Although the physical principles underlying gas exchange are set out in a variety of texts and reviews (Piiper et al. 1971; Farhi and Tenney 1987), in terms of insect gas exchange the most thorough treatment is provided by Kestler (1985). Among the 47 equations presented to facilitate theoretical investigations of gas exchange in insects, and on which Kestler (1985) bases his arguments regarding the relative contributions of diffusion and convection to gas exchange, and the scaling of water loss, several can be considered most essential in the broader context of insect responses to the environment.
Gas exchange and water loss
The molar rates of transport Mx (mmols-1), of gas x in a tube containing the medium m, are given, in the case of diffusion, by
where A is the cross-sectional area of the tube (cm2), L its length (cm), D'xm the effective diffusion coefficient (cm2 sec-1), and ^x m the capacitance coefficient (mmol cm-3 kPa-1) and Apx m the partial pressure difference (kPa). In the case of convection, the equation is
where Vm is the rate of volume flow (cm3s-1), which is the product of the frequency of volume changes ( f, s-1) and the volume change (AVm, cm3).
These equations represent the situation for pure diffusion and pure convection, respectively, and apply equally to N2, O2, CO2, and water vapour (Kestler 1985). Given that Dx,m and ^x m remain the same in a given medium for a given gas, it is clear that Mx can be altered in a pure diffusion system by changes in A, L and/or Apx,m, and in a pure convection system by changes in f, AVm and/or Apxm. This has considerable implications for gas exchange in insects, especially for a tracheal system that functions to exchange O2 and CO2, while conserving water (Kaars 1981).
For example, because the partial pressure difference for water is independent of metabolic rate (tissues remain saturated irrespective of metabolic rate), alteration of metabolic rate will not effect a change in the rate of water loss. However, if the partial pressure gradient for CO2 can be enhanced, then the same molar rate of CO2 transport can be maintained with a reduction in cross-sectional area of the spiracles. The latter often forms the major resistance to water loss (O2 is not considered here because partial pressure gradients are generally higher for O2 than for CO2, as is K (Kestler 1985; Lighton 1994; Wasserthal 1996)). In other words, changes in metabolic rate as a means to reduce or enhance water loss are only effective in a pure diffusion system in as much as they alter the area term in equation (1). In a pure convection system, any alterations to f or to AVm will have profound effects on water loss rates.
Based on similar reasoning, several null models for the likely extent of water loss in small and large terrestrial insects utilizing either pure convective or pure diffusive gas exchange have been developed (Kestler 1985). If metabolic rate scales with an exponent lying somewhere between m0 67 and m10 (Section 3.4.5), tracheal cross-sectional area scales as m0.67, and tracheal length as m0.33, in a pure diffusion system respiratory water loss should scale as m033. In a convective system, ventilation frequency does not scale with mass (unlike the situation in vertebrates—see Lighton 1991a; Davis et al. 1999), and ventilation volume scales as m10 (Kestler 1985; Lighton 1991a; Davis et al. 1999). Therefore, respiratory water loss scales as m10. To adjust both modes of oxygen flux to the same intensity, ventilation frequency must equal diffusive oxygen uptake, and net convective respiratory water loss should, therefore, be 80 per cent of diffusive loss (Kestler 1985). Notwithstanding this consistent difference, it is clear that according to the null model, respiratory water loss by diffusion will always be larger than convective water loss at small body sizes (Fig. 3.5). Therefore, from a purely theoretical perspective, selection should favour a system dominated by convective gas exchange in small insects.
However, water balance is not just a function of respiratory water loss. It is also dependent on the rate of cuticular transpiration, which scales as m0 67 (Chown and Davis 2003). When this transpiratory route is set to contribute half of the total water loss, then the difference between diffusion and convection remains pronounced, with diffusion resulting in greater water loss at small body sizes and convection showing the converse. However, if cuticular water loss makes up a large proportion of total transpiration (c.85-90 per cent), then the difference between rates of water lost by diffusion or convection are small, especially for small-bodied insects (see Chapter 4). Moreover, the theoretical analysis is not especially sensitive to alteration of tg o J
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