What Is The Probability That A Randomly Chosen Male Respondent Or His Partner Has Blue Eyes?
Pieter Maas
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A The probability a randomly chosen male respondent or his partner has blue eyes ## can be found by P(male_blue) + P(partner_blue) – P(both) ## = 114/204 + 108/204 – 78/204 = 144/204 = 70.59% ## 3.
Is assortative mating a non random mating pattern where individuals with similar genotypes?
Assortative mating is a nonrandom mating pattern where individuals with similar genotypes and/or phenotypes mate with one another more frequently than what would be expected under a random mating pattern. Researchers studying this topic collected data on eye colours of 204 Scandinavian men and their female partners.
What percent of Americans live below the poverty line and only speak English at home?
Chap2-Homework2 Defining Probability 2.6 Dice Rolls If you roll a pair of fair dice, what is the probability of There is 36 posible combianations when rolling a pair of fair dice
- getting a sum of 1? Ther is not possible combination to get a sum of on rolling a pair of dice
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- getting a sum of 5?
- Please see the following ways: 1,4; 2,3; 3,2; 4,1 so the changes are 4 times in 36 posible combinations which is 4/36
- The probability of getting a sum of 5 is 4/36
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- getting a sum of 12
- There is only one posible combination 6,6 out of the 36
- The probabilty of getting a sum of 12 is 1/36
2.8 Poverty and Language: The American Community Survey is an ongoing survey that provides data every year to give communities the current they need to plan investments and services. The 2010 American Community Survey estimates that 14.6% of Americans live below the poverty line, 20.7% speak a language other than English (foreing language) at home, and 4.2% fall into both categories.
- Are living below the poverty line and speaking a foreing language at home disjoint? Because the living below the poverty line and language spoken in the America community are events that have elements in common, one variable falls in the other one. they are not disjoint events.
- Draw a Venn diagram summarizing the variables and their associated probabilities?
library(VennDiagram) ## Loading required package: grid ## Loading required package: futile.logger library(grid) venn_sample <- draw.pairwise.venn(14.6, 20.7, 4.2, c("Foreing Language spoken", "Below poverty Line"), scale = FALSE, fill = c("blue", "red")); grid.draw(venn_sample); #grid.newpage()
- What percentage of Americans live below the poverty line and only speaks English at home? According to the Venn diagram for the two variables give ; 10.4 percent of Americans live below the poverty line and they are english speakers at home.
- What percentage of Americans live below the poverty line or speaks a foreign language at home? It would be 14.6 of Americans live below poverty leve plus 20.7 speaks foreing language minus 4.2 that meet both criteria, it means ( 14.6 + 20.7) – 4.2 = 31.1 percent of Americans live below the poverty or speak a foreing language.
- What percentage of Americans live above the poverty line and only speaks English at home? The percente of Americans live above the poverty line and only speaks English would be from 100 % – 31.1% = 68.9 %
- Is the event that someones lives below the poverty line independent of the event that a person speaks a foreing language at home? No, Those events are not independent, there is many possibilities that one variable falls in the other one.
Conditional Probability 2.20 Assortative mating.Assortative mating is a nonramdom mating pattern where individuals with similar genotypes and/or phenotypes mate with one another more frequently than what would be expected under a random mating pattern. Researchers studying this topic collected data on eye colors of 204 Scandinavian men and their female partners. The table below summarizes the results. For simplicity,,we only include heterosexual relationships in this exercise. ass_mating <- read.csv('https://raw.githubusercontent.com/jbryer/DATA606Fall2017/master/Data/Data%20from%20openintro.org/Ch%202%20Exercise%20Data/assortive_mating.csv') sampleblue = subset(ass_mating, partner_female == "blue") count1 = table(ass_mating$self_male, ass_mating$partner_female) t = as.data.frame(count1) names(t) = 'Self Male' names(t) = 'Partner Female' t ## Self Male Partner Female Freq ## 1 blue blue 78 ## 2 brown blue 19 ## 3 green blue 11 ## 4 blue brown 23 ## 5 brown brown 23 ## 6 green brown 9 ## 7 blue green 13 ## 8 brown green 12 ## 9 green green 16
What is the probabilty that a randomly chosen male respondent or his partner has blue eyes?
library(gmodels) # The gmodels packages has a function CrossTable with Tests for Factor Independece # prop.r If TRUE, row proportions will be included with(warpbreaks, CrossTable(ass_mating$self_male, ass_mating$partner_female, prop.r = TRUE, prop.c = FALSE, prop.t = FALSE, prop.chisq = FALSE)) ## ## ## Cell Contents ## |-| ## | N | ## | N / Row Total | ## |-| ## ## ## Total Observations in Table: 204 ## ## ## | ass_mating$partner_female ## ass_mating$self_male | blue | brown | green | Row Total | ## -|-|-|-|-| ## blue | 78 | 23 | 13 | 114 | ## | 0.684 | 0.202 | 0.114 | 0.559 | ## -|-|-|-|-| ## brown | 19 | 23 | 12 | 54 | ## | 0.352 | 0.426 | 0.222 | 0.265 | ## -|-|-|-|-| ## green | 11 | 9 | 16 | 36 | ## | 0.306 | 0.250 | 0.444 | 0.176 | ## -|-|-|-|-| ## Column Total | 108 | 55 | 41 | 204 | ## -|-|-|-|-| ## ##
- Acording to the table above we can summarize the assorting mating data set using the contingency table that contains a sample of 204 cases with two variables, A = self_male and B = partner_female
- Total of self male with blue eyes = 114 Total of self male with brown eyes = 54 Total of self male with green eyes = 36
- Total of partner female with blue eyes = 108 Total of partner female with brown eyes = 55 Total of partner female with green eyes = 41
- P(A or B) = P(A)+P(B)-P(A and B)
= (114/204)+(108/204)-(78/204)=,7059 =70.59% ((sum(ass_mating$self_male ==”blue”)/nrow(ass_mating)) + (sum(ass_mating$partner_female ==”blue”)/nrow(ass_mating)))- (sum(ass_mating$self_male ==”blue” & ass_mating$partner_female==”blue”)/nrow(ass_mating)) ## 0.7058824
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- What is the probability that a randomly chosen male respondent with blue eyes has a partner with blue eyes?
- I selected the number that correspondents in the table above to the self_male blue/partner blue = 78 divided by the total of self_male with blue eyes = 114
- P(A|B) = p(A and B)/P(B)
= 78/114 =,6842 = 68.42%
(sum(ass_mating$self_male ==”blue” & ass_mating$partner_female==”blue”)/nrow(ass_mating))/(sum(ass_mating$self_male==”blue”)/nrow(ass_mating)) ## 0.6842105
What is the probability that a randomly chose male respondent with brown eyes has a partner with blue eyes? I selected the number that correspondents in the table above to the self_male brown/partner blue = 19 divide by the Total of self male with brown eyes = 54 = 19/54 =,352 = 35.2%
(sum(ass_mating$self_male ==”brown” & ass_mating$partner_female==”blue”)/nrow(ass_mating))/(sum(ass_mating$self_male==”brown”)/nrow(ass_mating)) ## 0.3518519 What about the probability of a randomly chosen male respondent with green eyes having a partner with blue eyes? I selected the number that correspondents in the table above the self_male green/ partners blue = 11, divide by the Total of self male with green eyes = 36 = 11/36 =,306 = 30.6% (sum(ass_mating$self_male ==”green” & ass_mating$partner_female==”blue”)/nrow(ass_mating))/(sum(ass_mating$self_male==”green”)/nrow(ass_mating)) ## 0.3055556 Does it appears that the eye colors of male respondents and their partners are independent? Explain you reasoning. The probability that a random self male from the study has a blue eyes is 56% and the probability of randomly select a partner female with blue eyes is 52.4%, Both variables are dependent. Sampling from a Small population 2.30 Books on a bookshelf. The table below shows the distribution of books on a bookcase based on whether they are nonfiction or fiction and hardcover or paperback. book_class <- read.csv('https://raw.githubusercontent.com/jbryer/DATA606Fall2017/master/Data/Data%20from%20openintro.org/Ch%202%20Exercise%20Data/books.csv') with(warpbreaks, CrossTable(book_class$type, book_class$format, prop.r = TRUE, prop.c = FALSE, prop.t = FALSE, prop.chisq = FALSE)) ## ## ## Cell Contents ## |-| ## | N | ## | N / Row Total | ## |-| ## ## ## Total Observations in Table: 95 ## ## ## | book_class$format ## book_class$type | hardcover | paperback | Row Total | ## -|-|-|-| ## fiction | 13 | 59 | 72 | ## | 0.181 | 0.819 | 0.758 | ## -|-|-|-| ## nonfiction | 15 | 8 | 23 | ## | 0.652 | 0.348 | 0.242 | ## -|-|-|-| ## Column Total | 28 | 67 | 95 | ## -|-|-|-| ## ##
Find the probability of drawing a hardcover book first then a paperback fiction the second time without replacement?
The probability of drawing a hardcover book = 28/95 =,2947 = 29.47% the probability of drawing a paperback book fiction = 59/94 =,6276 = 62.76% The probability of the second time without replacement =,2947 X,6276 =,1849 = 18.49% (sum(book_class$format==”hardcover”))/sum(table(book_class)) * (sum(book_class$format==”paperback” & book_class$type == “fiction”))/(sum(table(book_class))-1) ## 0.1849944
Determine the probability of drawing a fiction book first and then a hardcover book second, when drawing without replacement.
The probability of drawing a fiction book 72/95 =,7578 = 75.78% the probability of dawing a hardbook = 28/94 =,2978= 29.78% the probability of drawing a fiction book then hardcover NO replacement is,7578 x,2978 =,2256 = 22.56% (sum(book_class$type==”fiction”))/sum(table(book_class)) * (sum(book_class$format==”hardcover”))/(sum(table(book_class))-1) ## 0.2257559
Calculate the probability of the scenario in part(b), except this time complete the calculaltions under the scenario where the first book is placed back on the bookcase before randomly drawing a second book.
The probability of drawing a fiction book 72/95 =,7578 = 75.78% the probability of dawing a hardbook = 28/95 =,2947 = 29.47% the probability of drawing a fiction book then hardcover WITH replacement is,7578 x,2947 =,2233 = 22.33% (sum(book_class$type==”fiction”))/sum(table(book_class)) * (sum(book_class$format==”hardcover”))/(sum(table(book_class))) ## 0.2233795
The final answers to parts b and c are very similar. Explain why this is the case.
the larger the samples the smaller the difference. Random Variables 2.38 Baggages fees: An airline charges the following baggage fees: $25 for the first bag and $35 for the second. Suppose 54% of passengers have no checked luggage, 34% have one piece of checked luggage and 12% have two pieces. We suppose a negligible portion of people check more than two bags.
Build a probability model, compute the average revenue per passenger, and compute the corresponding standard deviation.
num_bags <- c('no-bags', 'one-bags', 'two-bags') bag_fee <- c(0,25,35) pass <- c(.54,,34,,12) sample <- data.frame(num_bags, pass, bag_fee) average_revenue <- (sum((sample$pass*sample$bag_fee))/sum(sample$pass)) average_revenue ## 12.7 sqrt(0.54*(0-average_revenue)^2 + 0.34*(25-average_revenue)^2 + 0.12*(35-average_revenue)^2) ## 14.07871
About how much revenue should the airline expect for a flight of 120 passengers? With what standar deviation? Note any assumption you make and if you think they are justified. Total passengers 120 Assuming that 54% of passengers have no checked luggage, 34% have one piece of checked luggage and 12% have two pieces 65 passengers have no checked bag 41 passengers have one checked bag 14 passengers have two checked bag
avg120flight <- (65*0 + 41*25 + 14 *25 + 14 * 35) avg120flight ## 1865 x <- c(0, 1025,840) # Standar deviation of the revunue for a flight of 120 passengers sqrt(sum((x-mean(x))^2/(length(x)-1))) ## 546.2676 sd(x) ## 546.2676 Continuos Distribution 2.44 Income and Gender. The relative frequency table below displays the distribution of annual total personal income (in 2009 inflation-adjusted dollars) for a representative sample of 96,420,486 Americans. These data come from the American Community Survey for 2005-2009. This sample is comprised of 59% males and 41% females.
Describe the distribution of total personal income.
Income_range <- c("1 to $9999 or loss", "10,000 to 14,999", "15, 000 to 24,999", "25,000 to 34,999", "35,000 to 49,999", "50,000 to 64,999", "65,000 to 74,999", "75,000 to 99,999", "100,000 or more") total <- c(.022,,047, 0.158, 0.183, 0.212, 0.139, 0.058, 0.084, 0.097) x <- data.frame (Income_range, total) x ## Income_range total ## 1 1 to $9999 or loss 0.022 ## 2 10,000 to 14,999 0.047 ## 3 15, 000 to 24,999 0.158 ## 4 25,000 to 34,999 0.183 ## 5 35,000 to 49,999 0.212 ## 6 50,000 to 64,999 0.139 ## 7 65,000 to 74,999 0.058 ## 8 75,000 to 99,999 0.084 ## 9 100,000 or more 0.097 barplot(total)
- What is the probability that a randomly chosen US resident makes less than $50,000 per year? P(less than 50,000) = 2.2 + 4.7 + 15.8 + 18.3 + 21.2 = 62.2 %
- What is the probability that a randomly chosen US resident makes less than $50,000 per year and is female? Note any assumptions you make. P(less than 50,000 and gender = female) = P(less than $50,000) * P(gender= female) = 0.622 x 0.410 = 0.255 = 25.5%
- The same data source indicates that 71.8% of females make less than $50,000 per year. Use this value to determine whether or not the assumption you made in part (c) is valid. Gender and income are dependent variables,I am not able to calculate the probability of 71.8% of females making less than $50,000 because the total population making less than 50,000 (C) is 62.2%.
: Chap2-Homework2
What is an example of random mating?
Humans are an example of random mating because any male can select any female to mate randomly. The population of beetles where any beetle can choose any other beetle to mate irrespective of their external and internal conditions is also an example of random mating.
What is the difference between random and non-random mating?
Lecture 17 : Biology 102
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Assumptions of the Hardy-Weinberg principle
- The Hardy-Weinberg principle requires that there be:
- No migration
- No mutation
- No selection
- Large population
- Mating is random
Usefulness of the Hardy-Weinberg principle Hardy-Weinberg provides a theoretical benchmark against which real populations may be compared. Departures from the assumptions occur: Hardy-Weinberg provides a point of reference for evaluating the causes and consequences of the departures.
Genetic drift: random changes in gene frequencies Genetic drift means the random change of gene frequencies in a population. Some such changes are ” neutral “: changes in allele frequencies when the alleles have no immediate consequence to the biology of the population. Example: synonym codons code for the same amino acids and thus make exactly the same protein.
Examples of genetic drift Population bottleneck. Species temporarily reduced to very low number lose genetic diversity. Examples: cheetahs-low population during Pleistocene; elephant seals-hunted to near extinction during 19th century. Founder effect. Populations founded by just a few individuals have unusual gene frequencies.
- Significance of genetic drift Founder effect may start a new population with unusual gene frequencies which become the basis of new adaptations.
- Bottleneck causes reduced genetic diversity,
- For neutral alleles, genetic drift occurs in all populations and species.
- As a consequence, separated populations (and species) accumulate genetic differences,
Gene flow Gene flow means the movement of individual organisms from one population to another, or simply the movement of gametes (e.g. pollen). Gene flow brings the gene frequencies of adjacent populations closer together. Gene flow has the opposite effect of the founder effect: if it occurs, it prevents the accumulation of genetic differences,
- Mutations are spontaneous changes in the genetic material, These changes include:
- Point mutations : changes in a single base pair in the DNA
- Frame shift mutations : deletion or insertion of a single extra base pair (codon=3 bases).
- Chromosomal changes : duplication, deletion, inversion, translocation,
Significance of mutation Mutations introduce new alleles, Usually, the new alleles are deleterious, Some few, in a new environmental context, turn out to be beneficial, (Maybe not right away!) Some chromosomal mutations (e.g. inversion) produce barriers to reproduction between a new chromosomal arrangement and the ancestral arrangement.
Non-random mating The Hardy-Weinberg principle assumes random mating : mate selection without regard to genotype, Non-random mating means that mate selection is influenced by phenotypic differences based on underlying genotypic differences. Example of non-random mating: Sexual selection In some species, males acquire harems and monopolize females.
(Elk, elephant seals, horses, lions, etc.) Commonly, the males of such species are much larger than the females. In some species, females choose more attractive mates, (Peacocks, Woodducks, Picture-wing fruit flies, etc.) Significance of non-random mating.
- Genetic drift – random changes (founder effect, bottleneck, and neutral genetic drift).
- Gene flow – movement of alleles.
- Mutation – new genetic material.
- Non-random mating – sexual selection, etc.
- Natural selection – adaptive changes in the gene pool.
Hardy-Weinberg helps identify natural population processes.
- Each type of departure produces characteristic deviations from Hardy-Weinberg predictions.
- Example: selection produces changes in expected gene frequencies between new-born individuals and adult survivors.
- Hardy-Weinberg is the statistical “null hypothesis” used for testing population genetics data.
Evolution, natural selection, genetic drift
- Evolution is: changes in the gene frequencies of a population over several generations.
- Natural selection is a process : that occurs if a population has variation, fitness differences, inheritance.
- Genetic drift is: random changes in gene frequency from one generation to the next.
Evolution can be the result of. Natural selection, if the environment changes. Natural selection is responsible for adaptive evolution, Genetic drift, if random changes in gene frequencies occur. Genetic drift does not produce adaptive evolution. Neutral alleles change because of genetic drift.
What is a species? Individuals which belong to the same species are “similar” (but what about sexual dimorphism? conspicuous phenotypic differences?,,) A biological species is defined as a population or group of populations whose members have the potential to interbreed and produce fertile offspring,
Species: tied together by a common gene pool Mules are robust individuals produced by a cross between individuals from two different species: Horse x Donkey. But mules are sterile -hence the two species remain separated in spite of interbreeding. Eastern and western meadowlark look nearly the same, but courtship song is very different-they don’t interbreed,
- A species is.
- A group of individuals which interbreed and therefore represent a common gene pool.
- If there are reproductive barriers that prevent (permanently) two populations from interbreeding, they belong to separate species.
- An aside about spelling The singular of species is.
- Species The plural of species is.
Species Similar species are grouped together as a genus (singular). The plural is genera: two or more genera. Speciation: the division of a species into two or more species. A variety of mechanisms have been discovered which can cause speciation- the division of one species (ancestral) into two or more species (descendant).
The key is reproductive isolation, Mechanisms introduce barriers to reproduction. The barriers may be increased by selection, or erased by interbreeding. Time will tell which. Significance of reproductive barriers The significance of reproductive barriers is that they maintain genetic isolation between two populations.
If such barriers are complete, the populations represent distinct species. Barriers may arise by a variety of different means, Example: geographic isolation followed by drift, mutation, or selection until reproductive isolation is complete. The process of speciation Many different mechanisms have been studied.
- Two examples * Allopatric speciation-speciation based on geographic separation, and.
- Polyploidy-speciation based on a chromosome mechanism.
- Allopatric speciation Geographic isolation is one of the mechanisms which can bring about reproductive isolation.
- Allopatric speciation means: speciation which follows (over time) after geographic isolation.
The initial barrier to reproduction is physical separation, Given sufficient time (many generations) sufficient differences may accumulate to make separation permanent. Example of allopatric speciation Blue-headed wrasse (Caribbean) and the rainbow wrasse (Pacific) are closely similar.
- Their ancestral common population was split by the growth of the Isthmus of Panama about 5 million years ago.
- Since this allopatric separation occurred, the two species have changed independently.
- An ambiguous example Allopatric speciation is a process which can be interrupted before completion.
- Possible example: deermice.
There are 4 closely related populations in the Intermountain west. All 4 are distinct in some respects but interbreed, except : two of the subspecies do not interbreed even though they overlap. So are these species or just populations of the same species? Two of the populations (in Montana/Idaho) overlap but do not interbreed,
Hence, they must be different species. Both of these interbreed with the other two populations, so genes can flow from one to the other. The answer: Time will tell, With more divergence, speciation will occur. With more interbreeding, it will not occur. Speciation: a dynamic process Speciation is a dynamic process-it is taking place in many places in many populations, but it is being reversed in many places by interbreeding.
We should expect to see: populations with the potential to diverge (e.g. Snail p238), populations which have diverged horses and donkeys), populations which might be in the process (deermice). Reproductive barriers-many types. (see p241). Barriers to reproduction may prevent any mating : behavioral (courtship, etc.); habitat (populations choose different habitats, and never meet), etc.
Such barriers are prezygotic barriers, No fertilization. Barriers to reproduction may prevent subsequent reproductive success : sterility (hybrids die or are infertile), etc. Such barriers are postzygotic barriers. Significance of polyploidy The occurrence of diploid gametes (rare) can give rise to a polyploid individual after fertilization.
Many plants (e.g. Mendel’s peas) are hermaphroditic. Polyploidy can give rise to a new species : because of the incompatibility between parent and offspring, offspring are distinct. Polyploidy: common means of speciation in plants A common means of developing genetic isolation in plants is known as polyploidy.
- Haploid -half set of chromosomes
- Diploid -double set of chromosomes (the norm in typical sexual organisms)
- Triploid -3 sets of chromosomes (usually sterile, because pairing of chromosomes during meiosis is impossible).
Tetraploid -4 sets of chromosomes. (Meiosis OK for any even number ploidy.) Wheat: a case of polyploidy and speciation. Modern wheat is the result of two successive hybridizations (see figure 15.6). Hybridization 1: Einkorn wheat with a wild wheat. Einkorn wheat and the wild wheat each had 14 chromosomes.
How many people in the USA speak a language that is not English at home?
The number of people in the United States who spoke a language other than English at home nearly tripled from 23.1 million (about 1 in 10) in 1980 to 67.8 million (almost 1 in 5) in 2019, according to a recent U.S. Census Bureau report. At the same time, the number of people who spoke only English also increased, growing by approximately one-fourth from 187.2 million in 1980 to 241 million in 2019 (Figure 1).
The report, Language Use in the United States: 2019, uses American Community Survey (ACS) data to highlight trends and characteristics of the different languages spoken in the United States over the past four decades. Chinese, Vietnamese, Tagalog and Arabic speakers were more likely to be naturalized U.S.
citizens than not U.S. citizens. Spanish speakers were less likely to be naturalized U.S. citizens (18%) than not U.S. citizens (28%). In this article we refer to foreign-language “speakers” as those who report speaking a language other than English (LOTE) at home, not necessarily all those who can speak that language.
The Hispanic population is the largest minority group in the United States. So it is not surprising Spanish was the most common non-English language spoken in U.S. homes (62%) in 2019 – 12 times greater than the next four most common languages. Figure 2 displays the breakdown of age and nativity for the five most commonly spoken languages other than English in 2019.
Speakers of Spanish and Arabic, the first and fifth most common foreign languages spoken, had similar age compositions. Both had the greatest share (16%) of speakers ages 5 to 14 years and a small share of older speakers – 14% of Spanish speakers and 13% of Arabic speakers were ages 60 and over.
- In contrast, only 4% of Tagalog speakers were ages 5 to 14 but a third (33%) were 60 or older.
- More than half (55%) of Spanish speakers were U.S.-born, four times the share (13%) of Tagalog speakers.
- Chinese, Vietnamese, Tagalog and Arabic speakers were more likely to be naturalized U.S.
- Citizens than not U.S.
citizens. Spanish speakers were less likely to be naturalized U.S. citizens (18%) than not U.S. citizens (28%). In 2019, 51% of Tagalog and 54% of Chinese speakers had a bachelor’s degree or higher (these two groups were not statistically different from each other) compared to only 17% of Spanish speakers.
Figure 3 shows educational attainment for the U.S. population ages 25 years and older by language spoken at home. About a third (33%) of Spanish speakers did not graduate from high school, the largest share of speakers of the five most common languages other than English. Employment status of speakers ages 16 and over did not vary much across the five languages (Figure 3).
Less than 4% were unemployed in 2019 – not significantly different than the national average. The federal government relies on data on language use and English proficiency to provide language services under the Voting Rights Act, as well as to allocate educational funds to state English as a Second Language (ESL) programs.
Based on the 2019 data, 52% of people who spoke Chinese and 57% of those who spoke Vietnamese at home in the United States spoke English “less than very well,” compared to the other three common languages: Spanish 39%, Tagalog 30%, and Arabic 35% (Figure 4). This may have resulted from a recent increase in immigration from Asia and newcomers who have not had enough time to assimilate and master English yet.
In addition to individual differences, there were also differences in the U.S. households that spoke the five most frequently spoken non-English languages (Figure 5). A limited English-speaking household is one in which no members ages14 and over speak only English or speak English “very well.” About a third of Chinese (33%) and Vietnamese (31%) households were limited English-speaking households – four times greater than Tagalog households.
- In contrast, Tagalog-speaking households were more likely to be “non-limited” English speaking.
- About 92% of Tagalog-speaking households were non-limited English speaking and 8% were limited English speaking.
- The majority of households across all five languages were family households, defined as having at least two members (including the householder) related by birth, marriage or adoption.
On average, these households each had zero to one child under age 18 and three to four persons in the family. Among nonfamily households, defined either as a person living alone or one who shares the housing unit with nonrelatives such as boarders or roommates, a greater proportion (30%) of Chinese-speaking households were nonfamily compared to households speaking the other four languages.
- Half as many Tagalog-speaking households (17%) were nonfamily households.
- The American Community Survey is a nationally representative survey of households in the United States administered annually to a sample of approximately 3.5 million housing unit addresses (obtaining information about every household member).
In addition to language information, the ACS collects data on demographic and socioeconomic characteristics. For a comprehensive review at the individual languages and languages groups spoken in the United States, refer to the Language Use in the United States: 2019 report.
Which race has the highest rate of poverty?
In 2021, 19.5 percent of Black people living in the United States were living below the poverty line. This is compared to 8.2 percent of White people, and 8.1 percent of Asian people.
What state has the highest percentage of residents who speak a language other than English at home?
Share of U.S. population speaking a language besides English at home 2021, by state. As of 2021, about 43.9 percent of California’s population was speaking a language other than English at home. A ranking of the most spoken languages across the world can be accessed here.
How do you calculate random mating?
The Hardy-Weinberg Law – The unifying concept of population genetics is the Hardy-Weinberg Law (named after the two scientists who simultaneously discovered the law). The law predicts how gene frequencies will be transmitted from generation to generation given a specific set of assumptions. Specifically,
If an infinitely large, random mating population is free from outside evolutionaryforces (i.e. mutation, migration and natural selection), then the gene frequencies will not change over time and the frequencies in the next generation will be p 2 for the AA genotype, 2 pq for the Aa genotype and q 2 for the aa genotype.
Let’s examine the assumptions and conclusions in more detail starting first with the assumptions. Infinitely large population – No such population actually exists, but does this necessarily negate the Hardy-Weinberg Law? NO!! The effect that is of concern is genetic drift.
- Genetic drift is a change in gene frequency that is the result of chance deviation from expected genotypic frequencies.
- This is a problem in small population, but is minimal in moderate sized or larger populations.
- Random mating – Random mating refers to matings in a population that occur in proportion to their genotypic frequencies.
For example, if the genotypic frequencies in a population are MM=0.83, MN=0.16 and NN=0.01 then we would expect that 68.9% (0.83 x 0.83 X 100) of the matings would occur between MM individuals. If a significant deviation from this expected value occurred, then random mating did not happen in this population.
- If significant deviations occurred in the other matings (for example MM x MN or MN x NN), again the assumption of random mating will have been violated.
- In humans, at least, for many traits such as blood type, random mating will occur.
- Individuals do not consciously select a mate according to blood type.
But for other traits, such as intelligence or physical stature, this is the case. For these traits the population is not random mating. But this does not preclude the analysis of the population for those traits at which random mating is occurring. No evolutionary forces affecting the population – These forces may or may not be at work on a population, and we will discuss them in more detail later.
- As with random mating, some loci may be more affected by these forces.
- For these loci this assumption will be violated, whereas at those loci not affected by these forces this assumption will not be violated.
- The two conclusion of the Hardy-Weinberg Law can be mathematically demonstrated in the following table.
If p equals the frequency of allele A and q is the frequency of allele a, union of gametes would occur as follows:
p | q | |
---|---|---|
p | p 2 | pq |
q | pq | q 2 |
One of the predictions of the Hardy-Weinberg Law refers to the genotypic frequencies after one generation of random mating. In the above table the genotypic frequencies for AA is p ^2, the genotypic frequency for Aa is 2 pq and the genotypic frequency for aa will be q ^2. These are the values that are predicted by the law. The second prediction is that the frequencies of the two alleles will remain the same from generation to generation. The following is a mathematical proof of the second prediction. To determine the allelic frequency, they can be derived from the genotypic frequencies as shown above. p = f (AA) + f(Aa) (substitute from the above table) p = p 2 + (2pq) (factor out p and divide) p = p ( p + q ) ( p + q =1; therefore q =1 – p ; make this substitution) p = p (subtract and multiply) p = p Therefore, gene frequencies do not change in one generation. Analogous calculations would also show that the frequency of the a ( q ) allele would not change in one generation. In absence of any factors that change the allelic frequencies, the genotypic and allelic frequencies will remain the same from generation to generation. These two conclusions have been demonstrated experimentally to be valid and form the basis upon which all further population and evolutionary genetics research is based. Copyright © 1997. Phillip McClean
What does mating at random mean?
Random mating: Totally haphazard mating, with no regard to the genetic makeup ( genotype ) of the mate, so that any sperm has an equal chance of fertilizing any egg, Random mating rarely, if ever, occurs, but the concept is important in population genetics, Also known as panmixus,
What happens if mating is not random?
Non-Random Mating: Not Much of a Force – The last evolutionary force that we need to discuss is non-random mating. Non-random mating occurs when the probability that two individuals in a population will mate is not the same for all possible combinations of genotypes.
Non-random mating can be assortative, when individuals are more likely to mate with similar individuals ( e.g., individuals having the same genotype or phenotype), or it can be disassortative, when individuals prefer to mate with dissimilar individuals. Technically speaking, non-random mating is not an evolutionary force, because—unlike mutation, selection, drift, and migration—it does not actually cause any change in allele frequencies across generations.
It does, however, cause deviations from Hardy-Weinberg assumptions, because the frequency of genotypes do not match Hardy-Weinberg predictions when non-random mating is present. Therefore, non-random mating can have some indirect consequences for evolution.
- One of the most common forms of non-random mating is inbreeding, where offspring are produced by individuals that are closely related.
- The epitome of inbreeding is selfing (self-fertilization), which essentially represents strict genotype-specific assortative mating and is particularly common in plants.
If we assume a single, biallelic locus A, possible matings during selfing include AA x AA, Aa x Aa, and aa x aa, The consequences of selfing on the genotype frequencies across generations are depicted in Figure 6.10, As you can see, the frequency of heterozygotes declines rapidly until they are virtually gone after just 10 generations. Figure 6.10: Changes in genotype frequencies across generations when all individuals in a population self-fertilize. The degree of inbreeding can be described by the coefficient of inbreeding ( F ), which calculates the probability that two copies of an allele have been inherited from an ancestor common to both the mother and the father. You can find some examples for inbreeding coefficients in Table 6.1. Once we know F for a population, we can account for the effects of inbreeding on genotype frequencies by modifying the original Hardy-Weinberg formulas: \ Similarly, we can calculate the heterozygosity after inbreeding ( H ‘) based on F and the heterozygosity under Hardy-Weinberg assumptions ( H 0 ): \ Expected and Observed Heterozygosity Heterozygosity is a measure of genetic variability in a population. While there are multiple metrics of heterozygosity, the most commonly used one is expected heterozygosity H E (also known as gene diversity, D ). For a single locus with k alleles, expected heterozygosity is defined as: \ Hence, for a bi-allelic locus with allele frequencies p and q, expected heterozygosity is: \ H E can range from zero (when a population is fixed for a single allele) to almost 1 (when a locus has a large number of alleles with the same frequency). In practice, we can apply expected heterozygosity as a null model for inbreeding. Based on population level genotype data, we can calculate observed heterozygosity ( H O ) and allele frequencies, which allow us to also calculate expected heterozygosity ( H E ). If H E = H O, the observed heterozygosity matches the theoretical predictions, meaning that all Hardy-Weinberg assumptions are met. If H E ≠ H O, some evolutionary force must be acting on the particular locus. Most commonly, H E >> H O can be an indicator of inbreeding in a population. The degree of inbreeding is often quantified based on many loci in the genome, not just one. For m loci, genome-wide heterozygosity ( F ) is: \ Equation (6.11) allows us to simulate the effects of different levels of inbreeding on the observed heterozygosity across successive generations. As you can see in Figure 6.11, the rate of decline in heterozygosity across generations is dependent on F, and declines can be rapid when inbreeding is common. Declines in heterozygosity are particularly common in small populations where the pool of potential partners is limited, inadvertently leading to mating between related individuals. This is also the case for many managed populations, including those associated with captive breeding programs for endangered species. Hence, many species maintenance programs strategically share individuals for breeding across institutions to avoid inbreeding. Figure 6.11: Rates of decline in heterozygosity for different levels of inbreeding described by F (also see Table 6.1).
Is non random mating common?
Ch 6. Migration, Genetic Drift, Non-Random Mating Chapter 6. Mendelian Genetics in Populations II: Migration, Genetic Drift and Non-Random Mating Genetic Drift
Genetic drift – ” In small populations, chance events produce outcomes that differ from theoretical predictions” (p.165). In any population of finite size, “sampling error” will result in random changes in allele frequency from generation to generation. Consequences:
Especially for neutral alleles, frequencies drift to 1 (fixation) or 0 (elimination). The effect is strongest in small populations, but occurs in all populations Founder effect” is a special case of genetic drift: the small size of a founder population almost guarantees that its allele frequencies will not be identical to the parent population. “Bottleneck effect” occurs when populations undergo periodic crashes. Allele frequencies after the crash will probably differ from those before the crash.
Genetic drift causes random fixation of alleles and loss of heterozygosity. Fig 6.13 shows the trajectories of many populations, revealing that:
Each population follows a unique trajectory (evolutionary path). Some alleles become fixed in some populations, other alleles become fixed in other populations. Change in allele frequency is rapid in small populations, slower in large populations. Fixation occurs rapidly in small populations, more slowly in larger populations, but it eventually occurs no matter the population size. As alleles become fixed, there is an overall decline in heterozygosity as each population become homozygous for one or the other of the alleles. Note that selection can modify these outcomes by either facilitating or preventing fixation/extinction of alleles.
Some real examples:
Buri’s experiment with Drosophila (Fig.6.14). He began with most populations near p=.5, he ended with most populations near p=1 or p=0. This is exactly the outcome predicted by the computer simulations in Fig.6.13 Relict desert lizard populations in the Ozarks (Templeton, Fig.6.16):. Each population became fixed for a single multilocus genotype. Flowering plants (Young et al., Fig 6.17): There is a positive correlation between population size and genetic diversity (two measures of). Geospiza in the Galapagos: New population established by 3 males and 2 females. The new population differs morphologically from the source population.
Migration Migration – ” In an evolutionary sense, the movement of alleles between populations ” (p.157). Naturally, the alleles donut move by themselves – they move as organisms disperse from population to population. Note – don’t confuse migration in this sense with seasonal migrations, e.g.
In absence of selection (i.e. if alleles are selectively neutral) migration homogenizes allele frequencies among populations. If selection and migration tend to increase the frequencies of the same alleles, selection can amplify effect of migration. If selection and migration are opposed –
If selection is stronger than migration, than differences among populations will be maintained, even in the face of migration. If migration is stronger than selection, differences among populations will be reduced.
Some real examples:
Water snakes ( Nerodia sipedon ) on islands in western Lake Erie (Camin, Ehrlich, King; Fig.6.6, 6.7). Selection on the islands favors unbanded snakes, but dispersal of banded snakes from the mainland results in equilibrium frequencies of the two phenotypes. This is analogous to selection/mutation balance. Red bladder campion ( Silene dioica ) on Swedish islands (Giles and Goudet, Fig,6.9). This example address the interaction of drift and migration:
Diversity among young populations is due to founder effect. Migrations reduces diversity among populations of intermediate age. As populations shrink, chance extinction of alleles generates diversity among populations of old islands
Nonrandom Mating
Nonrandom mating occurs when the probability that two individuals in a population will mate is not the same for all possible pairs of individuals. When the probability is the same, then individuals are just as likely to mate with distant relatives as with close relatives – this is random mating. Nonrandom mating can take two forms:
Inbreeding – individuals are more likely to mate with close relatives (e.g. their neighbors) than with distant relatives. This is common. Outbreeding – individuals are more likely to mate with distant relatives than with close relatives. This is less common.
Inbreeding changes genotype frequencies, not allele frequencies:
Homozygotes increase in frequency, heterozygotes decrease in frequency. This is most easily seen in extreme case of inbreeding – selfing. When individuals self-fertilize, all of the homozygotes produce homozygotes, and half of the offspring of heterozygotes are homozygotes (only half are heterozygotes). Hence, the frequency of heterozygotes declines by 50% each generation. The same argument applies to sibling matings, half-sib matings, etc. Inbreeding in the malarial parasite Plasmodium falciparum (Fig.6.20, Tables 6.2, 6.3).
Strongly female biased sex ratios suggest parasite population is descended from a single foundress. If this is so, than all mating in the parasite population must be between siblings. The parasite population shows an excess of homozygote relative to Hardy-Weinberg expectation. This is the expected outcome of inbreeding.
F, the coefficient of inbreeding :
If mating is random, F=0 If all reproduction is by self fertilization, F=.5 F is between 0 and,5 for most populations. F can be calculated from genotype frequencies (because inbreeding depresses frequencies of heterozygotes) or from pedigrees (Fig.6.21).
Since inbreeding increases frequency of homozygotes, if deleterious recessive alleles are exposed to natural selection, mean fitness of population will be reduced. This is inbreeding depression, Examples:
Humans (Fig.6.22): children of first cousins have higher mortality rates than children of unrelated parents. Plants: inbreeding can be studied experimentally, yielding insights into inbreeding in general. Some generalizations:
Inbreeding depression most evident when plants are stressed. Inbreeding depression most evident as plants age and become independent of mother (seed parent), Fig.6.23. Inbreeding depression varies among lineages – not all posses deleterious recessive alleles.
Birds (Great Tit, Parus major ): hatching failure increases as function of inbreeding coefficient (F).
Inbreeding can be avoided by:
Dispersal (which may also diminish sibling competition) Separation of sexes (the rule in animals, less common in plants) to prevent self fertilization Self incompatibility in bisexual plants.
Conservation Genetics of the Prairie Chicken
Prairie chicken ( Tympanuchus cupido pinnatus ): a species endangered due to loss of habitat, habitat fragmentation, genetic drift and inbreeding depression. As prairie habitats shrink, total habitat area diminishes, but also habitat area become fragmented into smaller and smaller “islands” in a sea of farmland. There is little migration among populations, so these become genetically isolated from each other. Consequences:
In the small prairie chicken populations, genetic drift results in fixation of alleles. Some of these are deleterious, reducing mean fitness of population. As populations shrink, more matings occur among close relatives. This inbreeding increases frequency of homozygotes. As deleterious recessive alleles are exposed to selection, inbreeding depression results in lower mean fitness. As population mean fitness is reduced, population size shrinks, exacerbating the problems that caused it to shrink.
Evidence to support this explanation (the case of the Jasper County population):
From 1963 to 1990 there is a steady decline in hatching success (Fig.6.25). This could be due to inbreeding depression (there are other possibilities). If inbreeding depression/genetic drift is the culprit, genetic diversity (e.g. number of alleles per locus) should be lower in Jasper Co. individuals than in individuals from other, larger populations. It is (table 6.4). If inbreeding depression is the culprit, than introducing alleles from other populations should increase hatching success. It did – introducing individuals from from other populations had a dramatic impact (Fig.6.25)
: Ch 6. Migration, Genetic Drift, Non-Random Mating
Does random mating prevent gene flow?
Natural Selection – This red-eyed tree frog is well adapted for life in his habitat in Panama. Brad Wilson, DVM/Moment/Getty Images In order for a population to exist in Hardy-Weinberg equilibrium, natural selection must not occur. Natural selection is an important factor in biological evolution,
When natural selection occurs, individuals in a population that are best adapted to their environment survive and produce more offspring than individuals that are not as well adapted. This results in a change in the genetic makeup of a population as more favorable alleles are passed on to the population as a whole.
Natural selection changes the allele frequencies in a population. This change is not due to chance, as is the case with genetic drift, but the result of environmental adaptation. The environment establishes which genetic variations are more favorable. These variations occur as a result of several factors.
Is random mating Hardy Weinberg?
Population Genetics of Plant Pathogens Hardy-Weinberg Equilibrium The Hardy-Weinberg Law states: In a large, random-mating population that is not affected by the evolutionary processes of mutation, migration, or selection, both the allele frequencies and the genotype frequencies are constant from generation to generation.
Furthermore, the genotype frequencies are related to the allele frequencies by the square expansion of those allele frequencies. In other words, the Hardy-Weinberg Law states that under a restrictive set of assumptions, it is possible to calculate the expected frequencies of genotypes in a population if the frequency of the different alleles in a population is known.
The genotype frequencies are calculated using the square expansion of the allele frequencies. To illustrate this concept, assume that at some locus, A, you have two alleles, call them A 1, and A 2, Assume that the frequency of allele A 1 is p and the frequency of allele A 2 is q.
We can write this as: f(A 1 ) = p f(A 2 ) = q Under Hardy-Weinberg conditions, the expected genotypic proportions in the population are (p + q) 2 The square expansion of allele frequencies when there are two alleles is p 2 + 2pq + q 2 meaning that: f(A 1 A 1 ) = p 2, f(A 1 A 2 ) = 2pq, and f(A 2 A 2 ) = q 2 If there were a third allele, call it A 3, and it was present at frequency r, then the expected genotypic proportions would be (p + q + r) 2,
In other words, the expected genotypic frequencies would be: f(A 1 A 1 ) = p 2, f(A 2 A 2 ) = q 2, f(A 3 A 3 ) = r 2, f(A 1 A 2 ) = 2pq, f(A 1 A 3 ) = 2pr, and f(A 2 A 3 ) = 2qr. The implications of the Hardy-Weinberg Law are that:
The population is in a state of equilibrium. The frequencies of alleles in a population will remain constant from generation to generation. The genotypic frequencies will remain constant from generation to generation. The Hardy-Weinberg proportions will be reached in a single generation of random-mating.
As an example, consider a diploid pathogen such as an oomycete that has two alleles at an isozyme locus. If the frequency of the fast allele (F) is 0.40 and the frequency of the slow alleles (S) is 0.60, then the expected frequencies of the genotypes FF, FS, and SS would be 0.16, 0.48, and 0.36, respectively.
- The Hardy-Weinberg Law offers a model that is often used as a starting point for studying the population genetics of diploid organisms that meets the basic assumptions of large population size, random-mating, and no migration, mutation, or selection.
- Unfortunately, the Hardy-Weinberg Law cannot be applied to haploid pathogens.
If a population is found not to be in H-W equilibrium, then one of the assumptions in the Law has been violated. That is, there has been non-random mating, or selection or migration have affected the population. At this point, hypotheses are proposed and experiments are conducted to determine why a population is not at equilibrium.
What is the 3rd most spoken language in US?
3. Chinese (Mandarin, Cantonese, Hokkien and More) – The Chinese language, and the different varieties within it, is another prominent player in the diverse culture of the United States. With over 3.5 million speakers across the country today, Chinese is another dominant language and is the 3rd most spoken language in the United States right now.
Why do so many Americans only speak English?
U.S. identity, unlike that of other countries, is not rooted in ethnicity or race, and some Americans believe that national unity requires a national language. They see English as a national unifying bond.
What is the average black salary?
The median income in 2021 was at 48,297 U.S. dollars for black households.
What race has the lowest income?
In terms of broad ethnic groups, Black Americans have consistently had the lowest median income in the given years, while Asian Americans have the highest; median income in Asian American households has typically been around double that of Black Americans.
What percent of America is white?
Table
Population | |
---|---|
Persons 65 years and over, percent | 16.8% |
Female persons, percent | 50.5% |
Race and Hispanic Origin | |
White alone, percent | 75.8% |
Is assortative mating and non-random mating the same?
Assortative Mating – Assortative mating is nonrandom mating based on phenotypes rather than between relatives. Positive-assortative mating or negative-assortative mating occurs if the mated pairs in a population are composed of individuals with the same phenotype more often, or less often, than expected by random mating, respectively.
Positive-assortative mating is in some ways analogous to inbreeding in that similar phenotypes, which might have similar genotypes, are more likely to mate than random individuals from the population. Some types of assortative mating are also similar to inbreeding in that they do not change allele frequencies but do affect genotype frequencies.
On the other hand, negative-assortative mating may result in balancing selection and the maintenance of genetic variation. Many assortative mating models do change allele frequencies because the proportion of individuals in the matings differs from the proportion in the population.
An important point to remember is that assortative mating affects the genotype frequencies of only those loci involved in determining the phenotypes for mate selection (and genotypes at loci nonrandomly associated with those loci), whereas inbreeding affects all loci in the genome. In a survey of assortative mating studies, Jiang et al.
(2013) found that most of the examples of assortative mating were for positive-assortative mating. There appears to be positive-assortative mating for a number of traits in humans, such as height, skin color, and intelligence, although the consequent phenotypic correlation is often not very large.
- In addition, there also appears to be positive correlations among mates in humans that have particular phenotypes, such as deafness, blindness, or small stature.
- Of course, there are many different genetic (and nongenetic) causes for deafness, blindness, or small stature so that such a phenotypic correlation may not result in a genetic correlation (for deafness, see Nance and Kearsey, 2004 ).
Rather strong positive-assortative mating may occur in plants when a pollinator forages at a given height or is attracted to a given flower color and, as a result, tends to pollinate plants similar to the ones where the pollen was collected. Similar effects may also occur when flowering time is variable, and only plants that flower simultaneously pollinate each other.
- Jiang et al.
- 2013) found few examples of negative-assortative mating in their review.
- Some examples are, however, in some plants where successful fertilization occurs only between individuals with different flower types.
- Although less generally accepted, another example is in populations where rare males (or females) have a mating advantage over more common types.
Some reports suggest that negative-assortative mating in mammals and other vertebrates may be based on major histocompatibility complex (MHC) differences. The overall support for MHC-based, negative-assortative mate choice in humans is mixed and contentious.
- The most widely known example is the ‘t-shirt study’ in which female Swiss university students ranked the smell of t-shirts worn by male students on characteristics such as pleasantness ( Wedekind et al., 1995 ).
- The findings of this study suggested that females preferred the odor of males that differed at MHC genes, except when they were on birth control pills, in which case they preferred males that were similar at MHC genes! Further, a follow-up study examining some of the same pairs found no correlation between the rankings for the two different studies.
Several recent studies have examined the correlation of mates for MHC in humans compared to the correlation of genes in the rest of the genome. The first such study found a small but significant (partly due to high statistical power) negative correlation in 30 couples at the MHC region of −0.043 compared to the average in the rest of genome of −0.00 016 ( Chaix et al.
2008 ). However, this level of assortment appears small in a biological sense and nine other genomic regions had higher levels. Subsequently, Derti et al. (2010) concluded that the findings of Chaix et al. (2008) were not statistically robust and they found nonsignificant results in another small-sized, independent sample.
These sample sizes appear much too small to draw inference about genomic assortative mating but a study underway of assortative mating in about 10 000 pairs using genome-wide SNP data (P. Visscher, personal communication) should give definitive estimates.
- A striking example of negative-assortative mating is in wolves from Yellowstone National Park for gray and black coat color ( Hedrick et al.
- 2016b ).
- Black coat color in wolves is caused by a dominant allele at a beta-defensin gene.
- In the surveys of mating pairs at Yellowstone from 1995 to 2014, 166 out of 261 (64%) of the matings were between different color wolves, either gray males × black females or black males × gray females ( Table 3 ) with a significant negative correlation of −0.27.
Table 3, The number of matings observed between gray and black wolves in Yellowstone National Park from 1995 to 2014 ( Hedrick et al., 2016b )
Mating | Observed | Expected | Observed – Expected | |
---|---|---|---|---|
Male | Female | |||
Gray | Gray | 54 | 71.0 | −17.0 |
Gray | Black | 67 | 50.1 | 16.9 |
Black | Gray | 99 | 82.0 | 17.0 |
Black | Black | 41 | 57.9 | −16.9 |
Total | 261 | 261 |
Read full chapter URL: https://www.sciencedirect.com/science/article/pii/B9780128000496000238
What is non-random assortative mating?
Non-Random Mating: Not Much of a Force – The last evolutionary force that we need to discuss is non-random mating. Non-random mating occurs when the probability that two individuals in a population will mate is not the same for all possible combinations of genotypes.
Non-random mating can be assortative, when individuals are more likely to mate with similar individuals ( e.g., individuals having the same genotype or phenotype), or it can be disassortative, when individuals prefer to mate with dissimilar individuals. Technically speaking, non-random mating is not an evolutionary force, because—unlike mutation, selection, drift, and migration—it does not actually cause any change in allele frequencies across generations.
It does, however, cause deviations from Hardy-Weinberg assumptions, because the frequency of genotypes do not match Hardy-Weinberg predictions when non-random mating is present. Therefore, non-random mating can have some indirect consequences for evolution.
One of the most common forms of non-random mating is inbreeding, where offspring are produced by individuals that are closely related. The epitome of inbreeding is selfing (self-fertilization), which essentially represents strict genotype-specific assortative mating and is particularly common in plants.
If we assume a single, biallelic locus A, possible matings during selfing include AA x AA, Aa x Aa, and aa x aa, The consequences of selfing on the genotype frequencies across generations are depicted in Figure 6.10, As you can see, the frequency of heterozygotes declines rapidly until they are virtually gone after just 10 generations. Figure 6.10: Changes in genotype frequencies across generations when all individuals in a population self-fertilize. The degree of inbreeding can be described by the coefficient of inbreeding ( F ), which calculates the probability that two copies of an allele have been inherited from an ancestor common to both the mother and the father. You can find some examples for inbreeding coefficients in Table 6.1. Once we know F for a population, we can account for the effects of inbreeding on genotype frequencies by modifying the original Hardy-Weinberg formulas: \ Similarly, we can calculate the heterozygosity after inbreeding ( H ‘) based on F and the heterozygosity under Hardy-Weinberg assumptions ( H 0 ): \ Expected and Observed Heterozygosity Heterozygosity is a measure of genetic variability in a population. While there are multiple metrics of heterozygosity, the most commonly used one is expected heterozygosity H E (also known as gene diversity, D ). For a single locus with k alleles, expected heterozygosity is defined as: \ Hence, for a bi-allelic locus with allele frequencies p and q, expected heterozygosity is: \ H E can range from zero (when a population is fixed for a single allele) to almost 1 (when a locus has a large number of alleles with the same frequency). In practice, we can apply expected heterozygosity as a null model for inbreeding. Based on population level genotype data, we can calculate observed heterozygosity ( H O ) and allele frequencies, which allow us to also calculate expected heterozygosity ( H E ). If H E = H O, the observed heterozygosity matches the theoretical predictions, meaning that all Hardy-Weinberg assumptions are met. If H E ≠ H O, some evolutionary force must be acting on the particular locus. Most commonly, H E >> H O can be an indicator of inbreeding in a population. The degree of inbreeding is often quantified based on many loci in the genome, not just one. For m loci, genome-wide heterozygosity ( F ) is: \ Equation (6.11) allows us to simulate the effects of different levels of inbreeding on the observed heterozygosity across successive generations. As you can see in Figure 6.11, the rate of decline in heterozygosity across generations is dependent on F, and declines can be rapid when inbreeding is common. Declines in heterozygosity are particularly common in small populations where the pool of potential partners is limited, inadvertently leading to mating between related individuals. This is also the case for many managed populations, including those associated with captive breeding programs for endangered species. Hence, many species maintenance programs strategically share individuals for breeding across institutions to avoid inbreeding. Figure 6.11: Rates of decline in heterozygosity for different levels of inbreeding described by F (also see Table 6.1).
Is assortative mating nonrandom mating?
assortative mating, in human genetics, a form of nonrandom mating in which pair bonds are established on the basis of phenotype (observable characteristics). For example, a person may choose a mate according to religious, cultural, or ethnic preferences, professional interests, or physical traits.
Positive assortative mating, or homogamy, exists when people choose to mate with persons similar to themselves (e.g., when a tall person mates with a tall person); this type of selection is very common. Negative assortative mating is the opposite case, when people avoid mating with persons similar to themselves.
Assortative mating also occurs in nonhuman animal populations. Indeed, phenotypic similarity is thought to underlie mate selection in a variety of species, This article was most recently revised and updated by Kara Rogers,
What is an example of non-random mating?
Chapter Summary – We have already learned that natural selection and genetic drift are key mechanisms that cause evolution. Migration and nonrandom mating can also have impacts on genetic variation and relative proportions of genotypes. Migration is the movement from one locality to another.
It can alter genetic composition through genetic drift and alter allele frequencies in populations. For example, consider a population of green frogs in one pond and another population of white frogs in another pond. In the pond with green frogs the genotypes are heterozygous (Aa) or homozygous dominant (AA).
The pond with white frogs has the genotype homozygous recessive (aa). If a green frog migrates into the pond with white frogs it will mix in with the population, and the next generation of the pond will have a mix of frogs with genotypes of aa, and Aa.
This changes allele frequency of the pond because before all the frogs had the genotype aa, but now in the new generation the frogs in that pond could have aa or Aa. Over time, the allele frequencies change even more with the introduction of the new allele. When individuals migrate between different populations and results in changes in genetic composition of the population, it causes gene flow,
Click for a tutorial of gene flow and get a better idea. You can get a step by step guide to gene flow or have a narration. You can also take a 2 question quiz to check your understanding of gene flow. In previous sections, we have studied the Hardy-Weinberg equilibrium,
One of the conditions of the equilibrium is random mating, meaning that individuals mate randomly without thinking of the genotype or phenotype of their mate. However, there are many species of that do not mate randomly, they do nonrandom mating. Nonrandom mating is a phenomenon that individuals choose their mates based on their genotypes or phenotypes.
Examples of this kind of mating occur in species like humans, peacocks, and frogs. Nonrandom mating can happen in many different forms, one being assortative mating, This happens when individuals with similar phenotypes mate, which usually lower the proportion for heterozygotes, and increases the proportion of homozygotes.
- This is because similar phenotype usually means similar genotype.
- Another type of nonrandom mating is inbreeding.
- Inbreeding means to mate with genetically related relatives.
- These individuals choose their mates based on family history instead of phenotypes.
- This usually happens when the population becomes small and they are forced to inbreed due to lack of partners.
One thing about inbreeding is that, it doesn’t affect allele frequencies over short term. What this means is that inbreeding doesn’t cause allele frequencies to change if it happens once or twice in a pedigree, but when it happens over many generations, it decreases the likelihood of heterozygotes.
- This happens because the individual could inherit the two of the same allele from a common ancestor.
- There are many consequences to inbreeding, you may already know.
- Inbreeding lowers the fitness of the individual and the overall fitness of the population.
- Fitness can be described as the organism’s ability to survive, reproduce, and contribute to the gene pool.
It can be defined by its genotype or phenotype. Being a less fit individual can be harmful to the population, leading to inbreeding depression. Inbreeding depression is the phenomenon where inbreeding produces homozygotes that are less fit, therefore decreasing the reproductive success of the population.