The flight distance, flight time and individual flight activities of males and females of Dendroctonus armandi were recorded during 96-h flight trials using a flight mill system. The body weight, glucose, glycogen and lipid content of four treatments (naturally emerged, starved, phloem-fed and water-fed) were compared among pre-flight, post-flight and unflown controls. There was no significant difference between males and females in total flight distance and flight time in a given 24-h period. The flight distance and flight time of females showed a significant linear decline as the tethered flying continued, but the sustained flight ability of females was better than that of males. The females had higher glycogen and lipid content than the males; however, there was no significant difference between both sexes in glucose content. Water-feeding and phloem-feeding had significant effects on longevity, survival days and flight potential of D. armandi, which resulted in longer feeding days, poorer flight potential and lower energy substrate content. Our results demonstrate that flight distances in general do not differ between water-fed and starved individuals, whereas phloem-fed females and males fly better than water-fed and starved individuals.

We consider the number of trophic levels in a food chain given by the equilibrium state for a simple mathematical model with ordinary differential equations which govern the temporal variation of the energy reserve in each trophic level. When a new trophic level invades over the top of the chain, the chain could lengthen by one trophic level. We can derive the condition that such lengthening could occur, and prove that the possibly longest chain is globally stable. In some specific cases, we find that the possibly longest chain is such that the lower trophic level has a greater energy reserve than the higher has, so that the distribution of energy reserves can be regarded to have a pyramid shape, whereas, if any of its trophic levels is removed, the pyramid shape cannot be maintained. Further, we find the condition that arbitrary long chain can be established. In such unbounded case, we prove that any chain could not have the pyramid shape of energy reserve distribution.