Notation  Definition  Value 
x  Distance away from the wave front 

x_{max}  Width of the transition zone  2000 (m) 
b(x)  Colonial establishment rate 

n(a)  Number of individuals in a colony of age a 

m(a, t, z)  Average density per unit area of colonies, of age a, at spatial location z, at time t 

Z(t)  Location of the wave front at time t 

N(z, t)  Average density of individuals at spatial location z, at time t 

K  Environmental capacity  262 (ind. m^{−2}) 
r  Intrinsic growth rate  1.5 
c  Maximum colonial establishment rate 

c^{*}  Critical value of c 

n_{0}  Number of initial individuals in a colony  3 (ind. colony^{−1}) 
v  Speed of population spread 

V  Relative rate of population spread, V = v/x_{max} 
