Migration-selection balance
Whereas genetic variation is constantly removed each generation via purifying selection, it is continually renewed by mutation and migration. A multi-niche polymorphism describes how genetic variation can be maintained in a population though spatially-variable selection, where low-fitness alleles persist in a population given gene flow between niches that favour different optimal phenotypes (Maynard Smith 1970, Bulmer 1972). Having obtained estimates of environmental variance (VE) and additive genetic variance (VA) for traits in addition the genetic variance in fitness (γ), we can estimate the rate of migration (m) necessary to sustain these observed levels of variation given a range in the selection difference among niches (Bulmer 1985). If θ1 is the optimal phenotype in niche 1, and θ2 is the optimal phenotype in niche 2, then we can solve for \(m\), the proportion of the population that must migrate between niches each generation to maintain the polymorphism (Equation 2, from Bulmer 1985, Eq 10.65, pg. 181):
                       \(\left[{V_{A}+2m\left(V_{E}+\gamma\right)}^{2}\right]=m\left(1-m\right)\left(\theta_{1}-\theta_{2}\right)^{2}\left(V_{A}+V_{E}+\gamma\right)\)                       (2)
We calculated the rate of dispersal necessary to maintain the observed variation in frond area (Fig. 4A) and root length (Fig. 4B), over a range of selection differences (\(\theta_{1}-\theta_{2}\)), in the absence of mutation. The hyperbolic function indicates that, in the absence of mutation, there rate of dispersal of about 1% that is sufficient to sustain the observed diversity given a selection gradient of 7mm2 for frond area, and 15mm for root length). In a study on the genetic structure of L. minor populations in central Minnesota, Cole and Voskuil (1996) estimated much lower rates of gene flow, Nm =0.3, which suggests that mutation must play a critical role in maintaining the genetic variation we observed.