Table 1.

A list of important symbols

Symbol	Description
n	Population size
$W^i$	Fertility payoff function of the i-th type event
$d^i$	Mortality payoff function of the i-th type event
K	Carrying capacity (maximal environmental load)
$q_i$	Frequency of the i-th strategy
$W_i(q)$	Fertility payoff of the i-th strategy
$s_i(q)$	Pre-reproductive survival payoff function of the i-th strategy
$V_i(q)$	Mortality-fertility trade-off function for the i-th strategy
${\mathit{\tau }}_i$	Rate of occurrence (intensity) of the i-th type event
${\mathit{\tau }}_F$	Rate of occurrence (intensity) of the focal game event
${\mathit{\tau }}_B$	Rate of occurrence of the background event
$\mathit{\tau }$	Interaction rate from Argasinski and Broom (2012)—see “Appendix 1”
$\mathit{\theta }={\mathit{\tau }}_B/{\mathit{\tau }}_F$	Average number of background events between two focal events
$W_b$	Focal game background fertility (payoff based approach)
$d_b=1-s_b$	focal game background post-reproductive mortality (payoff-based approach)
$W_B$	Average background event fertility (dynamics-based approach)
$d_B=1-s_B$	Average background event mortality (dynamics-based approach)
$\mathrm{\Phi }=\mathit{\theta }{W}_B$	Rate of the average background fertility
$\mathrm{\Psi }=\mathit{\theta }(1-s_B)$	Rate of the average background mortality
S	Hawk–Dove example survival payoff matrix
$F=WP$	Hawk–Dove example fertility payoff matrix
$d=1-s$	Probability of death during a Hawk–Dove contest
${\tilde{q}}_h(n)$	Frequency nullcline describing the Nash equilibria
$\tilde{n}(q_h)$	Density nullcline describing the ecological equilibria