Exam Review II
Fall 2007 Amanda Ensminger
Materials for studying
Your lecture notes Your homework and quizzes Your notes from today Materials on Dr. Sargent's website "Population Biology Resources" "Populus " "Old Exam 2" "Review for Exam 2"
Subjects to study
Tradeoffs Life cycles & Williams' model Parental investment Theory Life tables Senescence Population Dynamics
Tradeoffs among fitness components
What are fitness components? Lack's tradeoff between....? clutch size in birds...? Williams' tradeoff between....? Biological examples illustrating Williams' tradeoff Sabat's experiments...? Balshine-Earn's experiments...?
Life cycle & Tradeoffs
zygote x=0
A
B
D
F
Adult x=1
C
Adult x=2
E
Adult x=3
G
Dead x=4
Where would you indicate.... Lack's tradeoff? Williams' tradeoff (as Sabat's expts showed)? Williams' tradeoff (as Balshine-Earn's expts showed)?
Practice (from old Quiz 3) Write "Lack's" or "Williams'" in the blanks below
A. _______ tradeoff is demonstrated if an increase in current brood size results in decreased survival of that brood. B. _______ tradeoff is demonstrated if an increase in current brood size results in decreased parental survival to the next breeding attempt. C. _______ tradeoff is demonstrated if an increase in current brood size results decreased size of the next brood.
Life cycle & Williams' Model
zygote x=0
A
B
D
F
Adult x=1
C
Adult x=2
E
Adult x=3
G
Dead x=4
Define variables: x Rx mx lx sx,x+1
Rx = Present RS + future RS Rx = mx + sx,x+1Rx+1
1 Rx = x ltmt t=x
R0 = ltmt
t=0
Practice (from old Quiz 4)
Let x=2, and refer to the life cycle depicted. In the blanks below, enter the letter(s) of the arrow(s) that F complete each sentence.
Dead x=4 Adult x=3 E Adult x=2
zygote x=0
D
B
A
C
Adult x=1
1) Arrow(s) ________ represent(s) Rx 2) Arrow(s) ________ represent(s) lx 3) A tradeoff between arrow(s) _______ would be a Williams' trade-off.
Parental Theory Investment & Williams' Model
Rx(E) = P(E) + F(E) (1-E) Rx(E) P(E) F(E) As E, P(E), F(E) Reproductive Success define: E
0
E
E*
1
Life tables
go to homework go to lecture notes
lx & Rx as x
1 Rx lx x x Why does Rx increase as x approaches age of first reproduction? Why does Rx decrease after age of first reproduction? Where is selection strongest? Why?
Senescence
Two hypotheses: 1. Medwar's "Mutation Accumulation" age-specific intensities of selection (note: accumulation in population, not individuals) specific example with fruit flies correlated response tradeoffs here
2. Williams' "Antagonistic Pleiotropy"
Population dynamics - overview
Geometric density INdependent Exponential density DEpendent Logistic dN dt Nt = N0t Nt = N0 ert K-N K
dN/dt
= rN
= r0N
DensityIndependent Growth Models N Geometric Growth
>1 =1
N0
Nt = N0t
<1
N
Exponential Growth
r > 0 (er > 1) r = 0 (er = 1) r < 0 (er < 1)
Nt = N0 ert
N0
Exponential Growth Model (still density INdependent) Integral form Nt = N0 ert Derivative form
dN/dt
= rN
N
dN/dt >0
N0
r>0
dN/dt Instantaneous slope at any time t
r=0 dN/dt =0 dN/...