Summary: 1. Plant growth is a fundamental ecological process, integrating across scales from physiology to community dynamics and ecosystem properties. Recent improvements in plant growth modelling have allowed deeper understanding and more accurate predictions for a wide range of ecological issues, including competition among plants, plant–herbivore interactions and ecosystem functioning.2. One challenge in modelling plant growth is that, for a variety of reasons, relative growth rate (RGR) almost universally decreases with increasing size, although traditional calculations assume that RGR is constant. Nonlinear growth models are flexible enough to account for varying growth rates.3. We demonstrate a variety of nonlinear models that are appropriate for modelling plant growth and, for each, show how to calculate function‐derived growth rates, which allow unbiased comparisons among species at a common time or size. We show how to propagate uncertainty in estimated parameters to express uncertainty in growth rates. Fitting nonlinear models can be challenging, so we present extensive worked examples and practical recommendations, all implemented in R.4. The use of nonlinear models coupled with function‐derived growth rates can facilitate the testing of novel hypotheses in population and community ecology. For example, the use of such techniques has allowed better understanding of the components of RGR, the costs of rapid growth and the linkage between host and parasite growth rates. We hope this contribution will demystify nonlinear modelling and persuade more ecologists to use these techniques.

Thermal sensitivity of tropical trees: A key uncertainty in climate change models is the thermal sensitivity of tropical forests and how this value might influence carbon fluxes. Sullivan et al. measured carbon stocks and fluxes in permanent forest plots distributed globally. This synthesis of plot networks across climatic and biogeographic gradients shows that forest thermal sensitivity is dominated by high daytime temperatures. This extreme condition depresses growth rates and shortens the time that carbon resides in the ecosystem by killing trees under hot, dry conditions. The effect of temperature is worse above 32°C, and a greater magnitude of climate change thus risks greater loss of tropical forest carbon stocks. Nevertheless, forest carbon stocks are likely to remain higher under moderate climate change if they are protected from direct impacts such as clearance, logging, or fires. Science , this issue p. 869

A mosaic of protected areas, including indigenous lands, sustainable-use production forests and reserves and strictly protected forests is the cornerstone of conservation in the Amazon, with almost 50 per cent of the region now protected. However, recent research indicates that isolation from direct deforestation or degradation may not be sufficient to maintain the ecological integrity of Amazon forests over the next several decades. Large-scale changes in fire and drought regimes occurring as a result of deforestation and greenhouse gas increases may result in forest degradation, regardless of protected status. How severe or widespread these feedbacks will be is uncertain, but the arc of deforestation in south–southeastern Amazonia appears to be particularly vulnerable owing to high current deforestation rates and ecological sensitivity to climate change. Maintaining forest ecosystem integrity may require significant strengthening of forest conservation on private property, which can in part be accomplished by leveraging existing policy mechanisms.

Advances in forest carbon mapping have the potential to greatly reduce uncertainties in the global carbon budget and to facilitate effective emissions mitigation strategies such as REDD+ (Reducing Emissions from Deforestation and Forest Degradation). Though broad-scale mapping is based primarily on remote sensing data, the accuracy of resulting forest carbon stock estimates depends critically on the quality of field measurements and calibration procedures. The mismatch in spatial scales between field inventory plots and larger pixels of current and planned remote sensing products for forest biomass mapping is of particular concern, as it has the potential to introduce errors, especially if forest biomass shows strong local spatial variation. Here, we used 30 large (8–50 ha) globally distributed permanent forest plots to quantify the spatial variability in aboveground biomass density (AGBD in Mg ha^–1) at spatial scales ranging from 5 to 250 m (0.025–6.25 ha), and to evaluate the implications of this variability for calibrating remote sensing products using simulated remote sensing footprints. We found that local spatial variability in AGBD is large for standard plot sizes, averaging 46.3% for replicate 0.1 ha subplots within a single large plot, and 16.6% for 1 ha subplots. AGBD showed weak spatial autocorrelation at distances of 20–400 m, with autocorrelation higher in sites with higher topographic variability and statistically significant in half of the sites. We further show that when field calibration plots are smaller than the remote sensing pixels, the high local spatial variability in AGBD leads to a substantial "dilution" bias in calibration parameters, a bias that cannot be removed with standard statistical methods. Our results suggest that topography should be explicitly accounted for in future sampling strategies and that much care must be taken in designing calibration schemes if remote sensing of forest carbon is to achieve its promise.