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**POPULATION GROWTH & MEASUREMENT**

AP Environmental Science Chapter 6

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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

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**Population Graphs measure status of populations**

J-curve or Exponential Growth Curve S-Curve or Logistics Curve

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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?

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**Population density Population Density =**

Number of Individuals (150 frogs) Unit Area (3 sq KM) = 50 bullfrogs per square kilometer!

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**Populations Dynamics Population Modeling**

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**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)

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**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

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

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

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**Exponential Increase (J-curve)**

In a J-curve, the popul keeps growing quickly (exponentially over time).

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**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.

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**Exponential Growth Math Model**

Change in N Change in time Initial Population Rate of reproduction Time

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**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

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Figure 06_03

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**Exponential Growth can Crash**

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

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**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.

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**S-curve (Logistics curve)**

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**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”.

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**Factors that keep populations within carrying capacity**

Migration

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**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

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**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!!!

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**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.

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**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!

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**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

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**Population Measurement in Review**

J-curve Exponential Curve S-curve Logistics Curve Carrying Capacity

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**Population Equilibrium**

Equilibrium: the balance between births and deaths within a population

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**Other Population Considerations**

Environmental Resistance Population Dispersal Reproductive Potential

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**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

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**Population Dispersal Definition**

Different patterns of how a species or population will inhabit a certain geographical location.

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**Population Dispersal is determined by:**

Random Uniform Clumped

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**POPULATION DISPERSAL A. RANDOM: 1. Least Common**

2. Found anywhere in envir. 3. High mobility such as wind blown Ex: Dandelions

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**POP DISPERSAL B. Uniform**

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

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**UNIFORM POPULATION DISP.**

Red-Tailed Hawk Orchards

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**CLUMPED POP DISPERSAL C. CLUMPED: Patchy, most common**

Protection, avail of natural resources, to survive Ex: Allelopathy, fish, plants, trees, etc.

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**Clumped Dispersal – Purple Loosestrife Patterns in US**

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**Reproductive Potential**

…Is an organism’s ability to grow at the fastest rate. (To replenish the species—innate!)

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**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

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REPRODUCTION TYPES K-SELECTED TYPE R-SELECTED TYPES

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**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

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**Reproductive potential – “K”**

Some species have higher reproductive potential!! K-Potential Gestation Times: Human= 9 months Elephants= 22 months Oppossum = days (marsupial)

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

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**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

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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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