Name: hardy-weinberg tests for population change
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Ohio’s Learning Standards and Model Curriculum

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Biology

Evolution

Mechanisms

Hardy-Weinberg and Genetic Drift

科学家曾一度困惑，为何像黄褐色长颈鹿斑点这样的显性性状并不会随着每一代的延续而变得更加普遍，从而取代深褐色斑点等隐性性状。在思考这一难题时，1908年，戈弗雷·H·哈代（Godfrey H. Hardy）与威廉·温伯格（Wilhelm Weinberg）在互不知情的情况下各自独立提出了一种理论，即如今所称的哈代-温伯格定律，并由以下方程表示。
该原理指出，在没有进化的条件下，即处于平衡状态时，一个群体的等位基因频率和基因型频率将从一代到下一代保持不变。为了理解这个方程，让我们回到长颈鹿的例子。大写字母 A 代表显性的褐色等位基因，小写字母 a 代表隐性的棕色等位基因。这两个等位基因在群体中的频率分别用 p 和 q 表示。那么我们如何确定等位基因频率呢？每个个体都有两个等位基因。在这个例子中，基因库中 40% 的等位基因是褐色的。因此，褐色等位基因的频率 p 为 0.4，棕色等位基因的频率 q 为 0.6。请注意，p 加 q 始终等于 1。
现在让我们回到哈迪-温伯格方程。方程中的每一项代表一种基因型的频率。纯合显性基因型的频率为 p²，纯合隐性基因型由 q² 表示。杂合基因型为 2pq。此处乘以 2 的原因是产生杂合基因型有两种不同的方式。这些频率加在一起代表了全部基因型，即总频率为 1（100%）。利用之前长颈鹿例子中计算出的 p 和 q 值，我们可以确定该长颈鹿群体中颜色基因等位基因的基因型分布。因此，根据哈迪-温伯格平衡定律，在达到平衡状态时，16% 的长颈鹿为纯合显性，48% 为杂合子，36% 为纯合隐性。
为了维持这种平衡，哈迪-温伯格平衡定律指出，一个群体应满足五个主要假设：随机交配、群体规模足够大、无突变、对所研究的基因无自然选择作用，以及无基因流进入或离开该群体。大多数自然群体至少违反了其中一项假设，因此平衡状态较为罕见……但尽管如此，该定律仍被用作群体遗传学中的零模型。通过将这些预期值与群体中实际的基因型频率进行比较，可以判断该群体是否处于哈迪-温伯格平衡状态。如果不符合，则意味着该群体正在发生某种形式的进化或等位基因频率的改变。
关于进化的一个普遍误解是，认为进化必须通过自然选择才能发生。然而，情况并非总是如此。遗传漂变就是一种无需自然选择也可导致进化的机制。它被定义为由于随机因素导致种群中等位基因频率发生变化。为了理解这一点，让我们回到长颈鹿种群的例子，并设想它们的浅褐色和棕色等位基因由两种不同颜色的弹珠来代表。我们假设每种颜色最初数量相等。如果我们从该种群中繁衍新一代，则需要将个体成对交配，从而每对组合中选出四个等位基因。如果我们随机选择一对进行繁殖，可能会得到每种颜色各两个弹珠。然而，仅凭偶然性，某些配对可能只包含一种颜色的弹珠，或三种一种颜色、一种另一种颜色。在多次配对产生新一代的过程中，这些偏离50-50比例的随机偏差可能导致下一代不再具有相等的等位基因混合比例。
正是等位基因频率随时间发生的变化定义了遗传漂变。因此，与适应性进化不同——在适应性进化中，等位基因频率的改变是为了筛选出更适应环境的性状，例如在寒冷气候中，因含有较多黑色素而具有更强吸热能力、从而生存能力更强的瓢虫——遗传漂变代表了一种完全由随机性变化驱动的进化类型。例如，由于灾难性事件导致种群中某一部分个体被随机移除。
在本实验中，您将通过计算机模拟和彩色珠子模拟来研究群体中哈迪-温伯格平衡和遗传漂变，并测试当平衡假设条件被打破时会发生什么情况。

哈迪-温伯格平衡与遗传漂变

研究进化变化非常有趣且重要，但种群的变化发生在漫长的时间尺度和广阔的空间范围内，因此极难进行测量。通常，研究此类现象需要使用数学模型，这些模型基于可方便测量的参数构建。然后利用这些模型预测系统变化可能对结果产生的影响。 
例如，物种在单个基因座上遗传等位基因频率的变化通常可在长时间尺度上观察到，但在较短的时间尺度内通常无法观察到。利用计算机模型，研究人员能够基于已收集的观测数据，预测物种基因库中的变化，并对种群进行理论上无限多代的模拟。这在人类寿命的时间范围内显然是不可能实现的。
<h4>哈迪-温伯格平衡定律</h4>
用于模拟种群的一个方程是哈迪-温伯格平衡方程。该方程于1908年由G. H. Hardy和Wilhelm Weinberg分别独立提出1,2。这个简单的方程描述了一个不在进化的种群中预期的等位基因频率。由于大多数真实种群都在自然选择压力下发生进化，该公式可作为一个有用的零假设。它被用来检验是否存在不同类型的自然选择。如果实测的等位基因频率与哈迪-温伯格方程预测的频率不同，则表明该基因正在经历进化改变。
哈迪-温伯格方程可以表示为 p2 + 2pq + q2 = 1，其中 p 代表显性等位基因的频率，q 代表该基因的隐性等位基因的频率。方程中的每一项代表三种可能的二倍体基因型之一的预测频率。纯合显性频率由 p2 表示，纯合隐性由 q2 表示，杂合子由 2pq 表示。如果将这些频率相加，总和为1，这是合理的，因为整个种群已被划分为这三个可选类别。
也可以仅根据两个等位基因来描述群体或基因库，而无需考虑它们在二倍体个体中的组合方式。该方程表示为 p + q = 1，即在一个群体中，显性等位基因和隐性等位基因的频率之和必须等于1。这一点是合理的，因为该模型仅包含两种等位基因的可能性。请注意，群体中基因型频率实际上就是等位基因频率的二次展开，因为 (p + q)2 = p2 + 2pq + q2。
哈迪-温伯格方程与大多数其他模型一样，需要一系列假设。如果实际数据与预测数据存在差异，则可以据此推断出哪一项初始假设不成立，这一点具有实际意义。哈迪-温伯格平衡方程的假设包括：1）种群规模非常大；2）种群是封闭的，即没有个体迁入或迁出该种群；3）所研究的基因不发生突变；4）种群内的个体随机交配——个体不会选择特定的配偶；5）不存在自然选择。需要再次强调的是，哈迪-温伯格平衡方程是一种零假设。现实中，真实的种群常常会违反其中一项或多项假设。该方程用于判断进化是否正在发生以及以何种方式发生。
<h4>遗传漂变</h4>
在相对较小的种群中，这一情况违反了哈迪-温伯格平衡的第一条假设，等位基因频率可能因偶然因素而产生变化。这种现象被称为遗传漂变。其中一种形式被称为奠基者效应。当少数个体迁移到一个孤立的地点并建立新的种群时，这些特定个体的遗传组成将决定后代的遗传特征。这个新的小型基因库可能与原始种群具有相同的等位基因频率，但也可能不同，甚至很可能不同。假设原始种群中显性等位基因和隐性等位基因各占50%。在极端情况下，如果迁移的奠基者群体中所有个体均为隐性纯合子，则显性等位基因将完全丢失，而隐性等位基因频率则变为100%。类似的现象称为瓶颈效应，可能在种群因自然灾害、人为干预或疾病导致数量急剧下降时发生。
重要的是，遗传漂变代表了一种不一定是适应性的进化类型。它并不会特异性地选择适应环境的性状。尽管如此，遗传漂变在个体数量较少的群体演化过程中仍是一种重要的进化力量，并会导致偏离哈迪-温伯格平衡的预测结果。在较大的群体中，若观察到与预测结果的偏离，则更有可能意味着该群体正在经历自然选择驱动的进化。在这种情况下，可进一步探讨导致该进化的具体机制。
哈代-温伯格模型的现代应用包括分析人类和动物群体，研究其免疫系统与对传染病易感性之间的关系3,4。许多研究团队正在对编码特定免疫系统分子（如CCR5和主要组织相容性复合体（MHC，在人类中称为人类白细胞抗原（HLA））的基因进行编目，并将这些信息与关于疾病及其进展的流行病学研究相关联3,5-6。通过比较这两类数据集，逐渐显现出一些模式，表明某些个体在遗传上对特定感染具有抵抗力，而另一些个体则更容易患病4。哈代和温伯格的模型对于这些数据的分析至关重要，并有助于我们理解感染如何影响了进化过程。
<h4>参考文献</h4>
<ol class="references">
	<li>哈代，G. H.（1908年7月）《混合群体中的孟德尔比例》 （PDF）。Science。 28 (706): 49–50. doi:10.1126/science.28.706.49. ISSN 0036-8075. PMID 17779291.</li>
	<li>Weinberg, W. (1908). 《论人类遗传的证明》 符腾堡祖国自然研究协会年鉴. 64: 368–382.</li>
	<li>Eguchi S, Matsuura M. 在HLA系统中检验哈迪-温伯格平衡。Biometrics. 1990年6月;46(2):415-26. PubMed PMID: 2364131.</li>
	<li>Phillips KP, Cable J, Mohammed RS, 等. 免疫遗传新颖性在宿主-病原体共同进化中赋予选择优势 美国国家科学院院刊. 2018;115(7):1552-1557.</li>
	<li>Lim JK, Glass WG, McDermott DH, Murphy PM CCR5：不再是一个“无用”基因——趋化因子对西尼罗河病毒感染的调控。Trends Immunol. 2006 Jul; 27(7):308-12.</li>
	<li><a target="__blank" href="https://hla-net.eu/tools/frequency-estimation/">https://hla-net.eu/tools/frequency-estimation/</a></li>
	<li>Santiago Rodriguez, Tom R. Gaunt 和 Ian N. M. Day。用于孟德尔随机化研究中生物学数据获取的哈迪-温伯格平衡检验。《美国流行病学杂志》提前访问，2009年1月6日发表，DOI 10.1093/aje/kwn359。http://www.oege.org/software/hwe-mr-calc.html</li>
</ol>
<h4>延伸阅读</h4>
Andrews, C. (2010) 哈迪-温伯格定律. Nature Education Knowledge 3(10):65 https://www.nature.com/scitable/knowledge/library/the-hardy-weinberg-principle-13235724

进化变化的研究既有趣又重要，但种群的变化发生在漫长的时间尺度和广阔的物理空间中，并且是……

Education

教育

JoVE Lab Manual

生物学

进化

Hardy-Weinberg 和遗传漂变

hardy-weinberg tests for population change

Hardy-Weinberg tests help scientists check whether a population is changing over time. Because evolution happens slowly and over large areas, researchers often use mathematical models to study it. These models use measurable data and computer simulations to predict how allele frequencies may shift across many generations.

The Hardy-Weinberg equilibrium equation is one common model. It was developed independently in 1908 by G. H. Hardy and Wilhelm Weinberg. The equation gives the expected allele frequency for a population that is not evolving, so it serves as a useful null hypothesis. If measured allele frequencies do not match the prediction, the gene may be undergoing evolutionary change.

The model is written as p2 + 2pq + q2 = 1. In this equation, p is the frequency of the dominant allele and q is the frequency of the recessive allele. The three terms represent the expected frequencies of the three diploid genotypes: homozygous dominant, heterozygous, and homozygous recessive. The allele version of the model is p + q = 1, since the two allele frequencies must total 1 in the population.

Hardy-Weinberg also depends on a set of assumptions. The population must be very large and closed, which means no individuals move in or out. There must be no mutations in the gene being studied. Individuals must mate at random, and natural selection must not be acting. When real data breaks one or more of these assumptions, the model can help point to what may be happening.

Genetic drift is one reason a small population can change by chance alone. This violates the large-population assumption of Hardy-Weinberg. One form of genetic drift is the founder effect. It happens when a small group leaves and starts a new isolated population. The genes carried by those founders shape future generations. In an extreme case, if the founders are all homozygous recessive, the dominant allele can disappear and the recessive allele can reach 100%.

A similar pattern is called the bottleneck effect. It can occur after a natural disaster, human intervention, or disease causes a major drop in population size. Genetic drift is not necessarily adaptive, because it does not specifically favor traits that fit the environment. Even so, it is an important evolutionary force in small populations and can create differences from Hardy-Weinberg predictions. In larger populations, those differences are more likely to suggest natural selection.

Scientists also use Hardy-Weinberg testing in modern studies of human and animal populations. One focus is how immune system genes relate to susceptibility to infectious disease. Researchers study genes such as CCR5 and the major histocompatibility complex, or MHC, called HLA in humans. By comparing genetic data with disease data, they can find patterns showing that some individuals are more resistant to certain infections while others are more likely to become ill. These studies have helped explain how infections have influenced evolution.

Hardy-Weinberg Tests for Population Change

hardy-weinberg-tests-for-population-change

natural selection

Fitness and Selection in Populations

Fitness and natural selection shape how traits spread through a population over time. Variation in inherited phenotypes gives evolution its raw material. When a trait is heritable and affects survival or reproduction, natural selection can change how common that trait becomes in later generations. Fitness means reproductive success compared with others in the same population. A heritable trait that improves fitness is called an adaptation. Individuals with higher lifetime reproductive success...

artificial selection

Selective Breeding in Dogs and Crops

Artificial selection, also called selective breeding, is the human choice of which plants or animals reproduce. It uses natural variation in a population to produce traits people want. Over many generations, this can create domesticated organisms that look very different from their wild ancestors. Natural selection is a different process, but it helps explain how change happens in nature. In adaptive evolution, differences in traits can lead to differences in survival and reproductive success.

hardy-weinberg and genetic drift

Hardy-Weinberg tests help scientists check whether a population is changing over time. Because evolution happens slowly and over large areas, researchers often use mathematical models to study it. These models use measurable data and computer simulations to predict how allele frequencies may shift across many generations. The Hardy-Weinberg equilibrium equation is one common model. It was developed independently in 1908 by G. H. Hardy and Wilhelm Weinberg. The equation gives the expected...

evolutionary relationships

DNA Evidence in Evolutionary Trees

DNA evidence helps scientists map evolutionary relationships between living things. Early classification began with Aristotle in the 4th century BC and was later improved during the Renaissance and by Carolus Linnaeus in the mid-1700s. These systems grouped species by physical similarity, such as the presence or absence of a backbone in vertebrates and invertebrates. Traits like a backbone are called synapomorphies, which are shared traits that likely came from a common ancestor. Physical...

plant diversity

Plant Adaptations for Land Life

Plant adaptations for land life explain how plants moved from water to land and diversified over time. Kingdom Plantae first appeared about 410 million years ago, when green algae began transitioning from aquatic environments to dry land. That shift was difficult, but land offered more light, more carbon dioxide, and far less competition than crowded oceans. Life on land forced plants to solve new problems. Aquatic plants can absorb water and nutrients directly from the surrounding liquid, use...

animal diversity

Animal Classification and Adaptation

Kingdom Animalia includes a wide range of organisms that share a few basic traits. Most animals are multicellular eukaryotes that move, consume organic matter, and reproduce sexually. Even with those shared features, animals are extremely diverse because each species adapts to a different niche. A niche is the place, role, and set of interactions a species has with living and nonliving parts of its environment. Specialization helps species survive, reproduce, and reduce competition with others...

microbial and fungal diversity

How Scientists Identify Bacteria and Fungi

Bacteria and fungi are highly diverse organisms, and scientists identify them by looking at their structure, growth, and role in health. Some species help people, while others can cause disease, so learning how to tell them apart matters in biology and medicine. Biological taxonomists group organisms by evolutionary relatedness. Life is divided into three domains: Bacteria, Archaea, and Eukaryota. Bacteria belong to the domain Bacteria, which includes single-celled prokaryotes. Prokaryotic...

evolution

Learn how Hardy-Weinberg testing uses allele frequencies, key assumptions, and genetic drift to show whether a population is evolving.

Hardy-Weinberg Tests for Population Change | JoVE K12

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New Jersey Student Learning Standards for Science

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Heredity: Inheritance and Variation of Traits

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Next Generation Science Standards

Florida Department of Education

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New York State Science Learning Standards

Inheritance and Variation of Traits

HS-LS3-3.

Natural Selection and Evolution

HS-LS4-1.

HS-LS4-3.

Georgia Standards of Excellence

SB6.d

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What is Natural Selection?

Natural selection is an evolutionary process in which individuals with survival-promoting traits reproduce at higher rates. These favorable traits become ...

Types of Selection

Natural selection influences the frequencies of particular alleles and phenotypes within populations in several different ways. Primarily, natural ...

Frequency-dependent Selection

When the fitness of a trait is influenced by how common it is (i.e., its frequency) relative to different traits within a population, this is referred to ...

Limits to Natural Selection

Organisms that are well-adapted to their environment are more likely to survive and reproduce. However, natural selection does not lead to perfectly ...

Natural Selection

Fitness
Widespread variation of phenotypes in natural populations provides the raw material for evolution, which is the change in the inherited traits of ...

Simulating Natural Selection
ExpandTo prepare for the lab, set out workstations for each student pair containing 6 white, 6 black, and 13 gray 12 inch ...

Simulating Natural Selection
ExpandTo begin, cut the white, black, and gray pipe cleaners into quarters, which should produce a total of 100 pieces that ...

Artificial Selection

Natural Selection and Adaptive Evolution
In natural settings, adaptive evolution takes place by natural selection, a process in which differences in ...

Observing Artificial Selection in Plants
ExpandTwo weeks before beginning the pollination experiments, collect a sufficient amount of small pots with a ...

Observing Artificial Selection in Plants 
ExpandTo begin the experiment, collect five two-week old grown plants from the generation one population that ...

What is Population Genetics?

A population is composed of members of the same species that simultaneously live and interact in the same area. When individuals in a population breed, ...

Hardy-Weinberg Principle

Diploid organisms have two alleles of each gene, one from each parent, in their somatic cells. Therefore, each individual contributes two alleles to the ...

Mutation, Gene Flow, and Genetic Drift

In a population that is not at Hardy-Weinberg equilibrium, the frequency of alleles changes over time. Therefore, any deviations from the five conditions ...

Genetic Drift

Natural selection&#x2014;probably the most well-known evolutionary mechanism&#x2014;increases the prevalence of traits that enhance survival and ...

Gene Flow

Gene flow is the transfer of genes among populations, resulting from either the dispersal of gametes or from the migration of individuals.

This ...

Evolutionary change is interesting and important to study, but changes in populations occur over long periods of time and in huge physical spaces and are ...


	Mathematical ModelingExpand
	
		
		Before beginning the mathematical modeling exercise make sure each computer has access to an either on or offline ...

Class Simulation
ExpandBegin by opening a new spreadsheet file. Following the Hardy-Weinberg equation where p is the frequency of a dominant allele A in a ...

Mechanisms
• Natural selection
• Mutation
• Genetic drift
• Gene flow (immigration, emigration)
• Sexual selection

Content elaboration: Natural selection is used to describe the process by which traits become more or less common in a population due to consistent environmental pressures upon the survival and reproduction of individuals with the trait. Mathematical reasoning is applied to solve problems (e.g., use Hardy-Weinberg principle to explain deviations in observed gene frequency patterns in a population compared to expected patterns based on the assumptions of the principle). Populations evolve over time. Evolution through natural selection is the consequence of the interactions of:
1. The potential for a population to increase its numbers; 
2. The genetic variability of offspring due to mutation and recombination of genes; 
3. A finite supply of the resources required for life; and 
4. The differential survival and reproduction of individuals based on phenotype(s). 
Mutations are described in the content elaboration for Heredity. Apply the knowledge of mutation and genetic drift to real-world examples. Biological evolution explains the natural origins for the diversity of life. Emphasis shifts from thinking in terms of selection of individuals with a particular trait to changing proportions of a trait in populations as a result of the mechanisms of natural selection, genetic drift, movement of genes into and out of populations and sexual selection.

Taxonomy

Taxonomy is the science of defining and naming groups of biological organisms based on shared characteristics. It uses a hierarchy of increasingly ...

Phylogeny

Phylogeny is concerned with the evolutionary diversification of organisms or groups of organisms. A group of organisms with a name is called a taxon ...

evolutionary-relationships-through-genome-comparisons

Evolutionary Relationships through Genome Comparisons

Genome comparison is one of the excellent ways to interpret the evolutionary relationships between organisms. The basic principle of genome comparison is ...

Genome Copying Errors

DNA replication is a well-evolved process that copies millions of base pairs with high fidelity during each cell division. Occasionally a wrong base or a ...

Phylogenetic Trees

Synteny and Evolution

John H. Renwick first coined the term &#8220;synteny&#8221; in 1971, which refers to the genes present on the same chromosomes, even if they are not ...

Multi-species Conserved Sequences

Next-generation sequencing technologies have created large genomic databases of a variety of animals and plants. Ever since the human genome project was ...

Gene Duplication and Divergence

The seminal work of Ohno in 1970 popularized the idea of gene duplication and divergence. DNA sequence comparison studies reveal that a large portion of ...

Exon Recombination

The evolution of new genes is critical for speciation. Exon recombination, also known as exon shuffling or domain shuffling, is an important means of new ...

comparing-copy-number-variations-and-snps

Comparing Copy Number Variations and SNPs

Sequencing of the human genome has opened up several best-kept secrets of the genome. Scientists have identified thousands of genome variations that exist ...

Speciation
• Biological classification expanded to molecular evidence
• Variation of organisms within a species due to population genetics and gene frequency

Content elaboration: Biological classification expanded to molecular evidence
Classification systems are frameworks, developed by scientists, for describing the diversity of organisms; indicating the degree of relatedness among organisms. Recent molecular sequence data generally support earlier hypotheses regarding lineages of organisms based upon morphological comparisons. Both morphological and molecular comparisons can be used to describe patterns of biodiversity (cladograms present hypotheses to explain descent from a common ancestor with modification). The concept of descent from a common ancestor with modification provides a natural explanation for the diversity of life on Earth as partially represented in the fossil record and in the similarities of existing species. 
Variation of organisms within a species due to population genetics and gene frequency
Different phenotypes result from new combinations of existing genes or from mutations of genes in reproductive cells. At the high school level, the expectation is to combine grade 8 knowledge with an explanation of genes and the function of chromosomes. Natural selection works on the phenotype. Heritable characteristics influence how likely an organism is to survive and reproduce in a particular environment. When an environment changes, the survival value of inherited characteristics may change. This may or may not cause a change in species that inhabit the environment. Use real-world examples to illustrate natural selection, gene flow, sexual selection, and genetic drift.

Speciation

Hardy-Weinberg Tests for Population Change

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