LMC.7 - Local Mate Competition (LMC). Here we are...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Local Mate Competition (LMC). Here we are interested in the question: how does the number of mates affect the proportion of resources that should be allocated by a hermaphrodite to male and females function in order to maximize individual fitness? DEFINING THE VARIABLES. .. a i = allocation to male function by the ith hermaphrodite in the population. a = average allocation to male function in the population (this was a* in lecture, but I can't use the star here, because it is used exclusively by Mathematica as the multiplication symbol.) R = Total resource base for reproduction k = the number of mates V = The reproductive value though male fuction W m = Fitness through male function W f = Fitness though female function (assuming Bateman's principle). W i = Fitness of the ith individual (Wf + Wm) FIRST WE DEFINE FITNESS THROUGH FEMALE FUNCTION, W f. (Put the cursor anywhere in the bracket below and press "SHIFT-RETURN." This will store W f in memory) Wf = R*(1 - ai) H 1 - ai L R NEXT DEFINE FITNESS THROUGH MALE FUNCTION, W m. V is the reproductive value of male function, which will be defined shortly. (Put the cursor anywhere in the bracket below and press "SHIFT-RETURN.")
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Wm = V*R*ai ai R V NOW DEFINE THE VARIABLE, V, AS THE RATIO OF EGGS IN THE POPULATION TO SPERM IN THE POPULATION. (Put the cursor anywhere in the bracket below and press "SHIFT-RETURN.") V = (k*(1 - a))/((k - 1)*a + ai) H 1 - a L k ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ai + a H - 1 + k L TOTAL FITNESS OF THE INDIVIDUAL IS THE SUM OF FITNESS THROUGH FEMALE + MALE FUNCTION. (Put the cursor anywhere in the bracket below and press "SHIFT-RETURN.") Wi = Wf + Wm H 1 - ai L R + H 1 - a L ai k R ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ai + a H - 1 + k L NOW CALCULATE THE FIRST DERIVATIVE OF INDIVIDUAL FITNESS WITH RESPECT TO ALLOCATION TO MALE FUNCTION. (Put the cursor anywhere in the bracket below and press "SHIFT-RETURN.") 2 LMC.7.nb
Background image of page 2
Firstder = D[Wi, ai] - R - H 1 - a L ai k R ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅÅÅÅÅÅÅ H ai + a H - 1 + k LL 2 + H 1 - a L k R ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ai + a H - 1 + k L CALCULATE THE SECOND DERIVATIVE OF INDIVIDUAL FITNESS AS A FUNCTION OF ITS ALLOCATION TO MALE FUNCTION. Remember, local stability requires a negative second derivative (Put the cursor anywhere in the bracket below and press "SHIFT-RETURN.")
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 07/01/2011 for the course L 567 taught by Professor Curtis during the Fall '10 term at Indiana State University .

Page1 / 16

LMC.7 - Local Mate Competition (LMC). Here we are...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online