Clarifying Baker's Law

Abstract

Background: Baker's Law states that colonization by self-compatible organisms is more likely to be successful than colonization by self-incompatible organisms because of the ability for self-compatible organisms to produce offspring without pollination agents. This simple model has proved very successful in plant ecology and has been applied to various contexts, including colonizing or ruderal species, islands colonizers, invasive species or mating system variation across distribution ranges. Moreover, it is one of the only models in population biology linking two traits of major importance in ecology, namely dispersal and mating system. Although Baker's Law has stimulated a large number of empirical studies reporting the association of self-fertilization and colonizing ability in various contexts, the data have not established a general pattern for the association of traits.

Scope: In this paper, a critical position is adopted to discuss and clarify Baker's Law. From the literature referring to Baker's Law, an analysis made regarding how mating success is considered in such studies and discrepancies with population genetics theory of mating systems are highlighted. The data reporting the association of self-fertilization and colonizing ability are also briefly reviewed and the potential bias in interpretation is discussed. Lastly, a recent theoretical model analysing the link between colonizing ability and self-fertilization is considered.

Conclusions: Evolutionary predictions are actually more complex than Baker's intuitive arguments. It appears that Baker's Law encompasses a variety of ecological scenarios, which cannot be considered a priori as equivalent. Questioning what has been considered as self-evident for more than 50 years seems a reasonable objective to analyse in-depth dispersal and mating system traits.

Fig. 1.

Measurements of mating success. Left: the self-fertilization allele is shown as closed circles and outcrossing allele as open circles. Transmission pathways from parent to offspring are shown as arrows; solid arrows represent gene transmission to progeny by the parent capable of self-fertilization, while dashed arrows represent transmission pathways for the outcrossing parent. Fitness is measured as the sum of gene copies transmitted by pollen and ovules. Assuming that the number of pollen grains produced is large relative to the number of ovules and that all the ovules are fertilized, a selfing genotype enjoys a 50 % advantage in gene transmission relative to a outcrossing genotype. This results in the cost of outcrossing (Fisher, 1941). Right: the large circles represent individual parents and their progeny. Arrows represent the production of discrete offspring by parents, with solid arrows representing pollinator-independent offspring production, and dashed arrows representing pollinator-dependent offspring production. Mating system is often equated with the number of seeds produced. Selfing ensures offspring production when lack of cross-pollinators limits seed-set (Darwin, 1876).

Fig. 2.

Joint evolution of dispersal and self-fertilization in a temporally heterogeneous pollination environment (from Cheptou and Massol, 2009; Massol and Cheptou, 2011). The model assumes an infinite island model where each patch is prone to temporally heterogeneous pollination because of the stochastic presence of pollinator (see Kalisz et al., 2004, for empirical support). We consider a basic mechanism of self-fertilization: plants self-fertilize a proportion, s, of their ovules while the proportion 1 – s can be fertilized by outcrossing only if pollinators are present, which occur with a probability (1 – e). Otherwise, the fraction 1 – s is left unfertilized (probability e). Seeds produced disperse at random among patch at rate d but only a fraction q survive to dispersal. Progeny produced by self-fertilization suffer from inbreeding depression (δ). Model outcome: the mathematical analysis (invasion analysis) reveals that only two syndromes of traits are possible: the ‘dispersal/outcrossing’ syndrome (d* = (e/[1 – q(1 – e)], s* = 0) and the ‘no-dispersal/selfing’ syndrome (d* = 0, s* = (2e/[2δ + e – 1])) (see Cheptou and Massol, 2009, for the influence of parameters). Pollination fluctuations suffered by out-crossers create among-patch variance and thus favour dispersal (see Comins et al., 1982). In contrast, selfers do not suffer from pollination heterogeneity, thus cancelling selection pressure for dispersal.