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Lecture 6Population Ecology
Eben Goodale
College of Forestry,
Guangxi University
So what did you think about sweaty T-shirts?
P = 0.023R2 = 0.09
2.3 out of 100 timesthis result will be foundby chance.
X explains 9% of theVariance in Y.
Where we are
• Definition（定义） of ecology: interactions between organisms and their environment.
• Started with physical environment
• Then looked at how individual organisms balanced temperature, water, obtained energy.
Where we are
• These organisms have adaptations to fit the environment.
• We talked about evolution（进化论） and how natural selection produces adaptations.
• Behaviors, too, are adaptations.
Where we are
• So do individuals adapt?• No, this is a something that happens with a
population（种群） , as the individuals with the best adaptations survive and reproduce best.
• We now move on to talking about populations and their properties: distribution（分布） (where they are), abundance（丰富） (how many), growth（生长） (how abundance changes), dynamics（动力学） (changes more complicated than growth).
Today’s outline:Population Ecology
• Population density（密度） and dispersion• Life tables• Population growth
– Exponential（指数）– Logistic（对数）
• Population regulation• The situation with human population growth
Population Ecology
Three main characteristics of a population:
– Density（密度）– Dispersion（离差） – Demography（人口统计学）
Density
• Density- Is the number of individuals per unit area or volume
Times Square
Abandoned town
• What are the factors that underlie this?
− Birth− Death− Immigration（迁入）− Emigration（迁出）
Density• How do we measure it?• Census（人口普查） =
everyone counted.• If can’t count all individuals,
estimate by area, and extrapolation
（推算） .• An example of sampling
（取样） .
If there are 12 kangarooIn 5 ha, how many in 5000 ha?
Density• How do we measure it?• But what if things are
difficult to detect?• “Distance” analysis helps
adjust for difference in detectability（检测能力）
X
Density• How do we measure it?• But what if things are
difficult to detect?• “Distance” analysis helps
adjust for difference in detectability
X
2 bird species (yellow and blue),blue loud; yellow soft and onlyheard nearby.
Probabilityof detection（检测概率）
Distance (m)
Density
• How do we measure it?
• Mark-recapture（标志重捕法） :
another example of sampling
− capture some animals. − let them go.− recapture.− estimate population size.
•
Mark-Recapture
N = (mn)/xx/n = m/N
Assumethatpopulationmixes fully（假设人口充分混合）
m = # marked（被标记的）
x = marked recaptured（抓到中被标记的）n = total captured 2nd time（被抓到总数）N = estimated population size（推算出的总数）
Exercise
We are counted the population of the yellow-bellied motmot. 5 motmots were marked originally. Of a sample of 6 captured the second time, 1 was marked. How many motmots are there?
A) 5
B) 7
C) 15
D) 30
Dispersion• Dispersion is the pattern of spacing among individuals • Random（随机分布 ), clumped（成群分布 ), or
uniform（均匀分布） .• Clumped and uniform interactions formed by
interactions among individuals
CompetitionTerritorial behavior
Facilitation（简易化）Grouping behavior
Most common
Dispersion: an example from Western North America
The creosote bush(Larrea tridentata)
Young: clumpedbecauseof seedsin groups.
Mediumage: competitionamongst seedlingshas ended clumping. Now random.
Old:Bushes get so bigroots come intocompetition with others.
End up evenly spaced.
Demography
• Demography is the study of the vital statistics（动态变化） of a population– And how they change over time
• Rates:– Birth rate– Death rate
A life table is an age-specific summary of the survival pattern of a population
Death rate can be seen through survivorship data
Survival data can also expressed as a survivorship curve（生存曲线）
1000
100
10
1
Num
ber
of s
urvi
vors
(lo
g sc
ale)
0 2 4 6 8 10Age (years)
Males
Females
Death rate can be seen through survivorship data
Survivorship curves can be classified into three general types
Types differ in the relative rates of juvenile and adult survival
I
II
III
50 10001
10
100
1,000
Percentage of maximum life span
Num
ber
of s
urvi
vors
(lo
g sc
ale)
III: These kindsof organismstend todie oftenas young
I: These kindsof organismstend to livelong and dieof old age
Where are r (mouse) and K (elephant) strategieson this graph?
Birth rate can be seen through reproductive data
A reproductive table describes the reproductive patterns of a population, by age group.
Calculating population growth through the life table
These original #sare a bitstrange andatypical of thispopulation
Because survivorship ofolder individuals is low, thismix of age classes is moretypical of this population
What happens after year 5?Is this population growing?
Calculating population growth through the life table
Nt + 1
Nt
λ =
This early instability causedby those weird initial numbers
Otherwise, constant mortality and fecundity leads to constant λ(λ = population growth) log
individuals
time
age 1 2 3 4 5 6 7 8 9 100 20 108 84 154 172 252 320 436 570 7621 30 6 32 25 46 52 76 96 131 1712 50 24 5 26 20 37 42 61 77 105
total 100 138 121 205 238 341 438 593 778 1038
λ 1.38 0.88 1.69 1.16 1.43 1.28 1.35 1.31 1.33
Calculating population growth through the life table
This early instability causedby those weird initial numbers
Otherwise, constant mortality and fecundity leads to constant λ
Important to recognize:-Different mortality（死亡率 ), fecundity（生殖力） leads to different kinds of rate of growth-In nature, mortality and fecundity are not constant-This kind of life table shows time in step (t = 1,2,3 etc.)
λ
Geometric growth（几何生长） : calculated for pulsed
reproduction（繁殖波动）
(Nt) λNt+ 1 = Rearrange
What’s Nt + 2? Nt+ 2 = (Nt+ 1) λ
= ((Nt) λ) λ
= Nt λ2
λ = Nt+1
Nt
λ is called thegeometric rate ofincrease
Generally Nt = Noλt
When λ is ____, the population is stable.
When λ is ____, the population is growing
When λ is ____, the population is shrinking
Different kinds of reproduction: pulsed vs. continuous
If all in one seasonal year, we consider this to be “pulsed”.
Larvae juveniles adults reproduction larvae juveniles adults reproduction
Season 1, after which all adults die Season 2
On the other hand, if individuals of different ages are reproducing at once, asin humans, we consider it “continuous” reproduction（连续繁殖）
Now let’s talk about continuous reproduction
r = per capita（人均） rate of increase of population (~ birth – death)
population
birth
Immigration
(animals dispersing in)
death
Emigration(animals dispersing
away)
Now let’s talk about continuous reproduction
r = per capita rate of increase of population (~ birth – death)
populationbirth death
Assume “closedpopulation” (no immigration, emigration), then
dN
dT= (b – d) (N)
Differential equation（微分方程） = change in N over time
Birth and deathrates times thepopulation present
Continuous reproduction leads to exponential（指数） growth
dN
dT= (b – d) (N)
When r is ____, the population is stable.
When r is ____, the population is growing
When r is ____, the population is shrinking
Can we solve for Nt, just as we did for geometric growth?
dN
dT= rmax (N)
rmax is the rate of growthfor the species under idealconditions and is by definition > 1
dN
dt= r (N)
Continuous reproduction leads to exponential growth
dN
dt= r (N)
dN
N= r (dt) Integrate both sides
ln (Nt/N0) = rt Where No is the population at time=0And Nt is the population at time=t
Nt/N0= er(t)
Nt = Noer(t) The exponential growth equatione = 2.718
Nt = Noλt Notice the similarity
Exponential growthNt = Noer(t)
What happens when r = 0?
Nt = Noer(t) Nt = Noe(0) Nt = N0
What happens when r > 0 … let’s say it’s 1…, and let’s look at t = 1.
Nt = Noert N1 = Noe(1) N1 = No(2.718)
What happens when r < 0 … let’s say it’s -1…, and let’s look at t = 1.
Nt = Noert N1 = Noe(.95) Nt = No(.368)
Exponential growth …let’s solve some problems
How many duckweeds in cm2 after 4 days?
Original amount = 10 per cm2
r = .20 duckweeds per day per cm2
Nt = Noert N4 = (10)(2.718^.8)
22 per cm2
Exponential growth …let’s solve some problems
Nt = NoertSolve for r
ln(Nt/No)
tr =
Pheasants on Protection Island went from 40 to 426 individualsIn 2 years …. What’s r?
ln(426/40)
2r =
r = 1.18
Doubling time
• Question: For a given growth rate r, how long before the population doubles?
• Recall Nt = N0 * ert, now we are asking, “what is the value of t such that Nt = 2N0?
• 2N0 = N0 * ert
• 2N0 / N0 = ert
• 2 = ert • ln(2) = rt• (ln2)/r = t (the natural log of 2 = 0.693147…)
ExerciseIf the human population is growing at a rate of
1.5% a year, the doubling（加倍） time is
A)13 years
B)46 years
C)102 years
D)105 years
Hint:First solve Nt = Noert
For t = 1, and find r
Then use (ln2)/r = t To find doubling time
This is the same equation we use for compounding interest.A savings account that receives 1.5% annual interest willdouble in 46 years.
Exponential population growth
• Let’s now explore what happens when population growth is highest; that is, when conditions are ideal:
dN/dt = rmaxN
• Let’s plot population size vs. time:
As population growth(dN/dt) is dependent on N, the size ofthe population, itkeeps escalatingas N gets bigger
Exponential population growth:does this really happen?
• This happens in rare situations, like when bacteria are just started to let multiply on an agar plate, or a population that was threatened is protected:
In other words, when there’s nolimiting factors（限制因子）
Elephants after hunting stopped
Logisitic growth（对数增长）• Exponential growth
• Cannot be sustained（持续） for long in any population
• (Otherwise we would be knee deep in fruit flies, or worse!)
• A more realistic population model• Limits growth by incorporating carrying
capacity（承载力）
Carrying capacity = maximum population size thata particular environment can sustain
Deriving the logistic equation
• We want an equation in which population growth decreases as density gets higher
Deriving the logistic equation
Line: r = mN + b
Plug in slope and intercept
Deriving the logistic equation
dN/dt = rmaxN
The logistic equation
What is K?
K is the “carrying capacity”
When N > K, what is dN/dt?
When N = K, what is dN/dt?
When N < K, what is dN/dt?
NdN
dt
= rmax (N) (1 - K
)
The logistic equation
dN
dt
N
What does this graph look like?
The logistic equation
OK, now say that you are managing a aquaculture farm, Raising fish. How many fish would you want to have?
Exercise
You’re a fish farmer and you have found out that the carrying capacity for the fish in your tanks is 3000 fish. At how many fish should you keep the population so that your annual harvest is best?
A)1,000
B)1,500
C)3,000
D)6,000
The logistic equation in reality
The Logistic Model and Real Populations
But other organisms shown a trend to overshoot（超过） the carrying capacity, and then had back down to it, settling up an oscillating（震荡的） pattern….
Indicates that there’ssome time-lag时间间隔） beforethe effects of thecarrying capacityare felt.
Some assumptions（假设） of the logistic growth model
• K always stays the same
• Every additional individual has the same effect on the resources.
• There is no time lag between reaching K and feeling the effects of K
A famous prediction of humanPopulation growth in the 1920’s(dashes; real data is circles)
Exercise
In the 1920’s, scientists used the logistic equation to estimate population growth. However, their estimates were much too low. What mistake did they make?
A) They miscalculated r.
B) They forgot that the effects of K had a time lag.
C) They didn’t realize K would change
Estimated population was the curved line; actual data the circles
Today’s outline:Population Ecology
• Population density and dispersion• Life tables（生命统计表）• Population growth
– Exponential– Logistic
• Population regulation• The situation with human population growth
Population Regulation（种群调节）
• What environmental factors stop a population from growing?– Density independent– Density dependent
• Why do some populations show radical fluctuations（波动） in size over time, while others remain stable?
Population Regulation
• Density-independent factors– Affect a species independent of its population
size• Disturbance（干扰） (landslide, fire)• Abiotic factors such as weather
Sedge grass (Vulpia membranacea):lives at certain position along dunes.die-backs occur when sand stormsexpose roots.
Population Regulation
• Density-dependent factors• Any kind of factor that increases as population
also increases:– Competition– Territoriality– Stress– Disease– Build up of toxins
Competition• In crowded populations, increasing
population density– Intensifies intraspecific competition for resources
Beware “group selection（群体选择）” arguments:like idea that individuals are suppressing their reproduction for “good of the group”.
Territoriality（领土权）
• A special case of competition for space (and hence food, mates)
• Idea of “floaters”: animals without territories. Often juveniles, often not able to reproduce.
Stress（压力）
• Animals raised in crowded diseases show hormonal imbalances.
• Hormones（激素） could be adaptive for some reasons – getting food – and not for others – giving birth.
From Chapman et al., 1998
• One word:
Duck, duck, duck, Achoose!!!
kindergarten!• “the daycare germfest”
Disease（疾病）
Toxic（有毒的） by-products
• Often the limiting agent for bacteria colonies living on a small plate.
• For humans, too?
Density-dependent birth rate
Density-dependent death rate
Equilibrium density
Density-dependent birth rate Density-
independent death rate
Equilibrium density
Density-independent birth rate
Density-dependent death rate
Equilibrium density
Population density Population density Population density
Birt
h or
dea
th r
ate
per
capi
ta
(a) Both birth rate and death rate change with population density.
(b) Birth rate changes with populationdensity while death rate is constant.
(c) Death rate changes with populationdensity while birht rate is constant.
Population regulation is often a mix of density-dependent and
independent factors
Looking for equilibrium point(平衡点 ) between birth and death rates
Remember the different kinds of strategies we talked about before?
A) Have lot of reproduction at one time (semelparous), with many of those young not surviving to adulthood (survival curve, cIass III)
B) Have a few offspring per time period (iteroparous), but live long into adulthood (survival class I) These species do
well in competitiveenvironments, whereyear after year they gather enough energyto compete. Few youngper year.
These species are goodat getting to a new place (many young dispersers)and then growing and reproducing again
Life history synthesis
Dynamic（动态的） , notfully colonizedareas: goodfor our dispersive（分散的） , semelparous （终身一胎的） , short-livedspecies = r species
Stable（稳定的）environments:good for ourCompetitive（竞争的） , Iteroparous（反复生殖的） ,long-lived species =K species.
Emphasizes importanceof disturbance（干扰） inecology
Today’s outline:Population Ecology
• Population density and dispersion• Life tables• Population growth
– Exponential– Logistic
• Population regulation• The situation with human population growth
The Global Human Population
The human population increased relatively slowly until about 1650 and then began to grow exponentially
8000 B.C.
4000 B.C.
3000 B.C.
2000 B.C.
1000 B.C.
1000 A.D.
0
The Plague Hum
an
pop
ulat
ion
(bill
ions
)
2000 A.D.
0
1
2
3
4
5
6
The Global Human PopulationThe rate of growth began to slow approximately 40
years ago
1950 1975 2000 2025 2050Year
2003
Per
cent
incr
ease
2.2
2
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
1.8
Regional Patterns of Population Change
• Some “developed”（发达的） (“industrialized（工业化）” , “urban”??) countries have low birth rates, low death rates
• Some “developing”（发展中的） countries show high birth rates, high death rate. But death rate coming down faster than birthrate, so big growth.
In traditional farming families,the farm is a family affair.
50
40
20
0
30
10
1750 1800 1850 1900 1950 2000 2050
Birth rateDeath rate
Birth rateDeath rate
Year
Sweden Mexico
Birt
h or
dea
th r
ate
per
1,00
0 pe
ople
Demographic Transition（人口过度）
Moving from high birth/death to low birth/death
Age StructureRapid growth Afghanistan
Slow growth United States
Decrease Italy
Male Female Male Female Male FemaleAge Age
8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8Percent of population Percent of population Percent of population
80–8485
75–7970–7465–6960–6455–5950–5445–4940–4435–3930–34
20–2425–29
10–145–90–4
15–19
80–8485
75–7970–7465–6960–6455–5950–5445–4940–4435–3930–34
20–2425–29
10–145–90–4
15–19
Difference between regions can be seen inpopulation pyramids
Estimates of Future Population Growth and Carrying Capacity
• The carrying capacity of Earth for humans is uncertain.• Increases in food production can increase the carrying
capacity, but only within limits.• How many people the earth can support depends on
the quality of life people wish to have or are willing to accept.
Homework
• For Saturday, Apr 11, Chapters 11 and 12.
• Begin to review for midterm next week:
• Lecture notes 1-5, Chapters 9-12
• 5 readings associated with first 5 lectures.
Key concepts
• A population can be characterized by its density, its dispersion and its demography.
• Population ecologists have several tools to estimate population sizes.
• A lifetable summarizes survival and fecundity (reproductive) data for a population.
• A rapid increase in a population is described by the exponential model (rare in nature).
• In the logistic equation a population reaches a stable density at the carrying capacity.
• Density-dependent factors keep a population from growing too large.
