Demographic and evolutionary consequences of mate-choice under Complementary Sex Determination constraints 

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Reduction in fitness components and/or increase in mortality

The first observed consequence of genetic load is a reduction of all components of fitness due to inbreeding and to the expression of mildly to fully deleterious mutations. Various models considered the impact of the reduction of one or several fitness components on the demography of populations engaged in an interaction.

Competitive interactions

In a competition interaction, the demographic response to a variation in fitness components depends mostly if resource consumption is mechanistically or phenomenologically described (Abrams, 2003). With competitive Lotka-Volterra equation, reduction in the fitness components of one competitor species is always beneficial to the persistence and abundance of the other. In models of interference competition, variations in mortality or reproductive abilities of competi-tors lead to the same results (Jensen, 1987).
However, species engaged in exploitative competition may respond very differently to vari-ation in their competitor’s fitness depending on the variety and variability of resources involved and of their own resource requirement. Abrams (2003) studied a variation in species consump-tion rate in a mechanistic model with two resources and two competitors, each one having a major and a minor resource consumed with a saturating functional response. HE demonstrated that an increase in one competitor ’s (species 1) attack rate on its major resource could have 3 different demographic responses, depending on resource requirement: i) (low resource re-quirement) species 1 declines while species 2 increases, because species 1 over-exploitation of species 2 major resource is relaxed; ii) (intermediate resource requirement) both species de-cline in abundances; iii) (high resource requirement) species 1 increases and species 2 decreases (Abrams, 2003). These results illustrate the variety of dynamical responses that may come from variation in one of the traits of a competitor species. Genetic load could traduce either as a decrease of one competitor attack rate or as an increase of its resource requirement – because reproductive abilities decrease, more resources are consumed to produce the same number of individuals. In this last assumption, genetic load may dramatically alter the dynamical response to competitor’s variations in consumption preferences.
When one consumer already primes on the system because it is extremely efficient, an in-crease of its mortality may allow other competitors to coexist, because available resources be-come more abundant and more diverse (Abrams, 2001). In this frame, a reduction of the best competitors’ s efficiency through genetic load could promote the species diversity in the ecosys-tem.

Antagonist interactions

Antagonist interactions encompass two trophic levels: a lower level, which suffers from the interaction (the prey or host) and a higher level, which benefits from the interaction (the preda-tor or parasite). Both positions have different consequences in terms of demography, and both will be studied distinctly.
Within the lower level In phenomenological models of predator prey interaction, such as Lotka-Volterra ’s or Rosenzweig and MacArthur (1963), a decrease in prey growth reduces the amplitude of predator prey cycles (Box 1). Prey mortality is thus considered as stabilizing for the system: Abrams (2003) interpreted this phenomenon as a form of Rosenzweig’s paradox of enrichment, in which an increase in resource availability (here the prey) is destabilizing for the system. Among the components of fitness, many are also associated with prey state, i.e its health and size. Prey state is known to directly affect the predation risk in a wide variety of systems, either because predators select low-state prey to minimize hunting costs (Christensen, 1996) or because they select high state prey to maximize energy income (Welton and Houston, 2001; Witter and Cuthill, 1993). A prey with a strong mutational load may have reduced quality and avoidance abilities, and is likely to be considered of low state. Subsequently, predation may act along or counter natural selection on deleterious mutations, whether predators select low state or high state prey. This indirect effect may impact the path of expression of deleterious muta-tions and their demographic consequences. Prey behavior can also vary with state and adapt to its predation risk, leading to adverse indirect effect of state on predation risk (Welton and Houston, 2001). Low state prey selection may yield another consequence: when the popula-tion becomes small and suffers inbreeding depression, prey state worsens, which may facilitate predation. These combined effects could produce a particular extinction vortex: as inbreeding depression decreases prey state, predation increases, prey population size decreases, which de-crease genetic diversity and increases inbreeding depression so prey state decreases, etc.

Modes of sex determination

Four categories of sex determination were considered: 1) haplodiploid mode of sex determination (model 3.1) with mated females fertilizing half of the eggs they laid (s0 Æ 0.5 (article 2) henceforward named “equilibrated haplodiploidy”), 2) an equilibrated diploid mode of sex determination (model 3.2 with s0 Æ 0.5), 3) a female-biased haplodiploid sex determination (s0 Æ 0.3) and 4) haplodiploid sex determination with mated females adjusting sex allocation to the proportion of virgin females in the population as follow: s0 Æ 1¡2p(Mt ) 2¡ 1¡p(Mt ) ¢ (3.6) (Godfray, 1990) The diploid mode of sex determination was considered as a reference to which each of the three haplodiploidy variants was compared.

Quantification of the extinction proneness

We quantified the extinction proneness for 11 ® values ranging from 0 to 100 (on a log scale) and for randomly drawn parameter sets. This quantification lay on two sets of currencies. First, we determined the relative extent of the conditions of persistence of the three haplodiploidy variants compared to diploidy when copingwithmate finding difficulties. For each haplodiploid variant and each ® value, we counted the number of parameter sets which (1) went extinct with diploid and haplodiploid reproductive systems, (2) went extinct with diploid but not with haplodiploid reproductive system, (3) persisted with diploid and haplodiploid reproductive system and (4) went extinct with haplodiploid but not with diploid reproductive system. To avoid an overestimation of the extinction risks, initial abundances had to be chosen close to the equilibrium values. However we were not able to estimate the equilibrium value if all parameters are random. For this reason we proceeded in two steps. First we randomly drawn 1000 parameter sets for b, K, k, and k1. Second, for each of these parameter sets, we screened the ¸¡a plane considering 2500 combinations. Second, for the parameter sets for which the population reachs a stable non-zero equilibriumdespite mate finding difficulties we evaluate the robustness of this persistence. For this we compute, for the different modes of sex determination: (i) the critical number of parasitoid necessary to establish (Fcr i t ) and (ii) the resistance of the host-parasitoid system to external causes of mortality (Fmin). The critical population size (Fcr i t ) was computed by progressively increasing the initial number of parasitoid females in the system when the host is set to its carrying capacity. The resistance of the host-parasitoid system to external causes of mortality is determined by the minimum fraction of female equilibrium abundance (with hosts set at their equilibrium) below which the population becomes unable to recover (Fmin). We address the impact of haplodiploidy on these two features by the representation of the ratio Fcr i t ,HD¡Fcr i t ,DD Fcr i t ,DD (resp. Fmin,HD¡Fmin,DD Fmin,DD ), i.e. the proportion of Fcr i t (resp. Fmin) that can be reduced by haplodiploidy.
In order to investigate further the conditions in which haplodiploidy is beneficial, we set up an analysis of the variance of the difference Fcr i t ,HD ¡Fcr i t ,DD(resp. Fmin,HD ¡Fmin,DD) depending on ® , the parameter b, k, and k1, and their interactions with ®, for each haplodiploidy variant.
We used an ANOVA and considered each parameter as qualitative variables, with 11 levels going from 0 to 100 on a log scale for ®, and respectively 2, 3 and 3 levels for b, k, and k1. The levels were chosen delimited as following:
– b Ç 2: under-compensated and b ¸ 2 overcompensated host competition.
– k · 1 (resp. k1 · 1) strongly aggregated, 1 Ç k ¸ 5 (resp. 1 Ç k1 ¸ 5): middy aggregated, and k È 5 (resp. k1 È 5) completely random host attacks (resp. parasitoid mate-choice) As developed in White et al. (2013), we will not consider the results and p-values of the linear model, since mathematical modeling allows for the multiplication of « experiments » until any parameter inducing a variation is significant. We will rather consider the proportion of variance of the difference Fcr i t ,HD ¡Fcr i t ,DD that can be explained by each parameter and its interaction, and compare these proportions to conclude which parameter has more effect on the impact of haplodiploidy.

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Relative invasibility of haplodiploids and diploids

In the second part of this article,we investigated howhaplodiploidy (equilibrated)may affect parasitoid ability to invade an already established population or to resist invasion. We considered resident and invader as distinct populations sharing the same host but with no possible reproduction events between them. Both resident and invader may be haplodiploid or diploid, resulting in four invasion scenarios. Dynamics of the resident population was iterated according to model 3.1 (or 3.2 depending on the resident reproductive system) for 1000 generations. If it persisted, the invader population was introduced and the joined resident / invader dynamic was followed for 1000 additional generations. Three issues were then possible: i) extinction of the whole host-parasitoid system, ii) extinction of the invader and maintenance of the resident or iii) successful invader excluding the resident (coexistence was tested but never lasted 1000 generations). Whenever resident and invader had different reproductive modes (one diploid, the other haplodiploid), their dynamics on the common host N were described by the followingmodel .

Table of contents :

I Introduction bibliographique 
1 Genetic load in interacting populations 
Introduction
1 Genetic load
2 Interacting populations
3 What could be genetic load impact in interacting populations?
Conclusion and perspectives
Parasitoïdes et mécanismes à faible densité
1 Les parasitoïdes et la lutte biologique.
2 Mécanismes de détermination du sexe
Organisation du manuscrit 49
1 Résultats (1) : Les effets Allee comportementaux
2 Résultats (2) : Le Complementary Sex Determination
3 Modèle hôte-parasitoïde de référence et limites de l’étude
II Conséquences démographiques d’un l’effet Allee comportemental chez les parasitoïdes 
2 Host-parasitoid dynamics and the success of biological control when parasitoids are prone to Allee effects.
3 Extinction proneness of diploid vs. haplodiploid parasitoid populations face tomate finding difficulties 
1 Introduction
2 Methods .
3 Results .
4 Discussion
III Conséquences démographiques et évolutives du Complementary Sex Determination chez les parasitoïdes 
4 No diploid male vortex in parasitic wasps: how a genetic load may favor parasitoid persistence 
1 Introduction
2 Methods .
3 Results .
4 Discussion
5 Appendix
5 What alters CSD impact on parasitoid populations? 
1 Introduction
2 Methods .
3 Results .
4 Discussion
6 Demographic and evolutionary consequences of mate-choice under Complementary Sex Determination constraints 
1 Introduction
2 Methods .
3 Results .
4 Discussion
Discussion Générale 
1 L’effet des mécanismes s’exprimant à faible densité : une question de dynamiques.
2 Quels facteurs d’extinctions pour les petites populations de parasitoïdes?
3 Pourquoi l’effet Allee et le CSD n’ont pas le même impact sur les populations de parasitoïdes cycliques? Effet Allee génétiques et effets Allee comportementaux .
4 Facteurs génétique chez les parasitoïdes et adaptation à l’hôte
5 Présence et persistance du CSD dans les populations d’hyménoptères parasitoïdes151
6 Alien vs. Predator (le fardeau génétique arbitre)
Conclusion
Bibliography

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