Table 1.

Definition of parameters

ParameterDimensionDefinition
BZ/DGradient in the environmental optimum
VsZ2TVariance of stabilizing selection
σD/TDispersal per generation
KT/DCarrying capacity for a well-adapted phenotype
rm1/TMaximum exponential growth rate
αZAllelic effect
μ1/TMutation rate
s1/TSelection per locus: sα2/(2Vs)
r*1/TRate of return to equilibrium population size: r*Nr¯/N|NN^=rmVG/(2Vs)
BEffective environmental gradient,
B=bσ/(r*2Vs)
NσsEfficacy of selection relative to strength of genetic drift
Nσr*Efficacy of population regulation relative to demographic stochasticity
  • Three scale-free parameters, B, Nσs, and Nσr* (bottom), describe the system; the top section gives seven parameters of the model before rescaling and the middle section defines two important composite parameters.

  • Dimensions: T stands for time, D stands for distance, and Z stands for trait. Note that, with a Poisson number of offspring, the effective population size Ne (which measures rate of genetic drift/coalescence) is identical to the N that regulates population growth due to crowding: hence, both carrying capacity K and population density N have units of T/D.

  • Mutation rate μ is set to be small, with minimal contribution to the dynamics, and, hence, μ/r* is neglected in the rescaled parameterization.