The law of constant final yield

Background/Question/Methods The law of constant final yield is an empirical generalization concerning the total biomass production of stands growing at different densities after a given period of growth. Total standing biomass initially increases proportionally with density, levels off and then remains constant at ever-higher densities. It is arguably one of the few well-established laws in plant ecology and its generality is surprising. We review the empirical basis for the law, mathematical formulations of it, and we clarify the relationship of the law to density- dependent mortality (“self-thinning”). Results/Conclusions At very high densities, constant final yield depends upon density-dependent mortality, but constant final yield is usually achieved at densities lower than those resulting in extensive self-thinning. Therefore a population undergoing self-thinning is at constant final yield. We describe four possible, non-exclusive mechanisms to explain the law: (1) modularity of plant growth form, (2) allometric growth and plasticity, (3) size-asymmetric competition among individuals and (4) density as a limiting factor in the conversion of resources into biomass. Only well-designed experiments can distinguish among these. From an evolutionary perspective, constant final yield occurs because competition for resources is an important determinant of plant fitness, so natural selection will usually result in the utilization of all available resources when density is sufficient to do so. Exceptions to the law may occur when non-resource-mediated mechanisms of "interference competition", such as allelopathy, dominate plant-plant interactions. While total biomass shows constant final yield, many biomass components do not: biomass allocation responds to density when total biomass doesn't. Reproductive allocation, for example, often decreases at high densities. Finally we argue that constant final yield is a key to understanding population- and community-level phenomena. Many plant communities in nature are at or near constant final yield, and the behavior of such communities may be much more predictable than behavior at lower densities. Establishing whether or not a plant community is at or close to constant final yield is important for understanding and predicting its behavior. Constant final yield represents the maximum biomass for a genotype in an environment after a period of growth and, as such, can serve as a base line for the measurement of disturbance in plant communities.