Table 1.

Descriptions and values for the model variables and parameters. Details for each parameter value can be found in Appendix 1.

Variable / parameter	Description	Default value	M. persicae	M. aeneus	F. occidentalis	Unit
I0	Initial density of insects each season	0.5	0.5	0.5	0.1	(insect plant-1)
K	Threshold density of the population	20	50	30	10,000,000	(insect plant-1)
β	Insect birth rate at low densities	0.1333	0.75	4	0.55	(insect day-1)
η	Rate of emergence from overwinter population	0.0	0.1	0.25	0.0	(day-1)
ξ	Insecticide decay rate	0.5	0.5	0.5	0.5	(day-1)
RR0	Initial proportion of homozygote resistant individuals	1e-8	1e-8	1e-8	1e-8	(1)
SR0	Initial proportion of heterozygote individuals	1e-4	1e-4	1e-4	1e-4	(1)
II	Immigration: untreated to treated population	0.0	0.01	0.01	0.0	(day−1)
ιE	Emigration: treated to untreated population	0.0	0.01	0.01	0.0	(day−1)
κ	Relative size of the untreated population	2.0	2.0	2.0	2.0
μE	Egg lifespan	NA	NA	5	6.7	(day)
μL	Larvae lifespan	10	7	7	9.8	(day)
μP	Pupa lifespan	NA	NA	12	5.2	(day)
μA	Adult lifespan	20	10	12	18.0	(day)
ωE	Natural mortality of eggs	NA	NA	0.01	0.0	(insect day-1)
ωL	Natural mortality of larvae	0.0	0.2	0.025	0.0	(insect day-1)
ωP	Natural mortality of pupae	NA	NA	0.01	0.0	(insect day-1)
ωA	Natural mortality of adults	0.0	0.2	0.01	0.0	(insect day-1)
tSpray	Day on which insecticide is sprayed	50	50	5	50	(day)
a [SS,SR,RR]	Intercept of logit-dose lines for each genotype	[0.5, −2, −4]	[2.5,0.85,−0.5]	[12.0,7.95,3.9]	[−1.0,−2.5,−6.0]
b [SS,SR,RR]	Gradient of logit-dose lines for each genotype	[1.5, 1.5, 1.5]	[2.0,2.0,2.0]	[1.5,1.5,1.5]	[2.5,2.5,2.5]
ϕ	Dominance of the resistance gene	0.25	0.45	0.5	0.5	(1)
	The number of days in a single season	200	100	60	70	(days)