# BIOL 290 Lecture Notes - Lecture 13: Sockeye Salmon, Fish Migration

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Geometric Growth

Tuesday, November 13, 2018

5:53 PM

• Lambda ( λ)

• Estimated growth rate

• Finite rate of increase

•

• N(t+1)= population size one year after N(t); one unit of time after N(t)

• N(t)= population size at year t

• N(0)= initial population size

• You can use estimate of lambda to make a mathematical prediction about how large the

waterhemp population will be in future years

o λN(t)

• Geometric Population Growth

• λ will be multiplied in each timestep to get an estimated population size in as

many timesteps in the future we want

• Examples:

o

o λ^2N(0)

o λ^t

• General formula

• Population changes in successive time steps by a constant ratio

• The geometric model works when populations are not limited in their growth; they

continue increasing at the same rate each unit of time

• This model assumes that there is only one discrete reproduction event per unit of

time for individuals (annual plants [waterhemp], mating events in some mammals)

Ex: N(0)= 10

λ= 1.35

What is the population size at year 10?

N(10)= N(0)x λ^t

= 201 plants

Who does the geometric population growth model

apply to?