Table 1 Symbols and definitions in the model with values of parameters.

x, y

xy coordinates location within the habitat

x = 1000–5000, y = 1000

I(λ)

The ambient illumination spectrum

-

S_m(λ)

The reflectance spectrum of the male nuptial color

-

S_e(λ)

The predominant ambient light spectrum

-

R_i(λ)

The absorption properties of the photoreceptor i

-

P(S)

The total sensitivity for an object with reflectance spectrum (S)

-

q_i

The quantum catch of photoreceptor i adapted to its background

-

k_R

The relative contributions to overall sensitivity by LWS cone opsin

-

k_G

The relative contributions to overall sensitivity by MWS cone opsin

-

k_B

The relative contributions to overall sensitivity by SWS cone opsin

-

λ_R1, λ_R2

The peak absorption wavelengths of allele 1 and 2 of LWS opsin gene

-

λ_G1, λ_G2

The peak absorption wavelengths of allele 1 and 2 of MWS opsin gene

-

λ_B1, λ_B2

The peak absorption wavelengths of allele 1 and 2 of SWS opsin gene

-

E_c

The mean (peak) of the distribution of I(λ)

-

σ_E

The width (standard deviation) of the distribution of I(λ)

6–16

σ_m

The width (standard deviation) of the reflectance spectrum of male coloration

6–16

G_E

The steepness of the gradient in predominant light color (peak wavelength)

0–0.225

G_s

The steepness with which the width of I(λ) decreases with depth

0.025

G_I

The steepness with which light intensity decreases with depth

0.0075

E_I

Light intensity

-

r

Reproductive rate of an individual

1.6

N

The number of individuals within home range (radius of home range = 50)

-

E_max

Maximum perception above which perception intensity cannot increase

22

K

Carrying capacity within the home range of an individual

5–15

V

Strength of selectioin

100

F(S)

The strength of female preference for males with reflectance spectrum S_m

-

M

A female's mating area

75–300

μ

Mutation rates per generation

10^-5,10^-3,10^-4, 10^-6, 10^-7, 10^-8

d

The standard deviation of a normal distribution in which random dispersal distances were generated.

50–225

α

The strength of female preference relative to perception intensity

1–14

f

The cost of mate preference: the strength of female preference for the preferred male is reduced by f

-

c

The coefficient of the cost for mating preference

0–0.00005