Beverton-Holt recruitment

[kimbero5]

please help me with this i'm not quite sure how to solve this i tried plugging the numbers in but it doesnt seem to come out right...

The Beverton-Holt recruitment curve is given by the recursion

N(t-1)= RN(t)/1+((R-1)/K)*N(t)

where R>1 and K>0. When N(0)>0, then lim(t)~>infinityN(t)=K for all values of R>0. To investigate how R affects the limiting behavior of N(t), find N(t) for t=1,2,3,...,10 for K=100 and N(0)=20 when

a.R=2
b.R=5

its kind of confusing but if you could help that would be great!~

 

[Gene]

It is confusing. I interpreted the equation as
N(t-1)= RN(t)/{1+((R-1)/K)*N(t)} and solved it as
N(t)=KN(t-1)/(KR-(R-1)N(t-1))
But it approaches zero as t increases, not K. Would you care to change the equation...

 

[kimbero5]

im still not sure what to do thats the problem in my book and i dont know if we could change the equation or not....

 

[Gene]

Is what I wrote what the book has? Do you see the difference between my first equation and yours?

 

[kimbero5]

it says we can have
N(t)= N(t+1)*((1/R)+(1-(1/R)/K*N(t))
or
N=RN(t)/(1+(R-1)/K*N(t)

does that make sense???

 

[Gene]

Not trying to be nitpicky. It is important that we start with the right formula. To make sense your (s must = your )s. Yours do not, in either! Count them.
Your original post started with N(t+1)/((1/R)...
Now you start with
N(t+1)*((1/R)
divided by vs times does make a difference. It shakes one's confidence :twisted:
--------------------
Gene

 

[kimbero5]

i'm sorry about that....the second post is what i copied right out of the book and if that's not answering your question im sorry im frusterating you but i'm frusterated too and not quite sure what to do...thanks

 

[Gene]

it says we can have
N(t)= N(t+1)*((1/R)+(1-(1/R)/K*N(t))
or
N=RN(t)/(1+(R-1)/K*N(t)

I'm sorry too. I find it difficult to believe the book has unballenced parens and the function keeps changing. In these two latest versions one is times and one is divided by and there are both an N(t) and an N(t+1) on the right side. One doesn't say N(of what). If there is anyone around who can compare the book to what you have typed, please have them do so before you hit Submit again.
--------------------
Gene