Population GrowthPopulation Growth

GoalsExponential Growth

Population DistributionLogistic Growth

Carrying CapacityCreated: 9/13/13 Revision: 9/13/13

Revision Number: 0

PopulationsPopulations

SamplingSampling

PlotPlot MarkMark

Density & Density & DistributionDistribution

ClumpedClumped

UniformUniform

RandomRandom

Growth Growth ModelsModels

ZeroZero ExponentialExponential LogisticLogistic

Carrying Carrying CapacityCapacity

Survivorship Survivorship CurvesCurves

Type IType I

Type IIType II

Type IIIType III

Population Concept Map

Life History Life History PatternsPatterns

KK

rr

GoalsGoals

• Why study population?

• Introduce real life issues with populations.

• Collect data on population box.

Who Studies Populations?Who Studies Populations?

Photos from http://www.ocearch.org/http://limnology.wisc.edu

Why Study Populations?Why Study Populations?

Photos from http://rogerbourland.com/http://www.ocearch.org/

Endangered SpeciesEndangered Species

COMMON NAME SCIENTIFIC NAME CONSERVATION STATUS ↓

Amur Leopard Panthera pardus orientalis Critically Endangered

Black Rhino Diceros bicornis Critically Endangered

Cross River Gorilla Gorilla gorilla diehli Critically Endangered

Hawksbill Turtle Eretmochelys imbricata Critically Endangered

Javan Rhino Rhinoceros sondaicus Critically Endangered

Leatherback Turtle Dermochelys coriacea Critically Endangered

Mountain Gorilla Gorilla beringei beringei Critically Endangered

Saola Pseudoryx nghetinhensis Critically Endangered

South China Tiger Panthera tigris amoyensis Critically Endangered

Sumatran Elephant Elephas maximus sumatranus Critically Endangered

Sumatran Orangutan Pongo abelii Critically Endangered

Sumatran Rhino Dicerorhinus sumatrensis Critically Endangered

Sumatran Tiger Panthera tigris sumatrae Critically Endangered

Vaquita Phocoena sinus Critically Endangered

Western Lowland Gorilla Gorilla gorilla gorilla Critically Endangered

Yangtze Finless Porpoise Neophocaena asiaeorientalis ssp. asiaeorientalis Critically Endangered

http://worldwildlife.org/

Hunting LimitsHunting Limits

why-youmad.com

deertagmuseum.com

Gain and Loses in Population Gain and Loses in Population SizeSize

• What are some factors that can affect the size of a population?

Ohio Treats Ohio Treats

Photo provided by: www.nytimes.com

PopulationsPopulations

• Populations = N

• Organisms of the same species that occupy a particular area and breed with one another more than they breed with members of other populations.

• Population size - is the number of individuals in a population.

Plot Sampling and Mark-Plot Sampling and Mark-RecaptureRecapture

• Video on mark-recapture

• Simulation

Photos provided by: www.junicoast.gr http://www.ocearch.org/

Population Density & Population Density & DistributionDistribution

• Population Density – number of individuals per unit area or volume.

• Clumped – A patchy distribution of resources encourages clumping.

• Near-Uniform- Competition for resources can produce a near-uniform distribution.

• Random – When resources are uniformly available and proximity to others neither benefits nor harms an individuals.

Name The Population Name The Population DistributionDistribution

Photos provided by: wps.pearsoncustom.com

A

B C

Population Box ActivityPopulation Box Activity• Goals of Activity:

– Collect data on population (N) size.– Collect data on population (b) births.– Collect data on population (d) deaths.– Graph data population size and time.– Observe the trends of the data.

www.dailymail.co.uk

Peppered Moth GamePeppered Moth Game

http://www.techapps.net/interactives/pepperMoths.swf

http://www.blackwellpublishing.com/

HomeworkHomework

• What is poaching? Reflection?

• Look up some info on shark finning and how it is affecting the population.

Population GrowthPopulation Growth

GoalsExponential Growth

Population DistributionLogistic Growth

Carrying CapacitySurvivorship

Created: 9/13/13 Revision: 9/13/13 Revision Number: 0

Mark-RecaptureMark-Recapture

• Video on mark-recapture

• Simulation

Photos provided by: www.junicoast.gr http://www.ocearch.org/

(# Captured First Run)(# Captured Second Run)---------------------------------------------------------------

(# Tagged from Second Run)

Zero Population GrowthZero Population Growth

• Anyone Know?

What is Exponential Growth ?What is Exponential Growth ?• Anyone know?

• As long as the rate is constant and greater than zero exponential growth will occur.

• Exponential growth when graphed out represents a J-shaped curve.

• The number of new individuals added increases each generation, although the growth rate stays the same.

• In exponential growth each generation is larger than the prior one.

Variables and EquationsVariables and Equations

http://www.supercoloring.com/

VariablesPopulation Size = N Time = tGrowth Rate = rBirths = bDeaths = d

Equationsr= (Births – Deaths) / NdN/dt= r(N)

Time Population

0 10

1

2

3

4

J-Shaped CurveJ-Shaped Curve

AssessAssess

• Supposed we have no deaths in a population of 1 and we have a birth of 1.

• What is the growth rate?

Problem of the day.Problem of the day.

Limiting Factor – is an essential resource that is in short supply acts as a limiting resource.

Populations obliviously can’t exponentially grow forever, there are factors that limit a population and its size, list some limiting factors that controls a populations growth.

Density - DependentDensity - Dependent

• Factor(s) that limits population growth and has a greater effect in dense populations than less dense ones.

flyrv7.com www.panoramio.com

Density-IndependentDensity-Independent

• Factor(s) that limits population growth and arises regardless of population density.

www.wildlandfire.com www.boston.com

AssessAssess

www.dailymail.co.uk

jonlieffmd.com

Carrying Capacity (K)Carrying Capacity (K)

• It is the maximum number of individuals of a population that a given environment can sustain indefinitely.

• Resources determine population size.

Question?Question?

• Do you think there is a carrying capacity for humans?

• One child policy

Exponential Growth (J-Shaped Exponential Growth (J-Shaped Curve)Curve)

Exponential EquationdN/dt = r(N)

t N dN/dt

0 2

30

http://www.supercoloring.com/

Logistic Growth (S-Shape)Logistic Growth (S-Shape)Carrying Capacity Equation

dN/dt = r(N)(K-N/K)t N K-N/K dN/dt

0 2r = 1K = 10

Logistic Growth (S-Shaped Logistic Growth (S-Shaped Curve)Curve)

peterhuff.wordpress.com

Inflection Point – Point at which in the logistic growth curve where population growth is maximal, and after this point the population starts to slow growth.

Rabbits and GrassRabbits and Grass

Bozeman Biology

Life History StrategiesLife History Strategies

Life History Pattern - How an organism allocates its resources between growth, maintenance, and reproduction over the course of its lifetime.

r-Selected Speciesr-Selected Species

• Adapted to conditions that change rapidly and unpredictably.

• Density Independent factors effect them the most.

• r-selected species produce multiple offspring at once, maximizing offspring quantity rather than quality.

r-Selected Speciesr-Selected Species

• Early Reproduction

• Less Parental Investment

• Short Life Span, high mortality rate

• Short Development

www.lemonbayconservancy.org info.franklinpestsolutions.com

K-Selected SpeciesK-Selected Species

• Adapted to life in a stable environment.• Allow population size to approach carrying

capacity of the environment.• Density-dependent factors limits individual

reproductive success.• Favors individuals who maximize their

reproductive success by producing high quality offspring capable of outcompeting others for resources.

K-Selected SpeciesK-Selected Species

• Long development

• Later reproduction

• More parental investment

• Longer life span lower mortality rate.

www.wildaid.org

Survivorship CurvesSurvivorship Curves

Cohort – Group of individuals born during the same time interval.

Survivorship Curve – Graph showing the decline in numbers of a cohort over time.

biology-forums.com

Asses Endangered SpeciesAsses Endangered Species

HomeworkHomework

Self-Quiz pg. 806-8072,3,6,10,11, and 13

Critical Thinking pg. 807A

1,5,7, and 9

VariablesGrowth Rate = rBirths = bDeaths = dPopulation = NCarrying Capacity = KTime = t

t N

0 10

1

1.) Starting population is 10.2.) We birth 5 rabbits, and 2 die.3.) Calculate growth rate. 4.) 5-2 / 10 = 0.3 = r5.) Calculate the change in population over time6.) ΔN/Δt = 0.3(10) = 37.) 3 + 10 = New Population = 13 8.) Starting population is 13.9.) Growth rate is constant10.) Use previously calculate r = 0.311.) Calculate the change in population over time12.) ΔN/Δt = 0.3(13) = 3.913.) 3.9 + 13 = New Population = 17

t N

0 10

1 13

2 17

Exponential Growth (J-Shape Curve)

Equations (Births – Deaths)r = ----------------------- N

ΔN----- = r (N)Δt

Data Given

VariablesGrowth Rate = rBirths = bDeaths = dPopulation = NCarrying Capacity = KTime = t

Equations (Births – Deaths)r = ----------------------- N

ΔN----- = r (N)Δt

1.) Starting population is 2.2.) We birth 2 rabbits, and 0 die.3.) Calculate growth rate. 4.) 2-0 / 2 = 1 = r5.) Calculate the change in population over time6.) ΔN/Δt = 1(2) = 27.) 2 + 2 = New Population = 4 8.) ΔN/Δt = 1(4) = 49.) 4 + 4 = New Population = 810.) ΔN/Δt = 1(8) = 8

Exponential Growth (J-Shape Curve) leading into Carrying Capacity K.

t N ΔN/Δt

0 2

t N ΔN/Δt

0 2 2

1 4 4

2 8 8

3 16 16

Use the r = 1 to take to the next slide

Data Given

VariablesGrowth Rate = rBirths = bDeaths = dPopulation = NCarrying Capacity = KTime = t

Equations (Births – Deaths)r = ----------------------- N

ΔN----- = r (N)Δt

ΔN (K-N)----- = r (N) --------Δt K

Logistic Growth Carrying Capacity K (S-Shaped Curve)

t N K-N / K

ΔN/Δt

0 2

t N K-N / K

ΔN/Δt

0 2 0.8 1.6

1 3.6 0.64 2.3

2 5.9 0.41 2.4

3 8.3 0.17 1.4

4 9.7 0.03 0.29

5 9.99 0.001

0.009

1.) Using r = 1 from previous slide2.) Solve K-N/K, 10-2/10 = 0.83.) Solve ΔN/Δt = r(N)((K-N)/N), ΔN/Δt = (1)(2)(0.8)= 1.64.) Solve 1.6 + N, 1.6+2 = 3.65.) Repeat Previous Steps6.) Solve K-N / K, 10-3.6 / 10 = 0.647.) Solve ΔN/Δt = r(N)((K-N)/N), ΔN/Δt = (1)(3.6)(0.64)= 2.38.) Repeat Previous Steps

Data r =1 K = 10

Notice how the population gets so close to the carrying capacity, I didn’t round any figures in this problem so we can observe the 9.99 value.

Data Given

• Equations and explanation from Bozeman Science, click the links (words) below for a step by step explanation.

• Exponential

• Logistic

Evidence of Life History Patterns

• Life History is a set of traits related to growth, survival, and reproduction, such as age-specific mortality, life span, age of first reproduction and number of breeding events.– Evolutionary Biologists J. Endler and D.

Reznick studied the effects of predation on life history traits.

– Pressures such as predation and commercial fishing may change life history patterns influencing the evolution of a species.

Human Population Growth

• The population growth rate of humans began to increase about 10,000 years ago and during the last 2 centuries it has SOARED.

• 3 Trends promoted the large increases – 1st Humans were able to migrate into new

habitats– 2nd Humans developed new technologies that

increased the carrying capacity.– 3rd Humans sidestepped some limiting factors

Human Populations

• Historically disease always kept population growth regulated (density dependent factor)

– 1300’s Black Death killed 1/3 of Europeans!!– Twelve disease that altered our history

Things began to change

– 1700’s Edward Jenner demonstrates the effectiveness of vaccines against small pox.

– Mid 1800’s Ignaz Semmelweis began urging surgeons to wash their hands between patients.

– 1800’s Louis Pasture popularized the idea that unseen organisms cause disease. (pasteurization)

– Late 1800’s first modern sewers in London divert waste water from drinking water areas.

– Early 1900’s chlorination and sterilization of drinking water.

Population Demographics• Total fertility rate of a human population is the

average number of children born to a woman during her reproductive years.

• Age structure greatly affects a population’s growth rate. – China and India have more than 1 billion people a piece.– Next highest is the US with 310 million.

• The broader the base of an age structure diagram, the greater the anticipated population growth.

Demographic Transition

• Demographic factors vary among countries, with the most highly developed countries having the lowest fertility rates and infant mortality and the highest life expectancy.

• Demographic transition models describe how changes in population growth often occur in four stages of economic development.

Stages of Demographic Transition

• Preindustrial stage- before technological and medical advances, birth and death rates are high, growth rate low.

• Transitional stage- industrialization begins, food production and healthcare improve, death rate drops fast, birth rate decline more slowly, population growth rate increases rapidly.

• Industrial stage- birth rates decline, move from farms to cities, birth rates move closer to death rates, population grows less rapidly.

• Postindustrial stage- populations growth becomes negative, birth rate falls below death rate and population size slowly decreases.

Sustainability

• Sustainability is the ability for a system to supply resources needed, while never running out of those resources.

• Per capita resource consumption rises with economic and industrial development.

• Ecological footprint is the amount of Earth’s surface required to support a particular level of development and consumption in a sustainable fashion.

• For everyone now alive to live like an average American would require four times the sustainable resources available on Earth.