Populations Growth pt. 1 Flashcards
What determines population growth?
the number of births, deaths, immigration, and emigration
Exponential population growth
a constant, positive rate of growth, r, causes the # of individuals in the population to grow exponentially because there are more individuals contributing to the population later in time
Total population growth rate =
of NEW individuals added per unit time
Per capita growth rate (r) =
of new individuals added (b, birth rate) MINUS # of individuals removed (d, death rate) per individual over time
Exponential growth equation
Nt = No (e^rt)
Nt = No (e^rt)
What does each unit stand for?
Nt = population size at future time, t
No = current population size
e = 2.72 (Euler’s constant)
r = growth rate per individual (b-d, birth-death)
t = amount of time over that passed between No and Nt
To find the growth rate at any one instant in time (dN/dt) you use the formula:
dN/dt = r x N
or
dN/dt = (b-d) x N
What is dN/dt also known as?
Instantaneous growth rate
slope of the line at Instant A or instant B
Exponential population growth:
r<0
population size decreases, slope is negative
dN/dt = -0.5 x 30
decreases by 15 individuals per unit time when N = 30
Exponential population growth:
r=0
population size does not change, slope is constant
dN/dt = 0 x 30
changes by 0 individuals per unit time when N = 30
Exponential population growth:
r>0
population size increases, slope is positive
dN/dt = 0.5 x 30
increases by 15 individuals per unit time when N = 30
What is the geometric growth equation?
Nt = Nolambda^t
What do the units stand for
Nt = Nolambda^t
Nt = population size at future time, t
No = current population size
lambda = a ratio of a population’s size in year 0 to its size in year 1
t = amount of time over which population grows (1 year, 2 years, etc.)
What does the geometric growth model describe?
it still describes exponential growth, but allows us to describe population growth for species that have specific breeding seasons
Geometric population growth:
lambda<1
population size decreases, slope is negative
lambda = 0.5
for every 1 individual in the population in year 1, there are only 0.5 individuals in year 2
Geometric population growth:
lambda=1
population size does not change, slope is constant
lambda = 1
for every 1 individual in the population in year 1, there is still 1 individual in year 2
Geometric population growth:
lambda>1
population size increases, slope is positive
lambda = 1.5
for every 1 individual in the population in year 1, there are 1.5 individuals in yer 2
What is the exponential growth model used to describe?
species that can breed continuously through the year
What is the geometric growth model used to describe?
species that have breeding seasons
