Realistic Choice of Annual Matrices Contracts the Range of λS Estimates

Abstract

In matrix population modeling the multi-year monitoring of a population structure results in a set of annual population projection matrices (PPMs), which gives rise to the stochastic growth rate λS, a quantitative measure of long-term population viability. This measure is usually found in the paradigm of population growth in a variable environment. The environment is represented by the set of PPMs, and λS ensues from a long sequence of PPMs chosen at random from the given set. because the known rules of random choice, such as the iid (independent and identically distributed) matrices, are generally artificial, the challenge is to find a more realistic rule. We achieve this with the a following a Markov chain that models, in a certain sense, the real variations in the environment. We develop a novel method to construct the ruling Markov chain from long-term weather data and to simulate, in a Monte Carlo mode, the long sequences of PPMs resulting in the estimates of λS. The stochastic nature of sequences causes the estimates to vary within some range, and we compare the range obtained by the “realistic choice” from 10 PPMs for a local population of a Red-Book species to those using the iid choice. As noted in the title of this paper, this realistic choice contracts the range of λS estimates, thus improving the estimation and confirming the Red-Book status of the species.

“Realistic Choice of Annual Matrices Contracts the Range of λS Estimates” under Reproductive Uncertainty Too

“…The citation in the title is taken from that of the former publication [1] devoted to the estimation of λ S , in which the stochastic growth rate of a population was calculated in the framework of a matrix population model (MPM, [2]).…”

“…. , (1) for the n-vector of a population structure that belongs to the positive orthant of the ndimensional Euclidean space. Matrix L(t) is non-negative and called the population projection matrix (PPM) [2,3]: "Each component of x(t) is the (absolute or relative) number of individuals in the corresponding status-specific group at time moment t, while the elements of L(t), called vital rates [2], carry information about the rates of demographic processes in the population.…”

“…Matrix L(t) is non-negative and called the population projection matrix (PPM) [2,3]: "Each component of x(t) is the (absolute or relative) number of individuals in the corresponding status-specific group at time moment t, while the elements of L(t), called vital rates [2], carry information about the rates of demographic processes in the population. They are time-dependent in general, but the zero-nonzero pattern of the PPM corresponds invariably to a single associated directed graph [4], which is called the life cycle graph [2] (LCG) as a condensed graphical representation of the biological knowledge involved into the model and the way the population structure is observed in the study" ( [1], p. 1) (see the next Section for a sample).…”

Potential-Growth Indicators Revisited: More Merits of Indication

“…However, the idea was fruitful, in this regard, when the task was to investigate the effects that uncertain parameters of the seed bank exert on the model outcome and to find the bounds of uncertainty in a case study of Androsace albana, another alpine short-lived perennial [14]. The R 1 (L) turned out linear w.r.t.…”

“…These two particular cases are however not exhaustive among PPMs, and since R 1 (L) has revealed certain "merit of indication" [2] motivated also by the current modeling practice [14], the challenge is to expand R 1 (L) to a wider class of PPMs or to propose another PGI simple enough in calculation. Aimed at responding this challenge, we present here a construction of a more general PGI by means of a general algorithm developed recently by V.N.…”