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c. Suppose a large population of turtles consists only of two species, snapping turtle and box turtle, but the percentage of the species in the population are unknown. What is the maximum possible value of the diversity index D for the population

Sagot :

Okpalawalter8idn

Answer:

[tex]D_m=1/2[/tex]      

Explanation:

From the question we are told that

2 species

Assuming that questions a and be are solved

Diversity index D=2p_1p_2

with [tex]p_1 +p_2 =1[/tex]

Mathematically

[tex]D=2p_1(1-p_1)[/tex]

[tex]D=2(p_1-p_1^2)[/tex]

[tex]D=2({\frac{1}{4} -(p_1-1/2)^2}[/tex]

Therefore

[tex]D=\frac{1}{2} -2(p_1-1/2)^2[/tex]

Giving

[tex]D_m=1/2[/tex]      

[tex]p_1=1/2[/tex]

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