POPULATION DYNAMICS

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UIC BioS 101 Nyberg

POPULATION DYNAMICS

Today we focus on population censuses and models that count all individuals equally (using the variable N only, i.e. without age or sex) and that do not measure resource availability.

Speaker Notes:

Exam 3 #5

UIC BioS 101 Nyberg

Reading

Chapter 52.2 and 52.3.
Box 52.3 (p1188) on Mark-Recapture
Review of the x1 07 lecture may be useful to understand population growth.
Chapter 52 starts with the more complicated models using age of individuals.

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UIC BioS 101 Nyberg

Changes in population size

In a sustainable world, we expect population sizes of animals and plant species to stay about the same, N constant thru time.
Reproduction gives organisms the potential to grow exponentially.
Exponential growth eventually exhausts the resources and maintenance of population is dependent on renewal of resources.

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Determining population size

Count all the individuals
- Generally tough to do
Sampling
- Create subpopulations (often based on area), count individuals in subpopulations, extrapolate to entire population/area
Mark-Recapture Studies
- Sample, mark, release, resample

Speaker Notes:

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Mark-recapture basics

Box 52.3 p1188
Perhaps simplest to understand in small lake
Capture individuals, mark(tag) them, release n1 marked individuals
Assume the marked animals disperse and mix with unmarked animals in lake
Capture n2 individuals, if m2 is # marked,
then N = total # in population = n1 • n2/ m2

Speaker Notes:

Mark-recapture example

You catch 14 butterflies and mark the thorax with white paint and then release the butterflies.
Two days later you go out and net 18 butterflies and find 4 of them marked.
The Estimate of the total population = 14 times (18/4) = 63 butterflies.

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Census Histories

The Census history is the record of the numbers of individuals through time
- Some populations show a pattern of constant doubling for a period of time.
- Many populations are stable in size.
- Some species have a pattern of steady decrease.
- Many insects have population “outbreaks” with large fluctuations from year to year

Speaker Notes:

Census history examples

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Speaker Notes:

Figure 52.9 in Freeman, 3rd Edition.

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Minimum Doubling Time

The time it takes for a species to double the number of individuals even when resources are abundant is called the doubling time.
Both geometric and exponential growth imply a constant doubling time, doubling time simply related to r, growth rate, is a parameter of the species.

Speaker Notes:

0.693/Doubling time = r or r = ln2/tD where tD is doubling time.

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Population Size at a particular time

N is the symbol for the variable population size
N t = means the population size at time t, as a subscript it implies the geometric or discrete time model.
N t + 1 = population size one generation after t
The exponential or continuous time model would be written as N(t), verbally ‘N as a function of time’.

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Population Change
using birth & deaths and migration

Plus Births, B is number of births
Minus Deaths, D is number that died
Plus Immigrants, I = # that moved in
Minus Emigrants, E = # that left

N t+1 = N t + B – D + I - E

If population is closed, N t+1 = N t + B – D

ΔN = N t+1 - N t = B – D = change in size

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The Whooping Crane

The species is ENDANGERED according to US law.
The population was once at least 10,000 birds (always rare).
The population was reduced to only 20 birds in the 1940s.
The population has been growing exponentially for about 60 years.

Speaker Notes:

Exponential growth is not automatically fast. Some species have long doubling times.

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Census history of Whooping Crane

Speaker Notes:

Notice that this population has increased from a very small size. Calculate r and doubling time for whooping cranes from N = 20 in 1941 and N = 518 in 2007.

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Geometric Growth Model

- Nt+1 = • Nt

, lambda,is the multiplier from one generation to the next.

If = 1, the population size stays the same = is constant.

Speaker Notes:

If lambda =1.4 what is the percent increase per unit time?

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Exponential Growth Model

- N(t) = N0•er•t
The parameter that measures growth is r, which measure the instantaneous per capita growth rate per unit time.
If r = 0.04 yr-1 the population grows 4% per year, as e0.04 = 1.04 approximately.
If r = 0, the population size does not change

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Exponential Growth Model

Can also be written in “differential” form:

dN/dt = r•N where dN/dt is the change in abundance per unit time change and r is the per capita growth rate.

Note that if r =0 the population is not changing in size, i.e. dN/dt =0, and if r is negative the population is decreasing.

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Relationships of and r

= ert or er if time is one unit long.
If < 1, then r will be negative, i.e. the population is declining (exponential decay).
If > 1, then r will be greater than zero and the population will increase geometrically.

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Modifications of growth model

Populations don’t grow indefinitely, but rather reach a maximum density.
The logistic model is a simple modification of exponential growth that leads to curve (sometimes referred to a ‘s’ shaped) that conforms to observations of batch cultures.

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The “logistic” model of growth

We take our exponential model (per capita growth constant) and add a new parameter, a, that reduces the growth rate in proportion to the population size
dN/dt = r•N – a•N2
per capita growth rate dN/N•dt = r – a•N

dN/N•dt

Speaker Notes:

What does the green line tell you?

Paramecium

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The Logistic Equation

Time

See Fig. 52.7a

Speaker Notes:

The basic idea of density dependence is that growth rate is a function of density = N.

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Metapopulations

Species are usually made up of patches of populations with few individuals found in the area between the patches.
The population is said to have a metapopulation structure if population extinction and colonization of empty suitable patches is frequent.

Speaker Notes:

Section 52.3 Glanville fritillaries

Meta-populations

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Population Abundance Cycles

Some populations show regular fluctuations of population size.
Evenly repeated highs and lows are known as population cycles.
The Lynx (a cat that eats hares) and hare (rabbit) populations cycle with an 11 year period. The Lynx hi and low trails the hi and low of the hare.

Speaker Notes:

Hare & Lynx populations

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Outbreaks

It is not unusual for populations of insects to vary greatly from year to year
Very great increases in abundance are called “outbreaks”
Examples in 2003 include the Painted Lady butterfly & the Asian Ladybug

Speaker Notes:

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Census History with Outbreak

Time

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Vocabulary

Constant Doubling time
Geometric growth
Exponential growth
metapopulations
parameter
Emigrants, immigrants

Census history
Outbreak
N0•er•t
Logistic growth
Cycle
, lambda

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