Problem 1. An ecological study focuses on the conservation of sea turtles in the eastern coast of India. There are two different populations of Olive Ridley turtles in the study: Gahiramatha population (Pop. A) and Chilika population (Pop. B). These turtles lay their eggs on the beach. After hatching, the baby turtles leave the beach and swim into the sea. These hatchlings are attacked by three different predators (say Q. W and R). The hatching rates (measured in number of hatchlings per minute) at different times of the day are: Morning: 0.25 (A), 0.5 (B); Afternoon: 0.25 (A), 0.1 (B); Evening: 0.25 (A), 0.25 (B); Night: 0.25 (A), 0.15 (B); The hunting rate per hatchling due to presence of different predator is given below in different times of the day: Morning: 0.3 (Q), 0 (W), 0.7 (R); Afternoon: 0.6 (Q), 0.1 (W), 0.3 (R); Evening: 0.1 (Q), 0.7 (W), 0.2 (R); Night: 0.1 (Q), 0.9 (W), 0 (R) Use matrices to calculate the following: (a) A matrix describing the total predation rate of each predator on each turtle population. Hint: You will be able to compute this as a matrix multiplication. When creating your matrices, pay attention to whether you want to use rows or columns for the different times of the day. (b) The total predation rate on each turtle population. For the sake of conservation, the scientists are using floating buoys to reduce preda- tion. The efficacy (in reducing hunting by any predator) of the buoys at different times of the day are Morning: 0.5; Afternoon 0.9; Evening: 0.3; Night: 0.1 (c) Create a new matrix describing the hunting rates for each predator for each time of the day when the buoys are used. More precisely, replace each hunting rate in the morning by 0.5 times that hunting rate, replace each hunting rate in the afternoon by 0.9 times that hunting rate, etc. (d) Compute a matrix describing the total predation rate of each predator on each turtle population if the buoys are used. (e) Compute the total predation rate on each turtle population if the buoys are used.

Problem 1. An ecological study focuses on the conservation of sea turtles in the eastern coast of India. There are two different populations of Olive Ridley turtles in the study: Gahiramatha population (Pop. A) and Chilika population (Pop. B). These turtles lay their eggs on the beach. After hatching, the baby turtles leave the beach and swim into the sea. These hatchlings are attacked by three different predators (say Q. W and R). The hatching rates (measured in number of hatchlings per minute) at different times of the day are: Morning: 0.25 (A), 0.5 (B); Afternoon: 0.25 (A), 0.1 (B); Evening: 0.25 (A), 0.25 (B); Night: 0.25 (A), 0.15 (B); The hunting rate per hatchling due to presence of different predator is given below in different times of the day: Morning: 0.3 (Q), 0 (W), 0.7 (R); Afternoon: 0.6 (Q), 0.1 (W), 0.3 (R); Evening: 0.1 (Q), 0.7 (W), 0.2 (R); Night: 0.1 (Q), 0.9 (W), 0 (R) Use matrices to calculate the following: (a) A matrix describing the total predation rate of each predator on each turtle population. Hint: You will be able to compute this as a matrix multiplication. When creating your matrices, pay attention to whether you want to use rows or columns for the different times of the day. (b) The total predation rate on each turtle population. For the sake of conservation, the scientists are using floating buoys to reduce preda- tion. The efficacy (in reducing hunting by any predator) of the buoys at different times of the day are Morning: 0.5; Afternoon 0.9; Evening: 0.3; Night: 0.1 (c) Create a new matrix describing the hunting rates for each predator for each time of the day when the buoys are used. More precisely, replace each hunting rate in the morning by 0.5 times that hunting rate, replace each hunting rate in the afternoon by 0.9 times that hunting rate, etc. (d) Compute a matrix describing the total predation rate of each predator on each turtle population if the buoys are used. (e) Compute the total predation rate on each turtle population if the buoys are used.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter10: Matrices

Section10.EA: Extended Application Contagion

Problem 2EA

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