Similarities and differences in demographic and genetic extinction patterns
Most ecological settings considered here had similar qualitative effects on demographic and genetic viabilities, in agreement with theoretical expectations. Large population sizes allow limiting demographic stochasticity  as well as the inbreeding and drift loads ; high dispersal rates are associated with demographic rescue and recolonization  and reduced drift load ; perturbations cause population bottlenecks that are directly associated with demographic extinction and inflate the genetic load ; high fecundity rates allow counteracting the effect of demographic and environmental stochasticities  and elevate the genetic extinction load threshold. Only fragmentation (N) has less obvious effects (see below). However, despite these similarities, the processes leading to "demographic" and "genetic" extinctions are fundamentally different. Demographic viability is related to the mean and variance of the rate of increase , which are primarily influenced by the perturbation regime and the basic growth rate (F and P). In contrast, genetic viability is associated with the inbreeding and drift loads, themselves primarily related to population size and fragmentation (K
and N, [14, 30]). The causes and implications of this are further developed below.
Demographic processes and hard selection models
While the genetic model presented here is a soft selection model (i.e., each local population contributes to the next generation independently of its mean relative fitness), the integration of demographic processes (i.e., the demo-genetic model) clearly adds a hard selection component (since the size and contribution of demes partly depend on their genetic loads). Theoretical work predicts that (1) With soft selection, population structure should reduce the efficiency of selection against mildly deleterious, nearly additive mutations  but will favor selection against severe and highly recessive mutations ; (2) With hard selection, structure should lead to reduced loads even with additive or nearly additive mutations .
While the present results are in agreement with predictions from soft selection models, the beneficial genetic effects of population structure expected under hard selection are not visible with the present demo-genetic model (i.e., increasing N and/or decreasing m has a negative effect on viability). This discrepancy is due to the fact that (i) the demo-genetic model is only a partial hard selection model, as local population size primarily depends on regulation processes (independent from genetic loads); (ii) potential genetic effects are masked by demographic effects (see, in particular, Figure 2c); (iii) the genetic and demo-genetic viabilities expressed in the present paper do not necessarily reflect expected equilibrium patterns. In particular, the purging processes leading to reduced inbreeding or drift load may be demographically costly, which implies that some metapopulations will have a low demo-genetic viability despite a small expected equilibrium load.
Why genetic models are insufficient to estimate viability
It is generally admitted in the theoretical literature that ecology-genetic interactions should strongly influence the persistence time of populations [15–18, 36, 37]. The demo-genetic interaction refers to the fact that the occurrence of genetic processes is affected by the demographic state of the population, and vice versa, leading to synergistic or antagonistic effects on viability. Here, the process of demo-genetic extinction may be decomposed in two phases: an accumulation phase, during which the overall genetic load increases while population size remains approximately equal to the carrying capacity, and an extinction phase during which the population declines to extinction. Demo-genetic interactions are important in both phases: (1) during the accumulation phase, stochastic variations in population size decrease the effective size and accelerate the rise of the genetic load; (2) during the extinction phase, the population decline increases the rate of mutation accumulation, which in turns accelerates population decline (the so-called mutational meltdown, formalized and discussed in refs [15, 16]).
The extinction phase (i.e., phase 3 in Lynch and colleagues papers) is generally assumed much shorter than the accumulation phase in theoretical genetic models, and the extinction time is assumed equal to the duration of the accumulation phase (i.e., the time necessary to obtain a deterministically decreasing population). Here, in all scenarios, the initial decrease in fitness was more rapid with the demo-genetic model as compared with the genetic model (see Additional file 5). This led to TDG < TG in two thirds of the scenarios investigated, in agreement with previous findings on the demo-genetic interaction. However, in the other third of the scenarios, demo-genetic viability was higher than genetic viability (Figure 1c). This comes from the fact that populations may be demographically resilient and persist several generations after their growth rate has become negative (Additional file 5). Therefore, fitness-based estimations of viability may lead to strong over- or under estimations of the risk of extinction, depending of the relative weights of the demo-genetic interaction and the demographic resilience on viability.
Why demographic models are insufficient to estimate actual viability
As expected, incorporating genetic considerations to the demographic model was unequivocally deleterious. However, the magnitude of the reduction in viability was highly variable. It is generally admitted that the proportional effect of genetic deterioration on viability should be larger for populations with a high demographic viability [17, 37–39]. While the present results are in clear agreement with this expectation, they highlight the critical need to distinguish the intrinsic and extrinsic ecological threats to population viability to estimate the effect of genetic problems on extinction. In some of the scenarios investigated, the demo-genetic extinction times were about half the demographic extinction times, while in other cases they were 10,000 times shorter. Typically, the first situation corresponds to large populations with highly variable, low quality environments (environmental stochasticity is the primary cause of extinction, with or without genetic deterioration), while the later corresponds to small, fragmented populations in stable, good quality environments (genetic deterioration is the primary cause of decline and extinction). In the context of the debate over the environmental versus genetic causes of species extinction, the present results demonstrate that the arguments of the partisans of the environment [1, 2, 40] and genetic [9–11] hypotheses are both theoretically justified. The net impact of genetic deterioration processes on extinction may be strongly variable among and within species, since it strongly depends on the ecological conditions faced by metapopulations (although it is clear that some variation in other factors such as mating systems, life history traits, dispersal pattern or demographic history, will further increase this variability). Importantly, however, many human induced environmental changes are likely to engender situations where genetic deterioration is the primary extinction cause, in particular where available habitats have been reduced in quantity, and not in quality.
The case of fragmentation
Contrary to other ecological settings (K
, m,...), fragmentation has non obvious (and potentially contradictory) qualitative effects on demographic and genetic viabilities. From a genetic view-point, most theoretical studies agree that subdivision has detrimental effects on fitness (i.e., few large patches perform better than many small patches [17, 19, 30]). In the ecological literature, conclusions are less clear . The optimal level of fragmentation depends on overall population size and dispersal ([42–44], see upper panels of Figure 2) as well as on the regime of perturbations [45, 46]. In the absence of fragmentation (single population), strong perturbations may rapidly drive the whole population to extinction, even if population size is large [33, 47]. In contrast, with very high levels of fragmentation (many small populations), environmentally induced extinction risk is spread over several units, but the probability of local extinction due to demographic stochasticity increases as local population sizes decrease. Thus, in many realistic situations, an intermediate level of fragmentations will be optimal. Theoretical work indicates that this general result remains true under a wide range of realistic conditions, provided that (i) the cost of dispersal is not too strong; (ii) environmental variations are not fully correlated among patches of habitats [43, 45, 46].
Consequently, (i) demographically optimal levels of fragmentation may be much higher than genetically optimal levels; (ii) demo-genetic optimal levels are, in most cases, intermediary between demographic and genetic optimal levels (Figure 2). This implies that optimal levels of fragmentations (e.g., in the context of reserve design) may be either under- or over-estimated when based on simple demographic or genetic approaches.