Suppose the Equations $\frac{d y}{d t}=2 y-x y$ And $\frac{d x}{d t}=x-x y$

question 31

Short Answer

Suppose the equations $\frac{d y}{d t}=2 y-x y$ and $\frac{d x}{d t}=x-x y$ describe the rates of growth of two interacting species, where x is the number of species A, measured in thousands, and y is the number of species B, measured in thousands.The slope field in the xy-phase plane is shown below.Consider the trajectory for the initial conditions x = 0.5, y = 1.5.(In other words, there are initially 500 of species A and 1500 of species B.)Is the population of Species B increasing or decreasing?

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Definitions:

Subpopulations

Distinct groups within a larger population that often have unique characteristics or genetic makeup.

Allele Frequencies

The relative frequencies of different alleles of a particular gene in a population, a fundamental concept in population genetics that helps explain the genetic diversity and evolutionary processes.

Oldfield Mice

A species of mouse, Peromyscus polionotus, known for its unique adaptations to sandy environments and its role in ecological and evolutionary research.

Mc1r Alleles

Variants of the melanocortin 1 receptor gene that play a significant role in determining the pigmentation of skin, hair, and eyes in organisms.