The document discusses using a Moran model to infer gene function from population genetics data. Specifically:
- The model differentiates reproductive fitness and lifespan independently for two phenotypes, considering reproduction and survival as separate functions.
- An equilibrium distribution for phenotype frequency is derived, depending on mutation rate, reproduction, and survival parameters.
- The equilibrium distribution explicitly gives the Wright distribution, providing a way to infer gene function from its population distribution parameters.
This document discusses using extreme value theory and Bayesian analysis to reassess hurricane risk in Puerto Rico after Hurricane Maria. It analyzes rainfall data from San Juan to estimate return levels for extreme rainfall events using maximum likelihood estimation and Bayesian modeling. The Bayesian analysis results in slightly more precise predictions of extreme rainfall amounts compared to the maximum likelihood estimates. Hurricane Maria dropped over 36 inches of rain in some areas of Puerto Rico in September 2017, the highest rainfall amount ever recorded from a hurricane in Puerto Rico.
The document discusses the renal (urinary) system and how it transports nitrogenous waste out of animals. The kidney filters blood and removes waste, which drains into the bladder via the ureters. The nephron is the basic functional unit of the kidney, containing a glomerulus and tubules that allow filtration, reabsorption, and production of urine. Different species excrete different forms of nitrogenous waste at varying concentrations depending on whether they live in freshwater, saltwater, or on land.
1) The document describes an experiment to test the vitamin C content of fresh orange juice and 4 brands of packaged orange juice using an indophenol indicator solution.
2) The results show that the actual vitamin C content of the packaged juices, as determined by the experiment, often did not match the claims on the packaging.
3) Differences between actual and claimed vitamin C levels could be due to factors like processing and storage conditions affecting vitamin levels in packaged juices over time compared to fresh.
This document outlines the topics to be covered in a unit on biology. Part 1 discusses cells at a basic level, including microscopes, differences between cell types, cellular structures, and transport. Part 2 delves deeper into cells, exploring membrane functions, enzymes, mitosis, and the cell cycle. Part 3 focuses on plants, covering photosynthesis, respiration, plant structures, and gas exchange. Part 4 examines body systems such as teeth, digestion, circulation, respiration, and excretion. Part 5 concludes with reproduction, including asexual, sexual, and comparative reproductive processes in various organisms.
This document describes an experiment to examine how water is transported through a celery stalk. Students cut sections of celery stalk that had been soaked in food dye and examined them under microscopes. They observed that the dye was concentrated in certain areas, indicating the paths of water transport. Upon higher magnification, they saw spiral or coiled structures in the vascular tissue and learned that these structures, like cartilage in the trachea, function to support water transport through the plant. The purpose of observing this transport system was achieved.
- Genes can be structural or regulatory, with regulatory genes controlling the expression of other genes.
- Homeotic genes control embryonic development and malfunctions can result in body parts appearing in abnormal locations.
- Gene expression involves transcription of DNA into mRNA, which is then translated into proteins. Regulatory elements and splicing modify gene transcripts.
Inferring microbial gene function from evolution of synonymous codon usage bi...Fran Supek
Introduction: Thousands of microbial genomes are available, yet even for the model organisms, a sizable portion of the genes have unknown function. Phyletic profiling is a technique that can predict their function by comparing the presence/absence profiles of their homologs across genomes. In addition, prokaryotic genomes contain an evolutionary signature of gene expression levels in the codon usage biases, where highly expressed genes prefer the codons better adapted to the cellular tRNA pools.
Objectives: We aimed to augment the existing phyletic profiling approaches by incorporating more detailed knowledge of gene evolutionary history, and create a very large database of predicted gene functions direcly usable for microbiologists.
Materials & methods: We used the OMA groups of orthologs and the paralogy relationships inferred through OMA's „witness of non-orthology“ rule. Genes were assigned to Gene Ontology categories and the phyletic profiles compared using the CLUS classifier that performs a hierarchical multilabel classification using decision trees. We quantified significant codon biases using a Random Forest randomization test that compares against the composition of intergenic DNA. Codon biases in COG gene families were contrasted between microbes inhabiting different enviroments, while controlling for phylogenetic inertia.
Results: The genomic co-occurence patterns of both the orthologs and the paralogs (the homologs separated by a speciation and by a duplication event, respectively) were informative and synergistic in a phylogenetic profiling setup, even though paralogy relationships are thought to conserve function less well. The resulting ~400,000 gene function predictions for 998 prokaryotes (at FDR<10%)> method to systematically link codon adaptation within COG gene families to microbial phenotypes and environments (thus functionally characterizing the COGs) and experimentally validated the predictions for novel E. coli genes relevant for surviving oxidative, thermal or osmotic stress.
Conclusion: Our work towards ehnancing phylogenetic profiling, as well as developing complementary genomic context approaches, will contribute to prioritizing experimental investigation of microbial gene function, cutting time and cost needed for discovery.
This document discusses using extreme value theory and Bayesian analysis to reassess hurricane risk in Puerto Rico after Hurricane Maria. It analyzes rainfall data from San Juan to estimate return levels for extreme rainfall events using maximum likelihood estimation and Bayesian modeling. The Bayesian analysis results in slightly more precise predictions of extreme rainfall amounts compared to the maximum likelihood estimates. Hurricane Maria dropped over 36 inches of rain in some areas of Puerto Rico in September 2017, the highest rainfall amount ever recorded from a hurricane in Puerto Rico.
The document discusses the renal (urinary) system and how it transports nitrogenous waste out of animals. The kidney filters blood and removes waste, which drains into the bladder via the ureters. The nephron is the basic functional unit of the kidney, containing a glomerulus and tubules that allow filtration, reabsorption, and production of urine. Different species excrete different forms of nitrogenous waste at varying concentrations depending on whether they live in freshwater, saltwater, or on land.
1) The document describes an experiment to test the vitamin C content of fresh orange juice and 4 brands of packaged orange juice using an indophenol indicator solution.
2) The results show that the actual vitamin C content of the packaged juices, as determined by the experiment, often did not match the claims on the packaging.
3) Differences between actual and claimed vitamin C levels could be due to factors like processing and storage conditions affecting vitamin levels in packaged juices over time compared to fresh.
This document outlines the topics to be covered in a unit on biology. Part 1 discusses cells at a basic level, including microscopes, differences between cell types, cellular structures, and transport. Part 2 delves deeper into cells, exploring membrane functions, enzymes, mitosis, and the cell cycle. Part 3 focuses on plants, covering photosynthesis, respiration, plant structures, and gas exchange. Part 4 examines body systems such as teeth, digestion, circulation, respiration, and excretion. Part 5 concludes with reproduction, including asexual, sexual, and comparative reproductive processes in various organisms.
This document describes an experiment to examine how water is transported through a celery stalk. Students cut sections of celery stalk that had been soaked in food dye and examined them under microscopes. They observed that the dye was concentrated in certain areas, indicating the paths of water transport. Upon higher magnification, they saw spiral or coiled structures in the vascular tissue and learned that these structures, like cartilage in the trachea, function to support water transport through the plant. The purpose of observing this transport system was achieved.
- Genes can be structural or regulatory, with regulatory genes controlling the expression of other genes.
- Homeotic genes control embryonic development and malfunctions can result in body parts appearing in abnormal locations.
- Gene expression involves transcription of DNA into mRNA, which is then translated into proteins. Regulatory elements and splicing modify gene transcripts.
Inferring microbial gene function from evolution of synonymous codon usage bi...Fran Supek
Introduction: Thousands of microbial genomes are available, yet even for the model organisms, a sizable portion of the genes have unknown function. Phyletic profiling is a technique that can predict their function by comparing the presence/absence profiles of their homologs across genomes. In addition, prokaryotic genomes contain an evolutionary signature of gene expression levels in the codon usage biases, where highly expressed genes prefer the codons better adapted to the cellular tRNA pools.
Objectives: We aimed to augment the existing phyletic profiling approaches by incorporating more detailed knowledge of gene evolutionary history, and create a very large database of predicted gene functions direcly usable for microbiologists.
Materials & methods: We used the OMA groups of orthologs and the paralogy relationships inferred through OMA's „witness of non-orthology“ rule. Genes were assigned to Gene Ontology categories and the phyletic profiles compared using the CLUS classifier that performs a hierarchical multilabel classification using decision trees. We quantified significant codon biases using a Random Forest randomization test that compares against the composition of intergenic DNA. Codon biases in COG gene families were contrasted between microbes inhabiting different enviroments, while controlling for phylogenetic inertia.
Results: The genomic co-occurence patterns of both the orthologs and the paralogs (the homologs separated by a speciation and by a duplication event, respectively) were informative and synergistic in a phylogenetic profiling setup, even though paralogy relationships are thought to conserve function less well. The resulting ~400,000 gene function predictions for 998 prokaryotes (at FDR<10%)> method to systematically link codon adaptation within COG gene families to microbial phenotypes and environments (thus functionally characterizing the COGs) and experimentally validated the predictions for novel E. coli genes relevant for surviving oxidative, thermal or osmotic stress.
Conclusion: Our work towards ehnancing phylogenetic profiling, as well as developing complementary genomic context approaches, will contribute to prioritizing experimental investigation of microbial gene function, cutting time and cost needed for discovery.
This document discusses the "hitch-hiking effect", where natural selection at one genetic site can impact variation at a nearby neutral site. It begins by defining the question precisely. It then reviews predictions in the absence of selection and introduces models of how selection changes these, including "classic sweeps" of new beneficial mutations and "soft sweeps" of standing variation. It discusses quantifying the process through the structured coalescent and simulating genealogies conditional on selective trajectories. Finally, it introduces the concept of "pseudo-hitchhiking" which ignores fixation time and models hitchhiking as occurring at a rate.
This document summarizes a study on extinction dynamics in two migratory populations. The researchers developed a stochastic model where two populations experience birth, death, and migration events. They derived the theoretical mean time to extinction using a master equation and WKB approximation. Simulations agreed well with the analytical results. Varying the migration rate affected extinction behaviors, including a "ping-pong effect" where one population goes locally extinct but is revived by migration from the other population. The study provides insights into managing infectious disease dynamics through population control and faster extinction times.
PG STAT 531 Lecture 5 Probability DistributionAashish Patel
This document provides an overview of probability distributions including binomial, Poisson, and normal distributions. It discusses key concepts such as:
- Binomial distributions describe experiments with two possible outcomes and fixed number of trials.
- Poisson distributions model rare events with sample sizes so large one outcome is much more common.
- Normal distributions produce bell-shaped curves defined by the mean and standard deviation. They are widely used in statistics.
2 Review of Statistics. 2 Review of Statistics.WeihanKhor2
This document provides an overview of discrete probability distributions, including the binomial and Poisson distributions.
1) It defines key concepts such as random variables, probability mass functions, and expected value as they relate to discrete random variables. 2) The binomial distribution describes independent Bernoulli trials with a constant probability of success, and is used to calculate probabilities of outcomes from events like coin flips. 3) The Poisson distribution approximates the binomial when the number of trials is large and the probability of success is small. It models rare, independent events with a constant average rate and can be used for problems involving traffic accidents or natural disasters.
The document discusses the classification of organisms and the binomial system of nomenclature. It explains that all organisms are classified based on their characteristics and relationships. Each organism is assigned a genus and species name, with the genus indicating the broader group it belongs to. Classification sorts organisms into a hierarchy of taxonomic ranks including species, genus, family, order, class, phylum, and kingdom. The example of chimpanzees and their taxonomic classification is provided to illustrate this system.
Thomas Lenormand - Génétique des populationsSeminaire MEE
This document summarizes a population genetics model for studying the evolution of recombination rates. The model considers three loci, including a modifier locus that can alter the recombination rates between two selected loci. Using recursion equations and assumptions like weak epistasis and separation of timescales, the model analyzes when and why the frequency of a recombination-increasing allele at the modifier locus may increase over time through indirect selection. The key results are that more recombination evolves if epistasis between the selected loci is weakly negative and their association is negative.
1. Population genetics and the Hardy-Weinberg equation can be applied to determine allele frequencies in a population and predict carrier risks for genetic diseases.
2. For examples like cystic fibrosis and hemophilia, the incidence of the disease is used to calculate the frequency of the recessive allele q and the dominant allele p. This allows predicting the frequency of carriers and different genotypes.
3. DNA fingerprinting also applies the Hardy-Weinberg equation to determine genotype frequencies and calculate the probability of a particular DNA combination, which can be used as evidence in criminal cases.
B.sc. agri i pog unit 4 population geneticsRai University
This document provides an overview of population genetics and principles of evolution. It discusses how genetic variation is maintained in populations through mechanisms such as sexual reproduction, genetic drift, mutation and natural selection. A key concept is that evolution occurs through changes in allele frequencies in populations over generations. The document also covers Mendelian inheritance, Darwinian evolution, the Hardy-Weinberg principle of genetic equilibrium, and factors that can lead to deviations from equilibrium, driving microevolutionary changes within populations.
Estimating the Evolution Direction of Populations to Improve Genetic AlgorithmsAnnibale Panichella
Meta-heuristics have been successfully used to solve a wide variety of problems. However, one issue many techniques have is their risk of being trapped into local optima, or to create a limited variety of solutions (problem known as ``population drift''). During recent and past years, different kinds of techniques have been proposed to deal with population drift, for example hybridizing genetic algorithms with local search techniques or using niche techniques.
This paper proposes a technique, based on Singular Value Decomposition (SVD), to enhance Genetic Algorithms (GAs) population diversity. SVD helps to estimate the evolution direction and drive next generations towards orthogonal dimensions.
The proposed SVD-based GA has been evaluated on 11 benchmark problems and compared with a simple GA and a GA with a distance-crowding schema. Results indicate that SVD-based GA achieves significantly better solutions and exhibits a quicker convergence than the alternative techniques.
This document defines key concepts related to probability distributions and random variables. It explains that a random variable can take on a set of possible values with different probabilities, and these probabilities are defined by a probability function. Probability functions for discrete random variables are called probability mass functions, while those for continuous random variables are called probability density functions. Both have cumulative distribution functions that give the probability that the random variable is less than or equal to a given value. Expected value and variance are used to characterize probability distributions. Examples are provided of common discrete and continuous distributions and how to calculate probabilities and expected values.
This document discusses probability distributions for random variables. It introduces discrete distributions like the binomial and Poisson distributions which are used for counting experiments. It also introduces continuous distributions like the normal distribution which are defined over continuous ranges of values. Key concepts covered include probability density functions, cumulative distribution functions, and how to relate random variables with specific parameters to standard distributions. Examples are provided to illustrate concepts like modeling the number of plant stems in a sampling area with a Poisson distribution.
This document discusses key concepts in population genetics, including defining a population as a group of the same species living in a specific area. It provides an example of studying the genetics of a population of racers lizards, looking at the frequency of dominant and recessive alleles for stripe color. The values for p (frequency of dominant allele) and q (frequency of recessive allele) are calculated based on observing 110 lizards with the dominant white stripe allele out of 200 total alleles observed. This yields values of p=0.55 and q=0.45 for this population.
This document discusses key concepts in population genetics, including defining a population as a group of the same species living in a specific area. It provides an example of studying the genetics of a population of racers lizards, looking at the frequency of dominant and recessive alleles for stripe color. The values for p (frequency of dominant allele) and q (frequency of recessive allele) are calculated based on observing 110 lizards with the dominant white stripe allele out of 200 total alleles observed. This yields values of p=0.55 and q=0.45 for this population.
This document discusses key concepts in population genetics, including defining a population as a group of the same species living in a specific area. It provides an example of studying the genetics of a population of racers lizards, looking at the frequency of dominant and recessive alleles for stripe color. The values for p (frequency of dominant allele) and q (frequency of recessive allele) are calculated based on observing 110 lizards with the dominant white stripe allele out of 200 total alleles observed. This yields values of p=0.55 and q=0.45 for this population.
The document discusses several probability distributions including the normal, binomial, and Poisson distributions. It provides information on who discovered each distribution and examples of how they are applied. The normal distribution describes how observations vary around a mean value and results in the familiar bell curve. The binomial distribution describes outcomes of binary events like coin flips that can succeed or fail. The Poisson distribution models rare, independent events occurring randomly in space or time.
This document discusses key concepts in population genetics, including defining a population as a group of the same species in a specific area. It provides an example of studying the frequencies of dominant and recessive alleles for stripe patterns in a population of lizards. The frequencies are used to determine if the population is evolving over time or remaining stable under certain conditions. Equations are presented to calculate allele frequencies (p and q) from sample data and determine percentages of genotypes.
The document discusses various probability distributions including the normal, binomial, Poisson, uniform, and chi-square distributions. It provides examples of when each distribution would be used and explains key properties such as mean, variance, and standard deviation. It also covers topics like the central limit theorem, sampling distributions, and how inferential statistics is used to generalize from samples to populations.
Introduction to conservation genetics and genomicsRanajitDas12
1) The document introduces population genetics and its application to conservation. It defines key terms like allele frequency, genotype frequency, and Hardy-Weinberg equilibrium.
2) Mutation, recombination, migration, and natural selection are described as the main forces that can drive evolution by changing allele frequencies over time. Mutation introduces new variants while selection favors advantageous variants.
3) Models of mutation, migration, genetic drift and natural selection are presented to explain how they impact allele frequency changes in a population both qualitatively and quantitatively over multiple generations. The interaction between mutation and selection is also described.
The document discusses different types of probability distributions including binomial, Poisson, and normal distributions. It provides examples of how to calculate probabilities for each distribution and approximations that can be used. It also defines common random variables like the number of successes in a binomial experiment and the number of events occurring in a Poisson distribution.
1. The document discusses basic probability concepts including classical, relative frequency, subjective probability, and properties of probability.
2. It provides an example to calculate unconditional, conditional, and joint probabilities using a table of frequency data.
3. The multiplication rule states that joint probability can be calculated as the product of marginal and conditional probabilities.
I argue in favour of an elementary analogy that links physical and biological systems. In two words, the interplay between reproduction and cooperation may turn out to be relevant to both physics and biology.
This basic analogy has probably been overlooked as a consequence of the "shut up and calculate" dogma which dominated 20th century physics.
The email is from ignacio@pofume.org and appears to be about the philosophical concept of eternal recurrence, which is the idea that the universe and all existence has been recurring, and will continue to recur infinitely. However, with no body text or additional context provided, the exact topic or viewpoint on eternal recurrence that the email concerns cannot be determined from the limited information given.
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This document discusses the "hitch-hiking effect", where natural selection at one genetic site can impact variation at a nearby neutral site. It begins by defining the question precisely. It then reviews predictions in the absence of selection and introduces models of how selection changes these, including "classic sweeps" of new beneficial mutations and "soft sweeps" of standing variation. It discusses quantifying the process through the structured coalescent and simulating genealogies conditional on selective trajectories. Finally, it introduces the concept of "pseudo-hitchhiking" which ignores fixation time and models hitchhiking as occurring at a rate.
This document summarizes a study on extinction dynamics in two migratory populations. The researchers developed a stochastic model where two populations experience birth, death, and migration events. They derived the theoretical mean time to extinction using a master equation and WKB approximation. Simulations agreed well with the analytical results. Varying the migration rate affected extinction behaviors, including a "ping-pong effect" where one population goes locally extinct but is revived by migration from the other population. The study provides insights into managing infectious disease dynamics through population control and faster extinction times.
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This document provides an overview of probability distributions including binomial, Poisson, and normal distributions. It discusses key concepts such as:
- Binomial distributions describe experiments with two possible outcomes and fixed number of trials.
- Poisson distributions model rare events with sample sizes so large one outcome is much more common.
- Normal distributions produce bell-shaped curves defined by the mean and standard deviation. They are widely used in statistics.
2 Review of Statistics. 2 Review of Statistics.WeihanKhor2
This document provides an overview of discrete probability distributions, including the binomial and Poisson distributions.
1) It defines key concepts such as random variables, probability mass functions, and expected value as they relate to discrete random variables. 2) The binomial distribution describes independent Bernoulli trials with a constant probability of success, and is used to calculate probabilities of outcomes from events like coin flips. 3) The Poisson distribution approximates the binomial when the number of trials is large and the probability of success is small. It models rare, independent events with a constant average rate and can be used for problems involving traffic accidents or natural disasters.
The document discusses the classification of organisms and the binomial system of nomenclature. It explains that all organisms are classified based on their characteristics and relationships. Each organism is assigned a genus and species name, with the genus indicating the broader group it belongs to. Classification sorts organisms into a hierarchy of taxonomic ranks including species, genus, family, order, class, phylum, and kingdom. The example of chimpanzees and their taxonomic classification is provided to illustrate this system.
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This document summarizes a population genetics model for studying the evolution of recombination rates. The model considers three loci, including a modifier locus that can alter the recombination rates between two selected loci. Using recursion equations and assumptions like weak epistasis and separation of timescales, the model analyzes when and why the frequency of a recombination-increasing allele at the modifier locus may increase over time through indirect selection. The key results are that more recombination evolves if epistasis between the selected loci is weakly negative and their association is negative.
1. Population genetics and the Hardy-Weinberg equation can be applied to determine allele frequencies in a population and predict carrier risks for genetic diseases.
2. For examples like cystic fibrosis and hemophilia, the incidence of the disease is used to calculate the frequency of the recessive allele q and the dominant allele p. This allows predicting the frequency of carriers and different genotypes.
3. DNA fingerprinting also applies the Hardy-Weinberg equation to determine genotype frequencies and calculate the probability of a particular DNA combination, which can be used as evidence in criminal cases.
B.sc. agri i pog unit 4 population geneticsRai University
This document provides an overview of population genetics and principles of evolution. It discusses how genetic variation is maintained in populations through mechanisms such as sexual reproduction, genetic drift, mutation and natural selection. A key concept is that evolution occurs through changes in allele frequencies in populations over generations. The document also covers Mendelian inheritance, Darwinian evolution, the Hardy-Weinberg principle of genetic equilibrium, and factors that can lead to deviations from equilibrium, driving microevolutionary changes within populations.
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Meta-heuristics have been successfully used to solve a wide variety of problems. However, one issue many techniques have is their risk of being trapped into local optima, or to create a limited variety of solutions (problem known as ``population drift''). During recent and past years, different kinds of techniques have been proposed to deal with population drift, for example hybridizing genetic algorithms with local search techniques or using niche techniques.
This paper proposes a technique, based on Singular Value Decomposition (SVD), to enhance Genetic Algorithms (GAs) population diversity. SVD helps to estimate the evolution direction and drive next generations towards orthogonal dimensions.
The proposed SVD-based GA has been evaluated on 11 benchmark problems and compared with a simple GA and a GA with a distance-crowding schema. Results indicate that SVD-based GA achieves significantly better solutions and exhibits a quicker convergence than the alternative techniques.
This document defines key concepts related to probability distributions and random variables. It explains that a random variable can take on a set of possible values with different probabilities, and these probabilities are defined by a probability function. Probability functions for discrete random variables are called probability mass functions, while those for continuous random variables are called probability density functions. Both have cumulative distribution functions that give the probability that the random variable is less than or equal to a given value. Expected value and variance are used to characterize probability distributions. Examples are provided of common discrete and continuous distributions and how to calculate probabilities and expected values.
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This document discusses key concepts in population genetics, including defining a population as a group of the same species living in a specific area. It provides an example of studying the genetics of a population of racers lizards, looking at the frequency of dominant and recessive alleles for stripe color. The values for p (frequency of dominant allele) and q (frequency of recessive allele) are calculated based on observing 110 lizards with the dominant white stripe allele out of 200 total alleles observed. This yields values of p=0.55 and q=0.45 for this population.
This document discusses key concepts in population genetics, including defining a population as a group of the same species living in a specific area. It provides an example of studying the genetics of a population of racers lizards, looking at the frequency of dominant and recessive alleles for stripe color. The values for p (frequency of dominant allele) and q (frequency of recessive allele) are calculated based on observing 110 lizards with the dominant white stripe allele out of 200 total alleles observed. This yields values of p=0.55 and q=0.45 for this population.
This document discusses key concepts in population genetics, including defining a population as a group of the same species living in a specific area. It provides an example of studying the genetics of a population of racers lizards, looking at the frequency of dominant and recessive alleles for stripe color. The values for p (frequency of dominant allele) and q (frequency of recessive allele) are calculated based on observing 110 lizards with the dominant white stripe allele out of 200 total alleles observed. This yields values of p=0.55 and q=0.45 for this population.
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The document discusses various probability distributions including the normal, binomial, Poisson, uniform, and chi-square distributions. It provides examples of when each distribution would be used and explains key properties such as mean, variance, and standard deviation. It also covers topics like the central limit theorem, sampling distributions, and how inferential statistics is used to generalize from samples to populations.
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1) The document introduces population genetics and its application to conservation. It defines key terms like allele frequency, genotype frequency, and Hardy-Weinberg equilibrium.
2) Mutation, recombination, migration, and natural selection are described as the main forces that can drive evolution by changing allele frequencies over time. Mutation introduces new variants while selection favors advantageous variants.
3) Models of mutation, migration, genetic drift and natural selection are presented to explain how they impact allele frequency changes in a population both qualitatively and quantitatively over multiple generations. The interaction between mutation and selection is also described.
The document discusses different types of probability distributions including binomial, Poisson, and normal distributions. It provides examples of how to calculate probabilities for each distribution and approximations that can be used. It also defines common random variables like the number of successes in a binomial experiment and the number of events occurring in a Poisson distribution.
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2. It provides an example to calculate unconditional, conditional, and joint probabilities using a table of frequency data.
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Similar to population genetics of gene function (talk) (20)
I argue in favour of an elementary analogy that links physical and biological systems. In two words, the interplay between reproduction and cooperation may turn out to be relevant to both physics and biology.
This basic analogy has probably been overlooked as a consequence of the "shut up and calculate" dogma which dominated 20th century physics.
The email is from ignacio@pofume.org and appears to be about the philosophical concept of eternal recurrence, which is the idea that the universe and all existence has been recurring, and will continue to recur infinitely. However, with no body text or additional context provided, the exact topic or viewpoint on eternal recurrence that the email concerns cannot be determined from the limited information given.
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(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 𝟏)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.
2. Mo'va'on
“Molecular
signatures
of
natural
selec0on”,
Nielsen
2005:
“inferences
regarding
the
paAerns
and
distribu'on
of
selec'on
in
genes
and
genomes
may
provide
important
func'onal
informa'on”
Wikipedia
entry
on
“sta0s0cal
thermodynamics”:
“The
goal
of
sta's'cal
thermodynamics
is
to
understand
and
to
interpret
the
measurable
macroscopic
proper'es
of
materials
in
terms
of
the
proper'es
of
their
cons'tuent
par'cles
and
the
interac'ons
between
them”
3. Mo'va'on
The
func'onal
importance
of
a
gene'c
sequence
can
be
inferred
by
its
popula'on
distribu'on
(for
example
from
its
degree
of
conserva'on).
Can
anything
more
be
said
about
the
gene’s
specific
func'on
(survival,
reproduc'on,
etc)?
distribu)on
of
genes
gene
func)on
macroscopic
proper)es
of
materials
proper)es
of
their
cons)tuent
par)cles
(size,
speed,
etc)
4. Moran
model:
Model
varia)on:
birth
death
change
in
frequency
for
a
given
phenotype
5. €
p−
€
p+
€
q−
€
q+
€
1− p−
− q−
€
p+
€
q+
We
have
two
phenotypes,
P1
and
P2
€
€
p−
, p+
: death and birth probabilities for P1
q−
, q+
: death and birth probabilities for P2
If
p - + q - < 1
in
some
intervals
nothing
happens.
If
a
death
happens,
a
birth
happens
instantaneously
(“musical
chairs”
process).
6. €
p−
€
p+
€
q−
€
q+
€
1− p−
− q−
€
p+
€
q+
We
have
two
phenotypes,
P1
and
P2
€
€
p−
, p+
: death and birth probabilities for P1
q−
, q+
: death and birth probabilities for P2
If
p - + q - < 1
in
some
intervals
nothing
happens.
If
a
death
happens,
a
birth
happens
instantaneously
(“musical
chairs”
process).
loop
7. €
p−
€
p+
€
q−
€
q+
€
1− p−
− q−
€
p+
€
q+
We
have
two
phenotypes,
P1
and
P2
€
€
p−
, p+
: death and birth probabilities for P1
q−
, q+
: death and birth probabilities for P2
If
p - + q - < 1
in
some
intervals
nothing
happens.
If
a
death
happens,
a
birth
happens
instantaneously
(“musical
chairs”
process).
loop
no
loop
8. €
p−
€
p+
€
q−
€
q+
€
1− p−
− q−
€
p+
€
q+
We
have
two
phenotypes,
P1
and
P2
€
€
p−
, p+
: death and birth probabilities for P1
q−
, q+
: death and birth probabilities for P2
If
p - + q - < 1
in
some
intervals
nothing
happens.
If
a
death
happens,
a
birth
happens
instantaneously
(“musical
chairs”
process).
loop
no
loop
9. €
p−
€
p+
€
q−
€
q+
€
1− p−
− q−
€
p+
€
q+
We
differen'ate
the
phenotypes’
reproduc've
fitness
and
life'mes
independently,
and
consider
reproduc)on
and
survival
as
two
different
func'ons.
€
W1 : offspring for type 1,
W2 : offspring for type 2,
⎧
⎨
⎩
T1 : average lifespan for type 1,
T2 : average lifespan for type 2.
⎧
⎨
⎩
reproduc,on
survival
u : mutation probability
and
we
are
interested
in
the
equilibrium
distribu'on
of
a
process
with
symmetric
reversible
muta)on
for
haploid
individuals
10. q+
=
W1
T1
u x +
W2
T2
(1− u)(1− x)
W1
T1
x +
W2
T2
(1− x)
.
€
q−
=
1− x
T2
.
p+
=
W1
T1
(1− u)x +
W2
T2
u (1− x)
W1
T1
x +
W2
T2
(1− x)
,
€
p−
=
x
T1
,
Death
probabili)es:
Birth
probabili)es:
€
p−
€
p+
€
q−
€
q+
€
1− p−
− q−
€
p+
€
q+
Variable
x
is
the
frequency
of
phenotype
P1
(so
frequency
of
P2
is
1 - x )
11. q+
=
W1
T1
u x +
W2
T2
(1− u)(1− x)
W1
T1
x +
W2
T2
(1− x)
.
€
q−
=
1− x
T2
.
p+
=
W1
T1
(1− u)x +
W2
T2
u (1− x)
W1
T1
x +
W2
T2
(1− x)
,
€
p−
=
x
T1
,
Death
probabili)es:
Birth
probabili)es:
€
p−
€
p+
€
q−
€
q+
€
1− p−
− q−
€
p+
€
q+
€
⇒ p−
+ q−
< 1
Variable
x
is
the
frequency
of
phenotype
P1
(so
frequency
of
P2
is
1 - x )
12. €
Nu N → ∞⎯ →⎯⎯ θ,
The
model
therefore
depends
on:
To
get
a
non
trivial
distribu'on
the
following
asympto'c
constraints
are
imposed
on
the
parameters:
€
θ (mutation), s (reproduction), λ (survival).€
For notational convenience we also define λ =
T1
T2
.
€
N
W1
W2
−1
⎛
⎝
⎜
⎞
⎠
⎟ u→ 0
⎯ →⎯⎯ s.
Asympto)c
parameters
13. €
Nu N → ∞⎯ →⎯⎯ θ,
The
model
therefore
depends
on:
To
get
a
non
trivial
distribu'on
the
following
asympto'c
constraints
are
imposed
on
the
parameters:
€
θ (mutation), s (reproduction), λ (survival).€
For notational convenience we also define λ =
T1
T2
.
€
N
W1
W2
−1
⎛
⎝
⎜
⎞
⎠
⎟ u→ 0
⎯ →⎯⎯ s.
Asympto)c
parameters
14. €
M = E[Xt +1 − Xt ] =
1
NT1
⋅
θ λ2
(1− x)2
+ λ s x(1− x) −θ x2
x + λ (1− x)
,
V = E (Xt +1 − Xt )2
[ ] =
2 λ
NT1
⋅
x (1− x)
x + λ (1− x)
.
15. €
M = E[Xt +1 − Xt ] =
1
NT1
⋅
θ λ2
(1− x)2
+ λ s x(1− x) −θ x2
x + λ (1− x)
,
V = E (Xt +1 − Xt )2
[ ] =
2 λ
NT1
⋅
x (1− x)
x + λ (1− x)
.
16. €
€
φ(x)= C⋅
1
V
⋅ exp 2
M
V
dx∫
⎧
⎨
⎩
⎫
⎬
⎭
,
€
φ(x)= Ceα x
xλ θ −1
(1− x)
θ
λ
−1
x + λ(1− x){ },
€
α = s +θ
1
λ
− λ
⎛
⎝
⎜
⎞
⎠
⎟.
which
explicitly
gives
where
The
Wright
equilibrium
distribu'on
for
large
N
is
Equilibrium
distribu)on
17. €
€
φ(x)= C⋅
1
V
⋅ exp 2
M
V
dx∫
⎧
⎨
⎩
⎫
⎬
⎭
,
€
φ(x)= Ceα x
xλ θ −1
(1− x)
θ
λ
−1
x + λ(1− x){ },
€
α = s +θ
1
λ
− λ
⎛
⎝
⎜
⎞
⎠
⎟.
which
explicitly
gives
where
The
Wright
equilibrium
distribu'on
for
large
N
is
Equilibrium
distribu)on
18. Typical
shapes
for
equilibrium
distribu)ons
rela've
frequency
of
“blue”
phenotypes
probability
density
€
low mutation
rela've
frequency
of
“blue”
phenotypes
probability
density
€
high mutation
rela've
frequency
of
“blue”
phenotypes
probability
density
€
mutation probability close to
1
N
19. Typical
shapes
for
equilibrium
distribu)ons
rela've
frequency
of
“blue”
phenotypes
probability
density
€
low mutation
rela've
frequency
of
“blue”
phenotypes
probability
density
€
high mutation
rela've
frequency
of
“blue”
phenotypes
probability
density
€
mutation probability close to
1
N
20. “u”:
probability
of
muta'on
per
site
sta'onary
points
€
λ =
T1
T2
=1 (life'mes
are
equal
for
the
two
phenotypes)
random
driR
muta'on/selec'on
balance
€
1
N
Sta)onary
points
21. “u”:
probability
of
muta'on
per
site
sta'onary
points
€
λ =
T1
T2
=1 (life'mes
are
equal
for
the
two
phenotypes)
random
driR
muta'on/selec'on
balance
€
1
N
Sta)onary
points
sta'onary
points
€
λ =
T1
T2
=
3
2
“u”:
probability
of
muta'on
per
site
€
1
N
random
driR
muta'on/selec'on
balance
22. “u”:
probability
of
muta'on
per
site
sta'onary
points
€
λ =
T1
T2
=1 (life'mes
are
equal
for
the
two
phenotypes)
random
driR
muta'on/selec'on
balance
€
1
N
Sta)onary
points
random
driR
muta'on/selec'on
balance
sta'onary
points
€
λ =
T1
T2
=
3
2
“u”:
probability
of
muta'on
per
site
€
1
N
€
λ =
T1
T2
=
3
2
€
1
N
23. Sta)onary
points
sta'onary
points
€
λ =
T1
T2
=
3
2
“u”:
probability
of
muta'on
per
site
€
1
N
random
driR
muta'on/selec'on
balance
€
1
N
24. Typical
shapes
for
equilibrium
distribu)ons
rela've
frequency
of
“blue”
phenotypes
probability
density
€
low mutation
rela've
frequency
of
“blue”
phenotypes
probability
density
€
high mutation
rela've
frequency
of
“blue”
phenotypes
probability
density
€
mutation probability close to
1
N
25. The
model
includes
one
more
parameter
than
the
standard
seTng,
so
it’s
desirable
expand
the
number
of
independent
sta)s)cs.
This
can
be
done
considering
the
amount
of
synonymous
varia'on
included
in
each
of
our
two
phenotypes,
and
considering
it
neutral
(as
done
by
Nielsen
and
colleagues
for
various
types
of
models).
The
amount
of
synonymous
varia'on
can
be
quan'fied
by
using
the
inbreeding
coefficient
concept.
€
Inferring λ =
T1
T2
from population statistics
26. phenotypes
P1
and
P2
genotypes
genotypes
Distribu)on
of
a
gene
throughout
a
popula)on
(Kreitman
1983)
27. x = relative frequency of P1
F1 = inbreeding coefficient for P1
F2 = inbreeding coefficient for P2
Sta)s)cal
quan))es
P1
P2
28. €
F1 /x +θ λ F1 /x − F1( )+ (L −1) F1[ ]− 1/x ≈ 0
F2 /(1− x) +θ
1
λ
F2 /(1− x) − F2( )+ (L −1) F2
⎡
⎣⎢
⎤
⎦⎥ − 1/(1− x) ≈ 0
A
result
by
Kimura
and
Crow
gives
that
for
only
one
phenotype
€
F ≈
1
1+ 2θ
This
can
be
extended
to
the
case
of
two
phenotypes
to
give
two
equa'ons:
where
θ
is
the
rescaled
muta'on
rate.
29. 0.5 1 1.5 20.75 1.25 1.75
0.5
1
1.5
2
.75
1.25
1.75
Real
Estimated
T1
= 2 T2
T1
= 1/2 T2
This
(hideous)
formula
can
be
used
to
derive
the
value
of
λ
from
combined
moments
of
quan''es
x ,
F1 ,
F2
es'mated
from
a
set
of
simulated
realiza'ons
of
the
process.
€
number of realizations per point =10000
€
running time = 5000 "generations"€
simulation parameters:
s = −5, θ = 7, N =1000, L (genotype length) = 40
and this relation leads to a quadratic equation that only admits one non-negative solution:
λ =
1
2Q1
(R − 1)(L − 1) +
(R − 1)2(L − 1)2 + 4RQ1Q2
. (4.5)
Figure 5 shows the result of using formula (4.5) to estimate λ, for a series series of
simulations where the real value of λ ranges from .5 (i.e. T1 = 1/2 T2) to 2 (i.e. T1 = 2 T2):
we see that the average values of such estimations are well aligned with the actual values.
The magnitude of the standard deviation for our estimations, on the other hand, is
considerable, especially in view of the fact the 10000 realisations of the process were used
to estimate each value of λ: it is clear that a substantial increase of efficiency will be
needed to make the theory relevant to actual empirical phenomena.
This practical consideration ought not to be allowed, however, to obfuscate the fact
that equation (4.5) provides a direct mathematical relation between combined moments
of the population quantities x, F1 and F2, and parameter λ = T1/T2, which arguably
contains information about the function of a genetic sequence.
5 Outlook
We have shown that the effect of differentiating the lifetimes of two phenotypes inde-
pendently from their fertility includes a qualitative change in the equilibrium state of a
wing auxiliary quantities
R =
F2
F1
·
1/x − F1/x
1/(1 − x) − F2/(1 − x)
,
Q1 =
F1/x
F1
− 1, Q2 =
F2/x
F2
− 1.
n terms of these quantities, the equation for λ takes the following form
R = λ
λQ1 + L − 1
Q2 + λ(L − 1)
,
his relation leads to a quadratic equation that only admits one non-negative solution:
λ =
1
2Q1
(R − 1)(L − 1) +
(R − 1)2(L − 1)2 + 4RQ1Q2
. (4.5)
igure 5 shows the result of using formula (4.5) to estimate λ, for a series series of
ations where the real value of λ ranges from .5 (i.e. T1 = 1/2 T2) to 2 (i.e. T1 = 2 T2):
e that the average values of such estimations are well aligned with the actual values.
he magnitude of the standard deviation for our estimations, on the other hand, is
derable, especially in view of the fact the 10000 realisations of the process were used
timate each value of λ: it is clear that a substantial increase of efficiency will be
ed to make the theory relevant to actual empirical phenomena.
his practical consideration ought not to be allowed, however, to obfuscate the fact
following auxiliary quantities
R =
F2
F1
·
1/x − F1/x
1/(1 − x) − F2/(1 − x)
,
Q1 =
F1/x
F1
− 1, Q2 =
F2/x
F2
− 1.
In terms of these quantities, the equation for λ takes the following form
R = λ
λQ1 + L − 1
Q2 + λ(L − 1)
,
and this relation leads to a quadratic equation that only admits one non-negative solution
λ =
1
2Q1
(R − 1)(L − 1) +
(R − 1)2(L − 1)2 + 4RQ1Q2
. (4.5
Figure 5 shows the result of using formula (4.5) to estimate λ, for a series series o
simulations where the real value of λ ranges from .5 (i.e. T1 = 1/2 T2) to 2 (i.e. T1 = 2 T2)
we see that the average values of such estimations are well aligned with the actual values
The magnitude of the standard deviation for our estimations, on the other hand, i
considerable, especially in view of the fact the 10000 realisations of the process were used
to estimate each value of λ: it is clear that a substantial increase of efficiency will b
needed to make the theory relevant to actual empirical phenomena.
This practical consideration ought not to be allowed, however, to obfuscate the fac
that equation (4.5) provides a direct mathematical relation between combined moment
30. Summary
• Playing
with
details
of
process
is
fun
• In
principle
“func'onal”
parameter
λ
=
T1 / T2
can
be
es'mated
from
“popula'on
observables”
x ,
F1 ,
F2
32. “Disclaimer”
…there
is
no
such
thing
as
the
“func'on
of
a
gene”,
like
there
is
no
such
thing
as
the
“meaning
of
a
word”.
For
example,
the
word
“Gene”
can
mean:
…but
dic'onaries
exist
(and
they
are
obsolete
(but
they’re
a
start
(or
maybe
not))).
or