Modelling the dynamics of introduced populations in the narrow-endemic Centaurea corymbosa: a demo-genetic integration

Authors

  • FLORIAN KIRCHNER,

    1. Muséum national d’histoire naturelle, UMR 5173, Conservation des espèces, restauration et suivi des populations, 55 rue Buffon, 75005 Paris, France
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  • ALEXANDRE ROBERT,

    1. Muséum national d’histoire naturelle, UMR 5173, Conservation des espèces, restauration et suivi des populations, 55 rue Buffon, 75005 Paris, France
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  • BRUNO COLAS

    1. Muséum national d’histoire naturelle, UMR 5173, Conservation des espèces, restauration et suivi des populations, 55 rue Buffon, 75005 Paris, France
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Florian Kirchner, Muséum national d’histoire naturelle, UMR 5173, Conservation des espèces, restauration et suivi des populations, 55 rue Buffon, 75005 Paris, France (fax + 33 1 40 79 38 35; e-mail florian.kirchner@voila.fr).

Summary

  • 1In the context of the restoration of an endangered species, population viability analysis represents a useful tool for assessing the effectiveness of different possible management strategies before implementation. However, despite the consensus that demographic and genetic mechanisms are both involved and interact in the process of extinction, few attempts have been made to examine their combined impacts on population viability in a particular species.
  • 2We integrated specific data resulting from 10-year multidisciplinary investigations into a descriptive model to simulate the dynamics of an introduced population of the rare self-incompatible plant species Centaurea corymbosa. The model allowed us to examine the interplay between demographic processes and genetic self-incompatibility in the particular habitat conformation of the species, alternating suitable and unsuitable sites within a population along cliffs. Population growth and extinction risk were compared for different introduction strategies.
  • 3Population persistence mainly depended on the number of introduced seeds and on their initial spatial distribution within the population (single vs. multisite introduction). In most cases, a multisite introduction resulted in faster population growth and higher viability than a single-site introduction.
  • 4As expected, a strong negative impact of the self-incompatibility system was observed on population dynamics and viability. However, because of positive feedback between demographic and genetic processes, this impact differed among introduction strategies: it was less severe when seeds were distributed among suitable sites, which also limited the loss of self-incompatibility alleles. Moreover, self-incompatibility contributed to the positive relationship between flowering plant density and fertilization rate.
  • 5 Synthesis and applications. Our results provide strong management guidelines for future introductions of C. corymbosa regarding the number of seeds required (> 800) and the benefits of introducing them into several sites to achieve population persistence. Further, the study highlights the general importance of integrating demography and genetics to compare the effectiveness of different management strategies.

Introduction

Population viability analysis (PVA) has become an extensively used tool for assessing the combined impacts of deterministic and stochastic factors on extinction risk in endangered species. However, although demographic and genetic mechanisms involved in the small population paradigm (sensu Caughley 1994) have largely been discussed in a general conservation framework, it remains difficult to evaluate their respective roles in the context of a particular species or population.

Among the various mechanisms impairing population viability, demographic stochasticity, caused by chance realizations of individual probabilities of death and reproduction events, is an important cause of extinction in populations smaller than a few 10s or 100s of individuals (Lande, Engen & Sæther 2003). Small and isolated populations are also prone to genetic deterioration, which has received much attention in recent conservation literature (reviewed by Frankham, Ballou & Briscoe 2002). The main effects associated with the genetic isolation of finite populations are the loss of genetic variation through drift and the increase in inbreeding that may eventually lead to a reduction of adaptive potential (Franklin 1980), inbreeding depression (Hedrick & Kalinowski 2000) and the accumulation of deleterious mutations (Lynch, Conery & Bürger 1995). In self-incompatible plant species, the loss of alleles at the self-incompatibility locus may further lead to a rapid reduction in fertilization success (Vekemans, Schierup & Christiansen 1998; Young et al. 2000). Moreover, both ecological (i.e. difficulties in finding mates and attracting pollinators) and genetic problems may cause a deterministic reduction in population growth rate at low densities (referred to as positive density dependence or the Allee effect). Positive density-dependence mechanisms have been documented in various animal and plant species (Courchamp, Clutton-Brock & Grenfell 1999) and may lead a small population to extinction (Engen, Lande & Sæther 2003).

There is now a compelling body of both theoretical (Hedrick 1994; Mills & Smouse 1994) and empirical (Saccheri et al. 1998; Oostermeijer 2000) evidence supporting the contention that genetic changes in small populations are significantly involved in the process of extinction and must be included in PVA. However, despite the consensus that a real mechanistic integration of genetics and demography is necessary to understand their interaction, the impact of genetic problems on population dynamics is generally oversimplified, with no real integration (Clarke & Young 2000; but for examples in plants see Burgman & Lamont 1992; Oostermeijer 2000). The main reason is that detailed empirical field data are often unavailable to parameterize models in a realistic way (Oostermeijer 2003).

Among many possible applications, simulation models of population dynamics can be used to optimize population restoration strategies (Bell, Bowles & McEachern 2003). Many reintroduction schemes have been carried out for plant species, but they have often proved expensive, time consuming and rarely successful in restoring self-sustaining populations (Pavlik 1994). Thus, it may be very useful to simulate the impact of various reintroduction strategies before implementation (Buckley, Briese & Rees 2003).

In this study, we integrated specific data from a 10-year demographic and genetic study into a descriptive model to simulate the population dynamics of newly introduced populations of the narrow-endemic Centaurea corymbosa Pourret (Asteraceae). Only six populations of this cliff-dwelling species are known and, because it has a very low colonization ability (Colas, Olivieri & Riba 1997), its survival probability should be greatly increased by the creation of new, viable populations. The demo-genetic model included a comprehensive life cycle, with demographic stochasticity on all parameters, seed dispersal within the population, intraspecific competition causing a negative density-dependence on two demographic parameters, positive density-dependence on fecundity, together with genetic self-incompatibility acting in connection with limited pollen dispersal.

We modelled the introduction of one population along the edge of a cliff offering six suitable sites arranged linearly, and addressed the following questions. (i) How do the initial number and spatial distribution (over one vs. six sites) of the introduced seeds affect population introduction success? (ii) What is the impact of the self-incompatibility system on population growth and extinction, and does this impact vary according to the distribution of the seeds introduced?

Methods

focal species

Centaurea corymbosa lives in the limestone Massif de la Clape located in southern France along the Mediterranean Sea. It appears on the French red list of endangered species (Olivier et al. 1995) and on the list of priority species of the European ‘Habitats’ Directive (Council Directive 92/43/EEC of 21 May 1992, OJ L206, 22.7.1992). The sizes of the six populations range from 17 to 198 flowering individuals (1995–2004 means) found on cliffs and in nearby rocky areas up the cliffs. All populations are within 3 km2, representing less than 10% of the massif area, although suitable cliffs seem to occur all over the massif (Colas, Olivieri & Riba 1997).

The species has a monocarpic perennial life cycle. Most seeds germinate in the autumn following summer dispersal, and individuals then grow as vegetative rosettes during 2 to ≥ 10 years (Fréville et al. 2004). They flower between May and mid-August, producing 1–200 capitula (mean 35) pollinated by insects (Kirchner et al. 2005) and die after flowering. Rarely, a plant may survive after flowering and flower a second time. The presence of a self-incompatibility system was detected by comparing fertilization success after manual self- and cross-pollination in controlled conditions (Fréville 2001). In one population, a paternity analysis revealed a natural self-fertilization rate of 1·6%, and a pollen dispersal curve indicating that 50% of the fertilizing pollen moves less than 11 m and 20% more than 43 m (Hardy et al. 2004b). Fertilization success is positively related to the density of flowering conspecifics within 10 m (Kirchner et al. 2005), mainly because of limited mate availability (Hardy et al. 2004a). On the other hand, negative density-dependence as a result of intraspecific competition within microsites (i.e. a few square centimetres of cleft in the rock) appeared to affect the survival of newly emerged seedlings and the flowering probability of rosettes (B. Colas, unpublished data). This competition partly results from restricted seed dispersal distances, most of the achenes (one-seeded dry fruits) falling within a few 10s of centimetres from the mother plant (Colas, Olivieri & Riba 1997). Genetic studies showed that populations are highly differentiated for both allozyme (Colas, Olivieri & Riba 1997) and microsatellite (Fréville, Justy & Olivieri 2001) markers, because of very limited seed dispersal and low pollen migration among populations despite their geographical proximity (0·3–2·3 km).

model parameters

We used a life cycle based on a pre-breeding census set in early June with a 1-year time step, considering three stages: seedlings (plants < 1 years old), rosettes (vegetative plants > 1 years old) and flowering plants (Fig. 1). The expected probability of transition from stage j to stage i was the product of survival probability (sj) of stage j from time t to time t+ 1 by the transition probability (αj or 1 − αj) from stage j to stage i conditional on survival. No seed stage was considered because < 5% of the seeds remain dormant for 1 year or more (Colas 1997). The mean survival rates and transition probabilities between stages were estimated from demographic data collected over 8 years (1994–2001) within 40 permanent quadrats located in the six natural populations, as described in Fréville et al. (2004). The mean and variance of the number of ovules produced per plant, the fertilization rate and the abortion rate were obtained from seed set data collected in 1995, 1996 and 2002 in the six populations (Colas, Olivieri & Riba 2001; Kirchner et al. 2005). Seed set data in 1995 and 1996 were also used to estimate seed production within demographic quadrats in these 2 years and to infer the emergence rate according to seedling recruitment following each flowering season (Colas 1997). Both years showed an identical emergence rate of 1·5% over all populations (the number of flowering plants within quadrats in each year was too low to get a good estimation of the emergence rate per population).

Figure 1.

Within-site life cycle of Centaurea corymbosa. Three plant stages are considered: seedling (S), rosette (R) and flowering plant (F). Solid arrows represent common transitions between stages, and dashed arrows stand for infrequent transitions. For each transition, the model parameters involved are indicated (see Table 1 for details and parameter values).

From 1995 to 2001, three populations out of the six showed an asymptotic growth rate λ > 1 (Fréville et al. 2004). We used the parameter values of one middle-sized population named Auzils, this choice being motivated by the good quantity of data available from this population and by its asymptotic growth rate > 1 that allowed us to model the dynamics of an intrinsically growing population. However, in Auzils, as in the other populations, data were lacking for accurate estimation of three of the demographic rates corresponding to rare events (the flowering probability of seedlings, α1, and the survival of flowering plants, s3) or involving a very small number of individuals (the probability of second flowering of flowering individuals, α3). So for these three vital rates, which all have a negligible contribution to the variation of λ (Fréville et al. 2004), the species’ means were used. The values of all parameters in the model are given in Table 1. We examined the sensitivity of our results to changes in the demographic rates by lowering or increasing their value by up to 10%.

Table 1.  Value of the model parameters
Model parameter Value
  • *

    Parameter value for individuals that are not affected by intraspecific competition.

  • Parameter value for individuals affected by intraspecific competition.

Survival s 0 0·640*/0·213
s 1 0·456
s 2 0·768
s 3 0·066
Flowering probabilityα10·002
α20·215*/0·108
α30·556
Number of ovules/individual#ov1500
Fertilization rate f 0·068 ln(1 + density) + 0·48
Abortion rate ab 0·1
Seed emigration rate m 0·001
Emergence rate e 0·015
Emergence rate at t= 0 e ini 0·334
Mutation rate u 10−4
Number of introduced seeds N 0 50–1000
Initial number of S alleles A 0 2–2N0
Number of pollen compatibility trials allowed per ovule Tr max 1–1000

structure of the model, demographic stochasticity, negative and positive density-dependence

We used an individual-based model in which each individual was described in terms of stage, location (site within population, see below) and genotype at the self-incompatibility locus. Each demographic event occurred stochastically at the individual level. Demographic stochasticity for survival and stage transitions resulted from Bernoulli sampling according to the mean rates si and αi presented in Table 1. The analysis of demographic data showed that intraspecific competition affected two parameters of the life cycle (B. Colas, unpublished data): the survival of newly emerged seedlings (s0) and the flowering probability of rosettes (α2). The protocol used to model negative density-dependence on these two vital rates is described in Appendix S1a in the supplementary material.

The transition probability from flowering plants to seedlings (fecundity transition) was the product of the number of ovules produced per plant (#ov), the fertilization rate (f), the probability of a fertilized ovule developing into a sound seed (1 − ab), the emergence rate (e) and the probability of newly emerged seedlings surviving until June (s0; Fig. 1). Demographic stochasticity in reproductive outputs was considered by drawing the number of ovules Otk produced by individual k at year t from a lognormal distribution with equal mean and standard deviation #ov (corresponding to the observed distributions in 1994, 1995 and 1996; B. Colas, unpublished data). The number of fertilized ovules (FOtk) of individual k was then obtained by drawing from a binomial distribution Bin(Otk, fti), where fti was the site-specific density-dependent fertilization rate of the plants in site i at year t, computed according to the positive density-dependence relationship found by Kirchner et al. (2005) (see Appendix S1b in the supplementary material). The number of viable seeds Vtk was then obtained from Bin(FOtk, 1 − ab), and the number of emerging plants Ftk from individual k was finally given by Bin(Vtk, e).

seed and pollen dispersal

We considered a habitat made up of six suitable sites arranged linearly. Sites can be seen as c. 300-m2 circular areas (diameter 20 m) separated from one another by 30 m of unsuitable land, forming together a discontinuous linear habitat stretching over 270 m. This spatial arrangement mimics the spatial structure of the actual populations that extend roughly linearly along the cliffs, displaying sites with high plant density as well as more sparse or unoccupied sites. The 270-m distance represents more or less the extent of the Auzils population. Each individual was characterized spatially by its location in one of the six suitable sites. We assumed for simplicity that plants within a site were randomly distributed over the whole site area. Field data showed that seed dispersal distances in C. corymbosa are very short, only 17% of them moving to more than 50 cm from the mother plant (Colas, Olivieri & Riba 1997). Long-distance seed dispersal by adhesion of the pappus to animals, although probably very rare (Colas 1997; Riba et al. 2005), may have a significant importance to population dynamics in the case of migration into unoccupied sites or into sites with few individuals. In the model, the annual emigration of seeds between adjacent sites separated by 30 m was fixed at a rate (m) of 0·001 and occurred stochastically through Bernoulli sampling. We conducted a sensitivity analysis of the model to this rough estimation. It must be noted that seed dispersal to unsuitable areas, such as the bottom of the cliffs, or to unsuitable microsites within suitable sites, is included in the estimation of the emergence rate (see above) because most seeds that do not emerge are seeds that failed to disperse to a suitable microsite (Colas 1997).

As regards pollen dispersal, the probability that an ovule in site i was fertilized by a pollen grain from site j depended both on the distance between i and j and on the number of flowering individuals in site j. After drawing the number of fertilized ovules per individual as explained in the previous subsection, the pollen donor for each fertilized ovule was determined as follows. First, a potential father was randomly drawn among all flowering individuals in the population, so that sites with many flowering individuals had a higher chance of being represented. Secondly, this individual was selected as the pollen donor if a uniform random number x drawn between zero and one was lower than P1ij (the probability that an ovule in site i was fertilized by a pollen grain from site j in the case where all sites have equal flowering plant densities). The probability matrix of P1ij values was obtained from the frequency distribution of effective pollen dispersal distances estimated after a paternity analysis in the Auzils population (Hardy et al. 2004b; see Appendix S2a in the supplementary material). Thirdly, if xP1ij, further sampling was repeated until a donor was found. In agreement with our data, another probability matrix, P2ij, was used instead of P1ij in the particular case where the fertilized individual was the unique flowering plant in its site (see Appendix S2b in the supplementary material).

integration of self-incompatibility

We examined the effect of self-incompatibility on short-term population dynamics and extinction risk. In the Asteraceae, the mechanism by which crosses are prevented when pollen and pistil share the same incompatibility phenotype is controlled by a single-locus (S locus) sporophytic system (Hiscock 2000; Young et al. 2000). In this system, the incompatibility phenotype of the pollen is determined by the diploid genotype of the donor plant at the S locus, and the incompatibility reaction therefore involves two diploid genotypes (four alleles). Dominance and/or codominance relationships between S alleles can be observed in the pistil and pollen, depending on the species considered (Richards 1986). We integrated a diploid self-incompatibility locus in the model, each individual being genetically characterized by its two S alleles represented by integer numbers. Different scenarios were investigated with respect to the initial number of S alleles (A0) present within the population. In particular, a scenario with a single copy of each allele (i.e. 2 N0 alleles in total, where N0 was the initial number of individuals in the population) was compared to situations with a restricted initial number of alleles. In the latter case, each allele initially present was drawn from a uniform distribution of integer numbers between 1 and A0. Mutations occurred stochastically at the S locus according to an expected mutation rate per generation u, each mutation giving rise to a new allele. The mutation rate u was fixed at 10−4 (Vekemans, Schierup & Christiansen 1998) and, again, we examined the robustness of our results to this estimation using a sensitivity analysis. Allele transmission at fertilization was stochastic, following Mendelian rules.

The fecundity of each plant depended on both the quantity of pollen available (density of flowering conspecifics, see above) and the quality of the pollen pool (interaction between the self-incompatibility phenotypes of the mother plant and of the potential fathers). We investigated different scenarios with respect to the type of allelic interactions determining incompatibility phenotypes (Nasrallah & Nasrallah 1993). In the ‘codominance’ scenario, codominance applied to alleles in both pollen and pistil, and pollen rejection occurred if at least one allele was shared by the two reproducing plants. In the ‘dominance’ scenario, dominance relationships between alleles applied in both pollen and pistil, and rejection occurred if the dominant allele was the same in the two plants (for each genotype, the dominant allele was the one with the highest integer number). In the ‘male-dominance’ scenario, codominance applied in the pistil and dominance in the pollen.

For each reproducing plant, once the fraction of fertilized ovules (fti, see above) was determined according to flowering plant density, we checked whether each ovule could find a compatible pollen grain or not, allowing a given maximum number of compatibility trials (Trmax) between the ovule and different pollen grains. Again, we compared several scenarios differing in Trmax, reflecting different levels of availability of insects carrying C. corymbosa pollen. For each fertilized ovule, a pollen donor was drawn from the population according to the procedure indicated in the pollen dispersal subsection, and the pollen and ovule phenotypes were compared. When not compatible, the pollen grain was rejected and another donor was drawn, and so on, until a compatible pollen grain was found or until the maximum number of trials allowed was reached. In that latter case, the ovule remained unfertilized, so that the number of ovules truly fertilized can be lower than the number initially drawn in the absence of self-incompatibility (FOtk). It should be noted that the presence of a self-incompatibility system here can only have a negative impact on population viability, because the demographic advantages of inbreeding avoidance were not incorporated.

initial conditions and simulation protocol

We modelled the population dynamics of an introduced population isolated from any possible external sources of seeds and pollen, which is close to the situation of natural populations given the strong genetic differentiation observed among them (Colas, Olivieri & Riba 1997; Fréville, Justy & Olivieri 2001). In all scenarios, we considered the introduction of a population from seeds placed by hand in suitable microsites. The chance of emergence in these conditions is much higher than after natural seed dispersal, as shown by data from experimental introductions in the Massif de la Clape (Colas 1997). The mean emergence probability eini at time 0 was estimated from these data (Table 1).

We investigated the impact of different scenarios of introduction on genetic characteristics, population dynamics and extinction risk. The different scenarios varied for the number of seeds introduced (N0), the initial diversity at the S locus (A0) and the strategy of spatial distribution of the seeds. In the ‘six-site strategy’, seeds were equally shared out among the six suitable sites, whereas in the ‘single-site strategy’ all seeds were introduced in one central site. The simulation program was developed in Pascal language and we used Monte Carlo simulations with 1000 stochastic population trajectories drawn over 100 years.

Results

population dynamics

Considering a strictly demographic model (without self-incompatibility), our simulations revealed a strong interaction between the number of seeds introduced and the spatial distribution strategy (single-site or six-site strategy) on the extinction risk. After 25 years, the six-site strategy led to higher extinction probabilities when considering a limited initial number of seeds (i.e. less than 600), but there was no difference between strategies for a larger number of seeds (Fig. 2a). However, the chances of long-term persistence were always higher with a six-site introduction (Fig. 2b). Near-zero 100-year extinction probabilities were obtained with a minimum of 800–1000 seeds in the six-site strategy, while the single-site strategy led to extinction rates higher than 20% for equivalent introduction efforts.

Figure 2.

Influence of the number of introduced seeds on (a) 25-year and (b) 100-year extinction probabilities, with the six-site (grey symbols) and single-site (black symbols) strategies. Codominance model; A0 = 20; Trmax= 3.

effect of self-incompatibility

This qualitative trend remains unchanged when including the effect of self-incompatibility alleles on population dynamics. Self-incompatibility increased the extinction risk whatever the number of seeds introduced (Fig. 2a,b). However, the negative effect of self-incompatibility on population dynamics appeared to be more drastic with the single-site strategy (Fig. 2b). Further, increasing the number of seeds increased the net negative effect of self-incompatibility when considering the single-site strategy, whereas it reduced its effect when considering the six-site strategy. Self-incompatibility had a minor effect on population dynamics if a large number of seeds was introduced using the six-site strategy. As an illustration, when considering 1000 introduced seeds distributed over six sites, mean overall population size (i.e. the total number of seedlings, rosettes and flowering plants over the six sites) reached after 100 years was 5828·02 (SE 11·95) in the absence of a self-incompatibility system in the model, whereas it was 5411·21 (SE 29·25) when self-incompatibility was taken into account. In the single-site strategy, mean population sizes after 100 years were 222·33 (SE 8·09) and 153·30 (SE 8·34) in the absence and presence of self-incompatibility, respectively.

Self-incompatibility affected the extinction risk through its effect on fecundity. It contributed significantly to the reduction of fertilization rates in small populations, as shown by the comparison of linear regressions of the number of newly emerged seedlings per flowering plant against the logarithm of the total number of flowering plants in the population, in the presence and absence of a self-incompatibility system. Regression slopes and intercepts were, respectively, 2·095 and 4·623 for the model without self-incompatibility, and 2·346 and 3·077 for the model including self-incompatibility. These slopes were significantly different (analysis of covariance P < 0·0001; results obtained after 50 years based on 6000 independent trajectories for each treatment; codominance model; N0 = 500; A0 = 20; Trmax= 3).

sensitivity analyses

To assess the generality and robustness of our conclusions, further analyses were performed varying genetic scenarios and demographic parameters. While all demographic aspects in the model were parameterized according to specific field data (Colas, Olivieri & Riba 1997, 2001; Fréville et al. 2004; Hardy et al. 2004b; Kirchner et al. 2005), our description of the self-incompatibility system and its quantitative impact on individual fitness relied on some assumptions. In particular, in the absence of specific information on the type of allelic interactions determining self-incompatibility phenotypes, we examined the effect of three different allelic interaction models (codominance, dominance and male-dominance). Demo-genetic projections indicated that the codominance model had the strongest negative effect on population viability, regardless of the demographic and genetic scenario considered. The dominance model had a substantially less detrimental effect on the chance of persistence, especially for a small initial number of alleles (A0 < 10), and the male-dominance model led to intermediate extinction probabilities. For example, after 100 years, the codominance, male-dominance and dominance scenarios led to extinction probabilities, respectively, equal to 0·961, 0·771 and 0·741 (with a six-site introduction; N0 = 250; A0 = 20; Trmax= 3). In the absence of self-incompatibility, the extinction probability was 0·670.

When considering an unrestricted initial number of S alleles (A0 = 2N0), the average number of alleles segregating in the overall population at the S locus after 100 years was five times greater with a six-site introduction (A100 = 57·68, SE = 0·29) than with a single-site strategy (A100 = 11·35, SE 0·12; Fig. 3). The influence of the initial number of alleles is illustrated in Fig. 4a for a large initial number of seeds (leading to little sampling effect on the number of alleles effectively present in the founding population). For both site strategies, a reduction in initial S allele diversity strongly reduced short- and long-term viabilities. However, in the six-site strategy the detrimental effect of self-incompatibility was rapidly overcome with the increase in initial diversity, and extinction probabilities dropped close to 0 for values of A0 above 10. On the other hand, escaping the impact of self-incompatibility in the single-site strategy required values of A0 higher than 20 alleles.

Figure 3.

Temporal evolution of the overall number of self-incompatibility alleles for both site strategies of introduction. Each allele is initially present as a single copy. Codominance model; N0 = 1000; Trmax= 3.

Figure 4.

Impact of (a) the initial number of S alleles and (b) the maximum number of trials allowed per ovule to draw a compatible pollen grain on the probability of extinction after 100 years, for both site strategies of introduction. Codominance model; (a) N0 = 1000; Trmax= 3; (b) N0 = 500; A0 = 20.

The maximum number of trials allowed for each ovule to draw a compatible pollen grain (Trmax) strongly affected the impact of self-incompatibility on fecundity. In particular, self-incompatibility no longer showed any effect on population viability for Trmax higher than 10 (Fig. 4b). Further examination of various combinations of values for A0 and Trmax showed 100% extinction after 100 years in all demographic scenarios (i.e. for both site introduction strategies and any value of N0) if A0 was lower than 6 or Trmax lower than 3. The sensitivity of the results to changes in the mutation rate was also assessed by varying u from 0·001 to 0·00001. It appeared that this rate had no impact on population dynamics at the conservation time scale considered.

We examined the effect of the population growth rate by increasing and decreasing the value of all demographic rates in the life cycle (Fig. 1) by up to 10%. This analysis indicated that the success of the six-site introduction (relative to the single-site introduction) was generally improved when lambda increased, as early local extinctions were less likely. But this did not qualitatively affect the conclusions. For 500 seeds introduced, the probabilities of extinction after 50 years for the single- and six-site introductions were, respectively, 0·99 and 0·93 as a result of a 5% decrease in lambda, and, respectively, 0·02 and 0·01 as a result of a 5% increase in lambda. When introducing 250 seeds, these probabilities were, respectively, 0·3 and 0·43 with a 5% increase in lambda, and reached 100% in both cases with a 5% decrease in lambda (all parameter values as in Fig. 2). For 500 seeds introduced, we also varied the annual emigration rate m from 0·001 to 0·01 but this did not modify the conclusions, seed migration remaining too low to influence population dynamics.

Discussion

interactions between demography, genetics and introduction strategy

Although the question of the optimal spatial restoration strategy has been addressed in previous studies (Gerber et al. 2003; Robert, Couvet & Sarrazin 2003), it remains difficult to draw general conclusions on this topic. Previous theoretical studies have examined the individual effects of different genetic and ecological processes on population viability, such as demographic stochasticity, positive and negative density-dependence, fragmentation and self-incompatibility. However, the qualitative assessment of their overall effect and the comparison of population viability under different management scenarios necessitate the examination of their interactions.

The viability of introduced populations depends on both local population dynamics (i.e. local growth rate, demographic stochasticity, positive and negative density-dependence) and metapopulation dynamics (i.e. colonization of empty sites and demographic rescue through seed dispersal). By definition, demographic stochasticity and positive density-dependence have a deleterious effect on viability when local density is low. For small numbers of introduced seeds, a single-site introduction allows maximization of transitorily local density in the introduction site, and therefore minimization of the short-term extinction rate. In contrast, for larger initial population sizes, if all seeds are introduced in the same site negative density-dependence limits local population growth and the limited seed dispersal in C. corymbosa results in low chances of colonizing empty sites. In this situation, the six-site introduction becomes the strategy that maximizes metapopulation growth and persistence.

However, adding some genetic considerations slightly complicates the conclusion. Overall, as expected, a negative impact of the self-incompatibility system on population dynamics and viability is observed. At the population level, the strength of this effect is because of both the limited number of effective founders and the spatial autocorrelation of self-incompatibility alleles arising as a consequence of limited intersite gene flow.

Self-incompatibility alleles are subject to strong frequency-dependent selection, and the number of alleles present in a subpopulation at drift-mutation equilibrium mainly depends on the metapopulation effective size (Schierup 1998). However, at the conservation time scale considered, the overall effect of genetic processes on population viability is related to transient rather than equilibrium genetic states. Following the introduction, the maintenance of allelic diversity at the S locus primarily depends on how quickly sufficiently large population sizes can be achieved, i.e. on the population growth rate in the first years. When considering a large number of introduced seeds, the six-site introduction leads to higher stochastic rates of increase for non-genetic reasons. This subsequently limits the loss of self-incompatibility alleles compared with the single-site strategy (Fig. 3), which in turn has a beneficial effect on population dynamics. Such positive feedback between demographic and genetic processes heightens the difference in extinction risk obtained between the two introduction strategies when self-incompatibility is taken into account (Fig. 2).

Overall, the optimal spatial strategy depends on the number of seeds introduced. However, in practice, the six-site introduction is the best when reasonable introduction efforts are considered (i.e. for initial numbers of seeds > 700–800, which ensure Pext < 10% within 50 years). Sensitivity analyses indicate that this conclusion is robust to uncertainties in various demographic and genetic parameters.

the demo-genetic approach in conservation biology

The importance of synergistic interactions between population genetics and dynamics was first pointed out by theoretical results (Lynch, Conery & Bürger 1995). In a PVA context, the mechanistic integration of genetic processes into demographic modelling (that allows modification of demographic rates according to genetic changes) may improve the realism of models, compared with PVA approaches simply based on a projection of current trends. A mechanistic understanding of extinction in terms of the combined impact of population genetics and population dynamics is virtually unexplored (Clarke & Young 2000). Our results on C. corymbosa illustrate the substantial effect of genetic processes on population dynamics and their potential interplay with management strategies.

However, in the context of applied conservation, such demo-genetic integration may give rise to technical difficulties and should be interpreted with caution. The main caveat to this approach is finding the best way to integrate demographic data and genetic aspects affecting species dynamics. As the effects of genetic problems are already included in the measured demographic rates, such integration may result in an overestimation of the extinction risk (Oostermeijer 2000). In the present study, it is likely that the impact of the self-incompatibility system is already included in the empirical relationship between local flowering plant density and fertilization success, leading to an overestimation of the positive density-dependence in demogenetic simulations. A similar problem was encountered by Robert et al. (2004) in a study aimed at modelling the impact of stochastic dynamics and mutation accumulation in a reintroduced population of griffon vulture Gyps fulvus, using real demographic data. The problem was partially solved by considering the effect of a relative rather than absolute genetic load on vital rates (i.e. the expected genetic load in each time step was divided by the genetic load at time zero).

Field ecological data suggest that positive density-dependence on fecundity in C. corymbosa is mainly because of pollen limitation (rather than pollinator limitation) caused by limited mate availability (Kirchner et al. 2005). An analysis of correlated paternity by Hardy et al. (2004a) using microsatellite data confirms that limited mate availability occurs in the populations and, along with simulation results, indicates that this limitation in mate availability is the result of several interacting mechanisms, including limited pollen dispersal, heterogeneity of pollen production and of phenology among plants, and self-incompatibility. Hence self-incompatibility is one factor, among others, contributing to the positive relationship between flowering plant density and fertilization rate. Therefore, projected persistence probabilities including the impact of the self-incompatibility system described in our model may be considered as upper limits for the extinction risk within the time frame considered.

Another caveat is the paucity of information on how genetic variation affects demographic rates (Beissinger & Westphal 1998). Although this lack of specific information is a general problem in conservation biology, it is less of a problem in the present study, which focuses on self-incompatibility. The self-incompatibility system has a well-described effect on reproduction, it is easy to model realistically on an individual basis, and its mechanistic effects on demography are not expected to change according to environmental conditions.

In spite of the difficulties mentioned above, the mechanistic integration of genetic processes into population dynamics is undoubtedly beneficial to applied and fundamental conservation, as it provides useful insights on: (i) how the genetic processes interact with various species’ peculiarities and how this can be generalized to other species; (ii) the sensitivity of the species’ dynamics to genetic processes, according to initial conditions, population size and structure; (iii) the erosion of genetic variation that may threaten the species’ persistence beyond the specified period of time (commonly 100 or 200 years); and (iv) the efficiency of different management options for minimizing these effects.

Although the precision of our quantitative projections of extinction probabilities and population sizes are directly related to the confidence intervals of input data, the relative comparisons of alternative management strategies certainly provide robust conclusions useful to decision making. It should be noted that the recommendation that population model projections should be used as qualitative (rather than quantitative) assessments applies to any PVA model, even those not including genetic considerations (Boyce 1992; Morris & Doak 2002).

insights to the conservation of c. corymbosa

Our simulations were performed with demographic parameters from the Auzils population, i.e. one of the three populations showing an asymptotic growth rate greater than one over 1995–2001 (Fréville et al. 2004). These parameter values may be among the more optimistic values we can expect for an introduced C. corymbosa population and do not allow us to predict the chance of success of a potential introduction in the Massif de la Clape. The choice of the parameters was justified by our goal of comparing relative introduction success for different demographic and genetic conditions, which implied simulation of the dynamics of intrinsically growing populations.

Two experimental populations located, respectively, 0·5 and 2 km away from the natural populations were created in 1994 and 1995 in the Massif de la Clape (Colas, Olivieri & Riba 1997). Four-hundred seeds distributed over eight sites and 1550 seeds over 31 sites (50 seeds site−1), respectively, were introduced along the two cliffs. Seedling and rosette survival appeared significantly higher in experimental populations than in natural ones (Kirchner 2005), suggesting that unoccupied cliffs in the Massif de la Clape are suitable for the establishment of individuals. Since 1998, several 10s of individuals have flowered in the introduced populations, but preliminary results showed that fertilization success was lower than in natural populations (Fréville 2001), resulting in a lower number of seedlings per flowering plant in introduced populations (Kirchner 2005). The results from experimental introductions cannot be used for the purpose of validating our simulation results because: (i) there were only two populations introduced (i.e. two replicates); (ii) the seeds were introduced into more sites (eight and 31) than in our model; and (iii) we have no information on the number of S alleles initially present in the introduced populations. However, simulation results can provide some insight concerning the deficit in reproductive success observed in experimental populations. It is unlikely that this deficit was because of a very low diversity at the S locus as introductions were carried out using a mix of seeds from four natural populations. On the other hand, according to the simulation results, introduction success is strongly influenced by the initial number and spatial distribution of the seeds. With 400 seeds introduced into eight sites (spread over 375 m) on one cliff, and 1550 seeds introduced into 31 sites (spread over 800 m) on the other cliff, it is likely that the initial conditions were not been optimal for successful reproduction. Pollen limitation, which is known to affect fertilization success in natural populations (Hardy et al. 2004a; Kirchner et al. 2005), must have been strong in experimental populations where only a few flowering plants were observed each year, many of which were isolated by 10s of metres. In 2002, for example, the mean number of flowering conspecifics found within 10 m around each flowering C. corymbosa was 6·5 in natural populations (Kirchner et al. 2005) but only 0·7 in experimental ones (Kirchner 2005). So, even if a six-site introduction ensures higher chances of success than a single-site strategy, increasing the number of introduction sites along the cliffs is not a good strategy (for an initial 400–1500 seeds) because this leads to low local densities of flowering plants suffering demographic stochasticity and pollen limitation.

For future population introductions, our results highlight the importance of the choice of the initial conditions. They indicate that the introduction of a great number of seeds (≥ 1000) distributed over a few sites should allow a probability of extinction close to zero over 100 years. Moreover, the extinction probability was strongly affected by the maximum number of random pollen grains drawn per ovule for compatibility trials. This suggests that pollinator abundance may play an important role in introduction success, especially if the initial S allele diversity is thought to be low. The availability of a significant pollinator community should be one of the points to check when identifying potential suitable habitats for population introduction.

Acknowledgements

This research was supported by a research fellowship from the French Ministry of Research (to FK). We wish to thank I. Olivieri, G. Oostermeijer and three anonymous referees for constructive comments that greatly improved the manuscript.

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