A long-standing hypothesis(1,2) posits that natural selection can favour tw
o female strategies when density cycles. At low density, females producing
many smaller progeny are favoured when the intrinsic rate of increase, r, g
overns population growth. At peak density, females producing fewer, high-qu
ality, progeny are favoured when the carrying capacity, K, is exceeded and
the population crashes. Here we report on the first example of a genetic r
versus K selection(3-5) game that promotes stable population cycles in liza
rds. Decade-long fitness studies and game theory demonstrated that two thro
at-colour morphs were refined by selection in which the strength of natural
selection varied with density. Orange-throated females, r strategists, pro
duced many eggs and were favoured at low density. Conversely, yellow-throat
ed females, K strategists, produced large eggs and were favoured at high de
nsity. Progeny size should also be under negative frequency-dependent selec
tion in that large progeny will have a survival advantage when rare, but th
e advantage disappears when they become common. We confirmed this predictio
n by seeding field plots with rare and common giant hatchlings. Thus, intri
nsic causes of frequency- and density-dependent selection promotes an evolu
tionary game with two-generation oscillations.