Unit 5 - Modelling Population Growth Flashcards
population growth rate
refers to the change in a population over a period of time
(+) growth
rate indicates the pop is increasing
(-) growth
rate indicates pop is decreasing
0 growth
indicates no change in pop size
zero population growth (ZPG)
a situation in which the death and the birth rate are in equilibrium
per capita growth rate (r)
the difference between the per capita birth rate and the per capita death rate of a population
Exponential Growth
a pattern of pop growth where organisms reproduce continuously at a constant rate
ecologist able to determine…
the instantaneous growth rate of the pop expressed in terms of the intrinsic (per capita) growth rate (r)
birth rate =
b
death rate =
d
r =
growth rate per capita
N
pop size
dN/dt =
instantaneous growth rate of pop
exponential growth; calculating doubling times
the doubling time of a pop is the amt of time that is need for a pop to double in size (the greater the rate of pop growth, the faster the pop will double)
constant
for any pop that is growing exponentially, the time that is needed for the pop to double in size is a constant
doubling time equation
td= 0.69/ r
Geometric Growth
(A) - pattern of pop growth where organisms reproduce at fixed intervals at a constant rate
A= fixed growth
N= pop in 1y
t= year
calculation pop w growth rate
N(t) = N(0)A
Modelling Logistic Growth
food, water, light, and space within an ecosystem are factors that limit pop growth as resources r consumed as the pop nears the ecosystem’s carrying capacityo
individual outnumbers the resources…
the pop tend to drop off as individuals compete for the remaining resources
so the growth rate drops below r(max) in this case
stable equilibrium
(birth = death) is often reached
k=
pop number at carrying capacity
Logistic Growth
is the most common growth pattern seen in nature as it represents the effect of carrying capacity on the pop growth logistic growth equation
logistic growth equation
dN/dt=r(max)N[(K-N)/K]
S-Shaped (sigmoidal) growth
sigmoid is an s-shaped curve, typical of pop growth that starts slow, accelerates or grows rapidly and then levels out over time
three distinct phase
lag phase
log phase
stationary phase
lag phase
occurs when pop is small and increasingly slowly
log phase
occurs when pop undergoes rapid growth
stationary phase
as available resources bc limited, pop experiences environmental resistance and stationary phase occurs in which the pop is at dynamic equilibrium (b=d)
