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Keywords:

  • Dispersal asymmetry;
  • evolutionarily stable strategy;
  • mate availability;
  • metapopulation;
  • pollination heterogeneity;
  • reproductive assurance

A few years after Baker's seminal paper (1955), Carlquist (1966) stated that “if dioecious stocks immigrated to the [Hawaiian] islands, Baker's law must be in part abandoned”. One year later, this led Baker to clarify his view in a famous paper published in the pages of Evolution (Baker 1967). More than 50 years after Baker's seminal paper, the commentary by Jeremiah Busch (2011) demonstrates that Baker's ideas are still debated in the field of plant mating systems. In this article, Busch discusses the discrepancies that arise between Baker's verbal predictions (Baker 1955, 1967) and our model predictions (Cheptou and Massol 2009; Massol and Cheptou 2011), even though pollination heterogeneity is at the heart of both theories.

Our theoretical models (Cheptou and Massol 2009; Massol and Cheptou 2011) did not aim at formalizing Baker's law per se. Because the literature dealing with dispersal/mating system trait association is replete with references to Baker's arguments, we are aware that our predictions will naturally be judged with regard to Baker's law, but we think it is important to clarify that we analyzed the evolutionary consequence of spatio-temporal variation in populations of a simple metapopulation, rather than Baker's law. Busch (2011) does not present an opposition to our metapopulation arguments and we think that the two points of view do not conflict. In the light of Busch's commentary, we endeavor to clarify some issues associated with Baker's ideas, especially focusing on the rationale behind Baker's arguments and its derivatives. We have identified three points that may help to clarify the debate surrounding the veracity of Baker's law and the association of outcrossing traits and dispersal traits in organisms. Because empirical data on selfing and dispersal have been discussed elsewhere (e.g., Price and Jain 1981; Barrett 1996; Van Kleunen et al. 2008), we will not review them here, focusing instead on logical arguments.

Intrinsic versus Extrinsic Determinants of Pollen Limitation

  1. Top of page
  2. Intrinsic versus Extrinsic Determinants of Pollen Limitation
  3. Dispersal Asymmetry and the Evolution of Self-Fertilization
  4. Optimality, Evolutionarily Stability, and the Demographic Advantage of Selfing
  5. Concluding Remarks
  6. ACKNOWLEDGMENTS
  7. LITERATURE CITED

Baker's law is often referred to for the advantage of selfing when mates are limiting. This is only half of the story. Baker (1955) proposed that (i) “With a self-compatible individuals a single propagule is sufficient to start a sexually reproducing colony”, and (ii) “Self-compatible flowering plants are usually able to form seeds in the absence of visits from specialised pollinating insects, which may be absent from the new situation”. These two arguments emphasize pollen limitation, which is relevant in natural populations (Holsinger 2000; Eckert et al. 2006), but are essentially different and do not produce similar responses. Although the former relies on intrinsic population properties (number of colonizers, growth rate, …), the latter relies on extrinsic properties (the occurrence of pollination agents).

Basing Baker's law on the number of initial colonizers is sound because, at low population density, the presence of an Allee effect linked to allogamy ensures selection for selfing (Pannell and Barrett 1998; Dornier et al. 2008). Because high dispersal types are expected to be associated with low-density populations when there is polymorphism in dispersal rates (Massol et al. 2011), a positive correlation between pollination efficiency and population density could lead to the association predicted by Baker's law. However, this argument is not simple and requires both Allee effects and kin competition to produce the appropriate selective pressures.

In contrast, when pollination agents are invoked, our predictions (Cheptou and Massol 2009; Massol and Cheptou 2011) conflict with Baker's because, as highlighted by Busch (2011), our models point out that selfing and dispersal influence each other at the landscape level in a particular way. Pollination uncertainty conveys a lethal cost for nondispersing outcrossing types. This cost can be overcome in two ways, either by dispersing and paying the cost of dispersal, or by selfing and paying the cost of inbreeding. Our models have made it clear that paying for both dispersal and inbreeding—as would be the case with Baker's law—is out of the evolutionary question because such a type would be outcompeted by mutants that disperse or self-fertilize less. Importantly the predicted syndromes are not the consequences of the joint evolution of both dispersal and selfing because the same associations are found when selfing is free to evolve and dispersal is fixed.

Dispersal Asymmetry and the Evolution of Self-Fertilization

  1. Top of page
  2. Intrinsic versus Extrinsic Determinants of Pollen Limitation
  3. Dispersal Asymmetry and the Evolution of Self-Fertilization
  4. Optimality, Evolutionarily Stability, and the Demographic Advantage of Selfing
  5. Concluding Remarks
  6. ACKNOWLEDGMENTS
  7. LITERATURE CITED

Baker's law is traditionally invoked in three different landscape contexts. First, as originally envisioned by Baker (1955), island/mainland systems provide the ideal case because dispersal is (supposedly) purely one-sided—there is no return of island types to the mainland. Second, landscapes involving asymmetric—but not completely one-sided—dispersal, such as populations at different distances from the center of a species’ geographical distribution, may suggest the application of Baker's law to explain the incidence of selfing types at range margins (Herlihy and Eckert 2005). Third, when dispersal is symmetric, as in metapopulation models, Baker's arguments are called on to predict that virgin patches should be first colonized by selfing species.

The first case (purely one-sided dispersal towards islands) seemingly offers the easiest case for Baker's law to apply because the absence of pollination agents on islands is a definitive filter selecting against self-incompatibility. However, we hold that Baker's law is more “ecological” than “evolutionary” in this instance. Indeed, isolated islands can be interpreted as “black hole sinks” (Holt and Gomulkiewicz 1997), that is, patches that do not contribute to the next generation at the landscape level and thus depend on the evolutionary trajectories of traits on the mainland. In other words, because islands do not send migrants to the mainland, the filtering process that selects for selfing on islands does not act on the evolution of mating systems at the landscape level. Therefore, purely one-sided dispersal provides a good ecological scenario for the selection of selfing, but provides a very bad situation for Baker's law to be evolutionarily significant.

The third case (metapopulations with symmetric dispersal) is the subject of our models (Cheptou and Massol 2009; Massol and Cheptou 2011). When accounting for the possibility of a “slow succession” in pollination states (Massol and Cheptou 2011), as would be implied if selfing were expected in sites just disturbed, we did not find a positive association between selfing and dispersal because, again, the model lacks a selective pressure for dispersal that would be higher for organisms that self-fertilize more. On the contrary, pollination uncertainty, even at a minimal level, provides the opposite selective pressure—it selects for dispersal with higher intensity when selfing rate is lower. Overall, selfing will not become evolutionarily associated with greater dispersal in a metapopulation unless some other ingredient is added to the model.

The second case (asymmetric distance-limited dispersal) is probably the most interesting of the three. Indeed, the outcome of the joint evolution of selfing and dispersal in a continuous population where dispersal is distance-limited is not obvious. Limited gene flow from the margins to the center, due to an asymmetry in population density might be counteracted by an asymmetry in dispersal rates, especially because individuals at the forefront of expanding ranges are expected to be selected for higher dispersal. A recent model (Burton et al. 2010) predicts that populations at range margins should display higher dispersal rate, higher fecundity, and lower competitiveness. Such a pattern could select for selfing/dispersal syndromes at range margins when inbreeding depression affects competitiveness and not fecundity. However, when pollination uncertainty due to an extrinsic pollination agent is superimposed on the geographic distribution of plants, we have very little intuition to guide us, and the opposite pattern may be true if for example, pollination efficiency varies more frequently at the margins than at the center of the distribution (Massol and Cheptou 2011).

Optimality, Evolutionarily Stability, and the Demographic Advantage of Selfing

  1. Top of page
  2. Intrinsic versus Extrinsic Determinants of Pollen Limitation
  3. Dispersal Asymmetry and the Evolution of Self-Fertilization
  4. Optimality, Evolutionarily Stability, and the Demographic Advantage of Selfing
  5. Concluding Remarks
  6. ACKNOWLEDGMENTS
  7. LITERATURE CITED

Baker's law states that selfing provides a demographic advantage under pollen limitation. Although this statement is true, its implicit interpretation is often that selfing should evolve as a way to maximize demographic attributes of populations. What is meant by demographic attributes can vary, but this idea that evolution should “optimize” the selfing rate pervades some of the existing literature as a general hand-waving argument for the existence of selfers. In truth, evolution does not proceed by optimization (Eshel 1983; Hofbauer and Sigmund 1990; Kisdi 1998). As an illustration, consider the evolutionarily stable selfing strategy obtained in our model, s*= Min [2e/(2δ− 1 +e), 1] with d*= 0 (eq. 9a in Cheptou and Massol 2009), and what would happen if a nondispersing species experiencing random pollination bluntly optimized its reproduction, that is, maximized a geometric average of fitness in pollinated and nonpollinated environments, inline image. The outcome of this optimization would be s= Min [e/δ, 1], contrary to evolutionary arguments. The discrepancy between these predictions stems from the fact that evolutionary stability and optimality are different properties.

More generally, mating system theory has shown that the dynamics of selfing genes (Fisher 1941) do not maximize population growth rate. Consequently, the presence of (even strong) pollen limitation in natural populations does not guarantee that selfing should be the evolutionarily stable mating strategy (Cheptou and Schoen 2007). Although seed production affects maternal fitness, there are many situations where pollen limitation leads to evolutionarily stable complete outcrossing, that is to situations where some ovules remain unfertilized (Lloyd 1979).

Concluding Remarks

  1. Top of page
  2. Intrinsic versus Extrinsic Determinants of Pollen Limitation
  3. Dispersal Asymmetry and the Evolution of Self-Fertilization
  4. Optimality, Evolutionarily Stability, and the Demographic Advantage of Selfing
  5. Concluding Remarks
  6. ACKNOWLEDGMENTS
  7. LITERATURE CITED

Our models tackle only part of the problem of dispersal rate/mating system syndromes because they do not account for all factors that can affect the evolution of these traits. Other factors that are likely to be important include kin competition and habitat selection. The intensity of kin competition as a selective pressure for dispersal decreases with population size, so it should be weak in very large populations (Frank 1986). However, the nature of selection—stabilizing or disruptive—drastically depends on the distribution of population sizes, even when the “average effect” of kin competition on the evolution of dispersal is small (Massol et al. 2011). Thus, even in very large populations, kin competition would still act on the emergence of dispersal polymorphisms. Habitat selection could also play a crucial part in the evolution of self-fertilization. Habitat selection may favor the emergence of protected polymorphisms in habitat specialization (Ravigné et al. 2004), and thus it could play an important part in the evolution of complete outcrossing (a specialist strategy) in a landscape with heterogeneous pollination.

Associate Editor: D. Fairbairn

ACKNOWLEDGMENTS

  1. Top of page
  2. Intrinsic versus Extrinsic Determinants of Pollen Limitation
  3. Dispersal Asymmetry and the Evolution of Self-Fertilization
  4. Optimality, Evolutionarily Stability, and the Demographic Advantage of Selfing
  5. Concluding Remarks
  6. ACKNOWLEDGMENTS
  7. LITERATURE CITED

We wish to thank J. Busch, M. Burd, and D. Fairbairn for giving us the opportunity to present these ideas and comments on the manuscript. FM was funded by CEMAGREF and EU Marie Curie Action (project DEFTER-PLANKTON, contract 236712). POC was funded by CNRS and the ADEPOL program (FRB funds).

LITERATURE CITED

  1. Top of page
  2. Intrinsic versus Extrinsic Determinants of Pollen Limitation
  3. Dispersal Asymmetry and the Evolution of Self-Fertilization
  4. Optimality, Evolutionarily Stability, and the Demographic Advantage of Selfing
  5. Concluding Remarks
  6. ACKNOWLEDGMENTS
  7. LITERATURE CITED