The structure of tropical forests and sphere packings

Abstract

The search for simple principles underlying the complex architecture of ecological communities such as forests still challenges ecological theorists. We use tree diameter distributions-fundamental for deriving other forest attributes-to describe the structure of tropical forests. Here we argue that tree diameter distributions of natural tropical forests can be explained by stochastic packing of tree crowns representing a forest crown packing system: a method usually used in physics or chemistry. We demonstrate that tree diameter distributions emerge accurately from a surprisingly simple set of principles that include site-specific tree allometries, random placement of trees, competition for space, and mortality. The simple static model also successfully predicted the canopy structure, revealing that most trees in our two studied forests grow up to 30-50 m in height and that the highest packing density of about 60% is reached between the 25-and 40-m height layer. Our approach is an important step toward identifying a minimal set of processes responsible for generating the spatial structure of tropical forests.tropical forest | forest size structure | stochastic geometry | tree crown packing | leaf area F orests are one of the world's best investigated ecosystems (1-4). However, despite all of the studies devoted to forests, mechanistic connections among important features of forest physiognomy are not fully understood. Of crucial importance for this are tree diameter distributions, which have been used for decades in ecology and forestry to characterize the state of forests. Tree diameter distributions are available for many forests of the world and allow together with tree allometries prediction of other important forest attributes like leaf area (5), basal area (6), above-ground biomass (7), tree density, and the presence or absence of disturbances (8). Tropical forests usually include many small trees and far fewer large ones (1, 9). Diameter distributions can also be predicted from dynamic forest models (10-13) in which the forest structure emerges from the interplay between the dynamic processes of mortality, regeneration, competition, and growth.In this study, we argue that tree diameter distributions of natural tropical forests can be predicted by stochastic packing theory-a method usually used in physics or chemistry-together with sitespecific tree allometries. Packing systems have a long history of use across a wide range of disciplines, going back as far as Kepler's analysis of regular packing of spheres (i.e., with a maximum of 74% filled volume). Irregular stochastic packing of spheres has been analyzed in the last decades and shows lower maximal packing densities (e.g., jammed sphere packing systems in physics, with 55-64% filled volume) (14, 15). We show here that simple principles of stochastic packing theory together with tree allometries and other simple structural rules allow for an accurate prediction of observed tree diameter distributions and related structural attributes for two tropical for...

Disentangling competitive vs. climatic drivers of tropical forest mortality

“…() and Taubert et al. (), explicitly considering three‐dimensional forest structure (Farrior et al., ; Taubert et al., ). Historically, studies of self‐thinning and competition have focused on temperate biomes and within these, monospecific, even‐aged stands (e.g.…”

“…Historically, studies of self‐thinning and competition have focused on temperate biomes and within these, monospecific, even‐aged stands (e.g. Aikman & Watkinson, ; de Kroon & Kalliola, ; Hynynen, ; Kenkel, ; Lonsdale & Watkinson, ), with little work on uneven‐aged stands of multiple species typical of tropical forests (but see, for example, Kohyama, ; Vanclay, ; Taubert et al., ). Our results show that even simple empirical approaches can be useful to investigate self‐thinning and competition in structurally complex tropical forests.…”

“…One of the main autogenic drivers of tree mortality is competition (Enquist, Brown, & West, 1998;Farrior, Bohlman, Hubbell, & Pacala, 2016;Long & Smith, 1984;Reineke, 1933;Taubert, Jahn, Dobner, Wiegand, & Huth, 2015;Vanclay, 1994). As a forest stand develops, individuals compete for increasingly scarce water, nutrient and light resources; this results in decreasing stand density, while survivors increase in size-a phenomenon referred to as "self-thinning" (Mohler, Marks, & Sprugel, 1978;Yoda, Kira, Ogawa, & Hozumi, 1963).…”

“…As a forest stand develops, individuals compete for increasingly scarce water, nutrient and light resources; this results in decreasing stand density, while survivors increase in size-a phenomenon referred to as "self-thinning" (Mohler, Marks, & Sprugel, 1978;Yoda, Kira, Ogawa, & Hozumi, 1963). An extensive body of work supports the occurrence of self-thinning in boreal and temperate forest ecosystems (Mohler et al, 1978;Pretzsch, 2006;Reineke, 1933;Westoby, 1984;Yoda et al, 1963), with less of an emphasis on tropical forests (but see, for example, Poorter et al, 2016), and a variety of mathematical descriptions of the process have been developed (Enquist et al, 1998;Reineke, 1933;Taubert et al, 2015;Westoby, 1984;Yoda et al, 1963).…”

Predicting coral community recovery using multi‐species population dynamics models

“…Our study expands seminal quantitative approaches to community dynamics in coral reefs (Tanner et al 2009;Ortiz et al 2014;Riegl et al 2017) and other ecosystems (Pacala et al 1996;Purves et al 2008;Adler et al 2010) by developing an IPM framework that facilitates realistic representation of the demography of assemblages of species with contrasting life-histories and regulated by density-dependent recruitment. By yielding a method to advance quantitative understanding, prediction and diagnosis of community dynamics, our empirical-modelling approach may assist managing for resilience of diverse communities, particularly for habitat-forming species whose spatial distributions and physical structures are crucial for the health and functions of ecosystems (Pacala et al 1996;Hastings et al 2007;Nash et al 2014;Taubert et al 2015).…”