Signalling Theory - Re-evaluating Biological Signalling Vs. Sports Handicapping

Re-evaluating Biological Signalling Vs. Sports Handicapping

Efforts to test the handicap principle empirically have not been decisive, partly because of inconsistent interpretations of Zahavi’s metaphor and Grafen’s marginal fitness model, and partly because of conflicting empirical results: in some studies individuals with bigger signals seem to be paying higher costs, in other studies they seem to be paying lower costs. Recent theoretical analyses have uncovered a possible explanation for the inconsistent empirical results. A series of papers by Getty shows that Grafen’s proof of the handicap principle is based on the critical simplifying assumption that signallers trade off costs for benefits in an additive fashion, the way humans invest money to increase income in the same currency. Grafen’s proof is formally similar to a classic monograph on economic market signalling by Nobel laureate Michael Spence. This assumption that costs and benefits trade off in an additive fashion might be valid for some biological signalling systems, but is not valid for the survival cost – reproduction benefit tradeoff that is assumed to mediate the evolution of sexually selected signals. Fitness depends on the production of offspring and this is a multiplicative function of reproductive success given an individual is still alive times the probability of still being alive, given investment in signals.

Survival-reproduction tradeoffs do not correspond to sports handicaps in any simple, useful way. Zahavi’s intuition was correct in the very general sense that "differences in costs" can stabilize the evolution of an "honest" signalling system, but in sexually selected signalling, "differences in costs" are properly decreasing proportional (or log) marginal costs. The mathematics can be interpreted to mean that higher quality signallers are more efficient at converting signal costs into reproductive benefits. This re-analysis undermines the idea that higher quality signallers are demonstrating their ability to waste more because the pattern of absolute signal costs across signallers of different quality remains undetermined. Depending on the specific form of the tradeoffs in any particular system, higher quality signallers might pay absolutely more or less for big signals than lower quality signallers pay for small signals. This might explain why the empirical data on the relationship between signals and costs are so inconsistent.