Table 1.

Definition of parameters

 Parameter Dimension† Definition B Z/D Gradient in the environmental optimum Vs Z2T Variance of stabilizing selection σ D/T Dispersal per generation K T/D Carrying capacity for a well-adapted phenotype rm 1/T Maximum exponential growth rate α Z Allelic effect μ‡ 1/T Mutation rate s 1/T Selection per locus: s≡α2/(2Vs) r* 1/T Rate of return to equilibrium population size: r*≡−N ∂r¯/∂N|N→N^=rm−VG/(2Vs) B — Effective environmental gradient, B=bσ/(r*2Vs) Nσs — Efficacy 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.