| Contents |
|
A process of habitat fragmentation of a population is modeled by a (non-autonomous) differential system that quantifies the abundance at each instant in patches forming. This postulated model is derived from assumptions of disturbance on demographic rates. In addition, some of its dynamic consequences are analyzed.
Given a final state ($ t = 1 $) when the habitat of a population is completely divided into fragments $A$ and $B$, from an initial ($ t = 0 $) fully pipelined, we can deduce:
$ $
\left\{
\begin{array}{rcl}
\dot {x}_{A}(t) & = & r x_{A}(t) \left\{1 - \ frac {x_{A} (t) + \eta (t) x_ {B}(t)} {K_ {A} + \ eta (t) K_{B}} \right \} x_{A}(t) \ \
\dot {x}_{B} (t) & = & r x_{B} (t) \left\{1 - \ frac {\eta (t) x_{A}(t) + x_{B}(t)} {\eta (t) K_{A} + K_{B}} \right \} x_{B} (t),
\ end {array}
\right.
$$
where $ x_{A} (t) $ and $ x_{B} (t) $ represent the abundances of subpopulations in training, and $ \ eta [0,1] \ to [0,1] $ is a decreasing function indicating a ``degree " of environmental resistance from the patch $ B $ to $ A $ subpopulation, and vice versa. Notice how this system connects as process, not fragmentation ($ \eta (0) = 1 $) with for a completely decoupled system ($ \eta(1) = 0 $). |
|