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Lecture 14

BIOLOGY 171 Lecture Notes - Lecture 14: Logistic Function, Carrying Capacity, Population Ecology

Course Code
Josephine Kurdziel

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Thursday, March 14, 2019
Ecology: The study of how organisms interact with one another and with their physical
•Many ecologists work on applied problems
–examples: invasive species, infectious diseases, fisheries, the effects of pollutants on
populations and communities, global climate change, etc.
Why does population ecology matter?
Sometimes we want to prevent population growth
Plasmodium parasite that causes malaria
Sometimes we want to promote population growth
Four Keys to population change
Only 4 things can change population size: vital rates affect population growth
•Birth (# births)/ time = B
•Immigration (# immigrants)/ time = I
•Death (# deaths)/ time = D
•Emigration (# emigrants)/ time = E
Population dynamics
N1= N0 + B – D + I – E
N1= number of individuals at time 1
N0= number of individuals at time 0
B = number of births between times 0 and 1
D = number of deaths between times 0 and 1
I = number of immigrants arriving between times 0 and 1
E = number of emigrants leaving between times 0 and 1
“BIDE” are the “vital rates”
Key Ecology Concept: Changes in population size reflect the sum of births, deaths,
immigration, and emigration.
ex. Pandas in the wild
2014: 1864 pandas in the wild
How can we predict how big the population would be in the future?
Imagine that, in 2015, 28 pandas were born, 1 died, 2 were released from captivity and none
were taken into captivity. Given that, what would the wild panda population size be at the end
of 2015?
!N1= N0+ B – D + I – E
2015= 1864+ 28 -1+2 -0
2015 = 1893 pandas
In reality, it is rarely possible to count all individuals & keep track of their births and deaths! What
else can we do?

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Thursday, March 14, 2019
Geometric population growth rate
Lambda is used for discrete breeders
CLICKER: 2014: 1864 pandas in the wild, 2015: 1893 (in our scenario from the previous slide)
What is lambda for giant pandas?
A) 0.985
B) 1.0156
C) 2.9
D) 29
Predicting one timestep into the future
•If there are 1893 pandas in 2015, how many would you predict there were in 2016?
Predicting further into the future
CLICKER: In 2014, there were 1864 pandas and λ = 1.0156. Based on that,
what population size would you predict in 2020?
A) 1870
B) 1893
C) 2045
D) 11358
More on the geometric rate of increase
Populations are growing when λ >1
Populations are stable when λ= 1 (population size is not changing)
Populations are shrinking when λ < 1
If λ=1.0156, what does that mean? (for pandas)
Population is growing, at a rate of 1.56 % per year
λ= 1 +c, where c = % increase in decimal form
Recap of lambda (λ)
Modeling population growth for species with discrete breeding seasons
λ is the geometric growth rate
Can use lambda to predict one time step (this year to next year)
Can use lambda to predict several time steps into future

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Thursday, March 14, 2019
ex. Of something that grows faster: Malaria & discrete population growth
Plasmodium (eukaryote) parasite that causes Malaria disease
Plasmodium has complex lie cycle, single cell eukaryotic
organisms that has many sexual and asexual phases
At particular lie history stage female mosquito that is infected
with the right stage of the parasite can bite a human and
injects particular stage into blood stream
traveling to liver
has round of asexual reproduction inside of liver cell
liver cells bursts, and new stage of parasite enters
blood stream
infects red blood cells —> stage we are focusing on
in mice:
~1 million cells when malaria leaves the liver
By 7 days later, ~1 billion cells
What is λ for malaria in mice?
Discrete vs. Continuous Population Growth
λ expresses a population’s growth rate over a discrete interval of time (e.g., 1 day, 1 year).
The population’s growth rate at any particular instant in time is r, which is known as the per
capita growth rate —> instantaneous rate of increase
Therefore, for continuously growing populations:
Calculating Population Growth
A population's growth rate is the change in the number of individuals in the population (ΔN) per
unit time (Δt).
Looking at change at two different periods we could take the slope of line
For continuous breeder, we might want to see how population is changing at a particular time
point dN/dt
When considering the rate of change over a very, very short interval, we typically use the notation
dN/dt rather than ΔN/Δt.
Exponential growth
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