Dynamics of the Oxygen, Carbon Dioxide, and Water Interaction across the Insect Spiracle

Abstract

This paper explores the dynamics of respiratory gases interactions which are accompanied by the loss of water through an insect’s spiracle. Here we investigate and analyze this interaction by deriving a system of ordinary differential equations for oxygen, carbon dioxide, and water vapor. The analysis is carried out in continuous time. The purpose of the research is to determine bounds for the gas volumes and to discuss the complexity and stability of the equilibria. Numerical simulations also demonstrate the dynamics of our model utilizing the new conditions for stability and instability.

Comparison of the tracheal systems ofAnopheles sinensisandAedes togoilarvae using synchrotron X-ray microscopic computed tomography (respiratory system of mosquito larvae using SR-μCT)

“…O 2 enters to the trachea and then it is replaced by CO 2 . The concentration of CO 2 increases, as O 2 is consumed (Simelane, Abelman, & Duncan, ). When the spiracles open, the two gases move in the opposite directions for exchange.…”

“…When the spiracles open, the two gases move in the opposite directions for exchange. Therefore, O 2 comes in and CO 2 leaves through the same opening (Simelane et al, ). In this study, A. sinensis larvae breathe more frequently than A. togoi larvae.…”

“…O 2 enters to the trachea and then it is replaced by CO 2 . The concentration of CO 2 increases, as O 2 is consumed (Simelane, Abelman, & Duncan, 2014).…”

Why do models of insect respiratory patterns fail?

“…Despite a rich history of theoretical models analysing gas exchange by insects (see Pickard, 1974, and references therein; Table 3), dating to early seminal work by Krogh (1920) and Wigglesworth (1935) on respiratory structures and their diversity, only later were comprehensive models of respiratory water loss developed by Kestler (1985). More recently, these have been extended to deal specifically with the dynamics of respiratory water loss at the spiracle (Simelane et al, 2014) or at the whole-animal level (Woods and Smith, 2010) and the latter was supported by a comprehensive null model developed from first principles of diffusive gas exchange. A non-exhaustive literature survey highlights that several approaches and types of models can be readily differentiated (Table 3), from hypothetical (e.g.…”

“…Some models tackle variation among respiratory patterns directly, whereas others simply aim to explain the fluxes of major gases (CO 2 , O 2 , H 2 O) in some specific part(s) of the insect respiratory system [e.g. in the tracheae (Simelane et al, 2014) or across the spiracles as a function of varying cross-sectional area (Snyder et al, 1995)]. Models are in some cases purely mathematical or hypothetical (e.g.…”