Pacific salmon populations have dis- crete breeding cycles in which they return

ID: 3202922 • Letter: P

Question

Pacific salmon populations have dis-
crete 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 size, assuming that there is

no mortality while at sea? You should count the popu-
lation immediately before the upstream journey.

(b) Suppose instead that bears prey on fish 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.)

a) given predation probability =d

offspring production= b (after offstream swimming)

additional hatch increase= m

Now lets take poplation size Nt and growth parameter R

then the equation is Nt+1 = RNt but the growth parameter depends on d therefore the expression changes into

logistic growth like Nt+1 = Nt(1+ R(1-Nt/K)) where K= (bR +m) -d

b) In this case d will be absent from the term K

that means

K= bR+m in the equation

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