A cost-benefit analysis of feeding in female tsetse

Three models for feeding in female tsetse are considered. Model I: there is a prolonged non-feeding phase after each meal followed by feeding at a constant rate, with a constant probability of dying as a consequence of feeding. Model II: the feeding rate increases linearly after each meal. Model III: the feeding rate increases exponentially after each meal. In Models II and III the feeding hazard is a linear function of the probability of feeding. Production of viable female offspring is estimated under each model, making allowance for losses of adults due to starvation and to background and feeding mortality, losses of pupae due to predation and parasitization, and losses of young flies if their mothers take insufficient blood during pregnancy. Under Model I, if females require three meals to produce viable pupae in 9 days, then for a non-decreasing population with a background mortality of 1%/day, and 25% pupal losses due to predation and parasitism, the feeding risk must be < or = 5%/feed. At this maximum level the non-feeding phase should be 2-2.5 days for optimal productivity, with a mean feeding interval of 60-72 h. If the background mortality is 2%/day, feeding losses cannot exceed 1%/feed for a non-decreasing population. If four or five meals are required for the production of fully viable pupae, the optimal values of the non-feeding phase and mean feeding interval tend towards 1 and 2 days respectively. Under Models II and III the mean feeding interval is 50-60 h for optimal productivity (with variances 3 times as large as for Model I), in good agreement with estimates from recent models for feeding and digestion. Field evidence suggests that feeding tsetse take greater risks as their fat levels dwindle. This should result in feeding (and feeding mortality) rates which increase during the feeding phase--as assumed in Models II and III but not in Model I. These models allow greater flexibility than Model I, because flies can feed early in the hunger cycle, at low probability, as long as the feeding risk is also low.