HOW DOES POLLEN VERSUS SEED DISPERSAL AFFECT NICHE EVOLUTION?

Authors


SUMMARY

In heterogeneous landscapes, the genetic and demographic consequences of dispersal influence the evolution of niche width. Unless pollen is limiting, pollen dispersal does not contribute directly to population growth. However, by disrupting local adaptation, it indirectly affects population dynamics. We compare the effect of pollen versus seed dispersal on the evolution of niche width in heterogeneous habitats, explicitly considering the feedback between maladaptation and demography. We consider two scenarios: the secondary contact of two subpopulations, in distinct, formerly isolated habitats, and the colonization of an empty habitat with dispersal between the new and ancestral habitat. With an analytical model, we identify critical levels of genetic variance leading to niche contraction (secondary contact scenario), or expansion (new habitat scenario). We confront these predictions with simulations where the genetic variance freely evolves. Niche contraction occurs when habitats are very different. It is faster as total gene flow increases or as pollen predominates in overall gene flow. Niche expansion occurs when habitat heterogeneity is not too high. Seed dispersal accelerates it, whereas pollen dispersal tends to retard it. In both scenarios very high seed dispersal leads to extinction. Overall, our results predict a wider niche for species dispersing seeds more than pollen.

A species’ niche can be defined as the range of environmental conditions in which it persists without immigration (Hutchinson 1957). Theory about niche evolution thus lies at the intersection of ecology and genetics, asking how demography constrains adaptation and, conversely, how local adaptation affects the distribution of population numbers across habitats (Holt 2009). In a landscape that is heterogeneous with respect to selection, the genetic and demographic consequences of dispersal jointly influence the evolution of niche width (see reviews in, e.g., Bridle and Vines 2007; Kawecki 2008; Sexton et al. 2009; Holt and Barfield 2011). Models of dispersal and adaptation in heterogeneous environments often characterize dispersal with a single parameter. Many organisms however display a life cycle with several dispersal stages. In plants with seed and pollen dispersal, demographic dispersal and colonization are partly uncoupled from gene flow (Thrall et al. 1998; Kremer et al. 2012).

In this paper, we investigate how dispersal through pollen versus seeds affects niche width evolution in a heterogeneous environment. We consider two scenarios of niche evolution. In the “secondary contact scenario,” two populations of the same species adapted to distinct habitats, previously isolated, come into contact: we examine the effect of pollen dispersal on the probability and dynamics of demographic collapse and niche contraction following contact. Study of this scenario may clarify the consequences of, for example, secondary contact between crops and their wild relatives (Ellstrand et al. 1999). In the “new habitat scenario,” the species colonizes a new habitat initially outside its niche, with persistent gene flow from the ancestral habitat: we examine the effect of pollen dispersal on the probability and dynamics of niche expansion. This scenario may offer insights into, for example, plant adaptation to extreme habitats such as mine tailings (Antonovics 2006). To fit the case of plant dispersal, we here focus on a species with sexual reproduction, dispersal before selection, and passive dispersal of propagules between habitats. We further assume that growth or decline in the sink is initially little affected by the local density and we allow local adaptation to depend on genetic variation at many loci.

In the absence of pollen limitation, pollen dispersal does not contribute directly to population growth. However, by disrupting local adaptation, pollen dispersal indirectly affects population dynamics via detrimental effects on fitness. Similarly, in animals with separate sexes, male dispersal has been predicted to differ from female dispersal in the effect on the process of adaptation to marginal habitats when only females directly contribute to population growth (Kawecki 2003). Pollen and seed dispersal are furthermore expected to exert different constraints on local adaptation (Nagylaki 1997; Hu and Li 2001, 2002; Lopez et al. 2008). First, the extent of pollen and seed dispersal, and therefore their relative contribution to gene flow, varies considerably among plant species (Ouborg et al. 1999; Petit et al. 2005). Second, for equal numbers of pollen grains and seeds dispersed, seeds carry twice as many nuclear genes as pollen (Hu and Ennos 1999). Finally, for the same number of gene copies dispersed, Lopez et al. (2008) predicted that, when selection is strongly divergent between habitats, the genetic load from pollen dispersal should be higher than that from seed, because of the relative inefficiency of purging of maladaptive alleles in heterozygotes formed from immigrating pollen. Yet, the previous authors did not explore the demographic consequences of the genetic load nor its impact on niche evolution.

Adaptation to marginal habitats leading to niche expansion (and failure to adapt leading to niche conservatism) has been intensively studied in the context of source–sink models (e.g., Holt and Gomulkiewicz 1997a; Gomulkiewicz et al. 1999; Tufto 2001; Ronce and Kirkpatrick 2001; Holt et al. 2003). Dispersal of individuals between source and sink populations tends to homogenize their sizes and genetic compositions, with antagonistic consequences for adaptation to marginal habitats (see reviews in Kawecki 2008; Holt and Barfield 2011). Influx of genes that enhance adaptation in the source may compromise fitness locally, maintaining the sink population in a state of severe maladaptation and low local abundance. Nevertheless, by boosting the sink population size, immigration of individuals from the source reduces the asymmetry of gene flow between source and sink, weakening the constraints on adaptation to marginal conditions. Furthermore, immigration from large and genetically diverse populations can facilitate adaptation to marginal conditions by increasing the amount of genetic variation exposed to selection in the sink. Many models integrating these multifarious effects of dispersal predict that the net effect of increasing the rate of seed dispersal between habitats is to facilitate and accelerate niche expansion (Holt and Gaines 1992; Kawecki 1995; Holt 1996a, b; Holt and Gomulkiewicz 1997a; Barton 2001; Ronce and Kirkpatrick 2001; Holt et al. 2003; Polechová et al. 2009). Exact effects of dispersal on niche expansion depend on the timing of dispersal within the life cycle, the pattern of dispersal between habitats, density-dependence of population growth in the sink, mating system, and genetic architecture of local adaptation (see review in Holt and Barfield 2011). Pollen dispersal is expected to differ from seed dispersal in its effects on population demography, the evolution of genetic variance and genetic divergence in marginal habitats (Lopez et al. 2008), which raises questions about its specific consequences for niche expansion. Hu and He (2006) found that, by affecting the spread of deleterious and advantageous mutations, pollen dispersal could slow down (when immigrating genes are maladaptive to recipient populations) or accelerate (when they are adaptive) range expansion in homogeneous environments. Butlin et al. (2003) found that pollen dispersal distances affect the probability of range expansion along environmental gradients (see also a short investigation of that question in Antonovics et al. 2001).

Conversely, niche contraction following secondary contact was described by Ronce and Kirkpatrick (2001) as a process called migrational meltdown. In strongly heterogeneous habitats, the genetic load generated by gene flow between two initially locally adapted populations can be large enough to cause demographic collapse. Small stochastic asymmetries in population sizes can be exaggerated by the stronger maladaptive effect of gene flow in smaller populations, resulting in a spiral of lower fitness and population size and the ultimate loss of a viable population in one of the habitats. The likelihood of migrational meltdown and niche contraction with pollen dispersal has not previously been explored. The higher genetic load found by Lopez et al. (2008) with pollen contribution to gene flow suggests that pollen and seed dispersal could differently affect migrational meltdown.

Here, we investigate the effects of pollen versus seed dispersal on niche width evolution, building on previous theory on niche evolution, in particular Ronce and Kirkpatrick (2001) and Holt et al. (2003). We explicitly model the feedbacks between population dynamics and adaptation, that is, that local adaptation is influenced by population size, and that, conversely, maladaptation results in reduction in population size. We consider a single quantitative trait under selection toward two different phenotypic optima in two distinct habitats. Genetic variance for this trait is critical to the process of niche expansion and contraction, because it both provides the potential for adaptation and depresses mean fitness. Following Gomulkiewicz and Houle (2009) who defined critical levels of genetic variance allowing an isolated population to adapt to an environmental change, we use an analytical model to identify critical levels of genetic variance leading to niche contraction (secondary contact scenario), niche expansion (new habitat scenario), or extinction (both scenarios). We confront these analytical predictions with individual-based simulations where the genetic variance freely evolves, and we examine the joint dynamics of adaptation and change in abundance.

Models

INVESTIGATED SCENARIOS

In the “secondary contact scenario,” we consider the contact of two genetically differentiated populations of the same species, initially living in two isolated, distinct habitats. Both populations are initially adapted to their local environment and at carrying capacity; the niche spanned by the species can be considered “wide.” We determine conditions under which both populations persist at carrying capacity, that is, the niche of the species remains wide. When this does not happen, either both populations go extinct, or niche contraction occurs. In the latter case, one habitat is a source (its population remains at carrying capacity), whereas the other one is a sink: due to maladaptation, its population cannot persist without immigration from the source. The niche spanned by the species can then be considered “narrow.”

In the “new habitat scenario,” we consider the possible invasion of a newly available habitat by a population initially adapted to a different habitat. The original habitat is initially a source, whereas the newly available habitat is a sink. The niche of the species is thus initially narrow. When adaptation proceeds to the point of persistence in both habitats, then the species’ niche has become wide, that is, niche expansion has occurred.

GENERAL ASSUMPTIONS

We consider self-compatible, annual, hermaphroditic plants with no seed bank. The environment consists of two habitat types. In each habitat, selection for an optimal phenotype acts on a single quantitative trait. The habitats are identical in all respects except that their optimal phenotypes, inline image and inline image, differ. Habitats are connected by pollen and seed dispersal: inline image and inline image are, respectively, the probability that a pollen grain or a seed changes habitat at the dispersal stage (see Table 1 for a summary of the notation). Dispersal probabilities are independent of the habitat, and there is no survival cost to dispersal.

Table 1.  Notation Parameter inline image is used in the analytical model only. Parameters K, L, U, and inline image are used in the simulation model only.
VariableDefinition
Ni Population size relative to carrying capacity in habitat i
inline image Mean maladaptation in habitat i
ParameterDefinition
inline image Seed dispersal probability
inline image Pollen dispersal probability
inline image Habitat heterogeneity, that is, difference between optimal phenotypes in the two habitats: inline image
inline image Width of the fitness function
inline image Genetic variance before selection
inline image Environmental variance
f Mean fecundity
K Carrying capacity
L Number of loci
U Mutation rate per genome
inline image Variance of the mutations size
Other notationDefinition
inline image Optimal phenotype in habitat i
ni Number of individuals in habitat i: ni=NiK
inline image Mean genotypic value in habitat 1: inline image
inline image Mean genotypic value in habitat 2: inline image
inline image Total gene flow: inline image
v Average survival probability of individuals with an average genotypic value at the optimum: inline image
inline image inline image

We define habitat heterogeneity inline image as the difference between the optimal phenotypes in the two habitats: inline image. Without loss of generality, we assume that habitat heterogeneity is positive. The phenotype of an individual is the sum of its genotypic value and a Gaussian environmental effect with mean 0 and variance inline image. We measure maladaptation in each habitat, inline image and inline image, as the distance between the mean genotypic value in each habitat, inline image and inline image, and its optimal value: inline image and inline image. Population size, measured relative to carrying capacity K, in habitat i is Ni=ni/K where ni is the number of individuals in habitat i.

We assume discrete and nonoverlapping generations with the following life cycle: (1) selection, (2) density regulation, (3) gametogenesis, pollen dispersal, and syngamy, and (4) seed dispersal. We found that reversing the order of density regulation and selection did not affect our qualitative conclusions. A juvenile with phenotype z in habitat i survives selection according to a Gaussian function with width inline image

image

(inline image is inversely related to the strength of selection).

We assume a “ceiling” form of density regulation: when the population size after selection in a given habitat exceeds its carrying capacity K, K individuals are randomly sampled, otherwise, all individuals survive density regulation. We also used a continuous density regulation function (Beverton–Holt, see Appendix S5). Fecundity does not depend on the habitat: each plant produces on average f ovules. It is assumed that pollen is not limiting, that is, all ovules are fertilized. We consider partial philopatry, that is, we use values of inline image and inline image lower than 0.5.

ANALYTICAL MODEL

In the analytical model, we assume a Gaussian distribution of genotypic values before selection with mean inline image in habitat i and fixed genetic variance inline image. The mean fitness in habitat i is then

image(1)

where inline image and inline image is the average survival probability of individuals with a genotypic value at the optimum. We ignore demographic stochasticity. Changes in mean phenotype and population size along the life cycle are detailed in Appendix S1.

We use the analytical model to determine critical levels of genetic variance leading to niche contraction (secondary contact scenario), niche expansion (new habitat scenario), or extinction (both scenarios).

SIMULATION MODEL

We have also simulated the two scenarios without any assumption regarding the distribution of genotypes, allowing the genetic variance to evolve. Simulations are individual-based and take into account stochastic effects due to limited population size.

The simulation model employed here has been described in detail elsewhere (Ronce et al. 2009). The individual’s genotypic trait value is the sum of allelic effects over L unlinked loci. During gametogenesis, mutations occur at a specified rate U per diploid genome. For a mutation occurring in a given allele, its effect is modeled as that of the original allele, plus a normal deviation with zero mean and variance inline image. Thus, there is no constraint on the number of alleles that might be segregating at a particular locus, nor is there a constraint on the allelic effect sizes, other than that imposed by selection. Consequently, the genetic variance of each population is free to evolve. At the fertilization stage, the number of juveniles generated in habitat i is taken as a Poisson random variable, with mean equal to f times the number of individuals after density regulation in habitat i.

In the secondary contact scenario, populations in the two habitats are allowed to evolve separately for 1000 generations to achieve mutation-selection-drift balance (as in Holt et al. 2003). We checked that this equilibrium was reached in our simulations (not shown). After 1000 generations, gene flow between populations begins. In the new habitat scenario, a single population is generated in habitat 1, with K individuals having their trait at the optimum inline image, and allowed to evolve for 1000 generations. At this point, dispersal begins between this population and habitat 2, initially empty.

After dispersal begins, the number of generations is counted before a new demographic equilibrium is reached. In the secondary contact scenario, we tally the number of generations until one or the other population drops in size to the point that it is maintained well below the carrying capacity (threshold set to 0.05 K) while the other remains at carrying capacity. In the new habitat scenario, we count the number of generations until the initially empty habitat harbors a population at carrying capacity. Simulations were stopped after 105 generations if still at the initial demographic equilibrium. Extinction was recorded when all individuals died. For a given scenario and set of parameter values, a minimum of 100 replicate simulations were run.

Results

SECONDARY CONTACT SCENARIO

Expected equilibrium at fixed genetic variance

In the secondary contact scenario, the niche of the species is initially wide. The populations in both habitats are isolated and are locally adapted. Dispersal between the two habitats then begins, and we investigate under which conditions the niche width is maintained, that is, under which conditions the wide niche equilibrium is viable and locally stable. In the analytical model, solving equation (S5) assuming N1=N2, we found population density and mean maladaptation, measured before selection, at the wide niche equilibrium:

image(2)

where inline image is the total gene flow, that is, the probability that a gene copy is dispersed to the other habitat via pollen or seed. Such a gene copy can originate from a dispersed pollen grain’s contribution to a nondispersed seed (probability inline image), from a nondispersed pollen grain’s contribution to a dispersed seed (probability inline image), or from an ovule’s contribution to a dispersed seed (probability inline image). Note that, as found in Lopez et al. (2008) (see also Nagylaki 1997; Hu and Li 2001), maladaptation at the wide niche equilibrium depends on the total gene flow, and not on the relative contribution of pollen and seed dispersal (see however Kawecki (2003) for different results when reproductive outputs vary between patches). Equation (2) shows that higher genetic variance inline image allows better local adaptation (lower inline image). Conversely, dispersal induces maladaptation in each population at the wide niche equilibrium (eq. 2). The wide niche equilibrium is viable (i.e., exists) and is locally stable (see Appendix S2) when

image(3)

For a specific combination of pollen and seed dispersal probabilities, Figure 1 shows the values of the genetic variance inline image for which the wide niche equilibrium is viable and locally stable, according to the analytical model: maintenance of a wide niche is impossible when inline image is either too small or too large. Too low inline image does not support response to selection that maintains sufficient adaptation of each population for them to persist (eq. 2). When inline image is too high, too few individuals survive selection for both populations to persist.

Figure 1.

Population density inline image (panel A) and mean maladaptation inline image (panel B) measured before selection at the evolutionary equilibrium as a function of the fixed genetic variance inline image for the secondary contact scenario. The niche of the species is initially wide; when niche contraction occurs, one population remains a source (solid line), the other one becomes a sink (dashed line). Letters W, N, and E indicate the parameter region corresponding to the wide niche equilibrium, narrow niche equilibrium, and to extinction of both populations, respectively. Results are obtained by numerically iterating equations (S1)–(S4) with almost symmetrical initial conditions (N1=f, N2=f−0.001, inline image, and inline image), mimicking a small perturbation at secondary contact of the two populations. Parameter values: inline image, inline image, inline image, inline image, f=2, inline image.

There are thus two critical values of the genetic variance, denoted inline image and inline image, below which and, respectively, above which, it is not possible to maintain a wide niche in the presence of dispersal (SC superscript stands for secondary contact scenario). The values of inline image and inline image are the solutions for inline image of equation (3) where the inequality is replaced by an equality. We were unable to solve equation (3) analytically for the genetic variance inline image; we obtained the critical genetic variances numerically.

At the wide niche equilibrium, because of the ceiling form of density regulation we assume, seed dispersal does not affect population size after density regulation. The stability of the wide niche equilibrium is consequently not affected by the demographic effect of seed dispersal, and the critical genetic variances are determined by the genetic effect of seed and pollen dispersal. In other words, the values of inline image and inline image depend on total gene flow inline image, but not on the specific pollen and seed dispersal probabilities (eq. 3 depends on inline image only). In Appendix S5, we consider a continuous density regulation function (Beverton–Holt) for which the stability of the wide niche equilibrium depends on the demographic effect of seed dispersal. Although the values of inline image and inline image then depend on the specific pollen and seed dispersal probabilities (at constant total dispersal, increasing seed dispersal tends to stabilize the wide niche equilibrium), the results described below are qualitatively unchanged and quantitatively weakly affected (Appendix S5).

The range of inline image for which a wide niche can be maintained (i.e., inline image) is reduced by total dispersal inline image. This is illustrated in Figure 2, which shows the variations of inline image and inline image as a function of pollen dispersal inline image (and corresponding total dispersal inline image), for different fixed values of seed dispersal inline image and habitat heterogeneity inline image. As total gene flow inline image increases, there may be no value of inline image allowing maintenance of a wide niche (on panels A and B of Fig. 2, inline image and inline image are not defined for inline image).

Figure 2.

Critical genetic variances inline image, inline image, inline image, inline image, inline image, and its approximation by equation (4), computed with the analytical model as a function of pollen dispersal inline image, for fixed values of seed dispersal inline image and habitat heterogeneity inline image. Solid regions indicate the parameter region where only one equilibrium is viable and locally stable: only the wide niche equilibrium (W), only the narrow niche equilibrium (N), or only extinction of both populations (E). Striped regions indicate bistabilities (WN and WE). Viability and stability of the wide niche equilibrium is determined from equation (3). Viability and stability of the narrow niche equilibrium is determined from numerical iteration of equations (S1)–(S4) with asymmetrical initial values corresponding to an empty sink and an adapted source (N1=f, N2= 0, inline image, and inline image). Parameter values: inline image, f=2, inline image.

As expected from previous literature (e.g. Ronce and Kirkpatrick 2001), Figure 2 reveals that the range inline image is reduced by increasing habitat heterogeneity and by stronger selection (panels A and B with inline image versus panels C and D with inline image, and Appendix S4).

When a wide niche is not maintained at secondary contact, niche contraction may occur (populations persist, but in a source–sink system), or both populations may go extinct. Figure 1 illustrates that there is a threshold value of the genetic variance, denoted inline image, above which the narrow niche equilibrium is not viable. Excessive genetic variance depresses mean fitness, resulting in the extinction of both populations. We derived an approximation for inline image assuming that, at the narrow niche equilibrium, close to extinction, the sink is a black-hole sink (i.e., no dispersal from the sink to the source; see Appendix S3):

image(4)

The approximation of inline image does not depend on pollen dispersal inline image because (1) it assumes a black-hole sink, which implies that the source does not receive pollen from the sink, and (2) we assume that pollen does not limit reproduction (all ovules in the source are fertilized). The accuracy of the approximation was checked by comparing it to the viability threshold found by numerical iteration of equations (S1)–(S4). The accuracy was found to be generally good, although the approximation given by equation (4) underestimates the value of inline image at high seed dispersal (see, e.g., Fig. 2).

The critical variance inline image decreases with increased seed dispersal (eq. 4, Fig. 2). Indeed, at the narrow niche equilibrium, most of the seeds dispersed from the source to the sink die. When seed dispersal increases, high genetic variance cannot be sustained because of the combined demographic loads due to the effects of selection and the loss of seeds to the sink through dispersal. Similarly, inline image decreases when selection becomes stronger (eq. 4, Fig. S2).

Figure 2 summarizes the parameter region where, depending on the value of the genetic variance inline image compared to the three critical genetic variances inline image, inline image, and inline image, the analytical model predicts the maintenance of the wide niche equilibrium (inline image) or not, and, in the latter case, if niche contraction or the extinction of both populations (inline image) is predicted.

Dynamics of genetic variance and consequences for niche width evolution

Figure 3 shows typical time series from our individual-based simulations with freely evolving genetic variance inline image, for two of the three possible outcomes in the secondary contact scenario. The genetic variance immediately increases at secondary contact, because of the initial genetic differentiation of the populations. Then, because dispersal quickly homogenizes the genotypic distribution between the two habitats, inline image tends to decrease, especially at high dispersal (Fig. 3, panel D). Then, the differentiation between the populations in each habitat increases in response to selection, so that the mean genetic variance increases again, until it reaches a quasi-stationary level denoted inline image. For parameter values such that the critical genetic variances inline image and inline image exist, we found that inline image was higher than inline image, but below or above inline image, depending on parameter values.

Figure 3.

Typical time series (simulation model, secondary contact scenario) ending by the maintenance of the wide niche equilibrium (panels A and B) and by niche contraction (panels C and D). Panels (A) and (C) show population density before selection Ni in each habitat and panels (B) and (D) show the mean genetic variance of the populations before selection. Horizontal lines show the critical genetic variances inline image (dotted lines), inline image (dashed lines), and inline image (solid lines), computed with the analytical model for the parameter values used in these simulations. Parameter values: K=400, inline image, inline image, f=2, inline image, inline image, U=0.1, L=10.

As predicted from the analytical model (Fig. 2), the populations remain at the wide niche equilibrium as long as inline image remains lower than inline image (Fig. 3, panels A and B). In simulations where inline image becomes higher than inline image (i.e., inline image), which may occur after a long time, the populations quickly leave the wide niche equilibrium (Fig. 3, panels C and D). Such conditions, under which niche contraction is possible, correspond to high habitat heterogeneity, strong selection (Appendix S4), and low to moderate total dispersal (Fig. 2, panels A and B). Once inline image, the growth rate of the populations was typically slightly below 1: the wide niche is lost when a stochastic demographic event induces a dispersal asymmetry large enough to result in the collapse of at least one of the two populations. This collapse is associated with a drastic decrease of the genetic variance. In simulations where inline image, we always observed that inline image became smaller than inline image, as illustrated in Figure 3 (panels C and D). The populations ultimately persist at the narrow niche equilibrium, that is, niche contraction occurred.

Considering simulations with approximately the same quasi-stationary genetic variance inline image but different values of inline image, smaller than inline image, we found that niche contraction was more likely and more rapid for lower values of inline image (Fig. 4). This suggests that when inline image is far from inline image, weak dispersal asymmetries are enough to destabilize the wide niche equilibrium.

Figure 4.

Cumulative distribution of the waiting time to the loss of the wide niche equilibrium (simulation model, secondary contact scenario). Each curve corresponds to a value of the critical genetic variance inline image indicated next to it. The different inline image are generated with different combinations of seed and pollen dispersal. In all simulations, the quasi-stationary genetic variance of the population inline image is approximately the same, about 1.25. Parameter values: K=400, inline image, inline image, f=2, inline image, inline image, U=0.1, L=10.

Because inline image decreases when inline image increases (Fig. 2), and niche contraction is more likely and faster for smaller values of inline image (Fig. 4), unsurprisingly, we found that niche contraction occurs faster when total dispersal increases (Fig. 5). In addition, Figure 5 shows that niche contraction proceeds more rapidly with increase in the proportion of pollen dispersal as a component of total gene flow. Dispersal through seeds can indeed delay niche contraction because, for the same number of gene copies dispersed, maladapted genes from immigrating seeds are more easily purged from the population than maladaptive alleles in heterozygotes formed from immigrating pollen. This is consistent with the higher genetic load with pollen dispersal observed by Lopez et al. (2008).

Figure 5.

Mean number of generations computed from simulations before niche contraction as a function of total dispersal inline image (secondary contact scenario). Each curve corresponds to a fixed value of inline image. A waiting time of 105 generations indicates that the populations were still at the wide niche equilibrium when simulations were stopped. Parameter values: K=400, inline image, inline image, f=2, inline image, inline image, U=0.1, L=10.

In simulations with parameter values such that there is no critical genetic variance inline image and inline image (high habitat heterogeneity, strong selection [Appendix S4], and high total dispersal [Fig. 2, panels A and B]), we observed that the populations always left the wide niche equilibrium, as predicted by the analytical model. We observed either niche contraction or extinction of both populations. The probability of an extinction of both populations shows a very sharp transition as seed dispersal increases (Appendix S6, Fig. S7). As expected from the analytical model, extinction occurs when the value of inline image (which decreases when inline image increases, eq. 4) becomes lower than the genetic variance in the source population at the narrow niche equilibrium.

NEW HABITAT SCENARIO

Expected equilibrium at fixed genetic variance

In the new habitat scenario, the niche of the species is initially narrow: one habitat is a source where individuals are on average perfectly locally adapted and the other habitat is an empty sink where immigrants are strongly maladapted. By numerically iterating equations (S1)–(S4) with initial values corresponding to this source–sink system (N1=f, N2= 0, inline image, and inline image), we can determine the parameter values for which the species’ niche remains narrow, for which niche expansion occurs (i.e., the species’ niche becomes wide, with both habitats as sources), and for which both populations go extinct.

For a specific combination of pollen and seed dispersal probabilities, numerical iteration of the analytical model shows that niche expansion occurs if the genetic variance is sufficiently large, but not too large (Fig. 6). Increasing the genetic variance improves the response to selection in the sink, so that the sink population may eventually become sufficiently adapted to persist in its habitat. At very high genetic variance, however, the wide niche equilibrium is not stable (and possibly not viable) because selection removes too many individuals.

Figure 6.

Population density inline image (panel A) and mean maladaptation inline image (panel B) at the evolutionary equilibrium as a function of the fixed genetic variance inline image for the new habitat scenario. Initially, one habitat is a source (solid lines), the other one is a sink (dashed lines). Letters W, N, and E indicate the parameter region corresponding to the wide niche equilibrium, narrow niche equilibrium, and to extinction of both populations, respectively. Results are obtained by numerically iterating equations (S1)–(S4) with initial conditions corresponding to an empty sink and an adapted source (N1=f, N2=0, inline image, and inline image). Parameter values: inline image, inline image, inline image, inline image, f=2, inline image.

There are thus two critical values of the genetic variance between which niche expansion is possible. The lower, denoted inline image (NH superscript stands for new habitat scenario), is the threshold above which the narrow niche equilibrium is unstable whereas the wide niche equilibrium is viable, locally stable, and reachable from initial conditions corresponding to an empty sink and an adapted source. The larger critical genetic variance, denoted inline image, is the threshold above which the wide niche equilibrium is unreachable from initial conditions corresponding to an empty sink and an adapted source. It is important to note that the wide niche equilibrium may be unreachable because it is inviable. In this case, the upper critical genetic variance for niche expansion is the critical variance inline image already defined for the secondary contact scenario. We were unable to determine inline image and inline image analytically. We obtained them by numerical iteration of equations (S1)–(S4). When inline image coincides with inline image, or when there is no inline image, niche expansion is not possible.

Consistent with previous literature (e.g., Ronce and Kirkpatrick, 2001), we found with the analytical model that there are values of the genetic variance allowing niche expansion for a large range of pollen and seed dispersal probabilities unless habitat heterogeneity is high and selection strong (Fig. 2 and Appendix S4).

The critical genetic variance inline image varies with pollen and seed dispersal (Fig. 2). Whatever the proportion of pollen dispersing, increasing seed dispersal decreases inline image. Because seeds contribute directly to population growth, initial demographic asymmetry between the habitats implies that seed dispersal directly increases the size of the sink population, which decreases demographic asymmetry. As a result, when inline image increases, the potential for adaptation is enhanced in the sink and compromised in the source, so that expansion of the niche can occur at lower genetic variance, that is, inline image decreases.

At low seed dispersal, increasing pollen dispersal strongly increases inline image (Fig. 2, panels A and C). Because pollen does not contribute to population growth, pollen dispersal does not directly affect population size. Pollen dispersal, however, increases maladaptation in the sink, which reinforces demographic asymmetries between the source and the sink population. The potential for adaptation is consequently compromised in the sink, so that niche expansion requires greater genetic variance, that is, when inline image increases, inline image increases. As pollen dispersal increases, the genetic variance that would allow niche expansion may be very high. Too few individuals may then survive selection for the wide niche equilibrium to be reachable from initial conditions corresponding to an empty sink and an adapted source (Fig. 2, panel C: inline image finally reaches inline image), or even to be viable (Fig. 2, panel A: inline image finally reaches inline image).

For higher values of seed dispersal, the effect of pollen dispersal on inline image is weaker (Fig. 2, panel D) because seed dispersal reduces the asymmetry in population size. In addition, increasing pollen dispersal first increases inline image, then decreases inline image. When pollen dispersal becomes high, pollen dispersal from the sink into the source also compromises adaptation of the source population to its local conditions. Pollen dispersed from the source has then a weaker maladaptive effect in the sink, and thus reduces demographic asymmetry. The potential for adaptation in the sink is consequently enhanced, so that niche expansion requires less genetic variance. This effect of increased pollen dispersal facilitating niche expansion appears only when seed dispersal is high enough: the sink population size is then sufficiently large, and gene flow from the sink to the source high enough, to generate significant maladaptation in the source.

The critical genetic variance inline image also varies with pollen and seed dispersal: it decreases with pollen dispersal and increases with seed dispersal (Fig. 2, panels C and D).

Figure 2 summarizes the parameter region where, depending on the value of the genetic variance inline image compared to the four critical genetic variances inline image, inline image, inline image, and inline image, the analytical model predicts that niche expansion is possible (inline image) or not, and, in the latter case, if populations are predicted to persist in a source–sink system or to go extinct (inline image). Note that there are parameter regions where the wide niche equilibrium is viable and locally stable, but not reachable from the initial conditions of the new habitat scenario (bistabilities indicated on Fig. 2).

Dynamics of genetic variance and consequences for niche width evolution

For parameter values identified in the analytical model such that critical genetic variances allowing niche expansion exist (not too extreme habitat heterogeneity nor too intense selection, Appendix S4), we found with simulations that a system initiated in a narrow niche state generally evolves to ultimately expand its niche. This can however occur after a very large amount of time. In some simulations, the system was still at the narrow niche equilibrium after 105 generations. The shift from the narrow to the wide niche equilibrium is associated with changes in the genetic variance, which increases progressively during the period before the sink population reaches carrying capacity. Once the genetic variance in the sink population reaches the critical genetic variance inline image, adaptation accelerates, and population growth in the new habitat is rapid. We observed that the genetic variance then stabilizes below the critical genetic variance inline image. Figure 7 shows a typical time series illustrating these dynamics.

Figure 7.

Typical time series from the simulation model for the new habitat scenario showing population density before selection Ni (panel A) and the mean genetic variance of the populations before selection (panel B). On panel (B), the horizontal line indicates the critical genetic variance inline image (computed with the analytical model for the parameter values used in this simulation). With the parameter values used in this figure, the upper critical genetic variance for niche expansion is inline image. Parameter values: inline image, inline image, K=400, inline image, inline image, f=2, inline image, inline image, U=0.1, L=10.

We found that the mean time to niche expansion depends on the difference between inline image and the genetic variance inline image at the time dispersal to the new habitat begins. Higher values of parameters that increase the initial genetic variance in the source (U, inline image, as well as inline image) decrease the time to adaptation to the sink (not shown). Figure 8 shows the cumulative distribution of waiting times to niche expansion for simulations with the same initial genetic variance but different values of inline image; at lower values of inline image, niche expansion proceeds more quickly. For high values of inline image, niche expansion may take thousands of generations, making niche conservatism more likely on a biologically relevant time scale (environmental changes may, e.g., occur before niche expansion can happen).

Figure 8.

Cumulative distribution of the waiting time to niche expansion (simulation model, new habitat scenario). Each curve corresponds to a value of the critical genetic variance inline image indicated next to it. The different inline image are generated with different combinations of seed and pollen dispersal. In all simulations, at the time dispersal begins, the genetic variance of the population is about 0.21. Parameter values: K=400, inline image, inline image, f=2, inline image, inline image, U=0.17, L=10.

Because seed dispersal decreases inline image (Fig. 2), and niche expansion is faster for lower values of inline image (Fig. 8), seed dispersal accelerates niche expansion (Fig. 9). Conversely, for most parameter values, pollen dispersal increases inline image (Fig. 2), and thus slows down niche expansion (Fig. 9). Figure 9 also shows that for high seed and pollen dispersal, pollen dispersal accelerates niche expansion; pollen dispersal decreases inline image in this case (Fig. 2).

Figure 9.

Mean number of generations computed from simulations before shift from narrow to wide niche equilibrium (new habitat scenario) as a function of pollen and seed dispersal probabilities. Parameter values: K=400, inline image, inline image, f=2, inline image, inline image, U=0.1, L=10.

In simulations with parameter values such that niche expansion was predicted as impossible by the analytical model (inline image coincide with inline image, or inline image does not exist), the system was still at the narrow niche equilibrium after 105 generations, or both populations went extinct. As in the secondary contact scenario, extinction of both populations occurred when the genetic variance inline image of the source population was higher than inline image, resulting in a sharp transition between narrow niche equilibrium and extinction as inline image increases (Appendix S6, Fig. S8).

Discussion

For organisms living in differentiated habitats, we find that enhancement of dispersal between the habitats can result in a shift from wide to narrow niche equilibrium or even in extinction. These shifts between equilibria are observed only when selection is severe and favors widely different phenotypes in the distinct habitats. Our model further shows that niche contraction is more likely and faster when total dispersal is high. Gene flow via pollen or seeds compromises local adaptation so that maintaining a viable population in both habitats may be impossible. Simulations show that, compared to gene flow through pollen, gene flow through seeds slows niche contraction, because seed dispersal generates a smaller dispersal load than pollen dispersal (see Lopez et al. 2008, for a detailed discussion of this phenomenon). Maladapted immigrant genes in seeds are more easily purged from the population than immigrant pollen genes, whose effects are partly masked in hybrids. However, our models also show that the higher the seed dispersal, the higher the probability of general extinction. As seed dispersal increases, and results in higher mortality of dispersing seeds, population viability depends on genetic variance being low enough to allow numerous individuals to survive selection.

Our results show that adaptation to the novel habitat requires sufficient genetic variance. When habitat heterogeneity and selection are not too strong, we found an increase of the genetic variance after dispersal to the new habitat begins, as also found in Barton (2001). This increase may take hundreds or thousands of generations when gene flow takes place predominantly via pollen dispersal. Antonovics et al. (2001) likewise found that, the greater the dispersal into a novel habitat via seeds, the faster the adaptation, whereas increasing dispersal via pollen impeded adaptation. As in Holt et al. (2003), the sink population remains maladapted until a shift to an adapted state occurs. Our results show that this shift occurs only after a minimal genetic variance is reached; adaptation per se then proceeds quite rapidly. At high pollen dispersal, however, it can take so long to reach the higher critical genetic variance, that the environment may change before adaptation to the new niche can proceed fully. The immediate genetic effect of pollen dispersal is to increase maladaptation in the sink, and thus to reduce population size in the sink. This reduces the efficacy of selection, even though the pollen-mediated gene flow increases the genetic variation in the sink. Gene flow via pollen predominates in many plant populations, as suggested by the differentiation among populations for molecular markers transmitted via seeds versus pollen (reviewed in Petit et al. 2005). Thus, by incorporating effects of pollen dispersal, our models help to address the challenge raised by Bradshaw (1991) of accounting for the prevalence of failures of plants to adapt to novel, harsh habitats, such as soils contaminated by heavy metals.

However, for plants whose seeds disperse more profusely than pollen, we find that adaptation to a selectively distinct habitat can proceed relatively quickly, in tens of generations. Because seeds contribute directly to population size, seed dispersal directly increases the size of the sink population (as animal dispersal does, see e.g. Holt and Gaines 1992; Kawecki 1995; Holt 1996a, b; Holt and Gomulkiewicz 1997a; Ronce and Kirkpatrick 2001; Holt et al. 2003). As a result, the potential for adaptation is enhanced in the sink and compromised in the source, so that relatively little genetic variation is required for adaptive expansion of the species’ niche. Plants having seeds with wings or other appendages that facilitate wind dispersal, or those whose seeds are frequently transported by animals may thus be especially likely to rapidly expand their niche under the circumstances of our models.

Although we have motivated this study by focusing on plants, we expect analogous conclusions to apply to other organisms for which male gametes and zygotes disperse (but not female gametes), and male gametes do not limit reproduction. Our conclusions may thus apply to some haplodiploid organisms, such as wasps with both male (haploid) and female (diploid) dispersal, or fungi dispersing both as haploids and diploids. In the case of animals having sex-specific dispersal rates, Kawecki (2003) showed that the fitness in absolute sink habitats is enhanced by female-biased dispersal but reduced by male-biased dispersal. This result relies on the fact that dispersal of both sexes has genetic consequences, but in the absence of parental care and sperm limitation, only females contribute directly to population growth. This situation is analogous to pollen (male) and seed (female) dispersal and explains the qualitative convergence of Kawecki (2003)’s results and ours. Quantitative differences are however expected because of important differences in the reproductive biology. In particular, pollen is haploid, whereas, apart from haplodiploids, male animals are not, and seeds carry alleles from the gametes produced by both parents, whereas when female animals disperse before mating, their progeny receives their paternal genetic complement from males encountered after dispersal. Kawecki (2003) concluded that the ecological niche of species with female-biased dispersal should be broader than that of species with male-biased dispersal. Similarly, according to our results, we expect the ecological niche of species dispersing predominantly via seeds to be wider than that of species dispersing predominantly via pollen. With individual-based simulations on a linear gradient, Butlin et al. (2003) also found that, at constant total dispersal, increasing the mating area (a circle around a female where she chooses a male for mating, which is analogous to pollen dispersal) makes the evolutionary equilibrium switch from an unlimited range to a limited range.

We know of no empirical study for which all of the components of our models have been estimated, clearly a challenging task. However, the new habitat scenario of our models may bear on the adaptation to metal-contaminated soil of some grass species from adjacent pasture populations (Bradshaw 1991). For two species of those that have evolved tolerance to the highly toxic metal-contaminated soils and that persist on the mine tailings, Anthoxanthum odoratum and Agrostis tenuis, gene flow via pollen between the populations on the different soils has declined greatly due to evolution of differences in flowering phenology (McNeilly and Antonovics 1968), which have persisted for four decades (Antonovics 2006), and to evolution of higher selfing rates on the mine tailings (Antonovics 1968). In the case of A. tenuis, McNeilly (1968) demonstrated ongoing seed dispersal between the two habitats. Our models suggest that such reductions of the exchange of pollen, while seeds continue to disperse, may have favored adaptation of these otherwise highly outcrossing, wind-pollinated plants to the contaminated soils. It remains to be tested whether high pollen dispersal explains the failure of adaptation for those many species that have not colonized such extreme habitats. For many invasive plants, pollen receipt is restricted via self-pollination and seeds are widely dispersed (Sakai et al. 2001), a combination that our models show is conducive to evolutionary niche expansion.

Our findings concerning the scenario of secondary contact between diverged populations indicate that adaptation to both habitats will be maintained under many circumstances, including differences in selection that are moderate and gene flow that comprises at least some seed dispersal. This conclusion, which accounts for both demography and genetics, reinforces the view of Frankham et al. (2011), based on genetic considerations alone, that outbreeding depression threatening population persistence should be expected under only restricted conditions, including when divergent populations occupy habitats that are selectively extremely different. Accordingly, these authors advocate for management that augments gene flow between isolated populations more often than it is currently practiced. Our findings tend to support this recommendation, particularly whenever gene flow is predominantly via seeds. When habitat differences are very strong, too high seed dispersal may however lead to extinction in both habitats and should be avoided.

Our main conclusions about the effect of seed and pollen dispersal on niche evolution appear to be robust to variation of several assumptions of our model. We ran simulations with mutations drawn from a truncated normal distribution with maximal mutation effect of inline image (rather than unbounded distribution), and found that this restriction on mutation effect size did not preclude adaptation in the sink (results not shown). This indicates that adaptation in the sink did not require mutations with extreme effects (in contrast to what previous authors have concluded, under different assumptions, e.g., Holt and Gomulkiewicz 1997b; Kawecki 2000; Holt and Barfield 2011; Yeaman and Whitlock 2011). Further analyses would be necessary to study the effect of seed versus pollen dispersal on the evolution of genetic architecture during adaptation. The order of life-history events is known to influence the likelihood and speed of niche evolution in animal models (Ronce and Kirkpatrick 2001; Kawecki 2008; Holt and Barfield 2011). We analyzed our models with a variant life cycle (density regulation before selection). We found that niche expansion was less likely and took longer when regulation occurs before selection, and niche contraction more likely and faster (results not shown). Our qualitative conclusions remain however unaffected: a wider niche is generally predicted for species dispersing seeds rather than pollen. Likewise, our models assume a ceiling form of density regulation that eliminates density-dependence effects at low density. Using a continuous density regulation function (Beverton–Holt), we checked that our results are robust with respect to a moderately strong form of density-dependence: niche contraction and niche expansion take only slightly longer with Beverton–Holt regulation (see Appendix S5).

If negative density-dependence is strong in low-density sink habitats, the demographic effect of seed dispersal could be globally negative, lowering the mean fitness of the populations, and preventing niche expansion. Similarly, our models assume that pollen is not limiting and, consequently, pollen dispersal has no direct demographic consequences, while it is not unusual in nature for pollen influx to contribute directly to seed production, particularly in marginal populations (Richards 2000; Wagenius 2004; Knight et al. 2005). Pollen limitation may lead to an Allee effect: sufficient pollen dispersal would then be required to increase local population size, and allow the evolution or maintenance of a wide niche. Conditions of severe density-regulation or pollen limitation would likely weaken our prediction of a wider niche for species dispersing seeds rather than pollen. A detailed analysis would be necessary to clarify the respective effect of seed and pollen dispersal on niche width evolution under such conditions.

Finally, our conclusions may be altered by consideration of additional factors, such as the genetic consequences of selfing (Charlesworth and Charlesworth 1995; Charlesworth 2003), or the effect of gene flow on inbreeding depression (Lopez et al. 2009; Ronce et al. 2009). We should also mention that our models assume constant pollen and seed dispersal rates. Dispersal is, however, a life-history trait subject to evolution, as predicted by models (e.g., van Valen 1971; Balkau and Feldman 1973; McPeek and Holt 1992; Ravigné et al. 2006) and as demonstrated by the various pollen and seed dispersal rates observed in natural populations (Ouborg et al. 1999; Petit et al. 2005). Because of its maladaptive effect, pollen dispersal could be selected against. Additional investigations would be required to determine the conditions under which pollen dispersal rate, as a trait under selection, might decrease enough to allow for niche expansion.

Associate Editor: K. Donohue

ACKNOWLEDGMENTS

We thank F. Débarre for productive discussions and useful comments on previous versions of this paper, and R. Law for his insights on implications of the model. We are very grateful to T. J. Kawecki and B. Holt whose comments significantly improved the quality of our work. RA was supported by the EVORANGE project (ANR-09-PEXT-01102) from the French “Agence Nationale de la Recherche” allocated to OR. We acknowledge support from RTRA BIOFIS (INRA 065609). FHS gratefully acknowledges research support from Hamline University. RGS gratefully acknowledges a sabbatical supplement from the University of Minnesota’s College of Biological Sciences and funding from the US National Science Foundation LTREB and IGERT programs. RGS and FHS thank members of ISEM for providing a stimulating context for this project. Part of the computations was run on the ISEM cluster. This is publication ISEM-2012-136 of the Institut des Sciences de l’Évolution.

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