Assume that $x ( t )$ and $y ( t )$ represent the populations of two competing species at time $t$ . The Lotka-Volterra competition model is
A) $\frac { d x } { d t } = r _ { 1 } x \left( K _ { 1 } + x - a _ { 12 } y \right) / K _ { 1 } , \frac { d y } { d t } = r _ { 2 } y \left( K _ { 2 } - y - a _ { 21 } y \right) / K _ { 2 }$
B) $\frac { d x } { d t } = r _ { 1 } x \left( K _ { 1 } - x + a _ { 12 } y \right) / K _ { 1 } , \frac { d y } { d t } = r _ { 2 } y \left( K _ { 2 } - y - a _ { 21 } y \right) / K _ { 2 }$
C) $\frac { d x } { d t } = r _ { 1 } x \left( K _ { 1 } - x - a _ { 12 } y \right) / K _ { 1 } , \frac { d y } { d t } = r _ { 2 } y \left( K _ { 2 } - y - a _ { 21 } y \right) / K _ { 2 }$
D) $\frac { d x } { d t } = r _ { 1 } x \left( K _ { 1 } - x - a _ { 12 } y \right) / K _ { 1 } , \frac { d y } { d t } = r _ { 2 } y \left( K _ { 2 } + y - a _ { 21 } y \right) / K _ { 2 }$
E) $\frac { d x } { d t } = r _ { 1 } x \left( K _ { 1 } - x - a _ { 12 } y \right) / K _ { 1 } , \frac { d y } { d t } = r _ { 2 } y \left( K _ { 2 } - y + a _ { 21 } y \right) / K _ { 2 }$

Question

Quizplus · Accepted Answer

The correct Lotka-Volterra competition model equations are given by $\frac { d x } { d t } = r _ { 1 } x \left( K _ { 1 } - x - a _ { 12 } y \right) / K _ { 1 }$ and $\frac { d y } { d t } = r _ { 2 } y \left( K _ { 2 } - y - a _ { 21 } y \right) / K _ { 2 }$, which accurately describe the population dynamics of two species competing for resources, where $r_1$ and $r_2$ are the intrinsic growth rates, $K_1$ and $K_2$ are the carrying capacities, and $a_{12}$ and $a_{21}$ are the competition coefficients.

Assume That x(t)x ( t )x(t) And y(t)y ( t )y(t) Represent the Populations of Two Competing Species at Time

Assume That $x ( t )$ And $y ( t )$ Represent the Populations of Two Competing Species at Time