Introduction to Populations #8: Exponential Growth, Geometric Growth

Question 1

Population

Answer 1

Population: Group of SAME species individuals that live in SAME area at SAME time and interact with each other

Note:
- Difficult/impossible to portray population w/ absolute precision b/c blurry (don’t know where every individual goes and interacts with)

Example:
- All 40 sockeye salmon populations feed in SAME Pacific Ocean at SAME time
- But spawn in DIFFERENT locations = considered separate populations
- Breeding location can determine population

Question 2

Exponential Growth

Answer 2

Exponential Growth: Continous reproduction
- Becomes straight line if plotted on log scale
- Populations can grow exponentially when conditions favourable
- Density independent
- Does NOT apply when out of resources

Example:
- Humans

Anti-Example:
- Daphnia observed population growth rate (r_obs) decreases as density increases

Question 3

Geometric Growth

Answer 3

Geometric Growth: Discrete-time periods
- Becomes straight line if plotted on log scale
- Populations grow geometrically when reproduction occurs at regular time intervals
- Density independent

Example:
- Annual plants

Question 4

Geometric Growth Equations

Answer 4

Geometric Growth Equations:
- N_t+1= (𝞴)(N_t)
- N_t = (𝞴^t)(N_0)

Variables:
- N_t = population size after t generations/periods (ex. years)
- N_t+1 = population size 1 year/period after t generations/periods
- 𝞴 = geometric population growth rate
- N_0 = initial population size

Question 5

Population Growth Rate (𝞴)

Answer 5

Population Growth Rate (𝞴):
- Ratio of population size in year t+1 (N_t+1) to population size in year t (N_t)
- 𝞴 = (N_t+1)/(N_t)

Note: 𝞴 does not have to same at every time period

Population Increasing:
- 𝞴 > 1

Population Decreasing:
- 𝞴 < 1

Population at EQ:
- 𝞴 = 1

Question 6

Exponential Growth Equations

Answer 6

Exponential Growth Equations:
- dN/dt = rN
- N(t) = N(0)e^(rt)

Variables:
- N(t) = population size each instant time t
- N(0) = initial population size
- dN/dt = rate of change in population size each instant time t
- r = exponential growth rate

Note:
- r = 0 when population stable
- When population starts very small (ex. after run of bad years for Australian mice/after new species introduction), initial population growth phase may be very close to exponential (B > D)
- Evolutionary/technological innovations can also lead to exponential population growth (B > D) (ex. Evolution of antibiotic resistance in microbes)

Question 7

Population Size Change

Answer 7

Populations Size Change:
- N_t+1 = N_t + (B - D) + (I - E)

Variables:
- B = Births
- D = Deaths
- I = Immigration (enter another habitat to live in permanently)
- E = Emigration (leave habitat to live in another)

Example:
- Greater precipitate = greater crop yield = more rate births = increased rat population size