Many ecological applications, like the study of mortality rates, require the estimation of proportions and confidence intervals for them. The traditional way of doing this applies the binomial distribution, which describes the outcome of a series of Bernoulli trials. This distribution assumes that observations are independent and the probability of success is the same for all the individual observations. Both assumptions are obviously false in many cases.I show how to apply bootstrap and the Poisson binomial distribution (a generalization of the binomial distribution) to the estimation of proportions. Any information at the individual level would result in better (narrower) confidence intervals around the estimation of proportions. As a case study, I applied this method to the calculation of mortality rates in a forest plot of tropical trees in Lambir Hills National Park, Malaysia.I calculated central estimates and 95% confidence intervals for species-level mortality rates for 1,007 tree species. I used a very simple model of spatial dependence in survival to estimate individual-level risk of mortality. The results obtained by accounting for heterogeneity in individual-level risk of mortality were comparable to those obtained with the binomial distribution in terms of central estimates, but the precision increased in virtually all cases, with an average reduction in the width of the confidence interval of ~20%.Spatial information allows the estimation of individual-level probabilities of survival, and this increases the precision in the estimates of mortality rates. The general method described here, with modifications, could be applied to reduce uncertainty in the estimation of proportions related to any spatially structured phenomenon with two possible outcomes. More sophisticated approaches can yield better estimates of individual-level mortality and thus narrower confidence intervals.
What causes individual tree death in tropical forests remains a major gap in our understanding of the biology of tropical trees and leads to significant uncertainty in predicting global carbon cycle dynamics. We measured individual characteristics (diameter at breast height, wood density, growth rate, crown illumination and crown form) and environmental conditions (soil fertility and habitat suitability) for 26 425 trees ≥ 10 cm diameter at breast height belonging to 416 species in a 52-ha plot in Lambir Hills National Park, Malaysia. We used structural equation models to investigate the relationships among the different factors and tree mortality. Crown form (a proxy for mechanical damage and other stresses) and prior growth were the two most important factors related to mortality. The effect of all variables on mortality (except habitat suitability) was substantially greater than expected by chance. Tree death is the result of interactions between factors, including direct and indirect effects. Crown form/damage and prior growth mediated most of the effect of tree size, wood density, fertility and habitat suitability on mortality. Large-scale assessment of crown form or status may result in improved prediction of individual tree death at the landscape scale.
The relative importance of tree mortality risk factors remains unknown, especially in diverse tropical forests where species may vary widely in their responses to particular conditions. We present a new framework for quantifying the importance of mortality risk factors and apply it to compare 19 risks on 31 203 trees (1977 species) in 14 one-year periods in six tropical forests. We defined a condition as a risk factor for a species if it was associated with at least a doubling of mortality rate in univariate analyses. For each risk, we estimated prevalence (frequency), lethality (difference in mortality between trees with and without the risk) and impact ('excess mortality' associated with the risk, relative to stand-level mortality). The most impactful risk factors were light limitation and crown/trunk loss; the most prevalent were light limitation and small size; the most lethal were leaf damage and wounds. Modes of death (standing, broken and uprooted) had limited links with previous conditions and mortality risk factors. We provide the first ranking of importance of tree-level mortality risk factors in tropical forests. Future research should focus on the links between these risks, their climatic drivers and the physiological processes to enable mechanistic predictions of future tree mortality.
Accurate estimates of forest biomass stocks and fluxes are needed to quantify global carbon budgets and assess the response of forests to climate change. However, most forest inventories consider tree mortality as the only aboveground biomass (AGB) loss without accounting for losses via damage to living trees: branchfall, trunk breakage, and wood decay. Here, we use ~151,000 annual records of tree survival and structural completeness to compare AGB loss via damage to living trees to total AGB loss (mortality + damage) in seven tropical forests widely distributed across environmental conditions. We find that 42% (3.62 Mg ha-1 year-1 ; 95% confidence interval [CI] 2.36-5.25) of total AGB loss (8.72 Mg ha-1 year-1 ; CI 5.57-12.86) is due to damage to living trees. Total AGB loss was highly variable among forests, but these differences were mainly caused by site variability in damage-related AGB losses rather than by mortality-related AGB losses. We show that conventional forest inventories overestimate stand-level AGB stocks by 4% (1%-17% range across forests) because assume structurally complete trees, underestimate total AGB loss by 29% (6%-57% range across forests) due to overlooked damage-related AGB losses, and overestimate AGB loss via mortality by 22% (7%-80% range across forests) because of the assumption that trees are undamaged before dying. Our results indicate that forest carbon fluxes are higher than previously thought. Damage on living trees is an underappreciated component of the forest carbon cycle that is likely to become even more important as the frequency and severity of forest disturbances increase.