suppose that the number of species s of a certain taxa on an island can be written as an allomet

Since the area of each island is different, the number of species of birds will also be differen

Suppose that the number of species s of a certain taxa on an...

Suppose that the number of species S (of a certain taxon) on an island can be written as an allometric function of the area A of that island as S = aA^beta. A) You are studying birds among a smaller cluster of islands and the first island has an area of 15 square miles, and you count 5 species of birds. The second island has an area of 110 square miles, and you counted 9 species of birds. Find the values of alpha and beta. (Round to 3 decimal places). B) If a third island has an area of 74 square miles, estimate the number of species of birds on that island. (Round to the nearest whole number).

Transcript

00:01 Hi, from the question given that, consider a allometric function of the area a of island is defined as s is equal to alpha a to the power of beta.

00:16 Here s represents the number of species and a represents the area.

00:20 So in part a it is given that let us consider a two island.

00:23 So first island as an area 15 square miles and it has a count of five species of birds.

00:35 So s is equal to five.

00:36 Let us consider the second island.

00:38 It has an area of 110 square miles and it has a counted s is equal to nine species of birds.

00:48 So from this information we need to find the alpha and beta value.

00:52 So let us substitute all the values in the.

00:54 Aboe expression so we have been 5 is equal to alpha times of 15 to the power of beta and similarly 9 is equal to alpha times of 110 to the power of beta now equate from this find the value of alpha so alpha is equal to 5 divided by 15 to the power of beta here alpha is equal to 9 divided by and 10 to the power of beta and then equate both the alpha values so we obtain 5 divided by 15 to the power of beta which is equal to 9 divided by 110 to the power of beta so this implies and redden 10 to the power of beta by 15 to the power of beta which is equal to 9 divided by 5 so 10 divided by 15 the old power beta is equal to 9 divided by 5 so 22 by 3 the old power beta is equal to 9 divided by 5 now taking natural algorithm on both sides so we have 10 of ln of 22 by 3 is equal to ln of 9 by 5 so beta is equal to ln of 9 by 5 divided by ln of 9 by 5 divided by l n of of 22 divided by 3.

02:31 So simplify this.

02:32 The value of beta is equal to 0 .29501...

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