a. Explanation Given : It is given that bears will swimming upstream, and predation occurs with probability d . After swimming upstream, each fish producesb offspring before dying. The stream is then stocked with m additional newly hatched fish before all fish then swim out to sea. Concept Used: In this we have to use the concept of difference equation. We use the formula of ( the previous salmon population - the salmon that died + the new born salmon). Calculation: The current salmon population is going to equal the previous salmon population minus the salmon that died, plus the new born salmon. As the fish swim upstream, the probability that they will be killed by bears is d .So, dP t fish die and are removed from the population .At this point, ( P t − d P t ) salmon are remaining in the population. Once the fish male it upstream, the fish remaining each produce b new fish.So, b ( P t − d P t ) Are added to the population. The fish that made it upstream then die after producing offspring, so ( P t − d P t ) fish are removed from the population b. To determine Find the discrete time recursion for the population dynamics, if bears prey on fish only while the fish are swimming downstream. c. To determine Explainwhether the recursions obtained in parts (a) and (b) predicts the largest increase in population size from one year to the next. You can assume that 0 < d < 1 a n d b > 0 .

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Question

Chapter 1.6, Problem 37E

To determine

Calculate the discrete-time recursion for the population size assuming that there is no mortality.

To determine

Find the discrete time recursion for the population dynamics, if bears prey on fish only while the fish are swimming downstream.

To determine

Explainwhether the recursions obtained in parts (a) and (b) predicts the largest increase in population size from one year to the next. You can assume that 0<d<1 and b>0 .

Expert Solution & Answer

Chapter 1 Solutions

Biocalculus

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Consumer Preference In a population of 100,000 consumers, there are 20,000 users of Brand A, 30,000 users of Brand B, and 50,000 who use neither brand. During any month, a Brand A user has a 20 probability of switching to Brand B and a 5 of not using either brand. A Brand B user has a 15 probability of switching to Brand A and a 10 probability of not using either brand. A nonuser has a 10 probability of purchasing Brand A and a 15 probability of purchasing Brand B. How many people will be in each group a in 1 month, b in 2 months, and c in 18 months?
Smokers and Non smokers In a population of 10,000, there are 5000 non-smokers, 2500 smokers of one pack or less per day. During any month, there is a 5 probability that a nonsmoker will begin smoking a pack or less per day, and a 2 probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10 probability of quitting and a 10 probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 5 probability of quitting and a 10 probability of dropping to a pack or less per day. How many people will be in each group a in 1 month, b in 2 months, and c in 1 year?
In Example 10, researchers selected five people at random from the population. What is the probability that all five people expected much of the workforce to be automated within 50 years?

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