# Lecture 20 Flashcards

what is the eq for pop growth?

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

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

delta N / delta t = rN

r = b-d

r = rate of increase per individual

b= birth rate

d= death rate

When does exponential growth happen in pops

- 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)

What is the eq for exponential growth

dN/dt = rN

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

explain what happened during the mouse plague in australia 2021

- 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

What does the carrying capacity (k) mean?

- 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

explain logistic growth

- 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!

- gwhat is the eq of a logistic growth curve?

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

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

- 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

What is the current global average fertility rate?

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

explain Anthropocene!!!

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