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Keywords:

  • dispersal;
  • evolution;
  • habitat selection;
  • phenotypic plasticity;
  • population age;
  • reproductive value;
  • senescence;
  • succession

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Model assumptions
  5. Analytical results
  6. Numerical results
  7. Discussion
  8. Conclusion
  9. Acknowledgements
  10. Supplementary material
  11. References
  • 1
    We use a deterministic model to explore theoretically the ecological and evolutionary relevance of plastic changes in seed dispersal along ecological succession. Our model describes the effect of changing disturbance regime, age structure, density and interspecific competition as the habitat matures, enabling us to seek the evolutionarily stable reaction norm for seed dispersal rate as a function of time elapsed since population foundation.
  • 2
    Our model predicts that, in the context of ecological succession, selection should generally favour plastic strategies allowing plants to increase their dispersal rate with population age, contrary to previous predictions of models that have assumed genetically fixed dispersal strategies.
  • 3
    More complex patterns can evolve showing periods with high production of dispersing seeds separated by periods of intense local recruitment. These patterns are due to the interaction of individual senescence with change in ecological conditions within sites.
  • 4
    Evolution of plastic dispersal strategies affects the patterns of density variation with time since foundation and accelerates successional replacement. An interesting parallel can be drawn between the evolution of age-specific dispersal rates in successional systems and the evolution of senescence in age-structured populations.
  • 5
    Seed dispersal plasticity could be a potential mechanism for habitat selection in plants and have implications for range expansion in invasive species because recently founded populations at the advancing front may show different patterns to those in the established range.

Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Model assumptions
  5. Analytical results
  6. Numerical results
  7. Discussion
  8. Conclusion
  9. Acknowledgements
  10. Supplementary material
  11. References

The widespread mechanisms that facilitate seed dispersal in plant species include pappi on achenes and spines on pods, as well as possession of samaras or elaiosomes. Genetic variation for dispersal-related traits has been documented in numerous cases within natural populations (Venable & Lawlor 1980; Clay 1982; Olivieri et al. 1983; Olivieri & Berger 1985; Schmitt et al. 1985), and phenotypic variation has also been reported for dispersal-related traits among populations in the same region. For example, dispersal ability of individuals may vary between recently founded and older populations. The average proportion of achenes of Carduus pycnocephalus and C. tenuiflorus that were equipped with a pappus declined along a successional gradient (Olivieri & Gouyon 1985) and comparison of the mass-area ratio of samaras of red maples (Acer rubrum) suggested that dispersal ability was significantly higher in populations located in early than in late successional environments (Peroni 1994). Dispersal-related morphological characteristics of diaspores of Lactuca muralis and Hypochaeris radicata also varied with population age (Cody & Overton 1996), with dispersal potential higher in young island populations but lower in older island populations than in the mainland population.

Theoretical studies in a metapopulation context (van Valen 1971; Olivieri et al. 1990; Olivieri et al. 1995) have suggested that these differences may result from genetic differences between young and old populations. They argue that, if genetic variation for dispersal behaviour is maintained in a metapopulation, we expect genotypes with the highest dispersal rate to be the most likely to colonize new empty patches of habitat and therefore to occur at high frequency in recently founded populations. However, because of the risk of landing in unsuitable areas, genotypes with a high dispersal rate will leave an occupied patch more often than they immigrate into it. As a result, within each local population, the frequency of genotypes with a high dispersal rate declines over time. Theoretical studies considering the effect of genetic polymorphism for dispersal thus predict that the average dispersal rate should be higher in young populations than in old populations (Olivieri et al. 1995), as is observed. However, none of the previous empirical studies actually proved that the observed differences in seed dispersal among populations had a genetic basis rather than simply being the expression of phenotypic plasticity.

An alternative hypothesis is that dispersal-related traits change with some environmental factor, which would covary with population age. The frequency of winged offspring in the pea aphid, Acyrthosiphon pisum, decreased in older populations (MacKay & Lamb 1979), but the lower migratory tendency in older populations was due to the higher frequency of old adults and thus to a maternal age effect on dispersal, rather than genetic differences. Although phenotypic plasticity for dispersal-related traits is generally poorly documented in plant species (see reviews in Olivieri & Berger 1985; Donohue & Schmitt 1998), contrasting with the abundant literature concerning environmental effects on dispersal behaviour in animals (see for instance the review by Dingle 1994; Mousseau & Fox 1998), similar environmentally controlled effects could affect seed dispersal patterns along ecological succession. For instance, maternal morphology, which determines seed dispersal distance, is affected by conspecific density in Cakile edentula (Donohue 1999). Partitioning of resources between seed mass and seed number changes with plant age in Cistus ladanifer (Acosta et al. 1997). The proportion of seeds equipped with a pappus increases with nutrient depletion in the heteromorphic species Crepis sancta (Imbert & Ronce 2001). Conspecific density, the age structure of the population and resource levels are all likely to change with time since population foundation.

Despite the existence of abundant theoretical literature on the evolution of dispersal traits (see Clobert et al. 2001), few models have investigated the evolution of phenotypic plasticity for dispersal. Most demographic or evolutionary metapopulation models have considered constant or entirely genetically determined dispersal rates. The very general model of McPeek & Holt (1992) predicts that, in heterogeneous environments, dispersal should increase with decreasing habitat quality, but does not consider the multidimensional nature of this parameter. Following the initial work of Levin et al. (1984), several recent models have studied the evolution and consequences of density-dependent dispersal in a metapopulation (Jánosi & Scheuring 1997; Johst & Brandl 1997; Travis et al. 1999; Metz & Gyllenberg 2001; Poethke & Hovestadt 2002). The general prediction reached is that the frequency of dispersal should increase with local crowding, with a complete absence of dispersal below some threshold density. Change in ecological conditions during succession cannot simply be reduced to change in conspecific density. For instance, the intensity of interspecific competition, recruitment rates, age structure and disturbance regime may all vary with time elapsed since initial colonization, and thus modify selection pressures on plastic dispersal strategies.

As a first approximation, successional replacement can be modelled by assuming that local populations can persist for a fixed maximal number of generations before going extinct due to competitive exclusion. Olivieri & Gouyon (1997) report simulation results, using such assumptions, where a genotype increasing its dispersal rate with population age was found to exclude a genotype with a fixed dispersal strategy. This predicts that mean seed dispersal rate should increase rather than decrease with population age, contrary both to theoretical predictions based on pure genetic determinism of dispersal strategies (Olivieri et al. 1995) and to previous empirical observations (Olivieri & Gouyon 1985; Peroni 1994; Cody & Overton 1996). The predictions of Olivieri & Gouyon (1997) have yet to be supported by empirical results. We have here built on their theoretical work by using an analytical model that is both more general and more realistic to verify the robustness of their prediction. We investigate the evolution of plastic dispersal strategies in a metapopulation with ecological succession and predict patterns of variation in dispersal as a function of population age when disturbance regime, density, age structure and interspecific competition vary with time since foundation of local populations.

Model assumptions

  1. Top of page
  2. Summary
  3. Introduction
  4. Model assumptions
  5. Analytical results
  6. Numerical results
  7. Discussion
  8. Conclusion
  9. Acknowledgements
  10. Supplementary material
  11. References

We use a deterministic model of metapopulation dynamics similar to that described by Olivieri et al. (1995). The main characteristic of this approach is that the dynamics at the landscape level (the disturbance and recolonization of patches of habitat) is modelled separately from the local dynamics (birth and death processes) within each extant population (see also Olivieri & Gouyon 1997; Ronce & Olivieri 1997; Brachet et al. 1999). We assume that local population sizes are large enough for us to ignore both demographic stochasticity and genetic drift. Inhabitants of the metapopulation are long lived and sedentary and only propagules disperse. The order of events in our discrete-time model is as follows: (i) reproduction, (ii) dispersal of propagules between patches, (iii) deaths of established individuals within patches, (iv) establishment of new individuals, and (v) disturbances of patches. Such a model is a good fit for species subject to seasonal disturbance (such as summer fires or autumn floods). A list of main notations and their definitions is given in Table 1.

Table 1.  List of notations used in the theoretical model
cCost of dispersal
g0Juvenile survival in absence of competition
αjCompetitive weight of a juvenile
αaCompetitive weight of adults per biomass unit
αzCompetitive weight of allospecific competitors per biomass unit
xmaxMaximal age of individuals
xfAge at first reproduction
k(x)Individual biomass at age x
f(x)Individual fecundity at age x
s(x)Individual survival probability at age x
imaxMaximal age of populations of the focal species
ezDisturbance probability of patches in the next successional stage
e(i)Disturbance probability for a population of age i
z(i)Biomass of allospecific competitors in a population of age i
V0Frequency of empty patches in the landscape
VzFrequency of patches occupied by the next successional stage
ViFrequency of patches occupied by a population of age i
g(i)Recruitment rate of juveniles in a population of age i
J(i)Number of juveniles present after dispersal in a population of age i
J(0)Number of immigrant juveniles per population
v(i)Reproductive value of an individual with age 1 in a population of age i
n(i,x)Number of individuals with age x in a population of age i
d(i)Dispersal rate of propagules born to an individual in a population of age i

landscape dynamics

The metapopulation evolves in a landscape composed of an infinite number of discrete patches. Local populations inhabiting the different patches are distinguished on the basis of their age only, i.e. the number of years elapsed since their foundation.

Disturbances

Disturbances are modelled by assuming that, due to some catastrophe, extinction of a whole population with age i occurs with probability e(i). We further assume that because of successional replacement, the lifetime of a local population is limited. Eventually, when a local population reaches age greater than imax, it goes extinct and the patch, now occupied by another species, remains uncolonizable until it is disturbed again. The probability of such a disturbance is assumed to be constant and, for consistency, equal to ez = e(imax). Figure 1(a) shows examples of age-specific probabilities of disturbance used in our model. When recently disturbed sites are more likely to be disturbed again (as on unstable river banks), the probability of disturbance is high in the years immediately after foundation but then decreases (case 1, Fig. 1a). In other environments, build-up of biomass in undisturbed patches may increase the probability of catastrophic fires, leading to an increase of the disturbance rate with population age (case 2, Fig. 1a).

image

Figure 1. Change in ecological characteristics of a patch as a function of time elapsed without disturbance, i (in years). (a) Change in per year probability of disturbance: in scenario (1) e(i) = 0.01 + 0.3e−0.25i; in scenario (2) e(i) = 0.008 + 0.0026e0.02i. (b) Change in the intensity of interspecific competition: (1) z(i) = 312.879(e0.01i − 1); (2) z(i) = 0.091 (e0.05i − 1); (3) z(i) = 0.009(e0.05i − 1). For all scenarios, imax = 200 years.

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Colonization

We assume an island model of migration (Slatkin 1977). As migrants are distributed evenly among patches, all empty patches are recolonized after dispersal, and the number of founders, J(0), is identical for all new populations. Dispersal is the only way to recolonize disturbed patches.

Age structure of the metapopulation

At equilibrium, the metapopulation is characterized by a stable age structure and the frequency in the landscape of populations with a given age is therefore constant from year to year (see Olivieri et al. 1995). After the occurrence of disturbance, we can distinguish three types of patches in the metapopulation: empty patches, patches occupied by our focal species and patches occupied by the next successional stage. We use Vi to denote the frequency, at equilibrium, of patches occupied by a population with age i, V0 the frequency of empty patches that have been just disturbed and Vz the frequency of patches occupied by another species (i.e. all patches that were last disturbed more than imax years ago). See Appendix A in Supplementary Material, equations A1 to A4, for the calculation of these frequencies.

life history

Age-specific survival, size and fecundity

Survival probability s(x), biomass k(x) and fecundity f(x) vary with individual age x (see Fig. 2 for a few examples). Age at first reproduction is xf and the maximal age reached by individuals is xmax. We assume that neither survival nor fecundity of established individuals depend on their population age.

image

Figure 2. Change in individual characteristics as a function of age, x (in years). (a) Change in adult size: (1) k(x) = 10/(1 + 99e−0.25x); (2) k(x) = 50/(1 + 99e−0.25x); (3) k(x) = 100/(1 + 99e−0.25x). (b) Change in annual survival rate: (1) xmax = 50, s(x) = 1 – 0.95e−0.25x – 0.00001e0.2306x; (2) xmax = 70, s(x) = 1 – 0.95e−0.25x– 0.00001e0.1645x; (3) xmax = 80, s(x) = 1 – 0.95e−0.25x– 0.00001e0.1439x.

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Dispersal

The fraction d(i) of dispersed propagules in the progeny of a sexually mature individual depends on the age of the population i where this individual reproduces. Dispersed propagules survive the migration episode with probability 1 − c, where c is the direct cost of dispersal. Propagules arriving in patches occupied by another species (such an event occurs with probability (1 − c)Vz) are lost, which represents another cost of dispersal.

Age structure of local populations

Because of founding of new populations by a single age class, local populations may take several years to reach a stable age structure. The number of individuals with age x in population with age i is denoted by n(i, x).

Recruitment

The number J(i) of propagules present after dispersal in a population with age i is simply the sum of the immigrant and philopatric propagules

  • image(eqn 1 )

The recruitment of propagules within patches is affected by both intraspecific and interspecific competition. More precisely, the number of new recruits in a population with age i+ 1 depends on the number of propagules present after dispersal in that same population J(i) and on the survival rate of such propagules to age 1, g(i)

  • image(eqn 2 )

Propagule survival, g(i), may depend on the numbers of competing adults and propagules from the same species present in the patch and on the number of individuals, z(i), from a competitively superior species also present in the patch. Figure 1(b) gives several examples where the intensity of interspecific competition increases along the succession. The dynamics of the competing species is modelled independently from the dynamics of our focal species. Recruitment is the only stage of the life cycle affected by density dependence. Propagules that fail to recruit in the year following their production die (no seed bank).

Appendix A shows how to compute the age structure n(i, x) of the different populations, given the functional form for g(i) and the basic life history and landscape parameters listed above.

Analytical results

  1. Top of page
  2. Summary
  3. Introduction
  4. Model assumptions
  5. Analytical results
  6. Numerical results
  7. Discussion
  8. Conclusion
  9. Acknowledgements
  10. Supplementary material
  11. References

We are interested in the evolution of the dispersal rate d(i) of propagules produced by an individual in a population with age i. As dispersal varies with population age, we focus on an ideal situation where individuals have complete information about their environment. Classic approaches of evolution in class-structured populations (see Appendix B in Supplementary Material) lead to a relatively simple marginal value argument for the evolutionary stability of age-specific dispersal rates (see also Ronce et al. 2000 for very similar arguments). If the strategy d(i) is evolutionarily stable (ES), then one of the following conditions is fulfilled

  • image(eqn 3a )
  • image(eqn 3b )
  • image(eqn 3c )

The terms Wr(i) and Wd(i) are the expected fitness gains associated with the production of, respectively, a non-dispersed or dispersed propagule by an individual in a population of age i. Equation 3 simply says that, at the ES strategy, gains associated with dispersal should equal those obtained through philopatry. In our model, those gains are

  • image(eqn 4a )

and

  • image( eqn 4b )

where v(i) is the reproductive value of new recruits in a population of age i. The fitness gain for a non-dispersed offspring depends on the probability of successful establishment in its natal population, its ability to survive disturbance and its reproductive value once established. Fitness gains associated with the production of non-dispersed individuals therefore depend on population age. For migrants, the gain depends simply on the cost of dispersal and on the average probability of establishment weighted by disturbance rates and reproductive values. This latter gain is the same whatever the age of population where the propagule was produced.

Assuming that, for all ages i, dispersal rates d(i) are ES and are strictly between 0 and 1, equations 1 to 4 lead to

  • image( eqn 5 )

Equation 5 defines d(i) only implicitly because reproductive values and population sizes are themselves functions of the dispersal rates. We thus solved this equation numerically to obtain the ES age-specific dispersal rates. Equation 5 shows that the fraction of philopatric propagules, 1 − d(i), in a population with age i increases with the number, n(i + 1,1), of new recruits in populations of age i+ 1 and with the reproductive values v(i + 1) of such new recruits. Everything else being equal, the number of non-dispersed propagules should be smaller in populations characterized by a high disturbance probability e(i) and in populations characterized by the local production of numerous propagules

  • image

Numerical results

  1. Top of page
  2. Summary
  3. Introduction
  4. Model assumptions
  5. Analytical results
  6. Numerical results
  7. Discussion
  8. Conclusion
  9. Acknowledgements
  10. Supplementary material
  11. References

We assume that growth is logistic and biomass does not increase much for older ages (Fig. 2a). Once reproduction has started, the yearly seed production is proportional to biomass (Greene & Johnson 1994). Survival may be low in young age classes (as is often the case before sexual maturity) and in old age classes (because of senescence, see Fig. 2b). We further assume that the competitive effect of conspecific adults on juvenile survival is proportional to their biomass. We chose a functional form for g(i) similar to the Beverton-Holt function

  • image(eqn 6 )

where g0 is the establishment rate of propagules in absence of competition, αj, αak(x) and αz are competitive weights for, respectively, another propagule, a conspecific adult with age x or a member of the competitively superior species. Equations 3 and 4 were solved numerically (see Appendix A and Appendix B for intermediate computations) using Mathematica 4.0 (Wolfram Research Inc.). Figure 3 presents possible evolutionarily stable reaction norms for propagule dispersal rate as a function of population age obtained for the combinations of landscape and life-history characteristics explored in Figs 1 and 2. The general trend emerging from these examples is that seed dispersal rate should increase with population age. Increased competition (both intraspecific and interspecific) in older populations results in decreases in probability of establishment (juveniles) and in reproductive value (established individuals), favouring escape from such deteriorating local conditions. ES reaction norms are characterized by two threshold ages: our model predicts that adults should disperse none of their offspring below the first, i.e. in recently founded populations, but all of them above the second (populations close to their maximal age). Between these two ages, intermediate dispersal rates are selected for, which can increase monotonically with time since foundation (e.g. Fig. 3a), or show more complex patterns (Fig. 3d).

image

Figure 3. Possible ES reaction norms of juvenile dispersal rate as a function of time since population foundation (in years), i, under different scenarios. Unless otherwise stated imax = 200, xmax = 50, c= 0.8, αa = αz = 1, αj = 0.001, xf = 3, f (x) = 500k(x), g0 = 0.3, with succession as Fig. 1b (2), growth as in Fig. 2a (1) and senescence as Fig. 2b (1). The left hand side (a, c, e, g) has disturbance rate decreasing with age (Fig. 1a (1)) and the right hand side has disturbance rate increasing with age (Fig. 1a (2)). (a) and (b): the effect of rapidity of successional replacement. Curves correspond to the appropriate scenario in Fig. 1 (b), (c) and (d): effect of fecundity per biomass unit. In (1) f (x) = 100k(x), (2) f (x) = 200k(x), (3) f (x) = 500k(x), (4) f (x) = 1000k(x), (5) f (x) = 2000k(x). (e) and (f): effect of life span in a competition-tolerant species (αa = 1). xmax = 50 in (1) and either 70 (e) or 80 (f) in (2). (g) and (h): as for (e) and (f) but for a competition-intolerant species (αa = 5).

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The threshold age above which dispersal does occur is lower if disturbance probability increases with population age (right vs. left hand side of Fig. 3). The threshold age above which dispersal is total is lower if successional replacement is faster (curve 1 in Fig. 3a,b) and if seed production per unit biomass is low (curve 1 in Fig. 3c,d). Lower fecundity also results in higher sensitivity of juvenile recruitment rates to variation in the intensity of competition with adults or other superior competitors. Decreasing seed production or increasing the competitive weight of adults can also result in the emergence of intermediate periods of decreasing dispersal, particularly if disturbance increases with age (as, for example, in Fig. 3d,h). The decline in dispersal starts when the original founders of the population reach their maximal age and massive adult death results in increased establishment opportunities for juveniles (in Fig. 3h maximal adult life span is 50 and 80 years, respectively, for curves 1 and 2). Such patterns are thus ultimately due to the combination of strong competitive effects of adults on juveniles, adult senescence and disequilibrium in age structure generated by foundation.

Evolution of dispersal rate as a function of population age is shaped in part by changes in reproductive values and population size with time since foundation. These patterns are, in turn, affected by changes in dispersal with population age. Reproductive values of new recruits decrease more slowly with population age when dispersal rates vary with the ES reaction norm, than when inhabitants of the metapopulation express a fixed dispersal strategy (see for example Fig. 4a). Evolution of plastic dispersal strategies thus tends to make reproductive values in different patches more similar, which is reminiscent of classical results of habitat selection theory and of the concept of Ideal Free Distribution (Fretwell 1972; Rousset 1999). Increased dispersal rates in older populations also tend to accelerate successional replacement (e.g. Fig. 4b), with a drop in population size preceding that observed for a fixed dispersal strategy, as recruitment in old populations is then limited not only by interspecific competition but also by the scarcity of non-dispersed seeds. Changes in dispersal can also greatly affect the evolution of the age structure of the population (see for instance Fig. 4c).

image

Figure 4. Comparison of population characteristics as a function of time since foundation (in years) when dispersal is a fixed strategy or when dispersal varies plastically with population age. Continuous line: population characteristics when all individuals disperse 5% of their progeny whatever the age of the population. Dashed line: population characteristics when individuals disperse their offspring according to the candidate ES reaction norm shown in Fig. 3c (5). All parameter values as in Fig. 3c (5). (a) Reproductive values of new recruits as a function of population age. (b) Population size, obtained by summing over all age classes after recruitment, as a function of population age. (c) Mean age of individuals, obtained by weighting each age class by its frequency in the population, as a function of population age.

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Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Model assumptions
  5. Analytical results
  6. Numerical results
  7. Discussion
  8. Conclusion
  9. Acknowledgements
  10. Supplementary material
  11. References

increasing dispersal with population age as a habitat selection strategy

In many species that either exploit an ephemeral and non-renewable resource or are subject to successional replacement, the very quality of the habitat deteriorates with time (Pascarella & Horvitz 1998; Valderde & Silvertown 1998). This led Olivieri & Gouyon (1997) to predict that dispersal in a metapopulation should increase with population age: most cases in our theoretical study verified this general prediction, contradicting the findings of models based on genetically fixed dispersal rates (Olivieri et al. 1995). An interesting parallel can be drawn between the evolution of plastic dispersal strategies as a function of population age in a metapopulation and the classic theory for the evolution of senescence. The latter theory predicts that in the presence of antagonistic pleiotropy, selection should favour genes increasing investment in reproduction or survival of young age classes with high reproductive values and decreasing the same vital rates in older age classes with low reproductive values (Rose 1991). Similarly, in the case of a metapopulation with successional replacement, the reproductive value of juveniles recruited in old populations is low, favouring the evolution of dispersal strategies such that investment in local recruitment is higher in recently founded populations. Evolutionary changes in age-specific dispersal accelerate successional replacement just as evolution of age-specific vital rates accelerates senescence (see a general discussion of habitat selection and senescence evolutionary theory in Holt 1996).

ideal reaction norms: complexity and limits of the theoretical approach

Our model predicts more complex patterns of dispersal change with population age than envisioned by Olivieri & Gouyon (1997). The prediction of threshold population ages, beyond which seed dispersal rate is either absent or total, is reminiscent of similar ‘bang-bang’ strategies (Hamilton & May 1977) predicted by evolutionary models for density-dependent dispersal in a metapopulation (Levin et al. 1984; Poethke & Hovestadt 2002). We also found cases where the optimal reaction norm for dispersal is not a monotonically increasing function of time since foundation, with several scenarios where there were intermediate phases of high local recruitment and low dispersal. Such events seem to be ultimately due to adult senescence and strong intraspecific competition. For similar reasons, in a stable habitat with intense mother-offspring competition, Ronce et al. (1998) predicted that senescent mothers should disperse a smaller fraction of their progeny than young mothers. Our model does not incorporate phenomena of kin competition, but the disequilibrium in age structure generated by founder events creates periods of locally high adult mortality, when a cohort becomes senescent, similarly favouring increased philopatry. Whether such complex shapes for dispersal reaction norms can be observed in nature is open to question. Our model predicts optimal reaction norms for dispersal as a function of population age, assuming that perfect information about time since foundation is available and in the absence of any mechanistic or physiological constraints acting on the shape of such reaction norms. In particular, the model does not consider which environmental cue triggers changes in seed dispersal in different aged populations. Departures of observed reaction norms from the ‘ideal’ patterns predicted by our model could nonetheless inform us about constraints acting on the evolution of plastic dispersal strategies.

ecological implications

Evolution of plastic seed dispersal strategies has several potentially important ecological consequences. First, our model predicts that environmental effects on seed dispersal might accelerate replacement and shorten the persistence time of fugitive species in ecological succession, although this would need to be investigated empirically. More generally, our model suggests that adaptation to local conditions in successional systems both affects, and is affected by, patterns of change in abundance for different species. Secondly, our predictions have implications for the understanding of the dynamics of expanding species. The rate of spread of an invasive species depends theoretically on both its net reproductive rate and its specific distribution of dispersal distance (Shigesada & Kawasaki 1997). Both parameters may, however, vary with ecological conditions, which may differ between older populations at the centre of the range and recently founded populations at the expanding margins. For instance, increased fecundity of isolated individuals in recently colonized areas, as observed in Scots pine (Debain et al. 2003), might accelerate spread rates. On the contrary, our prediction of decreased dispersal ability in recently founded populations should slow down the process of invasion (but see Debain et al. 2003 for an absence of variation in seed morphology related to dispersal in expanding range). More generally, phenotypic differences in dispersal ability among populations due to plasticity might develop much more rapidly than the build-up of genetic differences and could thus play an important role in the dynamics of populations that experience regular extinction and recolonization events.

empirical evidence

To our knowledge, patterns of increasing seed dispersal with increasing population age, as predicted by our model, have never been described empirically in successional systems. Preliminary data on invasive ash tree populations suggest that the dispersal ability of samaras is indeed lower at the advancing front than in presumably older populations (O. Ronce, S. Brachet, I. Olivieri, P.-H. Gouyon and J. Clobert, unpublished data). Previous reports of decreasing seed dispersal ability with increasing population age (Olivieri & Gouyon 1985; Peroni 1994; Cody & Overton 1996) do not agree with the general predictions of the present model. Observed patterns might be due to genetic differences as predicted by Olivieri et al. (1995), although genetic differentiation of old and young populations for dispersal traits remains to be demonstrated by common garden experiments in many of those cases. If it could be shown that dispersal variation was due to environmental effects in those cases, the adaptive value of such plasticity with respect to seed dispersal would still be unclear. We hope that the present theoretical study will stimulate more investigation of the patterns of environmentally driven variation in dispersal along succession.

Conclusion

  1. Top of page
  2. Summary
  3. Introduction
  4. Model assumptions
  5. Analytical results
  6. Numerical results
  7. Discussion
  8. Conclusion
  9. Acknowledgements
  10. Supplementary material
  11. References

Although, as yet, unsupported by experimental data, our model suggests that increased seed dispersal with age might represent a way for plants to escape the unfavourable conditions that develop as a species is displaced during succession. More generally, our theoretical findings point to the fact that changing ecological conditions during succession result in variation in the selection pressures acting on the evolution of life histories. Such changes in ecological conditions may allow the maintenance of diversity for life-history traits (Olivieri et al. 1995) or promote the evolution of plastic life-history strategies (the present paper). Despite recent interest in the metapopulation dynamics consequences of ecological succession (Johnson 2000; Amarasekare & Possingham 2001; Hastings 2003), the evolutionary consequences of such processes have as yet been little explored (Ronce & Olivieri 2004).

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Model assumptions
  5. Analytical results
  6. Numerical results
  7. Discussion
  8. Conclusion
  9. Acknowledgements
  10. Supplementary material
  11. References

This work was supported by the Ministère de l’Aménagement du Territoire et de l’Environnement (Contrats MATE n°98/153 and n°97/117 attributed to Isabelle Olivieri) through both the Bureau des Ressources Génétiques and the National Programme Diversitas, Fragmented Populations network, and by the European Union Fifth Framework through the program ‘Plant Dispersal’, contract EVK2-CT1999-00246 allocated to Ben Vosman. This is contribution number 2004–069 of the Institut des Sciences de l’Evolution de Montpellier.

Supplementary material

  1. Top of page
  2. Summary
  3. Introduction
  4. Model assumptions
  5. Analytical results
  6. Numerical results
  7. Discussion
  8. Conclusion
  9. Acknowledgements
  10. Supplementary material
  11. References

The following material is available from

Appendix A Age structure of the metapopulation.

Appendix B Condition for evolutionary stability.

References

  1. Top of page
  2. Summary
  3. Introduction
  4. Model assumptions
  5. Analytical results
  6. Numerical results
  7. Discussion
  8. Conclusion
  9. Acknowledgements
  10. Supplementary material
  11. References
  • Acosta, F.J., Delgado, J.A., Lopez, F. & Serrano, J.M. (1997) Functional features and ontogenic changes in reproductive allocation and partitioning strategies of plant modules. Plant Ecology, 132, 7176.
  • Amarasekare, P. & Possingham, H. (2001) Patch dynamics and metapopulation theory: the case of successional species. Journal of Theoretical Biology, 209, 333344.
  • Brachet, S., Olivieri, I., Godelle, B., Klein, E., Frascaria-Lacoste, N. & Gouyon, P.H. (1999) Dispersal and metapopulation viability in a heterogeneous landscape. Journal of Theoretical Biology, 198, 479495.
  • Caswell, H. (2001) Matrix Populations Models. Sinauer Associates, Sunderland, Massachusetts.
  • Clay, K. (1982) Environmental and genetic determinants of cleistogamy in a natural population of the grass Danthonia spicata. Evolution, 36, 734741.
  • Clobert, J., Danchin, E., Dhondt, A.A. & Nichols, J.D. (2001) Dispersal. Oxford University Press, Oxford.
  • Cody, M.L. & Overton, J.M. (1996) Short-term evolution of reduced dispersal in island plant populations. Journal of Ecology, 84, 5361.
  • Debain, S., Curt, T., Lepart, J. & Prevosto, B. (2003) Reproductive variability in Pinus sylvestris in southern France: implications for invasion. Journal of Vegetation Science, 14, 509516.
  • Dingle, H. (1994) Genetic analyses of animal migration. Quantitative Genetics Studies of Behavioural Evolution (ed. C.R.B.Boake), pp. 145164. University of Chicago Press, Chicago.
  • Donohue, K. (1999) Seed dispersal as a maternally influenced character: mechanistic basis of maternal effects and selection on maternal characters in an annual plant. American Naturalist, 154, 674689.
  • Donohue, K. & Schmitt, J. (1998) Maternal environmental effects in plants: adaptive plasticity? Maternal Effects as Adaptations (eds T.A.Mousseau & C.W.Fox), pp. 137158. Oxford University Press, New York.
  • Fretwell, S.D. (1972) Theory of habitat distribution. Populations in Seasonal Environments (ed. S.D.Fretwell), pp. 79114. Princeton University Press, Princeton, New Jersey.
  • Greene, D.F. & Johnson, E.A. (1994) Estimating the mean annual seed production of trees. Ecology, 75, 642647.
  • Hamilton, W.D. & May, R.M. (1977) Dispersal in stable habitats. Nature, 269, 578581.
  • Hastings, A. (2003) Metapopulation persistence with age-dependent disturbance or succession. Science, 301, 15251526.
  • Holt, R.D. (1996) Demographic constraints in evolution: towards unifying the evolutionary theories of senescence and niche conservatism. Evolutionary Ecology, 10, 111.
  • Imbert, E. & Ronce, O. (2001) Phenotypic plasticity for dispersal ability in the seed heteromorphic Crepis sancta (Asteraceae). Oikos, 93, 126134.
  • Jánosi, I.M. & Scheuring, I. (1997) On the evolution of density dependent dispersal in a spatially structured population model. Journal of Theoretical Biology, 187, 397408.
  • Johnson, M.P. (2000) The influence of patch demographics on metapopulations, with particular reference to successional landscapes. Oikos, 88, 6774.
  • Johst, K. & Brandl, R. (1997) Evolution of dispersal: the importance of the temporal order of reproduction and dispersal. Proceedings of the Royal Society of London B Biology Sciences, 264, 2330.
  • Levin, S.A., Cohen, D. & Hastings, A. (1984) Dispersal strategies in patchy environments. Theoretical Population Biology, 26, 165191.
  • MacKay, P.A. & Lamb, R.J. (1979) Migratory tendancy in aging populations of the pea aphid, Acyrtosiphon pisum. Oecologia, 39, 301308.
  • McPeek, M.A. & Holt, R.D. (1992) The evolution of dispersal in spatially and temporally varying environments. American Naturalist, 140, 10101027.
  • Metz, J.A.J. & Gyllenberg, M. (2001) How should we define fitness in structured metapopulation models? Including an application to the calculation of ES dispersal strategies. Proceedings of the Royal Society of London B Biology Sciences, 268, 499508.
  • Mousseau, T.A. & Fox, C.W. (1998) Maternal Effects as Adaptations. Oxford University Press, New York.
  • Olivieri, I. & Berger, A. (1985) Seed dimorphism and dispersal: physiological, genetic and demographical aspects. Genetic Differentiation and Dispersal in Plants (eds P.Jacquard, G.Heim & J.Antonovics), pp. 413429. Springer-Verlag, Berlin.
  • Olivieri, I., Couvet, D. & Gouyon, P.-H. (1990) The genetics of transient populations: research at the metapopulation level. Trends in Ecology and Evolution, 5, 207210.
  • Olivieri, I. & Gouyon, P.-H. (1985) Seed dimorphism for dispersal: theory and implications. Structure and Functionning of Plant Populations (eds J.Haeck & J.W.Woldendrop), pp. 7790. North-Holland Publications, Amsterdam.
  • Olivieri, I. & Gouyon, P.-H. (1997) Evolution of migration rate and other traits: the metapopulation effect. Metapopulation Biology: Ecology, Genetics, and Evolution (eds I.Hanski & M.E.Gilpin), pp. 293323. Academic Press, San Diego.
  • Olivieri, I., Michalakis, Y. & Gouyon, P.-H. (1995) Metapopulation genetics and the evolution of dispersal. American Naturalist, 146, 202228.
  • Olivieri, I., Swann, M. & Gouyon, P.H. (1983) Reproductive system and colonizing strategy of two species of Carduus (Compositae). Oecologia, 60, 114117.
  • Pascarella, J.B. & Horvitz, C.C. (1998) Hurricane disturbance and the population dynamics of a tropical understory shrub: megamatrix elasticity analysis. Ecology, 79, 547563.
  • Peroni, P.A. (1994) Seed size and dispersal potential of Acer rubrum (Aceraceae) samaras produced by populations in early and late successional environments. American Journal of Botany, 81, 14281434.
  • Poethke, H.J. & Hovestadt, T. (2002) Evolution of density- and patch-size-dependent dispersal rates. Proceedings of the Royal Society of London B Biology Sciences, 269, 637645.
  • Ronce, O., Clobert, J. & Massot, M. (1998) Natal dispersal and senescence. Proceedings of the National Academy of Sciences of the United States of America, 95, 600605.
  • Ronce, O., Gandon, S. & Rousset, F. (2000) Kin selection and natal dispersal in an age-structured population. Theoretical Population Biology, 58, 143159.
  • Ronce, O. & Olivieri, I. (1997) Evolution of reproductive effort in a metapopulation with local extinctions and ecological succession. American Naturalist, 150, 220249.
  • Ronce, O. & Olivieri, I. (2004) Life history evolution in metapopulations. Ecology, Genetics, and Evolution of Metapopulations (eds I.Hanski & O.E.Gaggiotti), pp. 227258. Academic Press, Amsterdam.
  • Rose, M.R. (1991) Evolutionary Biology of Aging. Oxford University Press, New York.
  • Rousset, F. (1999) Reproductive value vs sources and sinks. Oikos, 86, 591596.
  • Schmitt, J., Ehrhardt, C.W. & Schwartz, D. (1985) Differential dispersal of self-fertilized and outcrossed progeny in jewelweed (Impatiens capensis). American Naturalist, 126, 570575.
  • Shigesada, N. & Kawasaki, K. (1997) Biological Invasions: Theory and Practice. Oxford University Press, Oxford.
  • Slatkin, M. (1977) Gene flow and genetic drift in a species subject to frequent local extinction. Theoretical Population Biology, 12, 253262.
  • Taylor, P.D. & Frank, S.A. (1996) How to make a kin selection model. Journal of Theoretical Biology, 180, 2737.
  • Travis, J.M.J., Murrell, D.J. & Dytham, C. (1999) The evolution of density-dependent dispersal. Proceedings of the Royal Society of London B Biology Sciences, 266, 18371842.
  • Valderde, T. & Silvertown, J. (1998) Variation in the demography of a woodland understorey herb (Primula vulgaris) along the forest regeneration cycle: projection matrix analysis. Journal of Ecology, 86, 545562.
  • Van Valen, L. (1971) Group selection and the evolution of dispersal. Evolution, 25, 591598.
  • Venable, D.L. & Lawlor, L. (1980) Delayed germination and dispersal in desert annuals: escape in space and time. Oecologia, 46, 272282.