In This Lesson:
Population
Ecology
(Lesson 2 of 3)
Today is Wednesday,
September 30th, 2015
Pre-Class:
What’s the smallest biological unit in which
evolution can be detected?
Today’s Agenda
• Large scale biological interactions.
– Also known as “locking evolution, physiology, and
behavior together in a room and watching what
happens.”
• Where is this in my book?
– Chapters 52-53, but mostly 53.
By the end of the lesson…
• You should be able to identify the parameters
by which a population is measured.
• You should be able to describe limits to a
population’s growth.
• You should be able to solve mathematical
problems involving population growth and
density.
Populations: “What”
• So what’s a population?
• It’s a group of individuals of the
same species in the same place
at the same time.
– Finding the “boundaries” of the
population is based on whether
the individuals…
• draw on the same resources.
• interact.
• interbreed.
Populations: “Why”
• Like a good experiment, studying entire
populations automatically provides a high sample
size and therefore can lead to meaningful
understanding of what’s happening.
• Practically, this can also allow for population
management:
– Increasing populations (endangered species)
– Decreasing populations (pests, invasive species)
– Maintaining populations (global marine ecosystems)
Populations: “Factors”
• Complete analysis of a population requires
studying the abiotic factors…
– Climate
– Sunlight and photoperiod
– Soil and nutrients
• …as well as the biotic factors…
– Competition
– Prey/predator populations
– Disease
• …and the intrinsic factors…
– Genetics and evolution
Populations: “Descriptions”
• Populations are usually described through the
following characteristics:
– Range
– Density
– Size
• Range, to start, is how far a population spreads
and is limited by both abiotic and biotic factors:
– Temperature, food availability, predators, humans,
New Jersey, et cetera.
Population Range Case in Point
• Polar bears are migrating further south and
are interbreeding with grizzlies (!).
• Why? Because rising temperatures and ice
surface area (abiotic factors) are forcing them
to seek out prey (biotic factor) and land
further south.
Population Range Case in Point
• Case in point deux: Golden Lion Tamarins
• They are highly endangered largely because
their natural range is small.
– Human encroachment is shrinking it further.
http://ih2.redbubble.net/image.9367479.1727/flat,550x550,075,f.jpg
http://pin.primate.wisc.edu/fs/sheets/maps/leontopithecus_rosalia_range_large.gif
Population Spacing
• Are there packs? Are they loners? Do all the
males need a certain amount of territory?
• Importantly, with the answers to those
questions in mind, how do we deal with
habitat fragmentation.
http://www.eoi.es/blogs/mariagutierrez/files/2014/01/bridge.png
Population Spacing
• Clumped dispersion:
• Uniform dispersion:
• Random dispersion:
Population Dispersion
(same as “spacing”)
• Clumped is the most common in nature because it
indicates “oases” of resources or social behaviors.
• Uniform spacing, by the way, is usually distinguished
from random or clumped by the presence of
territoriality (or maybe something like trees that block
out too much sun…which is basically territoriality).
• Random is, well, random. Nobody’s territorial or overly
social either.
– Macaroni Penguins video! What kind of dispersion do they
exhibit?
– Note to students: That bit about the first egg being bad, but
possibly an insurance egg? Remember that. It’s coming back
later…
Population Size
• The size of a population is pretty easy to
define. More important is how it changes.
• Population size is determined/will change
based on:
– Sex Ratio (males vs. females)
– Generation Time (when is sexual maturity)
– Age Structure
Generation Time Case in Point
• Chilean Sea Bass (Patagonian Toothfish)
• If you see this on the menu, don’t order it!
• Why?
– They live to 50 years old, but they don’t reach
sexual maturity until around 20 years old.
– As Nature News said, fishing for them is “almost
like logging for trees.”
• Not a sustainable population!
http://graphics8.nytimes.com/images/2006/11/08/dining/08bass.600.jpg
Population Size
• All those factors (generation time, male/female
ratio, et cetera) are considered part of a
population’s demography.
• Take a look at the life table below:
Demography: Survivorship Curve
• Take that life table from the previous slide and
turn it into a graph. What do you get?
Demography: Survivorship Curve
1000
Survival per thousand
• Generally, three different
patterns may emerge
from a life curve:
I. High death rate but
after reproduction age.
II. Constant mortality rate.
III. High initial death rate
with longevity for
survivors.
Human
(type I)
Hydra
(type II)
100
Oyster
(type III)
10
1
0
25
50
75
Percent of maximum life span
100
Demography: Age Structure
• You’ve heard the term “baby boomer,” right?
– Terms like that describe a cohort of, in this case, people.
• What can you learn about the growth rates of these countries
using the graphs?
Demography: Age Structure
•
•
•
•
Kenya shows the birth rate is higher than the death rate.
The U.S. shows a slight increase in birth over death.
Italy has a birth rate equal to its death rate.
Key note: These graphs show the youngest cohort at the bottom.
Practicing Population Control
• Let’s try it with an appropriately-named
activity:
– Natural Population Controls
So what’s it all mean?
• Here’s the big idea, both for population
ecology and for biology as a whole:
• Life is a trade-off between costs and benefits.
– I’m going to say that again for emphasis.
• Life is a trade-off between costs and benefits.
– You know what? Here’s one more.
• Life is a trade-off between costs and benefits.
Trade-Offs
• How many kids do you (think you) want?
• Why?
• Whether we think consciously about it or not,
there’s always a trade-off in reproduction.
• From an evolutionary perspective,
reproduction is the ultimate goal, but exactly
how many offspring you churn out (especially
at one time) can be…interesting.
Costs/Benefits of Reproduction
• Benefits:
– Reproduction. Duh.
• Costs:
– Reproduction involves a lot of investment in
energy, resources, and behavior changes.
– Doing so may also lead to increased vulnerability
to predation or other risks.
– If it weren’t for reproduction, species wouldn’t
reproduce.
Case in Point: European Kestrels
• Researchers artificially
increased brood size
(number of chicks) in
European kestrels’
nests, then measured
how many birds
survived the next
winter.
• The results?
Life Histories
• Looking at these various traits – reproductive
strategies, timing of reproduction,
survivorship…these are all part of an organism’s
life history.
– Think of life history like “demography,” except
something evident in an individual and not just over a
population.
• Of course, the most obvious element of life
history is how an organism reproduces.
– Do they tend to have just one or two babies?
– Do they tend to “go big or go home?”
Reproductive Strategies
• Two main reproductive strategies:
• r Selection
– Reproduce early in life, have lots o’ babies, invest
little time in caring for offspring as a parent.
• Think insects, many plants, Finding Nemo sorta…
• K Selection
– Have relatively few offspring later in life, invest a
lot of parental care.
• Primates, elephants, coconuts.
Implications of r and K Selection
• r selected
– Environment is unstable
– Density does not adversely
affect interactions
– Organisms are small
– Relatively low energy needed
to reproduce
– Sexual maturity reached soon
– Many offspring
– Individuals reproduce only
once
– Type III survivorship curve
• K selected
– Environment is stable
– Density does affect
interactions
– Organisms are large
– High parental investment in
offspring
– Sexual maturity reached late
– Few offspring
– Individuals reproduce
multiple times
– Type I or II survivorship curve
http://www.bio.miami.edu/tom/courses/bil160/bil160goods/16_rKselection.html
r and K Selection
• Where did these variables come from?
• They come from the logistic growth equation.
– Population growth rate approaches zero as the
population size nears the maximum that can be
supported.
– r represents the growth rate of a population.
• So r selected populations have high growth rates.
– K represents the limit of population density.
• So K selected populations exist near the density limit.
Aside: Within-Species Patterns
• Here’s something weird:
• In biology, there is certainty of maternity (it’s
easy to tell who the mother of a child is), but
even if you witness a birth, there is
uncertainty of paternity.
• Males, therefore, across the animal kingdom
are never fully sure they’re the father, and
therefore they’re never fully sure they’ll be
caring for their genes as they are passed on.
Aside: Within-Species Patterns
• Therefore, most males, as we know, tend to
invest less in their offspring than females do.
• The interesting part?
• This applies even on a cellular level!
– Males churn out a TON of sperm that have
relatively small cell volumes and basically just
carry DNA.
– Females make fewer, relatively LARGE eggs that
contain nutrients and protective structures in
addition to the DNA.
Back to Population Size
• The growth of a population also takes a
predictable pattern, at least under idea (read:
fictional) conditions:
More on
these in a
little bit…
Population Growth
• That’s an exponential curve, of course, but it represents
ideal conditions that lack limiting factors.
• These have been achieved a few times, mainly for
endangered species:
Whooping Cranes (back from extinction)
African Elephants (banned hunting)
And those limiting factors are…?
• As you might guess:
• Density-Dependent:
– Competition (food, mates, nest sites, et cetera).
• Hint hint: Macaroni Penguins!
– Disease
– Predation
– Waste
• Density-Independent:
– Sunlight, temperature, rainfall.
Growth Equations
• You may have noticed what looked a little
like…calculus?...on those graphs.
– Stuff like dN/dt = 1.0N.
• These are equations that can help us discuss
population growth…quantitatively.
• You can expect some of these problems on the AP
Test as well as mine.
• Let’s explore the types of questions you may be
asked.
But first!
• You do need to remember two things:
• r is the growth rate.
• So r is positive for growing populations and negative for
shrinking populations.
• K is the carrying capacity.
• The formulas on the next few slides are given
to you for the AP Exam and for my tests too,
however, not all variables are identified on the
formula sheet.
• I’ll name them all here so you can learn them.
The Variables
• dN/dt = change in population size over time.
– This is an actual number, not a percentage.
• N = population size.
• b = per capita birth rate. [per individual]
• B = births.
– So B/N = b.
• d = per capita death rate. [per individual]
• D = deaths.
– So D/N = d.
• r = per capita growth rate [sometimes shown as rmax].
– So r = b – d.
• BUT! r ≠ B – D.
Example of Variables
• Suppose we have a population of 200 rainbow trout,
and in the next year 24 hatch while 8 die. Therefore…
•
•
•
•
•
•
•
N = 200
B = 24
D=8
dN/dt = 16 (that’s 24 born minus 8 dead)
b = 0.12 (or 24/200)
d = 0.04 (or 8/200)
r = 0.08 (or 0.12-0.04)
• Notice that 0.08 * 200 = 16!
The Equations (1 of 2)
• Population Growth
dN
 B- D
dt
– That’s births minus deaths.
• Exponential Growth
dN
 rmax  N
dt
– That’s the growth rate times population size.
The Equations (2 of 2)
• Logistic Growth
dN
K-N
 rmax  N  (
)
dt
K
– That’s growth rate times population size, adjusted for
how close the population is to carrying capacity.
• Population Density
individuals
Density 
unit area
– Measured as ___ per ___.
Population Growth Rate Example
• In a population of 312 Andean condors, 17 die over
the course of the year while 22 are born. What is
the growth rate of the population?
• The birth rate (b) is 22/312 = 0.071; the death rate
(d) is 17/312 = 0.054.
r b-d
r  0.071 - 0.054
r  0.017
• 0.017 tells us the population is slightly growing.
Exponential Growth Example
• A population of 43 mice exists in a predator-free
field. Each individual mouse has an average litter
size of 5 pups each month. How many mice will
there be next month?
• There’s no death rate here, so we’re expecting a
large number as an answer.
dN
dN
dN
 rmax  N
= 5· 43
= 215 258  215  43
dt
dt
dt
• This is an r selected population.
Logistic Growth Example
• An African elephant wildlife refuge has a carrying
capacity of 511 elephants. The population is
currently at 443 elephants. Assuming a growth rate
of 0.009 elephants/year, what will be the change in
population size this year?
• This is a K selected population.
dN
K-N
 rmax  N  (
)
dt
K
dN
 0.531 elephants
dt
dN
511 - 443
 0.009  443  (
)
dt
511
Population Density Example
• If there are 500 chameleons living in a 3 mi2
area, what’s the density?
• 166.67 chameleons/sq. mi.
Key Notes
• dN/dt is not itself a mini-formula. Think of it as one
variable.
– It represents the change in a population over a time
period, and frequently is a whole number (like 17).
• Think of r as the “rate” of growth, and dN/dt as the
“amount” of growth.
– r is typically, but not always, a decimal.
– dN/dt is expressed in terms of “individuals.”
• Round any answer that lists an amount of individuals.
– So it’s 134 turkeys, not 133.5 turkeys.
• Don’t round anything that’s population density.
Key Notes Deux
• If you’re wondering why the AP formulas seem to
have B and b (and D and d) flipped, it’s because,
well…
– …I don’t know.
• Everyone uses b and d as rates but College Board
seems to have decided on B and D.
• Similarly, they get a little weird with dN/dt too.
• Use whichever system you want as long as it’s not
College Board’s. You’ll still get the right answer.
Putting them together…
• Let’s try these on our own:
– Population Growth Problems 1
• The formula reference section at the top is identical to
what you’ll have on the test/AP Exam.
• This is the harder worksheet.
– Population Growth Problems 2
• This is the easier worksheet.
The (Introduced) Elephant in the Room
• One of the hottest topics of population ecology is
the effect of introduced species on a population.
• If the introduced species doesn’t really
survive…no big deal.
• If it does, however, it may become an invasive
species capable of dramatic ecological imbalance.
– Invasive species get their name because they tend to
explode in number once they find a new niche to
occupy in a different habitate.
Invasive Species Examples
• Brown Tree Snake
– Introduced to Guam around WWII.
– Nearly eliminated native Micronesian Kingfisher
population (yay Philadelphia Zoo!).
http://upload.wikimedia.org/wikipedia/commons/e/e2/Micronesian_Kingfisher_1644.jpg
http://photos.the-scientist.com/legacyArticleImages/2012/05/05_12_Notebook_snake01.jpg
Aside: Heads-Up!
• Heads Up to Invasive Pests - Poison Mice Are
Falling From the Sky article
Invasive Species Examples
• Zebra Mussel
– Native to East Europe/West
Russia.
– The only freshwater mussel
that can attach to objects.
– Can attach to and kill native
mussels, destroy equipment,
and eliminate larval fish food
supplies.
http://www.fws.gov/midwest/mussel/images/zebra_mussels_on_native2_620.jpg
http://3.bp.blogspot.com/-96Yfb0lrtFI/ToXwLf557wI/AAAAAAAAACM/Q7El411zveM/s400/zebra_mussel_shopping_cart.gif
Invasive Species Examples
• European Starling
– Introduced to Central Park, NYC,
by a woman who wanted the
park to have all the animals
mentioned in Shakespeare’s
plays.
– Not particularly harmful other
than providing an unnecessary
level of competition.
• Despised by lots of birders,
nevertheless.
http://www.allaboutbirds.org/guide/PHOTO/LARGE/european_starling_16.jpg
Invasive Species Effects
• Broadly:
– Exponential growth of introduced species.
• Lack of predators or adequate competition.
– Overall decline in biodiversity.
– Eradication of native species.
• Sound familiar?
• Humans are invasive species!
Humans are Invasive Species
http://www.pbfcomics.com
Back to Population Growth
• In the absence of predators, competition, and other limiting
factors, we know we’ll see exponential growth.
• In reality, populations reach a point at which their
environment and resources can no longer sustain further
expansion.
– Not to mention the predator population may start to become
overwhelming.
• This point is called the carrying capacity of a population, and
it’s geo-specific (depends on the environment).
– At carrying capacity, population growth can still fluctuate but
generally has little net change.
– One more thing: Carrying capacity is given, confusingly, by the
letter K.
Population Growth
Without Limiting Factors
With Limiting Factors
Typical Growth Curves
• Notice something different between the curves?
– Why is the seal curve relatively smooth, while the plankton one is
a vomit-eliciting roller coaster?
• Seal reproduction is K selected; plankton r selected.
Number of breeding male
fur seals (thousands)
K
Number of cladocerans
(per 200 ml)
– Seal populations level off nicely as death rates increase, but
plankton over-reproduce and then suffer big population crashes.
– KEY: Death rates increase slowly for seals, fast for plankton.
– Let’s draw approximate carrying capacities for each.
10
8
K
6
4
2
0
1915
1925
1935
Time (years)
1945
500
400
300
200
100
0
0
10
20
30
40
Time (days)
50
60
Classic Population
Growth Chart
• Canada Lynx and Snowshoe Hare
– Placing a carrying capacity line is tricky – it needs
to be above the valleys but below the peaks:
K
K
Hare-y Lynx?
• Now here’s where it gets more interesting:
– It’s easy to see why the lynx population rises and falls.
• FYI they do eat other stuff, but it’s not as easy for them.
– But why exactly the hare population expands and
contracts isn’t so clear. It’s not just predation pressure.
– A 2009 study showed that stressed pregnant hares were
exposed to stress, their bodies released more cortisol
(stress hormone) and reproductive output declined.
– Therefore, at least some reason for hare decline is
simply exposure to lynx.
• Other evidence suggests food supply changes.
http://www.britannica.com/blogs/2011/06/rise-fall-canada-lynx-snowshoe-hare/
Lag Time
• I’m sure you noticed a gap between population
peaks for lynx and hare.
• This gap is called “lag time (or “lag”), and it’s
something that can be calculated.
• Suppose…
Therefore, the lag
time of the
predator
population is
approximately 1/2
month.
Month 1
http://www.cfr.washington.edu/classes.esrm.450/Lecture13/Cycles.pdf
Month 2
Lag Time – Another Context
• Suppose we took that Kenyan population from
before and we eliminated childhood mortality.
• As you might imagine, that “bottom-heavy”
population bubble of children is going to lead to a
population boom.
– BUT! Not till they reach reproductive age.
• So there will be a lag time within the population
prior to growth.
• Let’s look at a graph. Again.
Lag Time – Another Context
• You can see a lag time when the population is low and
limited by reproductive age.
• Then it takes off and starts growing toward K.
• If I give you some more data, you can calculate the
average population growth rate during the exponential
phase.
Therefore, over 4
months, the
population gained 38
individuals, or 38/4 =
9.5 fish/month.
157
119
10/1
6/1
http://legacy.hopkinsville.kctcs.edu/instructors/Jason-Arnold/VLI/M4Apopulationecology/f30-11_logistic_growth-_c.jpg
The Opposite of Limiting Factors?
• Here’s something weird:
• Warder Clyde Allee noticed, in 1927 no
less, that population growth can
actually be limited by low population
density.
– What? Read that again.
• Allee is saying that having a denser
population can actually speed growth.
– In other words, the Allee Effect suggests
that fitness can be increased if the
population is denser, leading to increased
survival.
http://www.mudancasabruptas.com.br/EfeitoAllee4.JPG
W.C. Allee
Allee Effect Examples
• Having more lions around means more effective
cooperative hunting and thus magnified lion
population growth.
– Component Allee effect.
• Having more lions around means more efficient mate
locating.
– Component Allee effect.
• The two component effects comprise a demographic
Allee effect.
– Overall (for reasons given by the component effects), the
density of the population increases the fitness of the
individuals.
Aside: Collective Animal Nouns
• Open the pdf!
Human Population Growth
• Uh…carrying capacity? We’re at ~7 billion!
• We’re adding ~82 million people a year.
• WALL-E?
Human Population Clock
(click me like you mean it)
So what are our limiting factors?
• Here’s one:
Closure: Videos
• A couple last population ecology TED videos to
wind us down:
– Hans Rosling: Global Population Growth Block by
Block
– Jessica Green: We’re Covered In Germs – Let’s
Design for That