Nematostella stinging is regulated by predation while Exaiptasia stings for defense.A) Top: Nematostella burrows in the substrate and stings for predation. Bottom : We assumed the cost of stinging does not change with starvation state.
B) Left : Desirability of nutritional state, or reward, decreases with starvation. Three examples are shown: example 1, r (s ) = 10 tan −1 (1 − s ); example 2, ; and example 3, r (s ) = 3 – 3s2 . Right : Predicted optimal stinging obtained by solving equation (1) with numerical simulations (circles) and approximate analytical solutions (lines) assuming p (a ) = pM a (2−a ) and pM = 0.8 and c = c0 a with a constant cost for full discharge c 0 = 1. Colors match the corresponding reward in Left panels. For all three reward functions, optimal predatory stinging increases with starvation under broad assumptions (see Supplementary Information ).
C) Examples of optimal (blue) versus random (black) predatory stinging. Each agent (anemone) starts with s = 0.9, and stings sequentially for many events (represented on the x axis). The random agent almost always reaches maximal starvation before time 50 events (grey lines, five examples shown). In comparison, the optimal agent effectively never starves due to a successful stinging strategy optimized for predation (blue lines, five examples shown, parameters as in panel B, curve with matching color).
D) Top: Exaiptasia diaphana relies heavily on endosymbiotic algae for nutrients and stings primarily for defense. Bottom : We assumed there are two states, safety (L), and danger (D). The state of safety can transition to danger, but not the other way around. We assumed the agent obtains reward 1 in state L and penalty −1 in state D.
E) Left : Cost function, which is assumed to increase linearly with the fraction of nematocysts discharged cs (a ) = c 0 a The cost c 0 for full discharge is constant as in panel A, c 0 = 1 (example 1), or varies with starvation: c 0 (s ) = s (example 2), c 0 (s ) = 1 − (s − 1)2 (example 3) and c 0 obtained by fitting the experimental data (example 4) (see fitting procedure in Supplementary Information ). Right : Predicted optimal stinging obtained by solving equation (2) with numerical simulations (circles) and analytical solutions (lines). Colors match the corresponding cost in Left panels, and we assume p (a ) = PM a (2 − a ) and pM = 0.8 as before. Optimal defensive stinging is constant or decreases with starvation under broad assumptions (see Supplementary Information ).
F) Left: Nematostella nematocyte discharge was affected by prey availability while Exaiptasia stung at a similar rate regardless of feeding. p < 0.0001 for Nematostella , two-way ANOVA with post hoc Bonferroni test (n = 10 animals, data represented as mean ± sem). Right : Normalized optimal nematocyst discharge predicted from MDP models for both Exaiptasia (orange circles, using the cost function in E, example 4) and Nematostella (blue circles, using the reward function in B, example 2) fit the experimental measurements well. We match the last experimental data point to s = 0.5, the precise value of this parameter is irrelevant as long as it is smaller than 1, representing that animals are not severely starved during the experiment.