Population Growth and Regulation

Ecology exam 1

Intrinsic Growth Rate

“r”

-highest growth rate per capita

• =births-deaths

exponential growth equation

N(t) = N₀e^(rt)

-for ideal conditions and consistent breeding

Observed rate formula

dN/dt=rN

rate of growth at a specific moment in time

-use when given population and intrinsic rate of growth

Negatively growing population

more deaths than births

geometric growth model

N(t) = N(0) * λ^t

-used for species with a breeding season

λ

discrete population growth rate used for breeding seasons

λ = N(t)/N(t-1)

link two models

λ = e^r

convert between r and λ

r=ln λ

doubling time

-time for population to double in size

doubling time exponential model

doubling time geometric model

what does log e mean?

ln

density independent factor

mostly abiotic, like storms

-geometric and exponential models are density independent

Is indefinite growth possible?

No because of limited resources and abiotic factors

density dependent factors

are often biotic, like limited food resources and disease

negative density dependence

high population causes negative population growth

positive density depedence

low density causes decreased population

-difficulty finding mates or hunting in groups

“Allee effect”

carrying capacity “K”

-maximum population the ecosystem can support

-going over capacity starts reducing the population

-overshoot causes population collapse

logistic growth model

-early growth is exponential, then slows as it approaches K

logistic graph

inflection point

-point at which growths stops being exponential and starts to slow

-when N=K/2