A Reevaluation of the ‐3/2 Power Rule of Plant Self‐Thinning

Abstract

Abstract. The self-thinning rule predicts that for a crowded even-aged plant population a log-log plot of average plant mass vs. plant density will reveal a straight "self-thinning" line of slope -%. The rule is supported by examples from many individual populations, and by the existence of an interspecific relationship that yields a line of slope -% in a loglog plot displaying average mass and density data from many populations of different species. I examined and reanalyzed the evidence to evaluate the strength of support for this widely accepted rule.Some problems in fitting thinning lines and testing agreement with the rule have no truly satisfactory solution, but three improvements on commonly used methods were made: the analysis related stand biomass density to plant density because the alternative of relating average plant mass to plant density is statistically invalid; principal components analysis was used rather than regression, because regression relies on unrealistic assumptions about errors in the data; and statistical tests of hypotheses were used to interpret the results.The results of this reanalysis were that 19 of 63 individual-population data sets previously cited in support of the thinning rule actually showed no significant correlation between stand biomass density and plant density, and 20 gave thinning slopes significantly different ( P < .05) from the thinning rule prediction. Four other analyses provided additional evidence against a single quantitative thinning rule for all plants: slopes of the thinning lines were more variable than currently accepted, differed significantly among plant groups, were significantly correlated with shade tolerance in forest trees, and differed among stands of the same species. The same results held for the intercepts of self-thinning lines.Despite the failure of the thinning rule for individual populations, the combined data for all populations are still consistent with an interspecific relationship of slope -3/,; therefore, the existence of the interspecific relationship does not necessarily support the withinpopulation thinning rule. The within-population and interspecific relationships are apparently different phenomena that may arise from different constraints, so the two relationships should be tested and explained separately. power law.The self-thinning rule (also called the -% power rule or Yoda's law) describes a relationship between size and density in even-aged plant populations that are crowded but actively growing. If competition from other populations and crowding-independent stresses (drought, fire, disease, etc.) are absent, mortality or "thinning" is caused by competition within the population, hence the term "self-thinning." Yoda et al. Two lines of evidence support this relationship as an ecological "rule" or "law" governing even-aged plant populations. First, the slopes of many reported thinning lines are near y = -%, including data from monospecific populations ranging in size from small herbs to large trees , White and Harper 1970, Wh...

Un modèle générique des effets de l’éclaircie et de la densité des peuplements sur la croissance des forêts, la mortalité et l’accroissement net

“…For α a slightly higher value of -1.75 was chosen because this value is more in line with selfthinning studies that are based on much larger data sets than ours, e.g. (Weller, 1987). The results (Fig.…”

“…Although the existence of a universal α (slope of the self-thinning line) has been suggested based on empirical evidence (Reineke, 1933), theory for local competition and probability theory (Dewar and Porte, 2008), empirical studies have shown substantial variability in α, e.g. among species (Weller, 1987). In our analysis we allow α to vary among species.…”

Insights into plant size-density relationships from models and agricultural crops

“…These results offer a different perspective from many studies that have emphasized how competitive and successional processes vary across plant taxa, life forms, and environmental conditions (21,22,(24)(25)(26)(27)(28)(29)(30)(39)(40)(41)(42). They suggest to us that scaling exponents, when measured across orders of magnitude variation in plant size, are relatively independent of phylogenetic affiliation, growth habit, and abiotic environmental features.…”

“…For decades, plant scientists have debated the empirical form of the thinning line and the mechanisms that give rise to it (18,(21)(22)(23)(24)(25)(26)(27). Much of the debate has revolved around the value of the exponent, α.…”

Perspectives and Methods of Scaling

“…While this biomass-density relation has been held as a "law" for decades, recent studies have found little empirical evidence to support its universality and consistency (Weller 1987, Zeide 1987, Lonsdale 1990). In particular, the scaling exponent is not a constant, but rather a variable that is influenced by the shade tolerance of plants under study and taxonomic groups of choice.…”