Dynamic coexistence of sexual and asexual invasion fronts in a system of integro-difference equations

The role of long-range dispersal in the coexistence of sexual and asexual relatives in a population of hermaphrodite flowering plants is investigated. In these populations, growth and reproduction often occur during a sedentary stage that is then followed by dispersal of propagules. These two stages are clearly distinguishable and show strong seasonality. A modeling approach that accurately describes this kind of dynamics of mixed populations is a system of two nonlinear integro-difference equations. It is shown that this kind of model can accommodate coexistence of the two different reproductive types.

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.

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.

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.

In support of null hypothesis significance testing

Many criticisms have been levelled at null hypothesis significance testing (NHST). It is argued here that although there is reason to doubt that data subjected only to NHST have been subjected to sufficient analysis, the search for clear answers to well-formulated questions derived from substantive hypotheses is well served by NHST. To reliably draw inferences from data, however, NHST may need to be complemented by additional methods of analysis, such as the use of confidence intervals and of estimates of the degree of association between independent and dependent variables. It is argued that these should be seen as complements of, rather than as substitutes for, NHST since they do not directly test the strength of evidence against a null hypothesis.

Coexistence of Sexual and Asexual Conspecifics: A Cellular Automaton Model

Most previous models of populations mixed for reproductive mode have omitted important local interactions between sexual and asexual individuals. We propose a cellular automaton model where local rules focus on fertilization and colonization. This model produces rich sets of data which are then studied by means of spatial statistics. Results point to the fixation of one of the two reproductive modes in the landscape. However, some examples of coexistence of sexual and asexual conspecifics over long periods of time are also found. This model is an example of a CA that diverges from its mean field approximation. The formation of sexual and asexual clusters reduces effective colonization rate in the CA and may account for this behaviour.

Are sample sizes usually at least an order of magnitude too low for reliable estimates of leaf asymmetry?

Estimates of leaf size and asymmetry for individual trees are often obtained using sample sizes that are too small to take into account the possibility that size and asymmetry may be affected by the position of the leaf on the tree. This issue was addressed by exploring variation in leaf size and asymmetry within an individual of Alder (Alnus glutinosa). We found differences between branches for leaf size and for signed asymmetry but not for unsigned asymmetry. We also found that the size of a leaf was not correlated with its position on a branch and that the asymmetry of a leaf was not correlated with either its position on a branch or with the asymmetry of its neighbour. Repeated subsampling of a sample of 870 leaves showed that a subsample size approaching 500 leaves was required for consistently reliable estimates of the standard deviation of unsigned asymmetry. Smaller subsamples were required for consistently reliable estimates of mean unsigned asymmetry and of the mean and standard deviation of leaf size, but subsamples of less than 100 leaves provided consistently reliable estimates only of mean leaf size. For this species, reliable estimates of an individual's level of asymmetry are obtained only if several hundred leaves are sampled over several branches, but it is not necessary to sample the same sequence of leaves from each branch.