Class Notes (1,000,000)

US (420,000)

U of M (7,000)

BIOLOGY (500)

BIOLOGY 171 (100)

Josephine Kurdziel (60)

Lecture 14

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

by OC2537120

Department

BiologyCourse Code

BIOLOGY 171Professor

Josephine KurdzielLecture

14This

**preview**shows pages 1-3. to view the full**10 pages of the document.**Thursday, March 14, 2019

LECTURE 14

Ecology: The study of how organisms interact with one another and with their physical

environment

•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

!N

2015= 1864+ 28 -1+2 -0

!N

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?

1

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

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 time‐step 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

2

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

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

3

###### You're Reading a Preview

Unlock to view full version