An analysis of elasticity vector distribution specific to semelparous species using randomly generated population projection matrices and the COMPADRE Plant Matrix Database

The elasticity of population growth rate λ is a notable statistic in population projection matrix models and has been used by many empirical researchers. Silvertown and his collaborators published a paper in 1996 in which they mapped elasticity vectors of stasis, growth and fecundity for 84 plant species in a ternary plot and reported that the elasticity vector distribution of semelparous species (10 species) was located in the upper-left region of the ternary plot. To understand and clarify why the elasticity vectors of semelparous species were distributed in the upper-left region, we conducted three analyses. First, we used 68 matrices of semelparous species populations in the COMPADRE Plant Matrix Database and plotted their elasticity vectors in the ternary plot. Second, we constructed randomly generated population projection matrices for three archetypes, where several biological assumptions were made, and obtained their elasticity vector distributions. We showed that the high fecundity and/or immediate death after reproduction shifted the elasticity vector distribution to the upper-left region of the plot. Third, we examined the evolutionary change in the distribution using a population projection matrix model in which the trade-off between fecundity and adult survival was incorporated. The evolutionary trajectory derived from the trade-off model showed that the evolutionary consequence of semelparity was located in the upper-left more than was that of iteroparity in the ternary plot. Synthesizing the results derived from the three analyses, we concluded that the distinctive distribution of the elasticity vectors of semelparous species is the outcome of natural selection under the trade-off with low convexity, and the outcome of the resultant big-bang reproduction and immediate death after reproduction.