• mean of a population
o parameter
o (mu)
• mean of a sample
o statistic
o (x-bar)
• parameter --> population
• statistic --> sample
• sampling bias
o unbiased = the center of the sampling distribution is equal to the mean of the population
• sampling distribution
o the distribution of values taken by the statistics in all possible samples of the same size from the same population
• central limit theorem
o when n is large, (x-bar) is close to normal even if the population is not normal
o (n = sample size)
Tuesday, January 29, 2008
Stat. Geometric Distributions - Cooney
notes from textbook section 8.2: The Geometric Distribution
• a random variable X is geometric provided that the following conditions are met:
o each observation falls into one of just two categories, which for convenience we call “success” or “failure”
o the probability of a success, call it p, is the same for each observation
o the observations are all independent
o the variable of interest is the number of trials required to obtain the first success
• calculating geometric probabilities
o given that it’s geometric (see above), the probability that the first success occurs on the nth trial…
o P (X = n) = (1 – p)^(n-1) • p
• mean of a geometric random variable
o 1 / p
o a.k.a. the “expected value”
• variance
o (1-p) / p^2
• the probability that it takes more than n trials to see the first success is…
o P (X > n) = (1 – p)^n
• the sum of a geometric sequence
o (a) / (1 – r)
o a = probability (success)
o p = probability (failure)
• a random variable X is geometric provided that the following conditions are met:
o each observation falls into one of just two categories, which for convenience we call “success” or “failure”
o the probability of a success, call it p, is the same for each observation
o the observations are all independent
o the variable of interest is the number of trials required to obtain the first success
• calculating geometric probabilities
o given that it’s geometric (see above), the probability that the first success occurs on the nth trial…
o P (X = n) = (1 – p)^(n-1) • p
• mean of a geometric random variable
o 1 / p
o a.k.a. the “expected value”
• variance
o (1-p) / p^2
• the probability that it takes more than n trials to see the first success is…
o P (X > n) = (1 – p)^n
• the sum of a geometric sequence
o (a) / (1 – r)
o a = probability (success)
o p = probability (failure)
APES Population Growth - Shope
Thomas Robert Malthus
• late 1700s / early 1800s
• educated (Harvard); from England
• “Essays on the Principles of Populations”
o 1798
o he was concerned about the rapidly growing population (early stages of industrial revolution)
o originally concerned with food & carrying capacity
o then concerned with being able to afford the population
• “In nature, more offspring are produced than can survive.”
• developed our modern ideas about population & population growth
• logistic growth
o populations tend to expand until they reach the carrying capacity (k), then level off
o arithmetic
o “S” curve
• exponential growth
o how humans are reproducing
o geometric
o “J” curve
• overshoot growth
o population rises then suddenly… a dieback/crash
o after crash: either recovery or extinction
• late 1700s / early 1800s
• educated (Harvard); from England
• “Essays on the Principles of Populations”
o 1798
o he was concerned about the rapidly growing population (early stages of industrial revolution)
o originally concerned with food & carrying capacity
o then concerned with being able to afford the population
• “In nature, more offspring are produced than can survive.”
• developed our modern ideas about population & population growth
• logistic growth
o populations tend to expand until they reach the carrying capacity (k), then level off
o arithmetic
o “S” curve
• exponential growth
o how humans are reproducing
o geometric
o “J” curve
• overshoot growth
o population rises then suddenly… a dieback/crash
o after crash: either recovery or extinction
APES Demographic Transitions - Shope
• pre-industrial
o high birth rate
o high death rate
• transitional
o high birth rate
o low death rate
• industrial
o low birth rate
o low death rate
• post-industrial
o birth rate lower than or equal to the death rate
o zpg = zero population growth
o replacement fertility: 2.1 children per couple
o high birth rate
o high death rate
• transitional
o high birth rate
o low death rate
• industrial
o low birth rate
o low death rate
• post-industrial
o birth rate lower than or equal to the death rate
o zpg = zero population growth
o replacement fertility: 2.1 children per couple
APES Populations Vocab - Shope
• population
o a group of the same species in the same area
• demography (demographics)
o the statistical study of populations, especially with reference to size, density, distribution, and vital statistics (birth, death, age, sex, health)
• population momentum
o potential for growth as young members reach reproductive age
• population explosion
o an increase in population at an exponential rate, usually surpassing the carrying capacity
• population crash
o a sudden decline in population caused by predation, waste accumulation, disease, resource depletion, or environmental change
o a.k.a. dieback
• carrying capacity
o the maximum population that can be supported within a habitat
o graphically abbreviated as “k”
• natality
o birth or death rates
• crude birth rate
o the number of individuals born per 1000
o abbreviated: CBR
• crude death rate
o the number of individuals died per 1000
o abbreviated: CDR
• fertility
o the ability for reproduction
o almost synonymous with “fercundity”
• fercundity
o the capacity for reproduction
o almost synonymous with “fertility”
• prolific
o producing large numbers of offspring or reproducing frequently
o a group of the same species in the same area
• demography (demographics)
o the statistical study of populations, especially with reference to size, density, distribution, and vital statistics (birth, death, age, sex, health)
• population momentum
o potential for growth as young members reach reproductive age
• population explosion
o an increase in population at an exponential rate, usually surpassing the carrying capacity
• population crash
o a sudden decline in population caused by predation, waste accumulation, disease, resource depletion, or environmental change
o a.k.a. dieback
• carrying capacity
o the maximum population that can be supported within a habitat
o graphically abbreviated as “k”
• natality
o birth or death rates
• crude birth rate
o the number of individuals born per 1000
o abbreviated: CBR
• crude death rate
o the number of individuals died per 1000
o abbreviated: CDR
• fertility
o the ability for reproduction
o almost synonymous with “fercundity”
• fercundity
o the capacity for reproduction
o almost synonymous with “fertility”
• prolific
o producing large numbers of offspring or reproducing frequently
Thursday, January 3, 2008
APES Test Review - Shope
• vocabulary
o species
o population
o community
o habitat
o niche
o fundamental niche
o realized niche
o native / nonnative species
o indicator species
o keystone species
o resource partitioning
o niche overlap
o interspecific competition
o predation
o symbiosis
o mutation
o commensalisms
o primary succession
o secondary succession
o allogenic
o autogenic
o pioneer species
o early succession
o mid-succession
o late succession
o climax community
o speciation
o genetic persistence
o gene pool
o coevolution
o mass extinction events
• topics
o know the Hardy-Weinberg principle
o be able to compute gene frequency
o be able to describe natural selection
o be able to explain symbiosis
o know the four major geologic eras
o species
o population
o community
o habitat
o niche
o fundamental niche
o realized niche
o native / nonnative species
o indicator species
o keystone species
o resource partitioning
o niche overlap
o interspecific competition
o predation
o symbiosis
o mutation
o commensalisms
o primary succession
o secondary succession
o allogenic
o autogenic
o pioneer species
o early succession
o mid-succession
o late succession
o climax community
o speciation
o genetic persistence
o gene pool
o coevolution
o mass extinction events
• topics
o know the Hardy-Weinberg principle
o be able to compute gene frequency
o be able to describe natural selection
o be able to explain symbiosis
o know the four major geologic eras
APES Hardy-Weinberg Principle - Shope
• the frequency of a gene in a population will stay the same if:
1. there is no migration
2. there is random mating
3. there is no mutation
4. there is a large population
5. the phenotype (trait) does not affect survival
• p = most common gene – usually dominant
• q = least common gene – usually recessive
• p2 + 2pq + q2 available phenotypes
o p2 – homozygous dominant (usually)
o 2pq - heterozygous
o q2 – homozygous recessive (usually)
1. there is no migration
2. there is random mating
3. there is no mutation
4. there is a large population
5. the phenotype (trait) does not affect survival
• p = most common gene – usually dominant
• q = least common gene – usually recessive
• p2 + 2pq + q2 available phenotypes
o p2 – homozygous dominant (usually)
o 2pq - heterozygous
o q2 – homozygous recessive (usually)
APES Succession - Shope
• succession: a gradual change in species composition in a given area
• primary succession
o establishment of a biotic community in an area which has had no life before
• secondary succession
o re-establishment of life in an area where life was previously present
• pioneer species
o plants which attach to bare rock and begin the process of succession
• early successive plants
o moss, lichens, grasses
• mid successional plants
o shrubs, herbs, tall grasses
• late successional plants
o trees & shade-tolerant plants
• climax community
o the final stage of succession
o ex.: oak-hickory forest or maple-birch forest
• allogenic succession
o succession cause by an environmental change
• autogenic succession
o succession caused by an environmental change and a change in the plant life
• primary succession
o establishment of a biotic community in an area which has had no life before
• secondary succession
o re-establishment of life in an area where life was previously present
• pioneer species
o plants which attach to bare rock and begin the process of succession
• early successive plants
o moss, lichens, grasses
• mid successional plants
o shrubs, herbs, tall grasses
• late successional plants
o trees & shade-tolerant plants
• climax community
o the final stage of succession
o ex.: oak-hickory forest or maple-birch forest
• allogenic succession
o succession cause by an environmental change
• autogenic succession
o succession caused by an environmental change and a change in the plant life
APES Inter-Species Competition & Niche Overlap - Shope
(See worksheet.)
• results…
o competitive exclusion… one species must:
- migrate
- change (feeding or behavior)
- decline in population
- become extinct
o resource partitioning
• two types of competition
o interference
- one species limits resources access to other species
- territorialist
o exploitive
- one species is better at using a resource
• partitioning
o difference species use different parts of a resource
o ex.: birds in a tree
• variations in population
o stabilizing selection
- ex.: birds feed on largest and smallest spiders… thus stabilizing that population
o directional selection
- small-billed woodpeckers die off because their beaks are too short to reach
o disruptive selection
- “diversifying”
- selection against the average
- takes out middle values
- ex.: one hump to two humps (one high, one low)
• results…
o competitive exclusion… one species must:
- migrate
- change (feeding or behavior)
- decline in population
- become extinct
o resource partitioning
• two types of competition
o interference
- one species limits resources access to other species
- territorialist
o exploitive
- one species is better at using a resource
• partitioning
o difference species use different parts of a resource
o ex.: birds in a tree
• variations in population
o stabilizing selection
- ex.: birds feed on largest and smallest spiders… thus stabilizing that population
o directional selection
- small-billed woodpeckers die off because their beaks are too short to reach
o disruptive selection
- “diversifying”
- selection against the average
- takes out middle values
- ex.: one hump to two humps (one high, one low)
APES Communities, Populations, Interactions - Shope
• species
o organisms that are similar in nature and are capable of interbreeding and producing fertile offspring
- generalist species
• those with a broad niche
• can survive under varied conditions
- specialist species
• live in narrow, specific niches
o examples…
- horse and donkey are different species… their offspring (mule) is infertile
- all dogs are the same species
• population
o all members of a species living in a certain area
• community
o all of the different species (populations) living in a certain area
• niche (rhymes with “rich”)
o the lifestyle of species… where and how it lives
- fundamentalist niche
• the potential life if all parameters are optimal
- realized niche
• actual life of a species (after competition)
• species within ecosystems
o native
- organisms that normally live and thrive and have done so for some time
o nonnative
- a.k.a.: alien, exotic, invasive
- organisms that have been brought into an area, usually as a result of human activity
o indicator
- a species that can work (‘provide’) as an alert or warning of a problem
- ex. amphibians – occupy two habits (land & water)
o keystone
- a species that is more important than its biomass or abundance would indicate
- some people believe that there are no true keystone species
- alligator may be a keystone species
• competition
o interspecific
- a.k.a.: niche overlap
- competition between different species for the same resource
- predation
o symbiosis
- “same life”
- parasitism – one harmed, one benefited
- mutualism – two benefited
- commensalism – one benefited, one indifferent
o organisms that are similar in nature and are capable of interbreeding and producing fertile offspring
- generalist species
• those with a broad niche
• can survive under varied conditions
- specialist species
• live in narrow, specific niches
o examples…
- horse and donkey are different species… their offspring (mule) is infertile
- all dogs are the same species
• population
o all members of a species living in a certain area
• community
o all of the different species (populations) living in a certain area
• niche (rhymes with “rich”)
o the lifestyle of species… where and how it lives
- fundamentalist niche
• the potential life if all parameters are optimal
- realized niche
• actual life of a species (after competition)
• species within ecosystems
o native
- organisms that normally live and thrive and have done so for some time
o nonnative
- a.k.a.: alien, exotic, invasive
- organisms that have been brought into an area, usually as a result of human activity
o indicator
- a species that can work (‘provide’) as an alert or warning of a problem
- ex. amphibians – occupy two habits (land & water)
o keystone
- a species that is more important than its biomass or abundance would indicate
- some people believe that there are no true keystone species
- alligator may be a keystone species
• competition
o interspecific
- a.k.a.: niche overlap
- competition between different species for the same resource
- predation
o symbiosis
- “same life”
- parasitism – one harmed, one benefited
- mutualism – two benefited
- commensalism – one benefited, one indifferent
APES Extinction - Shope
• Endangered Species Act
o one of the most powerful pieces of legislation ever enacted (in US)
o controversial
o designed to protect habitats (and, therefore, species)
• we do not know all species, nor do we know how many there are (we can’t even accurately guess)
• 99.99% of all species to ever exist are currently extinct
• about 10 major mass extinctions in Earth’s history (60 % - 70% of species died)
• about 5 super (mass) extinctions
• eras (geological time scale… mya = million years old)
o Pre-cambrian (600 mya)
o Paleozoic (225 mya)
o Mesozoic (65 mya)
o Cenozoic (0.1 mya)
• Cambrian Explosion
o 500 mya
o invertebrate life (multi-cellular) started from bacteria & single-celled eukaryotes in ocean
o first fish
• biggest extinction in history
o about 250 mya
o wiped out about 96% of all life on earth
o just before time of dinosaurs
• KT Extinction
o end of the dinosaurs
o no one knows exactly what happened… asteroid? volcanoes? mammals feeding on dinosaur eggs?
• most extinctions (causes)
o change climate (getting hotter or colder)
o lots of dust in the air
o we don’t exactly know
• we may be starting the 6th massive extinction
o one of the most powerful pieces of legislation ever enacted (in US)
o controversial
o designed to protect habitats (and, therefore, species)
• we do not know all species, nor do we know how many there are (we can’t even accurately guess)
• 99.99% of all species to ever exist are currently extinct
• about 10 major mass extinctions in Earth’s history (60 % - 70% of species died)
• about 5 super (mass) extinctions
• eras (geological time scale… mya = million years old)
o Pre-cambrian (600 mya)
o Paleozoic (225 mya)
o Mesozoic (65 mya)
o Cenozoic (0.1 mya)
• Cambrian Explosion
o 500 mya
o invertebrate life (multi-cellular) started from bacteria & single-celled eukaryotes in ocean
o first fish
• biggest extinction in history
o about 250 mya
o wiped out about 96% of all life on earth
o just before time of dinosaurs
• KT Extinction
o end of the dinosaurs
o no one knows exactly what happened… asteroid? volcanoes? mammals feeding on dinosaur eggs?
• most extinctions (causes)
o change climate (getting hotter or colder)
o lots of dust in the air
o we don’t exactly know
• we may be starting the 6th massive extinction
APES Speciation and Natural Selection - Shope
• natural selection
o the principle that characteristics of species are determined by environmental conditions
- gradualist model = “slow change”
- punctuated equilibrium = “sudden change”
• adaptive radiation
o species evolving to fill niches (often following mass extinction)
• microevolution
o small genetic changes in a population
• macroevolution
o long term, large-scale changes
• background extinction (natural extinction)
o natural elimination of a species
o usually 1 – 10 species per year
• mass extinction
o widespread global extinction
o 25% - 75% of all species
• speciation
o development of 2 or more species from one ancestor
o geographic isolation: a population becomes divided by geologic events and evolves into different species
o reproductive isolation: within a population, genetic mutations prevent breeding
• genetic persistence
o retention and transfer of DNA material throughout time
• gene pool
o sum total of genes possessed by an individual or population
• coevolution
o 2 or more species interacting and causing each to change
o the principle that characteristics of species are determined by environmental conditions
- gradualist model = “slow change”
- punctuated equilibrium = “sudden change”
• adaptive radiation
o species evolving to fill niches (often following mass extinction)
• microevolution
o small genetic changes in a population
• macroevolution
o long term, large-scale changes
• background extinction (natural extinction)
o natural elimination of a species
o usually 1 – 10 species per year
• mass extinction
o widespread global extinction
o 25% - 75% of all species
• speciation
o development of 2 or more species from one ancestor
o geographic isolation: a population becomes divided by geologic events and evolves into different species
o reproductive isolation: within a population, genetic mutations prevent breeding
• genetic persistence
o retention and transfer of DNA material throughout time
• gene pool
o sum total of genes possessed by an individual or population
• coevolution
o 2 or more species interacting and causing each to change
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