Pacific salmon populations have discrete breeding cycles in which they return from the ocean to streams to reproduce and then die. This occurs every one to five years, depending on the species. (a) Suppose that each fish must first survive predation by bears while swimming upstream, and predation occurs with probability d. After swimming upstream, each fish produces b offspring before dying. The stream is then stocked with m additional newly hatched fish before all fish then swim out to sea. What is the discrete-time recursion for the population dynamics, assuming that there is no mortality while at sea? You should count the population immediately before the upstream journey. nt + 1 = (b) Suppose that, instead of preying on fish while they swim upstream, bears do so only while the fish are swimming downstream. What is the discrete-time recursion for the population dynamics? (Again assume there is no mortality while at sea.) nt+1 = (c) Which of the recursions obtained in parts (a) and (b) predicts the largest increase in population size from one year to the next? O recursion formula from part (a) O recursion formula from part (b)
Pacific salmon populations have discrete breeding cycles in which they return from the ocean to streams to reproduce and then die. This occurs every one to five years, depending on the species. (a) Suppose that each fish must first survive predation by bears while swimming upstream, and predation occurs with probability d. After swimming upstream, each fish produces b offspring before dying. The stream is then stocked with m additional newly hatched fish before all fish then swim out to sea. What is the discrete-time recursion for the population dynamics, assuming that there is no mortality while at sea? You should count the population immediately before the upstream journey. nt + 1 = (b) Suppose that, instead of preying on fish while they swim upstream, bears do so only while the fish are swimming downstream. What is the discrete-time recursion for the population dynamics? (Again assume there is no mortality while at sea.) nt+1 = (c) Which of the recursions obtained in parts (a) and (b) predicts the largest increase in population size from one year to the next? O recursion formula from part (a) O recursion formula from part (b)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Pacific salmon populations have discrete breeding cycles in which they return from the ocean to streams to reproduce and then die. This
occurs every one to five years, depending on the species.
(a) Suppose that each fish must first survive predation by bears while swimming upstream, and predation occurs with probability
d. After swimming upstream, each fish produces b offspring before dying. The stream is then stocked with m additional newly
hatched fish before all fish then swim out to sea. What is the discrete-time recursion for the population dynamics, assuming that
there is no mortality while at sea? You should count the population immediately before the upstream journey.
nt + 1 =
(b) Suppose that, instead of preying on fish while they swim upstream, bears do so only while the fish are swimming downstream.
What is the discrete-time recursion for the population dynamics? (Again assume there is no mortality while at sea.)
nt+1 =
(c) Which of the recursions obtained in parts (a) and (b) predicts the largest increase in population size from one year to the next?
O recursion formula from part (a)
Orecursion formula from part (b)
Justify your answer both mathematically and in terms of the underlying biology. You can assume that 0 < d < 1 and b > 0.
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