## INTRODUCTION

Because ambient humidity exerts a significant influence on stomatal aperture and, hence, the conductance of leaves to either water vapour (*g*_{(t)}) or CO_{2}, much effort has been focused on gas exchange measurements of *g*_{(t)} in response to variations in humidity. Most of these measurements have been made in the steady state, but it is often observed that, under certain conditions, an excitation in humidity causes oscillations in *g*_{(t)} [see Barrs (1971)]. This dynamic behaviour alludes to the functioning of feedback(s) in the response of stomata to changes in humidity and, therefore, provides a seductive insight into the mechanisms governing the system. Here and subsequently, the use of the term ‘system’ relates to the overall description of the response of stomata and the rate of water loss, *E*_{(t)}, to changes in humidity.

Because a wholly static analysis cannot address the fundamental dynamic nature of stomatal homeostasis, it seems more appropriate to utilize a dynamic systems approach to investigate the nature of the dynamic mechanisms that underlie the stomatal regulatory process. Surprisingly, however, there are relatively few examples of research into this topic that have exploited dynamic systems methodology. Farquhar (1973) described some experimental system identification of stomatal responses to both humidity and CO_{2} using sinusoidal perturbations in association with a frequency domain analysis. Also, Farquhar & Cowan (1974) manipulated the ‘environmental gain’ of the system in order to control the stability of the system response. Several simulation models of stomatal movement dynamics have been published which generate response characteristics that are qualitatively similar to the observed system dynamics (e.g. Cowan 1972; Delwiche & Cooke 1977; Haefner, Buckley & Mott 1997).

Cowan (1977), developing Farquhar’s (1973) earlier work, recognized the potential of using a more objective systems identification methods based on the estimation of transfer functions (TFs) from experimental data. Cowan (1977) assumed that *g*_{(t)} responds to *E*_{(t)} and, therefore, he estimated the dynamic relationship between the resultant *perturbations* of *E*_{(t)} and *g*_{(t)} [which we will denote by Δ*E*_{(t)} and Δ*g*_{(t)}] following a perturbational step increase in the leaf surface water vapour concentration gradient, Δ*D*_{(t)}. He proposed that, for cotton, this relationship was well described by a second-order TF composed of two, first-order, subsystems operating in parallel to one another: namely, a rapid stomatal opening and a persistent stomatal closure (with estimated time constants of 1·6 and 16 min, respectively). Cowan’s (1977) choice of *E*_{(t)} as the input is upheld by the findings of Mott & Parkhurst (1991) and the analysis of Monteith (1995), but it can be criticized at higher values of *D*_{(t)} [see Farquhar (1978)]. Also, Cowan (1977) concluded that, unless the modeller is very careful when identifying dynamic relationships between variables, it is easy to derive TFs that fit the data well yet may bear little relation to the processes being described.

Young and coauthors (e.g. Young & Lees 1992; Young 1993, Young & Beven 1994; Minchin *et al.* 1996 ; Young, Parkinson & Lees 1996) have developed a data-based mechanistic (DBM) method for modelling stochastic, dynamic systems which appears to satisfy Cowan’s (1977) requirement for a ‘proper statistical approach’ that avoids the kind of TF identification problems he describes. This DBM approach attempts to infer the nature of the dynamic system from the experimental data without undue reliance on *a priori* assumptions about the nature and order of the system. In this manner, it seeks to avoid over-reliance on current paradigms and minimizes the possibility that prejudicial judgements will be made in the formulation of the model. In particular, because the order of the TF model is identified statistically, by direct reference to the data, the DBM approach tends to yield a minimally parameterized or ‘parsimonious’ model that is well identified from the data and so avoids the possibility of over-parameterization and non-uniqueness.

The present paper employs DBM modelling methods to analyse data obtained from gas exchange experiments on leaves of Spanish cedar (*Cedrella odorata*). The aim of the analysis is to define the appropriate system inputs and outputs and to identify what mechanistic information is observable within a particular set of gas exchange time series. In this manner, we show that the dynamics of the stomatal response to a decrease in humidity is remarkably linear, with Δ*E*_{(t)}, rather than Δ*D*_{(t)}, being the appropriate input for the applied conditions ( Monteith 1995). Also, a similar parallel pathway model to that identified for cotton by Cowan (1977) is observed for *Cedrella*.