Calamagrostis model revisited: Matrix calibration as a constraint maximization problem

Abstract: A matrix model for age-stage-structured population dynamics of Calamagrostis canescens, a perennial grass species colonizing forest clear-cut areas, was calibrated before from a type of data called ‘identified individuals with unknown parents’ (Logofet, 2008) in order to estimate λ 1, the dominant eigenvalue of the projection matrix. A number of methods were applied to tackle the ‘reproductive uncertainty’ in data, and the output variety contained λ 1 both greater and less than 1 (Logofet, 2008), leaving the estimation uncertain. An ‘adaptation conjecture’ was then proposed that reduced the calibration to a nonlinear constraint maximization problem and provided for a satisfactory outcome. Two reasons have now caused revisiting. First, the maximization technique has been theoretically comprehended. In particular, an existence-uniqueness theorem has been proved that requires the maximizing solution to be reached at a vertex of the polyhedral of constrains. To facilitate searching for the solution in practice, I use the notion of potential-growth indicator and prove R 0 and R 1, the known indicators, to be certain linear functions of the uncertain fertility rates in a general class of projection matrix patterns. To solve a conjugate linear maximization problem under the same constraints as for λ 1 is both theoretically and technically simpler, and this causes a practical benefit from the indication along with calculation. Second, the former uniform (non-specific) estimate of the upper bounds for the status-specific fertility rates has now conceded to the age-stage-specific estimates inferred from a special case study. These more sophisticated constraints produce respectively more accurate calibration, hence a more reliable estimation of λ 1 as the growth potential inherent in the population in a certain environment at a given time. [Copyright &y& Elsevier]