POPULATION GROWTH & MEASUREMENT

AP Environmental ScienceChapter 6

WHAT IS A POPULATION?

A group of interbreeding individuals within a geographical location.

POPULATION SIZE is determined by:

a. #of births (based on fertility rates)

b. # of deathsc. # of indiv that enter or leave the

population

Population Graphs measure status of populations

J-curve or Exponential Growth Curve

S-Curve or Logistics Curve

POPULATION DENSITYDENSITY: number of

individuals per unit area or volume

Ex: Suppose there are 150 bullfrogs living in apond that covers an area 3 square km. What is the population

density?

Population density

Population Density =

Number of Individuals (150 frogs) Unit Area (3 sq KM)

= 50 bullfrogs per square kilometer!

Populations Dynamics

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Population Modeling

CARRYING CAPACITY

Max population that a habitat can support

(Level line)

DISEASE

DISAsTERS

=

PREDATORS

FOOD

Carrying Capacity Factors

These limiting pressures keep a population in check such as carrying capacity:1. # of Predators2. Amount of Food & Water ResourcesDiseaseNatural DisastersReproductive ability

Other factors – H I P P O can decrease in population!!

H=Habitat I= Invasive species P= Pollution P=Other interacting populations O=Overconsumption

Exponential Increase (J-curve)

In a J-curve,the popul keepsgrowing quickly(exponentially

over time).

What causes J-curve to occur?

Conditions:1. No enemies2. No competition.3. Plenty of food & water4. Low % of disease J-curve is usually a temporary

situation=Population crash.

Exponential Growth Math Model

Rate of reproduction

Initial Population

Time

Change in N

Change in time

dN/dt = rNTime (dt)

N(dN)

Rate (r)*

r x N Exponentially how does it look for a J-curve

T1 2 10 10x2 = 20 2x10

T2 20 10 10x20=200 2x10x10

T3 200 10 10x200=2,000 2x10x10x10

T3 2000 10 10x2,000=20,000 2x10x10x10x10

T4 20,000 10 10x20,000=200,000 2x10x10x10x10x10N=2 cockroaches (male and female)r= 2 cockroaches can produce 20 offspring in 3 months

a. The rate of growth (r) 20/2 adults or 10 per 1 adult.b. The growth rate (r) equals 10

Figure 06_03

Exponential Growth can Crash

When population can no longer sustain itself without food resources, pop decrease beneath the carrying capacity.

Population Crash

Isle Royale, MichiganNational Park

Moose popquickly in 1991-1995.

Wolf pop due toParvovirus passed on from domesticated dogs visiting the National Park.

Moose population Due to tick infestation.

S-curve (Logistics curve)

S-curve or Logistics Population

1. Population at equilibrium.

2. S-curve may change (increase & decrease) slightly, but is constant near the carrying capacity.

3. May be considered “restricted growth”.

Factors that keep populations within carrying capacity

Migration

Logistics Curve Model

dN = rN 1-N dt K

dN = change of population over timedtN = PopulationK= Current Carrying Capacityr= rate of change or reproductive rate of a speciesd

Logisitics/Carrying Capacity Connection

If the carrying capacity (K) = 100 wolvesIf the N = 100 wolves (wolves bred successfully to increase population)Look at the 1-N/K part: 1 - 100

100 1- 1 = 0

dN/dt = rN(0)=0!!!

Logistics & CC (continued)

There is no change in dN/dt-no population growth!

What if N=50? Plug it into 1-N/K to see how it affects the reproductive rate for a population. 1-50/100 = 1-1/2 = 1/2rN or half of the maximum reproductive rate for the wolves.

Logistics & CC (continued)

If N = 10…plug into 1-N/K(1- 10) = (1-.10) = .90 100dN = rN(.90) or dN is at a rate of dt dt

90% as fast as the max possible reproductive rate for the wolves!

Lincoln Peterson Population Estimate Model

Estimating population size by random sampling an ecosystem.Focus on population density or animal abundance. Model: n1 = m2 OR N= n1 x n2 N n2 m2n1=#animal marked & released 1st time n2=# animals captured during 2nd sessionm2-# animals captured during 2nd session & are marked.

Est Population

Population Measurement in Review

Population Equilibrium

Equilibrium: the balance between births and deaths within a population

Other Population Considerations

Environmental Resistance

Factors/pressures that limit a population’s ability to increase (CC)

Density Dependent Density Independent

Parasites Temperature

Disease Moisture, light, pH salinity

Competitors Weather

Predators Natural Disasters

Human Intervention Lack of habitat/territory

Population Dispersal Definition

Different patterns of how a species orpopulation will inhabit a certaingeographical location.

Population Dispersal is determined by:

POPULATION DISPERSAL

A. RANDOM: 1. Least Common2. Found anywhere in

envir.3. High mobility such

as wind blown Ex: Dandelions

POP DISPERSAL

B. Uniform1. Rare Occurrence but does occur

in nature! (Hawks, wolves)

2. Can indicate human impact a. Plantations, orchards, etc.

UNIFORM POPULATION DISP.

Orchards

Red-Tailed Hawk

CLUMPED POP DISPERSAL

C. CLUMPED:1. Patchy, most

common2. Protection, avail of

natural resources, to survive

3. Ex: Allelopathy, fish, plants, trees, etc.

Clumped Dispersal – Purple Loosestrife Patterns in US

Reproductive Potential

…Is an organism’s ability to grow at the fastest rate.

(To replenish the species—innate!)

REPRODUCTIVE

POTENTIAL COMPARISON

1. R-selectedHint: Rapid Reproa. Early reproductionb. Short life spanc. Hi mortalityd. Little/no parental caree. Large # of offspring

producedf. Inhabit lower trophic

levels (1st order consumers)

2. K-selected Hint: Longer Reproa. Late reproductionb. Long life spanc. Low mortalityd. High parental caree. Small # of offspring

produced

REPRODUCTION TYPES

K-SELECTED TYPE

R-SELECTED TYPES

Reproductive potential – “R”

Bacterium can produce 19 million descendants in a few days!!

Mosquitoes live 10-14 days laying eggs every 3 days.

Mosquito rafts have 200-300 eggs;. hatch in 48 hours

Reproductive potential – “K”

Some species have higher reproductive potential!!

K-Potential Gestation Times:Human= 9 monthsElephants= 22 monthsOppossum = 12-13

days (marsupial)

CRITICAL NUMBERS

Survival & recovery of population depends on a minimum population base—its critical number.

Factors Affecting Critical Number

C1. IMMIGRATION: movement of indiv into an areaC2. EMIGRATION: movement of individuals which leave

an area. Plus

Environmental Resistance Factors

Critical Numbers

If pop falls below critical number, breeding may fail and extinction could occur.

Threatened: species whose pops are declining rapidly

Endangered: near critical number and may become extinct.