Is the sky the limit? On the expansion threshold of a species’ range
Authors: Polechová Jitka 
Published: December 2017

AbstractMore than a hundred years after Grigg’s influential analysis of species’ borders, the causes of limits to species’ ranges still represent a puzzle that has never been understood with clarity. The topic has become especially important recently as many scientists have become interested in the potential for species’ ranges to shift in response to climate change – and yet, nearly all of those studies fail to recognise or incorporate evolutionary genetics in a way that relates to theoretical developments. I show that range margins can be understood based on just two measurable parameters: i) the fitness cost of dispersal – a measure of environmental heterogeneity – and ii) the strength of genetic drift, which reduces genetic diversity. Together, these two parameters define anexpansion threshold: adaptation fails when genetic drift reduces genetic diversity below that required for adaptation to environmental heterogeneity. When the key parameters drop below thisexpansion thresholdlocally, a sharp range margin forms. When they drop below this threshold throughout the species’ range, adaptation collapses everywhere, resulting in either extinction, or formation of a fragmented meta-population. Because the effects of dispersal differ fundamentally with dimension, the second parameter – the strength of genetic drift – is qualitatively different compared to a linear habitat. In two-dimensional habitats, genetic drift becomes effectively independent of selection. It decreases withneighbourhood size– the number of individuals accessible by dispersal within one generation. Moreover, in contrast to earlier predictions, which neglected evolution of genetic variance and/or stochasticity in two dimensions, dispersal into small marginal populations aids adaptation. This is because the reduction of both genetic and demographic stochasticity has a stronger effect than the cost of dispersal through increased maladaptation. Theexpansion thresholdthus provides a novel, theoretically justified and testable prediction for formation of the range margin and collapse of the species’ range.Author summaryGene flow across environments has conflicting effects: while it increases the genetic variation necessary for adaptation and counters the loss of genetic diversity due to genetic drift, it may also swamp adaptation to local conditions. This interplay is crucial for the dynamics of a species’ range expansion, which can thus be understood based on two dimensionless parameters: i) the fitness cost of dispersal – a measure of environmental heterogeneity – and ii) the strength of genetic drift – a measure of reduction of genetic diversity. Together, these two parameters define anexpansion threshold: adaptation fails when the number of individuals accessible by dispersal within one generation is so small that genetic drift reduces genetic diversity below the level required for adaptation to environmental heterogeneity. This threshold provides a novel, theoretically justified and testable prediction for formation of a range margin and a collapse of a species’ range in two-dimensional habitats.