Lecture 7: Life Tables & Population Growth

Question 1

Life history traits determine…

Answer 1

rate of population growth

Question 2

Variables for life table

Answer 2

• nx = # alive at start of age x
• lx = age-specific survival rate (nx/n0) = proportion surviving from age x from age 0
• dx = # dying in age interval x to x+1
• qx = per capita rate of mortality in age interval x to x+1 = dx/nx
• bx = mean # offspring for females aged x = age-specific birth rate

Question 3

Net reproductive rate (R0)

Answer 3

• avg # of offspring produced by an individual over life span

= (all)lxbx

Question 4

Mean generation time (G)

Answer 4

• mean time elapsed between parent production & offspring

= (all)lxbxx / (all)lx/bx
= (all)lxbxx / R0

Question 5

Calculating pop’s intrinsic rate of increase (r) from Ro & G

Answer 5

r = intrinsic capacity for increase = instantaneous growth rate

• predict pop growth trajectories
• compare predictions to natural growth rates
• compare pop growth across populations/species
• predict how fast a population may recover

r = (loge(r0))/G

Question 6

What causes population to grow/shrink?

Answer 6

• births, deaths, immigration/emigration

Nt+1 = Nt + B - D
* D = dN (d = instantaneous death rate)
* B = bN (b = instantaneous birth rate)

r = b - d (b & d constant)

Question 7

Exponential growth rate equation

Answer 7

dN/dt = rN
* dN/dt describes how pop size (N) changes over time

Question 8

Geometric growth rate equation

Answer 8

Nt = N0e^rt

Question 9

Iteroparous vs. Semelparous reproduction

Answer 9

Repeated; big-bang

Question 10

Cole’s Paradox

Answer 10

To have and equivalent impact on pop. growth:
b(annual) = b(perennial) + 1
* assume perfect survivorship, pop. growth of semelparous species will be equivalent to iteroparous if annual produces just one more offspring on avg @ age 1

Question 11

For annual and perennial to grow @ same rate…

Answer 11

• p(ad) : adult survival probability
• p(j) : juvenile survival probability

b(annual) = b(perennial) + (pad/pj)

• if juv survival high relative to adult –> itero + semel strategies have similar effects on pop. growth

Question 12

If there’s such a strong numerical advantage to investing slightly more into the first clutch, why by iteroparous?

Answer 12

• perfect survival is never true
• juv survival sometimes uncertain

Question 13

Reproductive value (Vx)

Answer 13

• expected reproductive contrinution of an individual of age x to next gen (same as R0)

Vx = bx + (all)(lt/lx)(bt)

• (all)(lt/lx)(bt) = residual reproductive value = expected future progeny