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# POPULATION GROWTH & MEASUREMENT

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POPULATION GROWTH & MEASUREMENT
AP Environmental Science Chapter 6

WHAT IS A POPULATION? A group of interbreeding individuals within a geographical location. POPULATION SIZE is determined by: #of births (based on fertility rates) # of deaths # 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 DENSITY DENSITY: number of individuals per unit area or volume Ex: Suppose there are 150 bullfrogs living in a pond 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 Population Modeling

CARRYING CAPACITY Max population that a habitat can support
E D A T O S F O D D I S E A D I S A s T E R = Max population that a habitat can support (Level line)

Carrying Capacity Factors
These limiting pressures keep a population in check such as carrying capacity: 1. # of Predators 2. Amount of Food & Water Resources Disease Natural Disasters Reproductive 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 keeps growing quickly (exponentially over time).

What causes J-curve to occur?
Conditions: No enemies No competition. Plenty of food & water 4. Low % of disease J-curve is usually a temporary situation=Population crash.

Exponential Growth Math Model
Change in N Change in time Initial Population Rate of reproduction Time

dN/dt = rN Time (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 10x20=200 2x10x10 T3 200 10x200=2,000 2x10x10x10 2000 10x2,000=20,000 2x10x10x10x10 T4 20,000 10x20,000=200,000 2x10x10x10x10x10 N=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, Michigan National Park Moose pop
quickly in Wolf pop due to Parvovirus 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. S-curve may change (increase & decrease) slightly, but is constant near the carrying capacity. 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 time dt N = Population K= Current Carrying Capacity r= rate of change or reproductive rate of a speciesd

Logisitics/Carrying Capacity Connection
If the carrying capacity (K) = 100 wolves If the N = 100 wolves (wolves bred successfully to increase population) Look at the 1-N/K part: 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) = .90 100 dN = 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 n m2 n1=#animal marked & released 1st time n2=# animals captured during 2nd session m2-# animals captured during 2nd session & are marked. Est Population

Population Measurement in Review
J-curve Exponential Curve S-curve Logistics Curve Carrying Capacity

Population Equilibrium
Equilibrium: the balance between births and deaths within a population

Other Population Considerations
Environmental Resistance Population Dispersal Reproductive Potential

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 or population will inhabit a certain geographical location.

Population Dispersal is determined by:
Random Uniform Clumped

POPULATION DISPERSAL A. RANDOM: 1. Least Common
2. Found anywhere in envir. 3. High mobility such as wind blown Ex: Dandelions

POP DISPERSAL B. Uniform
Rare Occurrence but does occur in nature! (Hawks, wolves) Can indicate human impact a. Plantations, orchards, etc.

UNIFORM POPULATION DISP.
Red-Tailed Hawk Orchards

CLUMPED POP DISPERSAL C. CLUMPED: Patchy, most common
Protection, avail of natural resources, to survive 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
R-selected Hint: Rapid Repro Early reproduction Short life span Hi mortality Little/no parental care Large # of offspring produced Inhabit lower trophic levels (1st order consumers) 2. K-selected Hint: Longer Repro Late reproduction Long life span Low mortality High parental care 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 days laying eggs every 3 days. Mosquito rafts have eggs;. hatch in 48 hours

Reproductive potential – “K”
Some species have higher reproductive potential!! K-Potential Gestation Times: Human= 9 months Elephants= 22 months Oppossum = 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 area C2. 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.

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