topic 3 - geometric pop growth Flashcards
how is population size modelled
in discrete time intervals (yrs,generations,etc)
Nt= N0R^t
Nt=N0λ^t
when is the geometric pop model useful?
• Model is especially useful when reproduction is discrete (eg once per year) and organisms have non overlapping generations ○ All individuals are same age (no age structure) ○ Adults die after reproduction Can use with organisms w age structures and overlapping generations if age-class distribution is constant
what is the geometric pop growth model
Nt=N0λ^t
what is geometric growth model if u wanna calc for further in the future?
Nt=N0λ^t Nt= pop size at time t N0= pop size at time 0 λ= geometric rate of increase model assumes wave is constant across generations - this is why pops grow geometrically (discrete form of exponential growth)
look at graphs for geometric. when is it increasing/declining based on λ
ok
λ is greater than 1 = grows
λ is less than 1 = declining
λ= 1 = unchanged
how do you calculate λ?
Nt=N0λ^t divide each side by N0 Nt/N0=λ^t, t = 1 bc λ is per generation Nt+1/Nt=λ λ= R0 for pops with discrete, non overlapping generations or stable age-class distributions
what does the model estimate?
• The model estimates population size at discrete points in time
We connect the dots for ease of interpretation ( doesn’t represent what is happening in nature)
what if discrete reproduction was measured continuously?
it would make a step-wise increase in NNot all individuals born in to a population are born or die at the same time
exponential form of the equation?
In Nt= In N0 + (Inλ)t
y intercept and slope in the exponential form?
InNt=InN0 + (Inλ)t y intercept is InN0 slope is (Inλ)
why do we use logs?
• Easier to see differences in population size over several orders of magnitude
- linearizes (y=mx+b) - easier to identify if rates are constant + easier to solve
how to find geometric doubling time?
In(2) / In(λ)= doubling time
only need to know λ or R0 to calculate it
assumptions of geometric pop growth model?
closed pop unlimited resources ans constant environment (b,d, R0, and λ constant) all individuals identical (b&d) or avearge b & d constant throughout time (stable age class distribution)
