Lecture 20

Question 1

what is the eq for pop growth?

Answer 1

delta N / delta t = births - deaths + immigrants - emigrants

Question 2

What is the eq for the rate of change in pop size

Answer 2

delta N / delta t = rN

r = b-d
r = rate of increase per individual

b= birth rate
d= death rate

Question 3

When does exponential growth happen in pops

Answer 3

• only occurs in pops with unlimited resources that are able to reproduce at a max rate, after:
  a) introduction to a new environment
  b) recovery from a disaster (few competitors)

Question 4

What is the eq for exponential growth

Answer 4

dN/dt = rN

differential rate eq in calc, where growth rate is independent of density

Question 5

explain what happened during the mouse plague in australia 2021

Answer 5

• wet year with high grain harvest
• lots of stored wheat that was invaded by mice that can produce new offspring every 3-4 weeks
• invading houses in search of more food as competition for food increases

Question 6

What does the carrying capacity (k) mean?

Answer 6

• max number of individuals that a particular environment can support
• k is affected by the availability of resources (ex. light, nutrients, water, territory, nesting sites, etc) and provides a limit to continued pop growth

ex. damaged coral reef = very low k for fish
productive reef = high k for fish

Question 7

explain logistic growth

Answer 7

• as a pop approaches k, density dependent factors will affect b and/or d, and N and other parameters.

Either:
- intraspecific (within species)
- interspecific (between species)

ex.
- competition for resources
- behavioural changes like conflicts, reproduction declines, infanticide, cannibalism
- disease or predation

• creates logistic curves!

Question 8

• gwhat is the eq of a logistic growth curve?

Answer 8

dN/delta t = rmaxN * (k-N)/k

when N is small, expression is close to 1 bc (1000-10)/1000 = 0.99 and exponential growth continues

when N is large, (1000-900)/1000 = 0.1, the expression gets smaller and slows the rate of growth (by 90%)

when N is at carrying capacity (k=N), the expression is 0, and growth stops

Question 9

What affects the carry capacity of humans? how can we increase k?

Answer 9

• food production capability (increase k!)
• increase agricultural areas? fish farms? greenhouse areas in non-arable land? etc.
  BUT
  all solutions have consequences, especially for non-humans

Question 10

What is the current global average fertility rate?

Answer 10

• 2.5 children per woman
• above the replacement rate of 2.1 children per woman, which replaces her and one male

Question 11

explain Anthropocene!!!

Answer 11

• an Earth whose future is controlled by activities of the human pop
• maximizing k for humans will have negative effects on most other species