1. BACKGROUND
• Populations are interbreeding groups; members of the same species in a geographic area
• Populations are dynamic; change in size due to:
births (natality)
deaths (mortality)
immigration (moving in)
emigration (moving out)
• Pattern of change can be linear, exponential or logistic, as evidenced by growth rate

2. S’math: Growth rate d*N dT r = B-D N 1. As change in population size
change in time
2. As per capita growth rate = Births - Deaths
Number in population
* delta, Δ
r = B-D N

3. 30 days dN dT r = r = B - D N 5 - 2 10 = 3 = 0.3 per capita 10
Ex: In a population of 10 ducks, 5 are born and 2 die in the month of April.
13 – = 3/mo = 0.3/day
30 days dN dT
r =
r = B - D N
5 - 2 10
= = 0.3 per capita 10
On the formula sheet it’s a single equation

4. Linear growth
• Change is constant, regardless of population size
• Population is increasing but # offspring produced is not
# of otters
2500
2000
1500
1000
500
+500
+500
+500
year

5. Exponential growth • Growth is proportionate to population size
• Populations growth in the absence of limits; biotic potential
• J shape to curve
Large population
rapid growth
+20,000 gen
population size
Fun fact: doubling time is the rate divided by 69. EX: 3% growth rate /69 = 23 years to double
Small population size, slow growth
+ 500 /generation
generation

6. Exponential growth dN dT rmax N =
• Amount of growth depends on the population size
population size dN dT
change in population size
rmax N =
growth rate per capita
Ex: duck population’s growth rate of 0.3 per capita
Fun fact: doubling time is the rate divided by 69. EX: 3% growth rate /69 = 23 years to double N
Math
Population change
New population size
1000
0.3(1000)
+300
1300
0.3(1300)
+390
1690
0.3(1690)
+510
2200
increasing

7. BIOTIC POTENTIAL UNLEASHED
Staphylococcus
Aureus
Cells would cover the Earth 7 feet
deep in 48 hours.
Audesirk & Audesirk, 1993

8. r-selected species opt for exponential growth
Small in size
Short life span
fast maturity
One reproductive event
many offspring
little energy invested in offspring
Organisms have two choices - maximize your chances in the short term in an unpredictable environment ‘(go with the flow’) or ‘cut and run’ to a more stable environment.
Suppose you stayed. Then, one thing you could do would be to increase the number of offspring. Make lots of cheap (requiring little energy investment) offspring instead of a few expensive, complicated ones (requiring a lot of energy investment). If you lose a lot of offspring to the unpredictable forces of nature, you still have some left to live to reproductive age and pass on your genes to future generations. Many invertebrates follow this strategy - lots of eggs are produced and larvae are formed but only a few survive to produce mature, reproductive adults. Insects and spiders also follow this strategy.
Alternatively, you could adapt to a more stable environment. If you could do that, you would find that it would be worthwhile to make fewer, more expensive offspring. These offspring would have all the bells and whistles necessary to ensure a comfortable, maximally productive life. Since the environment is relatively stable, your risk of losing offspring to random environmental factors is small. Large animals, such as ourselves, follow this strategy.
ex: insects
weeds

9. Reality: Limiting Factors
• checks on population size
• both biotic and abiotic
• both density dependent and density independent
‘disasters’
symbiotic relationships
space
predation

10. r-selected species/populations are limited by density independent factors
temperature change
fire
rapid growth
rapid decline
temperature change

11. K-selected species experience logistic growth
• Large size
• Long life span
slow to mature
• Reproduce multiple times
few offspring
dependent offspring
Organisms have two choices - maximize your chances in the short term in an unpredictable environment ‘(go with the flow’) or ‘cut and run’ to a more stable environment.
Suppose you stayed. Then, one thing you could do would be to increase the number of offspring. Make lots of cheap (requiring little energy investment) offspring instead of a few expensive, complicated ones (requiring a lot of energy investment). If you lose a lot of offspring to the unpredictable forces of nature, you still have some left to live to reproductive age and pass on your genes to future generations. Many invertebrates follow this strategy - lots of eggs are produced and larvae are formed but only a few survive to produce mature, reproductive adults. Insects and spiders also follow this strategy.
Alternatively, you could adapt to a more stable environment. If you could do that, you would find that it would be worthwhile to make fewer, more expensive offspring. These offspring would have all the bells and whistles necessary to ensure a comfortable, maximally productive life. Since the environment is relatively stable, your risk of losing offspring to random environmental factors is small. Large animals, such as ourselves, follow this strategy.
ex: trees
whales

12. In K populations limiting factors establish the ecosystems carrying capacity
• Sets the max population, size based on available resources
• Density dependent limiting factors
• Growth is logistic, creating an S-shaped curve

13. dN dT Calculations factor in the carrying capacity (K) K – N rmax N =
Ex: duck population’s growth rate of 0.3 per capita, and a carrying capacity of 2500 ducks N
Math
Change to population
Percent change
250
0.3(250)( /2500) 68 27
1000
0.3(1000)( /2500)
180 18
2000
0/3(2000)( /2500)
120 6

14. B>D B = births (and immigration) D = deaths (and emigration)
no growth
B=D
logistic growth
slow growth, linear even
B>D
time
exponential growth
B>D

15. Natural selection has produced a continuum of strategies
• extreme r-selection at one end of the spectrum
• extreme K-selection at the other end
1 offspring
5 years of care
500m eggs
No parental care

16. Survivorship curve of r vs K selected species
High survival probability in early and middle life, rapid decline in survival in later life. Typical of K – selected species
High mortality in early life – a bottleneck – typical of r – selected species

17. Population Case Study
• Galapagos finches, 1976 drought as limiting factor
• drought: abiotic, density independent
• change in food source: biotic, density dependent
Population decreases in size
Seed abundance
decreases
number of birds
Seed hardness
increases
Beak depth increases

18. Population Case Study
• Predator and prey as limiting factors on one another
• biotic, density dependent
Lag time