Pollen limitation or mate search need not induce an Allee effect.

When a process modelling the availability of gametes is included explicitly in population models a critical depensation or Allee effect usually results. Non-spatial models cannot describe clumping and so small populations must be assumed very diffuse. Consequently individuals in small populations experience low contact rates and so reproduction is limited. In Nature invasions into new territory are unlikely to be as diffuse as those described by non-spatial models. We develop pair approximations to a probabilistic cellular automata model with independent pollination and seed setting processes (equivalently mate search and reproduction processes). Each process can be either global (population-wide) or local (within a small neighbourhood) or a mixture of the two. When either process is global the resulting model recaptures the Allee effect found in non-spatial models. However, if both processes are at least partially local we obtain a model in which Allee effects can be avoided altogether if individuals are suitably strong pollinators and colonisers. The Allee effect disappears because small populations are dramatically more clumped when colonisation is local and less wasteful of pollen when pollination is local.

Space mediates coexistence of females and hermaphrodites.

In gynodioecious populations of flowering plants females and hermaphrodites coexist. Gynodioecy is widespread and occurs in both asexual and sexual species but does not admit a satisfactory explanation from classical sex ratio theory. In sexual populations male fertility restoring genes have evolved to counter non-nuclear male sterility mutations. In pseudogamous asexual populations pollen retention and increased self-fertilization can make male sterility costly. Both of these mechanisms can promote coexistence. However, it remains unclear how either of these mechanisms could evolve if coexistence was not initially possible. In the absence of these adaptations non-spatial models predict that females either fail to invade hermaphrodite populations or else displace them until pollen shortage drives the population to extinction. We develop a pair approximation to a probabilistic cellular automata model in which females and hermaphrodites interact on a regular lattice. The model features independent pollination and colonization processes which take place on different timescales. The timescale separation is exploited to obtain, with perturbation methods, a more manageable aggregated pair approximation. We present both the mean field model which recreates the classical non-spatial predictions and the pair approximation, which strikingly predicts different invasion criteria and coexistence under a wide range of parameters. The pair approximation is shown to correspond well qualitatively with simulation behaviour.

Endosperm triploidy has a selective advantage during ongoing parental conflict by imprinting.

The endosperm of the flowering plant mediates the supply of maternal resources for embryogenesis. An endosperm formed in sexual reproduction between diploid parents is typically triploid, with a 2 : 1 ratio of maternal genetic material (denoted as 2m : 1p). Variation from this ratio affects endosperm size, indicating parent-specific expression of genes involved in endosperm growth and development. The presence of paternally or maternally imprinted genes can be explained by parental conflict over the transfer of nutrients from maternal to offspring tissue. Genomic imprinting can, for example, provide the male parent of an embryo in a mixed-paternity seed pod, with an opportunity for expressing its preference for a disproportionate allocation of resources to its embryo. It has been argued that a diploid 1m : 1p endosperm was ancestral and the 2m : 1p endosperm evolved after parental conflict, to improve maternal control over seed provisioning. We present a population genetic model, which instead places the origin of triploidy early in the parental conflict over resource allocation. We find that there is an advantage to having a triploid endosperm as the parental conflict continues. This advantage can help to explain why the 2m : 1p endosperm prevails among flowering plants.