Self-thinning in overcrowded pure stands under cultivated and natural conditions (Intraspecific competition among higher plants XI). By Kyoji Yoda, Tatuo Kira, Husato Ogawa, Kazuo Hozumi, published in the Journal of Biology, Osaka City University (1963 14:107-129).
A longstanding goal in ecology has been to discover the mechanistic processes that underlie pervasive macroecological patterns [1, 2]. The process of Macroecology is synthetic and one of its central goals is to seek rules that underlie ‘emergent’ higher level patterns . Perhaps one of the early, and arguably successful, attempts to do so is by Yoda, Kira, Ogawa, and Hozumi in a paper they published in 1963 in an obscure Japanese ecological journal. Their paper has had, and will undoubtedly continue to have, far reaching implications in biology.
What I find so fascinating about this paper is that their approach is uniquely macroecological  and was so ahead of its time, especially within botany and plant ecology. Building on the insights of earlier work , the authors compiled several datasets in an attempt to find general statistical patterns. They then proposed a general theoretical model based on first principles for idealized plants to describe the pattern and compared the theory with experimental and synthetic data. Yoda et al. also elevated the concept of a ‘constraint’ on limiting variation and apply scaling principles to describe the dynamics of biology at this constraint– topics that continue to drive macroecology. Their theory is physics-like in approach  as it endeavors to ‘explain a lot with a little’ by mechanistically linking characteristics of idealized individuals with larger scale ecological, evolutionary, and ecosystem levels .
Simply put, the self-thinning rule describes plant mortality due to competition in crowded even-
aged (sized) stands – a topic long of interest in plant population biology, agronomy, and plant ecology . Thinning is mortality imposed on agricultural plants whereas self-thinning is the label applied to mortality from density-dependent processes – intraspecific competition . Yoda et al. assessed the generality of thinning on plant populations by documented the relationship of how the average size of a plant in a population is related to population density. They did this intraspecifically for several different species and identified that under ‘crowded’ conditions, where plants compete for resources, there emerged a general form of the size distribution.
The impact of the paper was initially slow, likely due to the journal where it was published, but with the ‘discovery’ of the work in the mid 70’s by western ecologists, its influence widened significantly. In a subtle nod to the unique synthetic and interdisciplinary nature of the work by Yoda et al. can be found in the footnote of the first page. The authors acknowledge that the “outlines” of this paper were presented at both the annual meetings of the Botanical and Ecological Society meetings of Japan. In the rest of the paper, Yoda et al. present a novel theory as well as experimental and compiled data
Yoda et al.’s argue three basic points : (i) There is an upper limit or constraint on the total amount of biomass that can be supported given a certain number of plants; (ii) That under this constraint, population mortality is driven by the growth rate of individual plants; (iii) The inverse relationship between size and density is general and originates in an equally general rule of how plant morphology scales or changes with plant size.
The academic core of the paper is the theoretical explanation for the origin of point (i). Yoda et al.
propose a general rule for the morphological scaling of how individual plants fill space. The mass of a plant, M, is proportional to its length, l , raised to the third power (M µ l3) and the area of ground over which a plant occupies, A, is proportional to a length measure squared, so that A µ l2. Under a steady state condition, where plants are tightly packed and assuming a self-similarity in plant morphological dimensions, the density of plants must be inversely proportional to the average area of ground occupied by a plant so that N µ A-1. Via substitution, the average size of a plant must be inversely related to the population density to the -3/2 power so that M µ N-3/2. Yoda et al. named the relationship “the 3/2th power law of self-thinning”. While bold in the generality of the argument, perhaps with an eye toward, future criticisms from a biological mindset too quick to point out exceptions rather than seek generality and appreciate the role of theory  they state that “The above conditions and assumptions may never be fulfilled in the strict sense but the universal applicability of the 3/2th power law indicates that the model could be accepted as a crude approximation.”
The significance of Yoda et al. (1963) is that the self-thinning rule provided a theoretical and empirical foundation to link organismal processes with population biology, evolutionary biology, community ecology, and even ecosystem ecology . In 1981 the ‘thinning rule’ was extended interspecifically  and seemed to provide the most convincing evidence that competition between individuals can have an important outcome on the structure of the entire population or community [7, 8]. The ‘thinning law’ makes clear linkages between several levels of biological organization. Showing how selection on plant traits and ‘emergent’ properties in ecosystems (biomass, stand productivity, turnover rates) communities (abundance) and populations could be mechanistically linked to morphological scaling and growth rates of individual plants. There was also clear way to link feedback from the environment via growth rate – low resource supply areas should then slow growth rates of plants which in turn should slow turnover and biomass accumulation rates.
After ~50 years Yoda et al.’s points (i) and (ii) appear largely accepted. However, our understanding of point (iii) now appears to have changed. First, their proposed model explicitly requires that plant morphology scales with mass according to Euclidean exponents so that A ~ M2/3. However, many aspects of plant form and function do not scale with mass according to geometric exponents but rather ‘quarter-power’ exponents . Second, larger datasets indicate that the thinning boundary is likely not -3/2 but instead closer to -4/3 [12-14] indicating that N ~ M-3/4. Third, Yoda et al. treat plant mass as the dependent variable. However, if growth rate and scaling of plant dimensions are more closely associated with how plants use resources as a function of their size and fill space with leaf area , then self-thinning should be driven by size-dependent processes and not by density per se. As a result, based on the above findings, the inverse relationship between size and density and a reworking of the theoretical basis [13, 14] appears to instead be functionally equivalent to the relationship between size and density that has been argued to hold in animals where N ~ M-3/4 [16-18]. Thus, plants and animals can be seen to share a common rule with a common explanation in terms of how organisms use and compete for resources as a function of their body size [13, 16-18].
The above new findings only refine the original theoretical argument for point (iii) and only underscore the importance of Yoda et al.’s approach and contribution. Remarkably, Yoda et al. appear to have anticipated these points by stating that their work “reveals . . . fundamental properties” of the process of self-thinning. And that the work will “add important knowledges for threoretical as well as applied . . .plant ecology.” In hindsight these statements are indeed correct. Yoda et al.’s paper is still a must read for any student interested in plant ecology let alone for macroecologists.
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