Studies on the population dynamics (changes in population size over time) of tropical tree species are being conducted intensively 1–8. The most common methods to study population dynamics is a population transition matrix approach (Cowell 2001). For this reason, this standard approach was used in this study.

These studies are often conducted empirically using forest inventory data obtained from tree censuses, and their census intervals are usually supra-annual (5 years in many cases) 1–3,5. In many studies, an annual census is not feasible because a census takes longer than 1 year and/or is expensive in terms of money and labor.

Some sophisticated methods have been proposed to estimate annual survival and/or recruitment rates from the forest monitoring data when census intervals are supra-annual 9–12. However, these studies have highlighted that conventional forest monitoring with supra-annual census intervals may result in serious and fundamental problems that cannot be overcome by those techniques, as shown below.

Supra-annual census intervals may lead to an unavoidable misinterpretation of tree population dynamics because of the characteristics of tropical rain forest ecosystems and climates. First, in relation to tree population dynamics, Silvertown, et al. 13 constructed population transition matrices for 66 perennial plant species with different life history characteristics. They compared the effects of growth, reproduction, and survival on population growth rates (lambda) among the species examined. They used elasticity analysis for their evaluation 13, a technique that can quantify the influence of matrix elements on lambda (de Kroon et al. 198614). Because the sum of all elasticities over the matrix elements is equal to 1.0 15, the relative influence of each of the matrix elements on lambda can be directly evaluated 16–18. Silvertown, et al. 13 grouped matrix elements into growth, fecundity, and survival and showed that lambda was almost exclusively affected by survival for trees 13. The same population dynamics have been repeatedly observed for many tropical tree species 2,19. This suggests that a change of just a few percent in the survival rate can have a substantial effect on lambda, resulting in a correspondingly large shrinkage or expansion in the tree population.

Second, the characteristics of tropical climates have a substantial effect on rain forest tree dynamics. A tropical rain forest climate is understood to be stable, hot, and humid throughout the year, but there is a substantial level of annual variability 20–26. For example, tropical rain forests in Southeast Asia experience severe droughts every few years, causing a substantial decline in the survival rate of trees 27–33. Consequently, occasional drought years have an important influence on the community structures and tree distribution patterns of tropical rain forests 20,34,35.

The combination of these two aspects can lead to important problems in modeling tree population dynamics. For example, if the survival rate drops by a few percent in a drought year, that decrease can have a significant effect on lambda. However, if the forest census interval is longer than 1 year (for example, 5-yearly), there may only be 1 severe drought year in census period while the remaining 4 years will reflect an average survival rate (Fig. S1). Naturally, the 5-year census interval will rarefy the substantial decline in survival rate in the one drought year by five times (5 years). However, the effect of this rarefaction does not equate to the simple averaging of observed population dynamics over 5 years that include a drought year. The impact of the survival rate on lambda is so great that the value may be changed by several tenths instead of a fifth. As a result, we may substantially underestimate the impact of drought (as a decrease in the survival rate) on the lambda of tropical tree species.

To summarize, there are important drawbacks to conventional forest monitoring with supra-annual census intervals. If the effect of drought-induced-mortality on lambda is reduced by several tenths by the rarefaction of the mortality rate because of the census interval, the impacts of drought on population dynamics may be hard to identify. Subsequently, this may lead to the erroneous conclusion that droughts have little effect on tropical tree species dynamics. However, a significant reduction in tree population size in a drought year has been observed.

As discussed above, supra-annual census intervals likely distort our understanding of the true population dynamics of trees. However, the level of strength of this effect remains unknown. Therefore, the current study had the following two aims:

(1) to quantitatively evaluate the size of the rarefaction effect of survival rate from census intervals on lambda; and

(2) to propose a forest observation method that was feasible and did not cause population dynamics to be misinterpreted.

To achieve the first aim, we used the observed survival rates in an average year (non-drought year) and a drought year in the Lambir Hills National Park, Sarawak, Malaysia. By combining the survival rates in the non-drought year with those in the drought year, datasets were simulated with different census intervals, including a drought year. With these datasets, several population transition matrices were created to simulate population dynamics with different census intervals, including a drought year. Using this approach, we quantitatively assessed the effect of rarefaction of the survival rate by supra-annual census intervals.