17 Population Modelling (Geometric, Exponential, Logistic, Carrying Capacity) Flashcards
What can be calculated using life tables and fecundity schecules?
Net reproductive rate (R⁰)
Geometric rate of increase (lambda)
Generation time (T)
Per capita rate of increase (r)
Generation time (T)
Average time when a female gives birth
Or
Average time from mother to daughter
Per capita rate of increase (r)
Per capita birth - per capita death
Measure of population growth
r = (lnR⁰)/T
What does r value mean for growth
r<0 pop decline
r=0 pop stable
r>0 pop growth
Geometric & Exponential vs Logistic growth
G&E= no environmental limitation, unlimited resources, density independent
L= limited environment, limited resources, density dependent
Geometric rate of increase
Ratio of population size at 2 points in time
Increasing at a constant rate (lambda) where reproduction is pulsed and generations do not overlap
J shaped curve
Geometric growth rate formula
λ = Nt+1/ Nt
Nt= population size at time t
Nt+1= population size at time t in the future
λ= geometric rate of increase
Geometric population size formula
Nt= N⁰λ^t
Nt= population size at time t
N⁰= population size at time ⁰
λ^t= geometric rate of increase raised to the power of t
Exponential population growth
Continuous growth with continuous reproduction and overlapping generations
Constant time intervals
J shaped curve
Exponential growth rate formula
dN/dt= rN
r= per capita rate of increase
N= population size
dN/dt= rate of population growth
Exponential population size formula
Nt= N⁰ e^rt
Nt= population at time t
N⁰= population at starting time ⁰
e= Eulers number
r= per capita rate of increase
t= time or # of time intervals
Logistic growth
Growth rate slows when resources become limited
Growth stops at carrying capacity (K)
S shape curve
Logistics population growth formula
dN/dT = rmax N (1– N/K)
dN/dT= rate of population growth
rmax= intrinsic rate of increase
N= population size at given time
K= carrying capacity
Logistic population size formula
Nt= K/1+((K/N)–1)e^–rmax^t
population rate of change
∂N/∂t = Nt+1 − Nt
