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.
Highlights
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 population projection matrices (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
Each component of x(t) is the number of individuals in the corresponding status-specific group at moment t, while the elements of L(t), called vital rates [1], carry information about the rates of demographic processes in the population. They are time-dependent in general, but the zero-nonzero pattern of the population projection matrix (PPM) corresponds invariably to a single associated directed graph [3], which is called the life cycle graph [1] (LCG), as a condensed graphical representation of the biological knowledge involved in the model and the way the population structure is observed in the study
Summary
Each component of x(t) is the (absolute or relative) number of individuals in the corresponding status-specific group at moment t, while the elements of L(t), called vital rates [1], carry information about the rates of demographic processes in the population They are time-dependent in general, but the zero-nonzero pattern of the population projection matrix (PPM) corresponds invariably to a single associated directed graph [3], which is called the life cycle graph [1] (LCG), as a condensed graphical representation of the biological knowledge involved in the model and the way the population structure is observed in the study (an example is given ).
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