Examples of decision making processes during fights. Black and grey lines depict two separate, independent fights. In the first fight (black data) the strength difference between both individuals (si - sj) was set to 1, and in the second fight (grey data) it was set to 0.3. In both fights the stronger individual is represented by a dashed line and the weaker one by a solid line. In each fighting round both individuals obtain a noisy estimation of their relative strength. This estimation is subtracted in each round from the decision variable d (on the y-axis), which measures the evidence of being weaker. Therefore, the decision variable of stronger individuals (dashed lines) tends to decrease over time and for weaker individuals it (solid lines) tends to increase. An individual is certain to be weaker and gives up when the value of d increases above the genetically determined giving-up threshold T, which in these examples is assumed to be three for all individuals (dotted line). The increase or decrease in the decision variable d is not always consistent because of the noise in the estimation of relative strength. In addition, the development of d strongly depends on the strength difference between both individuals. Thus, on average a smaller strength difference leads to longer fights as indicated by the differences in fight between black (3 rounds) and grey data (13 rounds). Also note that a higher giving-up threshold leads on average to longer fights, but also to a lower risk that the stronger individual erroneously becomes certain to be weaker and gives up.
Franz et al. BMC Evolutionary Biology 2011 11:323 doi:10.1186/1471-2148-11-323