Chapter 5: Estimating Population Growth Rates Flashcards
exponential (or geometric) growth
- (per capita) rate of change in abundance that is not affected by density
- growth = increase or decrease
examples of exponential decline
- Hawaiian monk seal: 3.9% decline per year
- Devil facial disease
Malthus dilemma
contrast between exponential growth vs arithmetic growth
Malthus dilemma: geometric growth
- population
- increases by a constant factor of 2
Malthus dilemma: arithmetic growth
- food
- increases by constant difference of 2
λ =
Nt + 1 / Nt
when λ = 1
the population is stationary
when λ < 1
the population decreases geometrically
when λ > 1
the population increases geometrically
% change per year =
(λ-1) * 100
NT =
No * λT
discrete time
change in N over 1 year
discrete time equation
Nt + 1 = Nt (λt)
continuous time
instantaneous change
continuous time equation
dN/dt = rN
r =
slope of a line
continuous (exponential) growth equation
dN/dt = rN
continuous (exponential) growth
- the rate of change in population size at each instant in time
- the instantaneous per capital growth rate
per capita growth rate
the average contribution each individual makes to population change
how to convert between λ and r
r = ln(λ)
λ = e^r
when r = 0
the population is stable
when r < 0
the population decreases exponentially
when r > 0
the population increases exponentially
advantages of λ
translates easily into ‘percent annual growth’ an easily understandable metric
disadvantages of λ
cannot average over consecutive values
advantages of r
- center around 0
- successive r values can be added or averaged over time
- r values can be divided to convert to different time scales
disadvantages of r
a hard to explain logarithm of the proportionate population change per time step
when use an exponential growth model for wild populations?
- often used as a null model to then identify deviations
- unaffected by density
- in newly established populations
- populations recovering from catastrophic declines
- invasive, pest outbreaks
population growth is often ________
variable (stochasticity)
what causes stochasticity in growth rate over time?
- sample variance
- process variance
sample variance
- aka observation error
- nature is not varying, but our estimation error makes it seem like it
process variance
the one actually affecting changes in abundance & the one we care about
internal drivers of process variance
- age structure
- density dependence
- connectivity
process variance: changes from interacting species
- predation
- competition
- parasitism
- human harvest
process variance: stochastic factors
- environmental stochasticity
- demographic stochasticity
demographic stochasticity
due to random deviation from mean birth and death rates
where is demographic stochasticity especially important
small population
where does demographic stochasticity arise from?
strictly from population size & not from any variability in the environment
demographic stochasticity can cause …
declines in small populations
environmental stochasticity
- due to extrinsic factors that cause mean vital rates to change randomly over time
- effects less dependent on population size
environmental stochasticity examples
- early springs
- summer droughts
- hurricanes
- forest fires
