EXAM 2 (4) Population growth part 2

Population growth rate dN/dt

change in the number of individuals in a population per unit time

intrinsic growth rate (b-d)=r

r is the per capita rate of increase(measures how fast a population would grow per individual)

The highest possible per capita growth rate for a population.

birth rate and death rate for each individual 

rmax: occurs when birthrate is at its highest and deathrate is at its lowest 

When B=D r=0

when deathrate is higher than birthrate=-r

exponential growth equation

(dN/dt)=rN

founding populations

when you have a new population in a habitat

recovering populations 

population basically crashed (Ex. disease)

what are some assumptions of exponential growth

unlimited space

unlimited resources 

small population (as populations become larger reosurces become more unlimited)

very little competition

includes birth and death rates

logistic growth equation

(dN/dt)-rrelN(k-N)/K)

rrel- relative growth rate, how an individual can reproduce relative to the influence population size has on that individual

carrying capacity (k)

max number of individuals a habitat can support

k is not constant

whats the population growth when N=K

zero

whats the poulation growth rate when N>K

negative. the population is larger than the environment can support, resources become limited and there are more deaths=negative growth

whats the population growth rate when N<K

positive, the population is less than the carrying capacity. resources arent limited so the population can grow

density independence

doesn’t depend on population size, affects the population no matter what 

limits population size regardless of the populations density

alter birth and death rates

usually environmental changes

exponential model: population grows without being limited by its size

ex. storms drought, wildfires

if r is constant, the number of individuals added to the population changes, but the rate of increase in the same

Density dependence 

Factors that affect population size in relation to the population’s density.

alters survivorship and fecundity based on density

affects the population more when there are lots of individuals

logistic growth curve

defines k

*examples with terns and the islands

logistic growth model graph

includes density dependence

inflection growth

the population size where growth is fastest, halfway to the carrying capacity 

tern population

example of negative density dependece

As the tern population expanded in Buzzards Bay, Massachusetts, it colonized Bird Island. Rapid growth of the population filled most of the available nesting sites, and the birds then colonized Ram Island. Once again, the population grew and occupied most of the available nesting sites. The terns then colonized Penikese Island.

Negative density dependence

When the rate of population growth decreases as population density increases