A single theory explains two empirical laws applicable to plant populations

Two empirical laws, formulated independently, are known to be well satisfied in even-aged plant monocultures. One relates yield to plant density in different plant populations, and the other relates cumulative plant mass to cumulative plant number from the largest individual within a population. In this paper, we construct a mathematical model of plant growth under asymmetric competition between individuals in a population, where large individuals grow larger than small individuals because they pre-empt resources, especially light. The model categorizes influences on the growth of a plant into those from individuals larger than itself, and those from all individuals in the population. We derive the two laws from our model. Thus, individual growth, determined by asymmetric interaction between individuals in a population, can explain the two different laws relating to plant populations.