Extensions of Lefkovitch matrix for modeling invasive Cestrum aurantiacum population Dynamics

Abstract

Modeling of invasive species using stage based matrix methods can be exploited to understand population dynamics of plants using stage based Leftkovitch matrix models. This study reviewed and extended the stage based matrix incorporating invasion variables of invasive Cestrum aurantiacum across different forest types, ecological zones and altitudes.  The estimation of eigenvalues of the extended stage based Lefkovitch matrix and its corresponding right and left eigenvectors representing stage structure and reproductive value respectively were determined. The results shows the growth rates for Kiptogot λ =4.84 and Kimothon λ =3.21, Suam λ=2.89, Kitale λ =3.91 and Saboti λ=3.58. The  stable  stage  distribution of  individuals  species  in each  of  the  three life  stages  for  Kimothon  forest  block is  84.6% for seedling, 12.9% sapling and 2.5% mature trees while Kiptogot was 88.9% seedling, 9.7% sapling, 1.3% mature trees. Suam block was 82.8% for seedling, 16% sapling, 1.2% mature trees. This study provides various extensions of stage based matrix for estimation and projection of the invasive tree population and information for managing invasive trees species within the forests ecosystems.

Keywords: Lefkovitch matrix, growth rate, Stable stage distribution, extension of stage based matrix.