6. Part 1: Population growth & Regulation

Change in number of individuals in a population over time, driven by rates of births, deaths, and migrations

Population growth

Populations in which immigration/emigration occurs

open populations

Populations where there is no migrations or rates in/out are equal

Closed populations

N =

number of individuals in the population

t =

time

Nt =

number of individuals in the population at a given time

B = 

number born each time step

D =

number of deaths each time step

To calculate new population size over just one time step, use what equation?

N1 = No + B - D

Per capita birthrate (b) is the

births per individual per unit time

Per capita death rate (d) is the

Deaths per individual per unit time

b =

B/No

d =

D/No

N2 given N1, b, and d is

N2 = N1 + (N1 * b) - (N1 * d)

There are two general models of population growth (exponential vs geometric) because species have different

life histories

Growth model used for populations with continuous reproduction and/or overlapping generations

Exponential growth

Growth model used for populations with reproduction occurring at discrete intervals (breeding seasons)

Geometric growth

Under ideal conditions (unlimited resources, maximum reproduction, minimal death rates), you can the variable r to represent

intrinsic growth rate

r = 

b - d

r is the

per capita growth rate (intrinsic growth rate)

In populations experience exponential growth, r is

constant over time

Net change in individuals per current individual per unit time

per capita growth rate ( r )

when r = 0,

population size does not change

when r < 0,

population decreases exponentially

when r > 0,

population grows exponentially

in a physics analogy to exponential growth models, population size is like _____ and intrinsic growth rate ( r ) is like ______

velocity
acceleration

Exponential or geometric growth equation?
Nt = No * e^rt

Exponential

In exponential model, the instantaneous growth rate is calculated by

r * N

What is this the equation for?
t = ln(2) / r

doubling time for exponential growth

Exponential or geometric growth equation?
Nt = No * (lambda)^t

geometric

When lambda = 1,

the population size does not change

When lambda < 1,

the population decreases exponentially

When lambda > 1,

population grows exponentially

When r = 0, lambda = 

1

lambda is known as the

Discrete population growth rate, per individual

Limiting factors to population growth can be ______ or ____

density-dependent
density-independent

Factor that affects growth rate regardless of population size
Often environmental factors (temp, precip, natural disasters)

Density-independent

Factor that affects growth rate of large populations differently than smaller populations

Density-dependent

Rate of population growth decreases as population density increases (limited resources, predation, disease)

negative density-dependent factors

Rate of population growth increases as population density increases (reproductive success, pollen-limiting)

Positive density-dependence