J O Nyakinda’s scientific contributions

The Lefkovitch stage specific matrix population models are divided into discrete stage classes defined by a growth variable such as size, height and diameter at breast height for trees. In matrix model, the deterministic matrix projection models are used to estimate growth rate, stable size distribution, reproductive values, and sensitivities of the growth rate to changes in vital rates. This study sampled five forest blocks (Kiptogot, Kimothon, Suam, Saboti and Kitale within Mt. Elgon forest ecosystem) and used stage base matrix models to estimate asymptotic growth rate, sensitivity and elasticity values of invasive tree population within the forest ecosystem. The result concludes that the dominant eigenvalue is more sensitive to transition probabilities from stage 2 (sapling) to stage 3 (Mature trees) stages of Cestrum aurantiacum than to transition probability of stage 1 (seedling) to stage 2 (sapling) and lower in fertility of the stage 3 (Mature trees). The results further shows that the growth parameters in the forest blocks shows that Kiptogot block had the largest elasticity values than the other blocks, indicating that the invasive tree growth survival probabilities had greatest impact on population growth.

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.