Understanding height-structured competition in forests: Is there an R* for liaht?

Tree species differ from one another in, and display trade-offs among, a wide range of attributes, including canopy and understorey growth and mortality rates, fecundity, height and crown allometry, and crown transmissivity. But how does this variation affect the outcome of interspecific competition and hence community structure? We derive criteria for the outcome of competition among tree species competing for light, given their allometric and life-history parameters. These criteria are defined in terms of a new simple whole life-cycle measure of performance, which provides a simple way to organize and understand the many ways in which species differ. The general case, in which all parameters can differ between species, can produce coexistence, founder control or competitive exclusion: thus, competition for light need not be hierarchical as implied by R* theory. The special case in which species differ only in crown transmissivity produces neutral dynamics. The special case in which species differ in all parameters except crown transmissivity gives hierarchical competition, where the equivalent of R* is Ẑ*, the height at which trees enter the canopy in an equilibrium monoculture.