Predatory benefit is modeled as the probability of capturing prey per encounter:
B(T,eco)=Egainphunt(T,tprey),B(\mathbf{T}, \Theta_{eco}) = E_{gain} \cdot p_{hunt}(\mathbf{T}, \mathbf{t}_{prey}),B(T,eco)=Egainphunt(T,tprey),
with:
phunt(T,tprey)=(1T1+2T3+3T41tprey,12tprey,2),p_{hunt}(\mathbf{T}, \mathbf{t}_{prey}) \;=\; \sigma\!\Big(\alpha_1 T_1 + \alpha_2 T_3 + \alpha_3 T_4 \;-\; \beta_1 t_{prey,1} - \beta_2 t_{prey,2}\Big),phunt(T,tprey)=(1T1+2T3+3T41tprey,12tprey,2),
where (x)=1/(1+ex)\sigma(x) = 1/(1 + e^{-x})(x)=1/(1+ex) is a sigmoid function bounding the probability between 0 and 1.
T1,T3,T4T_1, T_3, T_4T1,T3,T4 are predator traits contributing to prey detection, maneuvering precision, and aerodynamic performance.
tprey,1,tprey,2t_{prey,1}, t_{prey,2}tprey,1,tprey,2 represent prey speed and evasive agility.
i\alpha_ii and i\beta_ii are weighting coefficients that quantify trait importance.
EgainE_{gain}Egain is the energetic return per successful hunt.
This formulation ensures that predatory success emerges from relative advantage: a predator's traits must exceed prey defenses to yield substantial benefit.
2. Cost Function: Trade-Offs
Adaptive traits are not free. Increased wing loading, for example, may reduce maneuverability; enhanced neuromuscular control may incur high metabolic demand. We represent such trade-offs with a quadratic cost function:
C(T)=1T22+2T32+3(T4)2,C(\mathbf{T}) \;=\; \lambda_1 T_2^2 + \lambda_2 T_3^2 + \lambda_3 (T_4 - \theta)^2,C(T)=1T22+2T32+3(T4)2,
where:
i\lambda_ii are cost coefficients reflecting energetic or structural burden.
T2T_2T2 (respiratory capacity) incurs metabolic cost at high values.
T3T_3T3 (neuromuscular precision) scales quadratically with neural investment.
T4T_4T4 (wing morphology) has an optimal aerodynamic design \theta; deviations reduce efficiency.
This structure embeds biological realism: extreme values may reduce fitness as much as deficiencies, capturing the principle that adaptation requires balance across modules.
