Peter - Population growth

Question 1

Four processes that determine the number of individuals, N

Answer 1

Birth (B), immigration (I), emigration (E) and death (D). B and I increase, E and D decrease.
Nnow = Nthen + B - D + I - E

Question 2

Closed population growth equation

Answer 2

What is normally studied. Assume I and E are very small.
Nt+1 = Nt + B - D

Question 3

Discrete model

Answer 3

All results of conditions, resources and competition are calculated at one specific time point, eg once each year. B and D is measured as “rates”, time interval = one generation.

Question 4

Discrete model equation

Answer 4

F = fertility, the number of offspring produced per individual at time t that survives to time (t+1), next generation.
S = survival, the fraction of adult individuals at time t than survives to (t+1).

Number of animals in next generation:
Nt+1 = Nt x F + Nt x S = Nt x (F + S)

S + F is defined as R, meaning
Nt+1 = Nt x R
R = fundamental net reproductive rate.

Question 5

R, fundamental net reproductive rate

Answer 5

Also called lambda.
R is the factor by which a population increases to the next generation.
R = 1: population is stable
R > 1: population increases
R < 1: population decreases

If R is constant, then
Nt+2 = Nt+1 x R
or
Nt x R x R = Nt x R^2
which leads to exponential growth for discrete reproducing populations.

Question 6

Exponential growth (discrete)

Answer 6

N change by a constant factor, in this case R.
Nt = N0 x R^t
t = number of time intervals.

Question 7

Continuous model

Answer 7

Time intervals are very small, and in each time interval B and D are calculated.
Nt+1 = Nt + B - D meaning
Nt+1 - Nt = B - D
We measure B and D as rates, but with time steps (not generation time).
Nt+1 - Nt = (b - d) x N (lower case to indicate continuous)
r = b - d
dN/dT = r x N meaning
Nt = N0 x e^rt

Question 8

Two ways to describe exponential growth

Answer 8

Nt = N0 x R^t (discreet)

Nt = N0 x e^rt (continuous)

R^t = e^rt
R = e^r
lnR = r (a way to translate R into r)

Question 9

Population control by resources

Answer 9

Resources control population growth: b increase and d decerase with increasing resources. The resources are reduced by population growth. This feedback leads to a dampening of population growth, ie population regulation.

Question 10

Population control by conditions

Answer 10

Conditions affect both b and d and the resources, but is not affected by population density. Conditions are therefore not regulating.