the environmental niche. In the case of constant environmental change or of ecosystem disturbance, AF can instead destabilize the communities because of its intrinsic cost. However, in such cases AF becomes itself counter-selected, which ultimately cancels out its negative effect on stability.

Furthermore, we show that the evolutionary diversification of resources and consumers shaped by AF produces a wider array of communities, with biomass and productivity characteristics much more heterogeneous than communities without AF. As a result, the relationships between diversity and biomass, and between diversity and productivity can be positive, negative or unimodal. Although the evolution of AF always promotes diversity, it also leads to a more complex picture than the standard positive relationship between diversity, biomass and productivity.

The multi-directional causal mechanisms involved in our study emphasize that the relationships between ecosystem characteristics, in particular adaptive foraging, productivity and stability, are not necessarily fixed for a given ecosystem, and that the existence of eco-evolutionary feedback loops can turn these relationships dynamics and historical.
IV.2.6 Appendix

<figure><img src="image_53.png" /><figcaption>Figure IV.12 – Relationship between niche overlap and adaptive foraging. a) Niche overlap according to foraging trait value. For each foraging trait value, there is a community with a single foraging trait value and no evolution of that trait. b) Niche overlap as a function of foraging strategy diversity. The niche overlap is measured for a community with a single maximum foraging trait value (z = 1), then the measure is repeated with a community with two foraging traits (z = 1, 0.9), and so on until a community with all possible foraging trait values is reached.</figcaption></figure>

<figure><img src="image_54.png" /><figcaption>Figure IV.13 – Difference in functional regularity between communities where the evolution of AF is allowed by the diffusion of the foraging trait and communities where the evolution of AF is inhibited. The difference is made from 500 pairs of communities that emerged with 500 different parameter sets.</figcaption></figure>
# CHAPITRE V

## CONCLUSION GÉNÉRALE ET PERSPECTIVES

Dans ce dernier chapitre notre objectif est de dépasser les discussions détaillées incluses à l'issue de chacun des chapitres pour créer, à l'image de ce qui a été fait dans l'introduction générale, des liens conceptuels entre ces trois chapitres.

### Causalité réciproque

L'élément fondamental qui émerge de l'ensemble des travaux de cette thèse est l'importance du principe de causalité réciproque dans les systèmes complexes. Nous montrons dans trois contextes biologiques différents comment peuvent émerger de l'ensemble des interactions parties-parties, parties-tout et tout-parties, des causalités réciproques qui ont un rôle fondamental dans les propriétés de ces systèmes complexes. Pour rappel, dans le chapitre II nous montrons que les propriétés du système buis-pyrale reposent sur la causalité réciproque entre les communautés et la métacommunauté. La dynamique de la metacommunauté émerge des interactions entre les communautés via la dispersion de la pyrale et du buis, tandis qu'en retour les dynamiques locales sont également influencées par la dynamique globale de la métacommunauté, et notamment les extinctions de certaines communautés de buis à cause d'invasions successives de la pyrale. Dans le chapitre III nous montrons que la transition du parasitisme vers le mutualisme du système hôtes-symbiotes dépend de bouclages causaux entre les dynamiques écologique et évolutive ainsi qu'entre trois niveaux d'organisations différents. Ainsi, l'apparition par mutations d'une faible proportion de mutualistes, malgré leur désavantage initial, entraîne une augmentation de la compétition entre les hôtes, qui à son tour change la dynamique écologique des différents couples hôtes-symbiotes, au profit final du phénotype mutualiste. Enfin, dans le chapitre IV nous montrons le rôle de la causalité réciproque entre écologie et évolution dans l'émergence de communautés. Plusieurs bouclages causaux peuvent être décrits, le principal concernant la diversité de la communauté et l'évolution de l'adaptive foraging (AF). L'émergence d'une diversité de ressources suffisante en conditions environnementales favorables, va favoriser l'évolution de l'AF chez certains consommateurs, et l'AF à son tour va induire une pression de sélection sur les ressources se traduisant par une plus grande diversification. Ce premier point mérite d'être remis dans la perspective de notre introduction, qui montrait les limites d'une vision réductionniste, y préférant une vision dialectique. Effectivement, dans les trois contextes biologiques étudiés les propriétés des systèmes complexes ne dépendent pas uniquement des propriétés des parties. C'est l'ensemble des interactions, et les causalités réciproques qui en découlent, qu'il faut considérer pour appréhender ces systèmes. Poussée à l'extrême, la vision dialectique suggérerait que les parties ne puissent même pas être con-
sidérées en l'absence de l'ensemble des bouclages causaux avec le tout, puisque leurs propriétés sont constamment remodelées par ces bouclages. Néanmoins, l'usage de la modélisation nécessite de définir des parties, en incluant deux catégories : les variables d'état et les relations qui existent entre elles. Pour être plus concret, nous pouvons développer l'exemple du modèle de métacommunauté du système pyrale-buis qui nécessite que les communautés soient numériquement définies en l'occurrence sous forme de cellules de matrice. A l'opposé l'approche dialectique décrirait la métacommunauté plutôt comme un ensemble d'interactions plus ou moins fortes, aux contours mouvants. Cependant, nous tenons à souligner que nos méthodes de modélisation laissent une part importante au principe d'émergence (du mutualisme, de communautés, de structures spatiales), de telle sorte que les parties constitutives des systèmes complexes étudiés ne sont pas définies a priori. Irrémédiablement les parties sont représentées par des objets numériques distincts, mais en revanche le nombre de parties et les interactions entre elles sont des propriétés émergentes de nos modèles. Même dans le modèle de métacommunauté, bien qu'un nombre maximal de parties soit défini en conditions initiales (le nombre de peuplement de buis), les processus d'extinction et recolonisation restructurent ensuite le système en changeant ce nombre et leurs interactions.

## Persistance

Le deuxième point de convergence entre les chapitres est la question de la persistance de ces systèmes complexes. Comme décrit dans l'introduction (section I.4) cette question peut être envisagée comme un ensemble de sous-questions : de quoi dépend la persistance d'un système complexe, de ses parties, de son tout ? Mais le prisme de la vision dialectique impliquant que tout système contienne un changement, comment concilier ces notions de changement et de persistance ?

Dans l'introduction, nous avons apporté des éléments de réponse en proposant un cadre dans lequel l'individualité d'un système complexe, c'est-à-dire ce qui persiste, est défini non seulement par ses propriétés mais également par ses interactions, et notamment les causalités réciproques. Nous avons également utilisé comme synonyme la notion de processus. Ce qui définit un système, et donc ce sur quoi la persistance est évaluée, c'est que le système continue à réaliser les mêmes processus au cours du temps. Par exemple la persistance du système buis-pyrale est représentée par le maintien des interactions entre les deux espèces et entre les communautés, ainsi que par la causalité réciproque avec la métacommunauté. Nous suggérons alors la proposition "It's the song, not the singer" (Doolittle and Booth, 2017; Doolittle and Inkpen, 2018); autrement dit, l'important ce n'est ni les parties, ni le tout, mais l'ensemble des relations causales qui réalisent la "musique" du système et les propriétés qui conditionnent ces relations.

Cet élément de réponse à la question "qu'est-ce qui persiste ?" fournit également une réponse à cette autre question "qu'est-ce qui détermine la persistance d'un système complexe ?". Effectivement, puisque le système qui persiste peut être représenté par l'ensemble des relations causales, alors la persistance ne repose sur aucun élément du système en particulier mais sur l'ensemble des relations causales. Autrement dit, il est imaginable de considérer un système dont des parties changent, mais dont les interactions, et causalités réciproques, seraient inchangées. Cependant, les relations causales du système étant tout de même conditionnées par ses propriétés (par exemple le nombre d'espèces dans le système), un changement trop important des parties induira irrémédiablement un changement des relations causales et donc d'individualité du système. Ainsi, l'individualité ne repose pas uniquement sur la composition en parties, mais celle-ci joue tout de même un rôle.

Une analogie peut-être envisagée avec le mythe du bateau de Thésée raconté par Plutarque
toutes les planches de ce bateau sont progressivement remplacées au cours du temps, de sorte que la question se pose de savoir s'il s'agit toujours au final du bateau de Thésée. Nous considérons que tant que le bateau flotte, tant qu'il est propulsé par le vent, tant qu'il peut se manoeuvrer dans différentes directions, c'est-à-dire tant qu'il peut réaliser tous les processus normalement réalisés par le système "bateau de Thésée" grâce a ses propriétés (par exemple l'agencement des planches de telle sorte à former une coque), alors il s'agit toujours du même bateau.

Il est important de considérer que la vision de l'individualité et de la persistance des systèmes complexes que nous décrivons ici implique une prise en compte de l'historicité du système. Premièrement par le fait que nous soulignons l'importance des relations causales, dans l'individualité comme dans la persistance. Ces relations causales ne pourront être perçues que si elles s'expriment à travers le temps. Autrement dit, une photo instantanée d'un système, disons une communauté par exemple, ne montrera que les parties du système, pas les relations causales. De plus, nous avons précisé que l'individualité reposait non seulement sur l'ensemble des relations causales, mais aussi sur les propriétés les conditionnant. Ces propriétés qui jouent un rôle dans les relations causales du système ne peuvent être qu'une partie de l'ensemble des propriétés du système et nous pouvons les qualifier de propriétés fondamentales du système. Pour définir ces propriétés il est également nécessaire de considérer l'historicité du système.

Dans chacun des chapitres nous avons testé la persistance du système étudié, selon cette vision "dialectique" de la persistance. Dans le chapitre II cette vision s'exprime par la considération que le système persiste dès lors que les deux espèces coexistent en interaction dans le système complexe formé de la causalité réciproque entre communautés et métacommunauté. Dans le chapitre III, nous nous sommes intéressés à la persistance du mutualisme, non pas sous le prisme de la persistance du phénotype mutualiste, qui lui n'est qu'une partie du système complexe, mais sous le prisme de la persistance des relations causales permettant la formation du système avec une forte proportion de mutualistes. Ce système est constitué des populations d'hôtes et de symbiontes, parasites et mutualistes, qui sont en perpétuel changement. De plus, la structure spatiale change continuellement puisque des clusters s'effondrent alors que d'autres se forment. Malgré ces changements quantitatifs des différentes parties du système, l'ensemble des relations causales persiste de telle sorte que le mutualisme soit sélectionné. Notons que dans ce modèle nous considérons que la transition du parasitisme vers le mutualisme s'est produite à partir du moment où il y a 10% de symbiontes mutualistes dans la population. Le fait que ce critère soit quantitatif peut sembler aller à l'encontre de notre propos. Cependant, ce critère quantitatif, indispensable d'un point de vue méthodologique, cache des relations causales et donc un véritable changement de système selon notre définition. Ainsi, quantité et qualité entretiennent aussi une relation dialectique. Effectivement, le passage d'une proportion de symbiontes mutualistes d'environ 2%, lorsque les mutualistes sont contre-sélectionnés et simplement résultat de la variabilité phénotypique due aux mutations, à une proportion supérieure à 10% lorsque le mutualisme est sélectionné, n'est possible qu'à condition que la causalité réciproque entre le paysage (la compétition globale entre les hôtes), les clusters et les individus devienne suffisamment forte. Ainsi, les deux situations - avant et après transition - correspondent à deux systèmes différents. Lorsque nous perturbons le système avec une extinction des populations d'hôtes et de symbiontes dans une partie de l'espace, au-delà des changements quantitatifs engendrés, nous perturbons en fait la causalité réciproque entre le paysage et les sous-parties. Nous montrons que celle-ci peut néanmoins se reconstituer pour reformer le même système.

Enfin dans le chapitre IV, nous n'avons pas mesuré la persistance de trait ou d'espèces comme le veut la tradition associée à l'exploration de la stabilité de réseaux trophiques (Dunne
et al., 2002; Eklöf and Ebenman, 2006; Kondoh, 2003a; Sole and Montoya, 2001), mais celle des interactions dans les communautés. Effectivement, le modèle considéré impliquant une dynamique éco-évolutive il n’est pas possible de mesurer des extinctions d’espèces après une perturbation puisque l’évolution va pouvoir recréer ces espèces ensuite. De plus, à cause des causalités réciproques entre les niveaux trophiques et les dynamiques écologique et évolutive, les abondances au sein des communautés sont très dynamiques. Les communautés sont donc des systèmes complexes dont les parties sont en constant changement. Nous avons considéré qu’à travers l’extinction de l’ensemble du niveau trophique des consommateurs le système devenait réellement différent, à cause de la perte de la causalité réciproque non seulement entre les deux niveaux trophiques mais également entre l’AF et les propriétés de la communauté. Nos résultats sur la réponse des communautés face à la perturbation de changement brutal et ponctuel de l’environnement sont les plus explicites par rapport au cadre conceptuel précédemment décrit. En effet, face à cette perturbation, la persistance de la communauté repose sur la causalité réciproque entre l’évolution de l’AF et la diversité de la communauté. La diversité est à l’origine de l’évolution de l’AF qui se traduit par une plus grande diversité, elle-même responsable d’une persistance améliorée.

Ce cas particulier de la perturbation brutale (niche-jump) dans le chapitre IV permet d’illustrer le lien entre relations causales au sein du système et les propriétés assurant une meilleure persistance du système. En synthèse, le système génère les conditions favorables à sa propre persistance.

En fait, cette caractéristique se retrouve également dans les deux autres chapitres. Lorsque le système buis-pyrale du chapitre II est placé dans un espace initialement saturé en buis, la dynamique globale va induire l’extinction de certains peuplements de buis, autrement dit la disparition de certaines parties du système. Cette dynamique d’extinction du buis, et également de recolonisation, va perdurer jusqu’à atteindre un équilibre où l’espace sera constitué de groupements de peuplements de buis répartis à peu près équitablement. Cette structure spatiale favorise la persistance du système par rapport à la structure initiale caractérisée par des oscillations très prononcées de la population de pyrale, et donc sensible à d’éventuelles perturbations stochastiques en période de faible abondance. Pour ce qui est du chapitre III, la création par le système mutualiste des conditions permettant sa persistance selon un processus de construction de niche a déjà été discutée.

Dans le chapitre introductif (section I.3.2) ce phénomène était déjà présent dans notre extension du modèle de Pepper and Smuts (2002). Dans ce modèle l’apparition des consommateurs modérés à partir d’une situation initiale avec des consommateurs gourmands et sans structure spatiale est explorée. Nous montrons que la dynamique entre ressources et consommateurs gourmands génère une structure spatiale à travers la mortalité des ressources lorsqu’elles sont sur-exploitées. Cette structure spatiale permet ensuite l’émergence du phénotype modéré, qui devient même dominant dans la coexistence des deux phénotypes. Si nous considérons que le système est formé de la coexistence des deux phénotypes, dans ce cas celui-ci génère effectivement les conditions favorables à sa persistance. L’originalité tient à l’opposition entre chacune des parties du système - phénotype modéré vs phénotype gourmand - et aux conditions favorables à l’autre phénotype induites par chaque phénotype. Effectivement, le phénotype gourmand entraîne une forte mortalité des ressources créant une structure spatiale favorisant le phénotype modéré. À l’inverse, le phénotype modéré détruit la structure spatiale en entraînant la régénération de ressources non sur-consommées, favorisant ainsi le phénotype gourmand. Cette causalité réciproque positive entre les deux phénotypes, à travers la causalité réciproque avec la structure spatiale, est la source des oscillations des densités de chaque phénotype.
## Perspectives

Cette notion de systèmes complexes favorisant sa propre persistance permet maintenant d'aborder les perspectives de cette thèse dans le cadre de sa problématique principale, l'évolution des écosystèmes par sélection naturelle.

Nous avons brièvement évoqué en introduction les verrous conceptuels préalables à toute tentative de réponse à cette question. La théorie de l'évolution par sélection naturelle repose sur le trépied : variabilité (différents phénotypes), sélection (différentes valeurs sélectives), et hérédité (transmission du phénotype du parent au descendant). S'agissant du niveau d'organisation de l'écosystème, le principe de variabilité est facilement adaptable, en revanche les principes de sélection selon la valeur sélective (fitness) et d'hérédité sont plus complexes à envisager. Les travaux empiriques concernant cette question ont pu s'affranchir de ces difficultés grâce à une méthodologie permettant de traiter les écosystèmes comme des organismes (Blouin et al., 2015; Swenson et al., 2000a,b). Dans ces manipulations l'individualité des écosystèmes est crée par leur isolement (par exemple avec des écosystèmes microbiens isolés dans des tubes à essai différents), et la reproduction est assurée par l'expérimentateur en prenant un échantillon de chaque écosystème et en le laissant se développer dans un nouveau milieu. Ces manipulations montrent que l'évolution par sélection artificielle au niveau des écosystèmes est possible. À présent, l'approche conceptuelle et par modélisation cherche à s'affranchir des conditions restrictives de la sélection artificielle pour correspondre à la sélection naturelle.

Nous avons proposé l'idée que la fitness, habituellement mesurée comme la capacité à produire de nombreux descendants, pouvait en fait s'exprimer par la notion de persistance (Bouchard, 2008). La reproduction ne serait alors qu'une des composantes de la fitness, une manière de persister. Ainsi, la difficulté d'imaginer qu'un écosystème puisse se reproduire - en considérant le terme de reproduction dans le même sens que pour des organismes - n'empêche pas de penser qu'il puisse tout de même exprimer une fitness à travers sa capacité à persister (Bouchard, 2011, 2014; Dussault and Bouchard, 2017; Lenton et al., 2021). La persistance des écosystèmes peut elle-même être divisée en deux composantes : la capacité à persister localement et la capacité à se re-produire (ce qui correspond à une variante de la reproduction organismique).

La première composante peut s'exprimer comme une capacité à conserver les propriétés et relations causales qui font son identité en tant que système face aux perturbations. La conséquence sera alors sa persistance dans le temps au même titre qu'un phénotype avantageux perdurera grâce à des générations successives de descendants. Le lien est ainsi évident avec le principe de système générant, et préservant, des conditions permettant sa propre persistance. Ce principe s'apparente à une notion d'homéostasie des écosystèmes, ceux-ci se construisant sur des relations causales qui assurent le maintien de conditions permettant leur persistance (Boyd, 1999; Ibanez, 2020). La seconde composante de re-production consiste à accepter que les écosystèmes ne puissent pas se reproduire dans le sens organismique du terme, mais qu'un procédé analogue est concevable (Doolittle and Inkpen, 2018; Ibanez, 2020). La re-production repose sur la manière dont l'individualité des systèmes complexes a été définie plus haut, c'est-à-dire que les propriétés fondamentales et les relations causales sont à prendre en compte tout autant que la composition du système en terme de parties constitutives. (Doolittle and Booth, 2017; Doolittle and Inkpen, 2018; Ibanez, 2020). Ainsi, la dispersion d'organismes depuis un écosystème "parent" peut être comparée à la dispersion de propagules de cet écosystème. Si ces organismes finissent par former un ensemble, dans une localité différente de l'écosystème parent, mais de telle sorte que les propriétés fondamentales et relations causales de l'écosystème parent soient re-produites, alors il est possible de considérer que l'écosystème parent s'est re-produit. Et ceci malgré des différences possibles dans l'assemblage des organismes qui seraient provoquées par des dispersions d'organismes venant d'autres écosystèmes. Nous pouvons remarquer que les deux composantes de la fitness envisagées : persistance et re-production, sont étroitement
liées puisque le principe de re-production nécessite que l'écosystème parent ait une certaine persistance. Cette vision de la fitness des écosystèmes permet de prédire que les écosystèmes qui sont en mesure de générer les conditions favorisant leur persistance seront sélectionnés. Alors que dans les trois chapitres précédents cette capacité des systèmes à générer leur propre persistance est une propriété émergente non-sélectionnée, celle-ci pourrait être une propriété sélectionnée dans un contexte de méta-écosystème soumis à l'évolution par sélection naturelle.

Pour conclure, nous envisageons une approche par modélisation capable d'explorer cette question de l'évolution des écosystèmes par sélection naturelle.

Le principe serait de considérer un méta-écosystème, c'est-à-dire un assemblage d'écosystèmes en interactions à travers des flux biotiques et abiotiques. La différence avec le concept de métacommunauté et communautés résiderait dans la prise en compte supplémentaire du compartiment abiotique, alors que les communautés ne sont constituées que du compartiment biotique. En intégrant ce compartiment, des possibilités supplémentaires de dynamiques de type construction de niche sont créées, dans lesquelles l'écosystème générerait des conditions favorisant sa persistance, par exemple à travers des cycles biogéochimiques (Barot et al., 2016; Doolittle, 2017; Loeuille et al., 2017). Ces écosystèmes émergeraient de sorte que leurs différentes histoires évolutives mènent à une diversité d'écosystèmes. On peut imaginer qu'en conditions initiales l'environnement abiotique soit hétérogène afin de permettre cette diversité initiale à l'émergence. Par exemple Girardot et al. (2020) montrent comment l'environnement, en l'occurrence représenté par le taux de croissance d'une ressource basale, peut permettre la génération de réseaux trophiques aux propriétés variées à travers leur histoire évolutive. Les organismes auraient ensuite la possibilité de remodeler leur environnement selon une vision constructiviste de celui-ci. Les flux biotiques et abiotiques entre les écosystèmes assureraient leur mise en compétition et les écosystèmes les moins persistants pourraient être remplacés par la re-production des plus persistants.

Des travaux récents se plaçant dans le cadre de l'hypothèse Gaia (Lovelock and Margulis, 1974) - mais dans une version moins idéaliste, à l'image de la théorie de sélection multi-niveaux par rapport à la sélection de groupe naïve - ont posé les premières pierres en explorant comment des organismes peuvent rendre leur écosystème plus persistant ou productif (Arthur and Nicholson, 2017; Boyle et al., 2012; Doolittle, 2017; Lenton et al., 2018; zu Castell et al., 2019). Ces travaux amènent des réflexions conceptuelles et des résultats en modélisation intéressants. Cependant, les modèles sont généralement fondés sur des présupposés propres au milieu microbien ou bien formés d'écosystèmes minimalistes. De plus, ils ne considèrent pas systématiquement plusieurs écosystèmes en compétition. Or, au même titre que l'exploitation d'individus altruistes par des individus tricheurs, la question peut se poser de l'exploitation d'écosystèmes de type Gaia par des "écosystèmes tricheurs". Un élargissement de ces résultats à des modèles incorporant des interactions plus complexes et des écosystèmes en compétition dans un méta-écosystème nous semble la prochaine étape.

Enfin, considérer la possibilité de conflit entre niveaux de sélection, par exemple entre le niveau de l'individu et celui de l'écosystème semble une composante importante. Effectivement, si les phénotypes des individus assurent en même temps la sélection de ces individus et la sélection des écosystèmes composés de ces phénotypes alors il est difficile de différencier si la sélection agit uniquement au niveau de l'individu ou également au niveau de l'écosystème. Il est tout à fait possible que la sélection agisse dans la même "direction" aux deux niveaux, ce qui représente alors le versant "facile" de l'exploration de la sélection au niveau des écosystèmes. Idéalement, nous aimerions aborder le versant "difficile", c'est-à-dire lorsque les forces de sélection entre les différents niveaux de sélection sont opposées. Par exemple, la sélection au niveau individuel pourrait favoriser des phénotypes très compétitifs au sein des différents
niveaux trophiques, mais en situation de dominance de ces phénotypes, la persistance de l'écosystème serait fragilisée pour diverses raisons (un recyclage des nutriments moins efficace par exemple). Ainsi, ces individus très compétitifs seraient potentiellement en mesure d'envahir des écosystèmes au sein du méta-écosystème, mais les écosystèmes contenant une proportion trop importante de ces individus verraient leur compartiment abiotique dégradé et serait contre-sélectionné par rapport à d'autres écosystèmes plus persistants et productifs.

Notre contribution à cet édifice grâce à la pierre apportée avec le chapitre III sur l'évolution du mutualisme est ainsi illustrée car la dynamique décrite dans ce chapitre est en plusieurs points similaire à celle imaginée ici. Resterait à dépasser le stade de l'écosystème minimaliste en modélisant un écosystème écologiquement plus riche, par exemple en considérant plusieurs niveaux trophiques avec potentiellement des interactions variées (antagonistes et mutualistes), ainsi qu'un compartiment abiotique avec un cycle des nutriments.
## RÉSUMÉ

Les domaines de l'écologie et l'évolution sont constitués de systèmes complexes – organismes, espèces, communautés – qui se prêtent mal à une approche réductionniste. Ces systèmes ont des propriétés émergentes qui dépassent la somme des propriétés de leurs parties. Leur étude demande alors de s'intéresser aux interactions entre les parties et le tout de ces systèmes. Par exemple, l'étude d'une métacommunauté ne peut pas se limiter à l'étude stricte du tout (la métacommunauté) ou l'étude stricte des parties (les communautés composant la métacommunauté). La compréhension de cet système complexe demande de considérer le tout, les parties, et les interactions entre eux. De plus, ces interactions peuvent être multidirectionnelles, elles ne sont pas exclusivement des parties vers le tout, la causalité réciproque est possible, le tout influençant alors les parties. Dans cette thèse nous explorons à travers trois systèmes biologiques distincts comment les interactions entre le tout et les parties définissent ces systèmes. La thèse est donc constitué de trois chapitres. Dans le premier nous explorons un modèle de métacommunauté simulant l'invasion de la pyrale du buis, un insecte herbivore invasif en Europe, et étudions les interactions entre les échelles spatiales locale et globale. Ce modèle écologique de dynamique des populations est calibré à partir de mesures empiriques sur le terrain et à travers une manipulation en mésocosme. Notre modèle reproduit l'instabilité des dynamiques locales. En effet, localement l'insecte s'éteint irrémédiablement à cause de sa sur-exploitation de sa ressource (le buis). Cependant, notre modèle montre que les interactions entre les communautés, grâce à la dispersion de l'insecte, peut mener à la persistance du système à l'échelle de la métacommunauté. De plus, nous montrons que la structure de la métacommunauté émerge des interactions entre les dynamiques locales. Le deuxième chapitre explore dans quelle mesure une interaction mutualiste entre un hôte et un symbionte peut émerger à partir d'une interaction parasitique en coévoluant avec la dispersion. Nous développons un modèle éco-évolutif individu-centré dans un espace spatialisé en 2D et considérons comme condition initiale une population d'hôtes en interaction avec une population de symbiontes parasitiques. Nous montrons que grâce à l'évolution d'une dispersion locale une structure spatiale peut émerger de la dynamique du système hôte-symbionte. L'émergence de cette structure spatiale induit la formation de plusieurs niveaux d'organisation en interactions entre eux : le niveau de l'individu, le niveau du regroupement spatial, et le niveau du paysage. Tandis que le niveau de l'individu favorise l'évolution du parasitisme, les deux niveaux supérieurs du regroupement spatial et de l'ensemble du paysage favorise l'évolution du mutualisme. Nous montrons que selon la force de la structure spatiale, modulée par l'intensité de la compétition à l'échelle du paysage, la transition du parasitisme vers le mutualisme peut se produire. Enfin, le dernier chapitre s'intéresse à l'évolution d'une stratégie d'acquisition de ressource chez des consommateurs dans un modèle éco-évolutif consommateurs-ressources. La littérature montre que la capacité des consommateurs à moduler activement leur manière de consommer les différentes ressources est un processus important dans le fonctionnement des écosystèmes, notamment leur stabilité. Cependant, ces résultats sont obtenus à partir de modèles de communautés fixes ce qui prive l'étude de certaines interactions potentielles entre le niveau de l'individu et celui de la communauté. À partir de notre modèle d'émergence de communautés nous montrons que la stratégie d'acquisition des ressources des consommateurs a un effet sur des propriétés de la communauté, notamment sa biomasse, sa productivité, sa diversité et sa stabilité. De plus, la structure de l'ensemble de la communauté module l'évolution des stratégies des consommateurs.
# ABSTRACT

The fields of ecology and evolution are made up of complex systems - organisms, species, communities - that do not lend themselves well to a reductionist approach. Indeed, these systems may have emergent properties that exceed the sum of the properties of their parts. Their study then requires an interest in the interactions between the parts and the whole of these systems. For example, the study of a metacommunity cannot be limited to the strict study of the whole (the metacommunity) or the strict study of the parts (the communities composing the metacommunity). Understanding this complex system requires considering the whole, the parts, and the interactions between them. Moreover, these interactions can be multidirectional, they are not exclusively from the parts to the whole, reciprocal causality is possible, the whole then influencing the parts. In this thesis we explore through three distinct biological systems how the interactions between the whole and the parts define these systems. The thesis therefore consists of three chapters. In the first we explore a metacommunity model simulating the invasion of the boxwood moth, an invasive herbivorous insect in Europe, and study the interactions between local and global spatial scales. This ecological model of population dynamics is calibrated from empirical field measurements and through mesocosm manipulation. Our model reproduces the instability of local dynamics. Indeed, locally the insect is irreversibly extinguished due to its over-exploitation of its resource (boxwood). However, our model shows that interactions between communities, thanks to the dispersal of the insect, can lead to the persistence of the system at the scale of the metacommunity. Furthermore, we show that the structure of the metacommunity emerges from the interactions between local dynamics. The second chapter explores the extent to which a mutualistic interaction between a host and a symbiont can emerge from a parasitic interaction by co-evolving with dispersal. We develop an individual-centred eco-evolutionary model in a 2D space and consider as initial condition a host population interacting with a population of parasitic symbionts. We show that through the evolution of a local dispersal a spatial structure can emerge from the dynamics of the host-symbiont system. The emergence of this spatial structure induces the formation of several interacting levels of organisation: the individual level, the spatial cluster level, and the landscape level. While the individual level favours the evolution of parasitism, the two higher levels of spatial cluster and the landscape favour the evolution of mutualism. We show that depending on the strength of the spatial structure, modulated by the intensity of competition at the landscape level, the transition from parasitism to mutualism can occur. Finally, the last chapter focuses on the evolution of the evolution of adaptive foraging among consumers in a consumer-resource eco-evolutionary model. The literature shows that the adaptive foraging is an important process in the functioning of ecosystems, especially their stability. However, these results are obtained from models of fixed communities, which deprives the study of some potential interactions between the individual and community levels. From our model of community emergence we show that the resource acquisition strategy of consumers has an effect on community properties, including biomass, productivity, diversity and stability. Furthermore, the structure of the whole community modulates the evolution of consumers' strategies.
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