The model was run under a ‘null’ scenario, whereby all genotypes are equally fit (). Even in the absence of a selective advantage to hybrid genotypes, the relative frequency of the native declines through hybridization (and the frequency of the exotic undergoes a similar decline). How rapidly the native decreases in frequency depends strongly on the fecundity of the population, the initial ratio of native and exotic genotypes and the relative compatibility of different genotypes.
Figure 1 Decline in the relative frequency of the native genotype in a neutrally selective environment (i.e. all genotypes are equally fit). The default parameter values (dashed line) for vegetative growth rate and fecundity are, respectively, R=1.05 and S=0.1. (more ...)
When a life-history trait of a plant is a function of its genotype, the effects on both the population growth rate (a) and genetic structure (b) can be dramatic. Most notably, an apparent accelerating population growth rate may be observed (a). In the case where hybrids exhibit an elevated growth rate relative to the native, the fastest-growing genotype increases rapidly in frequency within the population. This results in an increase in the frequency of pollen and ovules produced by this genotype, which in turn results in higher production of seedlings with this genotype. The net population growth rate therefore increases to approach that of a population consisting entirely of the fittest genotype. The results illustrated here are for elevated vegetative growth rate of hybrids, but sufficiently large changes in seedling vigour and ovule production can also result in faster-than exponential population growth.
Figure 2 Effect of elevated hybrid vegetative growth rate on (a) the total population growth rate and (b) the genetic structure of the population after 50 generations. The growth rate is varied by changing the proportional difference between the growth rate of (more ...)
The addition of compatibility constraints can delay, or even prevent, the invasion of novel genotypes. If hybridization does eventually occur, the invasion continues at the same rate as if all genotypes were equally compatible (a, cf. dashed and circled lines). Thus, reduced compatibility between genetically distant congeners may help to explain the ‘lag-time’ observed between the introduction of an exotic and the subsequent appearance of hybrids.
The location of the fitness maximum in genotype space strongly influences the resulting genetic structure of the population. In the above example, the fittest genotype is also the most commonly produced genotype in F1 hybrids, and hence this genotype rapidly dominates the population. When the location of the maximum is skewed, such that it is unlikely to appear in the initial round of hybridization (c,d), the fittest genotype takes longer to emerge, and may not become the dominant genotype within an ecologically relevant timescale. When fecundity is low (c), relatively little hybridization occurs over the first 50 generations. The exotic becomes the dominant genotype (since in this case it is fitter than the native) even though it is not the fittest possible genotype. Some F1 hybrids eventually appear, but further introgression does not occur within this time-frame. When fecundity is increased by an order of magnitude (d), there is a noticeable shift in the population structure towards the fittest genotype, although the population remains genetically very variable.
In reality, we might expect certain life-history traits to be genetically linked. For example, average inflorescence length varies with genotype in Spartina, resulting in more pollen and ovule production per unit area for those genotypes with large inflorescences. In this model, elevated hybrid pollen production alone does not affect the rate of population increase, since the number of seeds produced is assumed proportional to the number of ovules (it does, however, strongly influence the genetic structure of the population). Elevated ovule production can result in accelerating population growth (a, dashed line), but when both pollen and ovule production are genetically correlated (pluses), the ensuing population growth rate is considerably more rapid as the two mechanisms feed back on each other to select for the fittest genotype.
Figure 3 (a) Effect of elevated hybrid life-history traits on population growth when two traits (pollen production, Nm and ovule production, Nf) are genetically linked. The default vegetative growth and fecundity parameters are R=0.6 and S=0.5. When pollen production (more ...)
When two elevated fitness traits attain their maxima at different genotypes (through, for example, a trade-off between resources allocated to vegetative growth and reproduction), more interesting dynamics can ensue (b). If one of the elevated life-history traits has a stronger effect on population growth than the others, the population will tend to converge on that genotype (not shown). However, when two opposing life-history traits have similar effects on population growth, a wide range of phenotypically distinct genotypes can persist over many generations (b). Such trade-offs between genotypes may help to explain the existence of ‘hybrid swarms’, whereby hybrids with very different life-history characteristics appear to coexist.