Table 1.

Definitions of variables and functions.

fa(μa, ma, za)	Energy budget constraint at age a excluding transfers
fa,μ; fa,m; fa,z	Partial derivatives of fa with respect to μa, ma, za
μ a	Instantaneous death rate, d ln (la) /da
ma	Birth rate
za	Rate of change of body size, ẉa
la	$\text{Probability of surviving from birth to age a},\text{exp}(-{\int }_0^a{\mu }_{s}ds)$
ζa (wa)	Energy flow generated as a function of body size
ζ a,w	Partial derivatives of ζa with respect to wa
wa	Body size
ρ	Steady state population growth rate or intrinsic rate of natural increase
ϕ a	Costate variable associated with la
ψ a	Costate variable associated with wa
λ a	Rate of instantaneous time preference at age a
ga(Ra)	Amount of usable energy derived from receipt of a transfer Ra
Ra	Transfer made or received
K	If K > 0 then transfers raise fitness (for specific pair of ages)