Models of vegetation function are widely used to predict the effects of climate change on carbon, water and nutrient cycles of terrestrial ecosystems, and their feedbacks to climate. Stomatal conductance, the process that governs plant water use and carbon uptake, is fundamental to such models. In this paper, we reconcile two long-standing theories of stomatal conductance. The empirical approach, which is most commonly used in vegetation models, is phenomenological, based on experimental observations of stomatal behaviour in response to environmental conditions. The optimal approach is based on the theoretical argument that stomata should act to minimize the amount of water used per unit carbon gained. We reconcile these two approaches by showing that the theory of optimal stomatal conductance can be used to derive a model of stomatal conductance that is closely analogous to the empirical models. Consequently, we obtain a unified stomatal model which has a similar form to existing empirical models, but which now provides a theoretical interpretation for model parameter values. The key model parameter, g 1 , is predicted to increase with growth temperature and with the marginal water cost of carbon gain. The new model is fitted to a range of datasets ranging from tropical to boreal trees. The parameter g 1 is shown to vary with growth temperature, as predicted, and also with plant functional type. The model is shown to correctly capture responses of stomatal conductance to changing atmospheric CO 2 , and thus can be used to test for stomatal acclimation to elevated CO 2 . The reconciliation of the optimal and empirical approaches to modelling stomatal conductance is important for global change biology because it provides a simple theoretical framework for analyzing, and simulating, the coupling between carbon and water cycles under environmental change.

Summary1. The Standardised Major Axis Tests and Routines (SMATR) software provides tools for estimation and inference about allometric lines, currently widely used in ecology and evolution. 2. This paper describes some significant improvements to the functionality of the package, now available on R in smatr version 3. 3. New inclusions in the package include sma and ma functions that accept formula input and perform the key inference tasks; multiple comparisons; graphical methods for visualising data and checking (S)MA assumptions; robust (S)MA estimation and inference tools.Key-words: common slope testing, model II regression, principal component analysis, robust estimation, standardised major axis Biologists often wish to estimate how one variable scales against another and to test hypotheses about the nature of this relationship and how it varies across samples. The most common example of this is allometry (Reiss 1989); hence, we refer to this problem as one of estimation and testing about allometric lines. An example is given in Fig. 1a, where we wish to understand how leaf lifespan (longev) scales against leaf mass per area (lma) and how this relationship changes across sites with different rainfall (rain). longev and lma are log-transformed prior to analysis and are approximately linearly related on the transformed scale. This is common in allometry, and it means that their relationship approximately follows a power law, longev¼ alma b . The 'scaling exponent' b is the slope on log-transformed axes, and the magnitude of this parameter describes how steep the leaf lifespan-leaf mass per area relationship is. The 'proportionality coefficient' a, related to the elevation on log-log axes, is needed to understand how longlived leaves of a given mass per area will be.Estimating a and b is not a simple linear regression problem because we are not interested in predicting one variable from another -we are interested in estimating some underlying line of best fit (Warton et al., 2006 ). Another way to understand this is to see that the problem is symmetric -the basic problem does not change if we plot lma on the Y axis instead of the X axis (Smith 2009). Hence, the appropriate methods for analysis have more in common with principal component analysis, a multivariate approach, than with linear regression (Warton et al., 2006). Common approaches to estimating the line of best fit are standardised major axis (SMA) and major axis (MA) estimation, which will be collectively referred to as (S)MA, and which are widely used in ecology and evolution.Warton et al. (2006) reviewed (S)MA techniques, proposed routines for comparing the parameters a and b amongst groups and developed software to implement the methods. The Standardised Major Axis Tests and Routines (SMATR) software, available in both R (R Development Core Team 2010) and C++, has since been used in over 200 publications. We have made significant improvements to the software in the recently released version 3 of the smatr R package, and this paper briefly describe...

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Contents Summary I. Introduction II. Comparison of various definitions and measurement techniques of minimum conductance III. Cuticular conductance IV. Contribution of stomata V. Environmental and ecological variation in minimum conductance VI. Use of minimum conductance in models VII. Conclusions Acknowledgements References SUMMARY: When the rate of photosynthesis is greatly diminished, such as during severe drought, extreme temperature or low light, it seems advantageous for plants to close stomata and completely halt water loss. However, water loss continues through the cuticle and incompletely closed stomata, together constituting the leaf minimum conductance (g ). In this review, we critically evaluate the sources of variation in g , quantitatively compare various methods for its estimation, and illustrate the role of g in models of leaf gas exchange. A literature compilation of g as measured by the weight loss of detached leaves is presented, which shows much variation in this trait, which is not clearly related to species groups, climate of origin or leaf type. Much evidence points to the idea that g is highly responsive to the growing conditions of the plant, including soil water availability, temperature and air humidity - as we further demonstrate with two case studies. We pay special attention to the role of the minimum conductance in the Ball-Berry model of stomatal conductance, and caution against the usual regression-based method for its estimation. The synthesis presented here provides guidelines for the use of g in ecosystem models, and points to clear research gaps for this drought tolerance trait.