Using Zebrafish to Learn Statistical Analysis and Mendelian ...zfic.org/classroom...

16
Original Articles Using Zebrafish to Learn Statistical Analysis and Mendelian Genetics Samantha Lindemann,* Jon Senkler,* Elizabeth Auchter, and Jennifer O. Liang Abstract This project was developed to promote understanding of how mathematics and statistical analysis are used as tools in genetic research. It gives students the opportunity to carry out hypothesis-driven experiments in the classroom: students generate hypotheses about Mendelian and non-Mendelian inheritance patterns, gather raw data, and test their hypotheses using chi-square statistical analysis. In the first protocol, students are challenged to analyze inheritance patterns using GloFish, brightly colored, commercially available, transgenic zebrafish that express Green, Yellow, or Red Fluorescent Protein throughout their muscles. In the second protocol, students learn about genetic screens, microscopy, and developmental biology by analyzing the inheritance patterns of mutations that cause developmental defects. The difficulty of the experiments can be adapted for middle school to upper level undergraduate students. Since the GloFish experiments use only fish and materials that can be purchased from pet stores, they should be accessible to many schools. For each protocol, we provide detailed instructions, ideas for how the experiments fit into an undergraduate curriculum, raw data, and example analyses. Our plan is to have these protocols form the basis of a growing and adaptable educational tool available on the Zebrafish in the Classroom Web site. Introduction U ndergraduate laboratory courses provide valuable opportunities for hands-on learning, the application of concepts learned in lectures and textbooks, and an introduc- tion to the complexity of science and experimental design. Mendelian genetics has long been taught through laboratory experiments, with protocols for using Drosophila melanogaster in the classroom published as early as 1918. 1 Here we present two protocols that use the zebrafish model system to give students the opportunity to analyze Mendelian and non- Mendelian inheritance patterns and rigorously test their hy- potheses through statistical analysis. The difficulty of these protocols can be easily adapted to students at different levels, and the material requirements are low, making them acces- sible to a wide range of classrooms. Zebrafish are being increasingly used for education, and in particular have many advantages for genetic experiments. 2–7 They are easy to raise, and a single pair often produces 100 embryos or more when mated, making it possible for each student to have their own fish. Since adult fish live over 2 years, the same fish can be used over many semesters, either directly when the adult fish express viable phenotypes or to produce clutches containing mutant embryos for analysis. Many zebrafish mutant and transgenic strains are available commercially and from the Zebrafish International Resource Center, and there is a wealth of information about how to successfully raise and maintain them (zebrafish.org/zirc/ home/guide.php). 8–10 Our first protocol uses GloFish, a brightly colored and fluorescent strain. GloFish are readily available in pet stores (www.glofish.com/), making it possi- ble to carry out challenging genetic experiments in schools without access to a research zebrafish facility. Several excellent protocols already exist for using zebrafish to teach genetics (www.bioeyes.org/) (www.insciedout.org/) (www.glofish.com/classroom.asp). 2–7 Our protocols build upon this earlier work by giving students background in how genetic screens are used to find new mutants, bringing in the analysis of several phenotypes in a single cross, and including inheritance patterns that do not fall into basic recessive and dominant patterns. Finally, these protocols add richness to the study of genetics by challenging students to form their own hypotheses, and then rigorously test these hypotheses through the use of chi-square statistical analysis. Chi-square analysis requires only the use of basic mathematic techniques, making it appropriate for middle school and high school students. Knowledge of mathematics is becoming even more important to biologists as they tackle increasingly complex problems and Department of Biology, University of Minnesota Duluth, Duluth, Minnesota. *These authors contributed equally to this work. ZEBRAFISH Volume 8, Number 2, 2011 ª Mary Ann Liebert, Inc. DOI: 10.1089/zeb.2010.0686 41

Transcript of Using Zebrafish to Learn Statistical Analysis and Mendelian ...zfic.org/classroom...

  • Original Articles

    Using Zebrafish to Learn Statistical Analysisand Mendelian Genetics

    Samantha Lindemann,* Jon Senkler,* Elizabeth Auchter, and Jennifer O. Liang

    Abstract

    This project was developed to promote understanding of how mathematics and statistical analysis are used astools in genetic research. It gives students the opportunity to carry out hypothesis-driven experiments in theclassroom: students generate hypotheses about Mendelian and non-Mendelian inheritance patterns, gather rawdata, and test their hypotheses using chi-square statistical analysis. In the first protocol, students are challengedto analyze inheritance patterns using GloFish, brightly colored, commercially available, transgenic zebrafish thatexpress Green, Yellow, or Red Fluorescent Protein throughout their muscles. In the second protocol, studentslearn about genetic screens, microscopy, and developmental biology by analyzing the inheritance patterns ofmutations that cause developmental defects. The difficulty of the experiments can be adapted for middle schoolto upper level undergraduate students. Since the GloFish experiments use only fish and materials that can bepurchased from pet stores, they should be accessible to many schools. For each protocol, we provide detailedinstructions, ideas for how the experiments fit into an undergraduate curriculum, raw data, and exampleanalyses. Our plan is to have these protocols form the basis of a growing and adaptable educational toolavailable on the Zebrafish in the Classroom Web site.

    Introduction

    Undergraduate laboratory courses provide valuableopportunities for hands-on learning, the application ofconcepts learned in lectures and textbooks, and an introduc-tion to the complexity of science and experimental design.Mendelian genetics has long been taught through laboratoryexperiments, with protocols for using Drosophila melanogasterin the classroom published as early as 1918.1 Here we presenttwo protocols that use the zebrafish model system to givestudents the opportunity to analyze Mendelian and non-Mendelian inheritance patterns and rigorously test their hy-potheses through statistical analysis. The difficulty of theseprotocols can be easily adapted to students at different levels,and the material requirements are low, making them acces-sible to a wide range of classrooms.

    Zebrafish are being increasingly used for education, and inparticular have many advantages for genetic experiments.2–7

    They are easy to raise, and a single pair often produces 100embryos or more when mated, making it possible for eachstudent to have their own fish. Since adult fish live over 2years, the same fish can be used over many semesters, eitherdirectly when the adult fish express viable phenotypes or toproduce clutches containing mutant embryos for analysis.

    Many zebrafish mutant and transgenic strains are availablecommercially and from the Zebrafish International ResourceCenter, and there is a wealth of information about how tosuccessfully raise and maintain them (zebrafish.org/zirc/home/guide.php).8–10 Our first protocol uses GloFish, abrightly colored and fluorescent strain. GloFish are readilyavailable in pet stores (www.glofish.com/), making it possi-ble to carry out challenging genetic experiments in schoolswithout access to a research zebrafish facility.

    Several excellent protocols already exist for using zebrafishto teach genetics (www.bioeyes.org/) (www.insciedout.org/)(www.glofish.com/classroom.asp).2–7 Our protocols buildupon this earlier work by giving students background in howgenetic screens are used to find new mutants, bringing in theanalysis of several phenotypes in a single cross, and includinginheritance patterns that do not fall into basic recessive anddominant patterns. Finally, these protocols add richness to thestudy of genetics by challenging students to form their ownhypotheses, and then rigorously test these hypotheses throughthe use of chi-square statistical analysis. Chi-square analysisrequires only the use of basic mathematic techniques, makingit appropriate for middle school and high school students.Knowledge of mathematics is becoming even more importantto biologists as they tackle increasingly complex problems and

    Department of Biology, University of Minnesota Duluth, Duluth, Minnesota.*These authors contributed equally to this work.

    ZEBRAFISHVolume 8, Number 2, 2011ª Mary Ann Liebert, Inc.DOI: 10.1089/zeb.2010.0686

    41

  • large data sets.11–13 This has led to a call for greater integrationof mathematics into the undergraduate curriculum.13–15 Ourprotocols enable the introduction of mathematics into theundergraduate curriculum during the freshman or sophomoreyear, providing a foundation for more complex mathematicalapproaches in subsequent courses.

    The two protocols reported here were developed for asophomore level undergraduate genetics laboratory course.This course met for one 4-hour laboratory session each weekof the semester, and all of the students (*60 students/semester, 10–20 students/laboratory section) either had takenor were concurrently taking a genetics lecture course. How-ever, these experiments will coordinate with virtually everygenetics course, as they incorporate the concepts that form thebasis of all genetics studies. In addition, these laboratories arestudent-driven and problem-based without being extremelylabor intensive for the instructors. Thus, they will fit well intocourses aiming to eliminate ‘‘cook-book’’ laboratories fromtheir curriculum. Further, the raw data we have included canbe used to introduce active learning and problem solving intolecture courses, which has been shown to have a positiveimpact on the ability of students to retain knowledge and theirlong-term achievement.16 Our goal is to make this an evolvingand growing collaborative protocol on our Zebrafish in theClassroom Web site (www.zfic.org) that includes variationson how to use these ideas in the classrooms for students atdiverse levels in their development as scientists.

    Materials and Methods

    All procedures have been approved by the University ofMinnesota IACUC Committee. A copy of the approved pro-tocol is available on the Zebrafish in the Classroom Web site(www.zfic.org/common%20techniques/IACUC-teaching-all.pdf). In addition, students complete vertebrate animal safetytraining before starting the laboratories (Supplementary Ma-terial 1; Supplementary Data are available online at www.liebertonline.com/zeb).

    Fish stocks

    Parental fish stocks included the wild-type (WT) strainzebrafish Danio rerio (ZDR) (Aquatic Tropicals, Plant City,FL), and strains carrying the following mutations and trans-genes: cyclopsm294 (cyc)17; squintcz35 (sqt),18 mylz2:YellowFluorescent Protein (GloYFP),19 mylz2:Red Fluorescent Protein(GloRFP),19 golden (gol),20,21 and long fin (lof).22,23 Adult fishwere maintained using standard protocols.10 Fish to be raisedwere maintained for 8–9 days postfertilization (dpf) in Petridishes at 28.58C, and then placed in a 10 L tank within a re-circulating, multi-rack aquarium system (Aquatic Habitats,Apopka, FL) in our fish facility. From 9–14 dpf they were fedtwice daily with live paramecium10 and a pinch of a powdercontaining one part dried Spirulina and one part ArgentChemical Laboratories Hatchfry Encapsulon Grade 0.24

    Natural matings

    Adult fish were set up in single pair or group matings in theafternoon, and monitored for spawning until late afternoonthe following day. At that time, adult fish were placed backinto their home tanks, and any embryo produced were col-

    lected into deep (100�20 mm) Petri dishes (Cat. #M090501;Laboratory Products Sales, Rochester, NY), one dish for eachclutch of eggs. To do this, the adult fish and the insert in themating tank were removed and the eggs allowed to settle. Themajority of the water was poured out slowly so that noeggs were lost. When about 20 mL of water was left, the re-maining water and eggs were poured quickly into a Petri dish(www.zfic.org/common%20techniques/mating.html). Thefertile eggs were sorted from infertile eggs and waste prod-ucts using a dissecting microscope with transmitted light.Embryos were moved to the middle of the Petri dish usingthe ‘‘embryo swirl’’ (www.zfic.org/common%20techniques/embryo%20swirl.html). The good eggs, which appearedtranslucent and had normal morphology, were sorted intoone area of the Petri dish using an embryo loop (www.zfic.org/common%20techniques/Embryoloops.html), andwaste and infertile eggs removed. Healthy embryos weremoved to a new Petri dish containing clean aquatic systemwater using a transfer pipet, and the Petri dish placed in anincubator at 28.58C or in the aquatic fish facility until the fishwere ready to be imaged or raised in a large tank.

    Scoring the phenotype of cyc and sqt mutants

    Between 2 and 3 dpf, developing embryos were countedand scored by their eye phenotype using a dissecting micro-scope, with normal embryos having two eyes and mutantembryos having more closely spaced or cyclopic eyes.

    Imaging

    Fish were photographed without anesthesia or with a shortincubation in 0.017% tricaine methanesulfonate (MS-222)dissolved in aquatic system water. Larvae were photo-graphed using a Leica S6 D stereo light microscope fitted witha Nikon Digital Sight DS-SM camera. For all adult picturesexcept the progeny in Figure 5 and all fish in Figure 14, the fishwere netted onto a flat surface with a small amount of water,and then photographed using Panasonic DMZ-TZ3 digitalcamera. Images in Figure 5 were captured with a CanonEOS Rebel XS 18-55IS digital camera. For Figure 14, adult fishwere netted onto the glass plate of an Olympus SZX12stereomicroscope connected to a Cannon PowerShot A520through one eye piece. Images were taken with white lightillumination from above or with fluorescence microscopy.

    Results

    Laboratory 1: analysis of Mendelian inheritancepatterns using GloFish

    This laboratory is designed to be the opening laboratory ofthe semester. Students analyze sibling groups of adult zeb-rafish by counting the number of fish with each phenotype,generate hypotheses about the inheritance of the relevantgenes based on these data, and test their hypotheses using chi-square statistical analysis (Supplementary Materials 1–7). Tomake this engaging, and to bring in the concept of transgenes,it uses GloFish, a commercially available strain containingtransgenes that make the fish brightly colored (Table 1)(www.glofish.com).19,25,26 In the most challenging siblinggroup, students make hypotheses about the inheritance pat-terns of three different genes that when combined togetherproduce eight different phenotypes in a single clutch of sib-

    42 LINDEMANN ET AL.

  • lings (Trihybrid Crosses 1 and 2 below). The experiments inthis protocol are accessible to teaching laboratories that do nothave an association with a research zebrafish facility withmany mutant strains, as all needed materials can be easilyfound in pet stores. For instance, the GloFish available frompet stores carry transgenes and mutations that enable theanalysis of recessive, dominant, and incomplete dominanceinheritance patterns, making it easy to build both simple andcomplex crosses for student analysis.

    The Glo transgenes, which give these fish their name, usethe muscle-specific fast skeletal light chain 2 (mylz2) promoterto drive expression of Green Fluorescent Protein (GFP), YellowFluorescent Protein (YFP), or Red Fluorescent Protein (RFP/dsRed), making the body color of the fish green-yellow, yel-low, or red, respectively.19,25,26 GloFish purchased from petstores are typically homozygous for the recessive gol mutation,which causes them to have very light or non-existent stripes(Table 1).20 To create trihybrid crosses, we crossed GloFishto WT zebrafish, which introduces the WT striped allele ofthe gol gene, and into a line carrying the dominant lof mutation,which causes all of the fins to undergo unregulated growth(Table 1).22,27–30 WT zebrafish and fish carrying the lof muta-tion are also readily available in pet stores. Because all of thesegenetic changes in our crosses produce viable phenotypes,inheritance patterns can be followed over several generationsand students can be challenged to interpret the inheritancepatterns of several genes in one cross.

    The experimental design and set up for the laboratory arerelatively simple (See GloFish Instructor’s Key: Supplemen-tary Material 2). Students prepare by completing vertebrateanimal safety training, and by reading an introduction to thelaboratory (Supplementary Materials 1 and 4). At the start ofclass, the students are given a short PowerPoint presentationthat puts the GloFish experiment into context, lists the goalsfor the day, and gives examples to illustrate important con-cepts in statistical analysis (Supplementary Material 3).

    A worksheet guides students through the steps of the lab-oratory and at the same time teaches them how to keep anaccurate and complete laboratory notebook (SupplementaryMaterials 5 and 7). Briefly, students move in small groupsaround the laboratory and together sort tanks of sibling fishinto phenotypic classes and count the number of fish in eachclass. After this is complete, the groups together generate nullhypotheses about the inheritance patterns in each tank, andtest these hypotheses using chi-square analysis. The final stepin the protocol, which is typically done a week or more later, is

    for students to set up their own single pair mating designed totest one of their hypotheses (Supplementary Materials 5 and6). The last day of the semester, the students have the chanceto examine the progeny of these crosses and determine if theirhypothesis was correct and their experimental design sound(Supplementary Material 2)

    Students are encouraged to work together throughout thelaboratory, but the written assignments are to be completedindividually by each student. The written assignments in-clude the laboratory worksheet, which counts as their labo-ratory notebook entry, and a homework in which they designan experiment to test one of their hypotheses about inheri-tance patterns (Supplementary Materials 5–7). Here, we haveprovided raw data and analyses for four GloFish crosses thatcould be used for this laboratory.

    Dihybrid cross 1

    The first experiment in this laboratory enables students tostart with analysis of recessive and dominant genes, thesimplest Mendelian inheritance patterns. It analyzes a dihy-brid cross between a WT male and a female heterozygous forthe GloYFP transgene and homozygous for gol mutation(Fig. 1). Thus, the male is gray with stripes, whereas the fe-male is yellow and lacks stripes (Fig. 1). Of 14 progeny, 57%were yellow and 43% were gray, and all were striped (Fig. 1,Table 2, Supplementary Fig. 1).

    The next step in the experiment is for the students to gen-erate a hypothesis about the inheritance patterns in this cross,and test their hypothesis with chi-square statistical analysis.In chi-square analysis, the hypothesis about the inheritancepattern of a gene or genes is termed the null hypothesis. Thechi-square test produces a probability value ( p-value) thatreports the probability that the observed distribution of val-ues is the same as the expected distribution. For instance, ap-value of 0.40 means that there is a 40% chance that the ob-served distribution is consistent with the null hypothesis, anda 60% chance that it is not. A p-value of 0.05 or less is needed toreject the null hypothesis. In other words, if there is a 5% orlower probability that the observed distribution is consistentwith the null hypothesis, the null hypothesis can be rejected. Itis important to note that the converse is not true. A p-valueabove 0.05 does not prove the null hypothesis. To rigorouslyprove the null hypothesis, one would have to disprove all ofthe other possible hypotheses by showing that they produce ap-value less than 0.05.

    Table 1. Summary of Mutations and Transgenes Used in These Laboratory Experiments

    Gene name AbbreviationType

    of genetic changeHomozygous

    phenotypeHeterozygous

    phenotypeInheritance

    pattern

    mylz2:YFP GloYFP Transgene Yellow body Yellow body Dominant(or incompletely dominant)

    mylz2:RFP GloRFP Transgene Red body Red body Dominant(or incompletely dominant)

    no transgene Glo- None Gray body N/A Recessivegolden gol Mutation Attenuated stripes Normal stripes Recessivelong fin lof Mutation Long fins Long fins Dominantcyclops cyc Mutation Cyclopia Normal eyes Recessivesquint sqt Mutation Cyclopia Normal eyes Recessive, incompletely

    penetrant

    STATISTICAL ANALYSIS AND MENDELIAN GENETICS 43

  • gol;Glo- gol;Glo- gol;GloYFP gol;GloYFP

    genotype phenotype+/gol;Glo-/Glo- striped, grey body (WT)+/gol;Glo-/GloYFP striped, yellow body

    C+;Glo- +/gol;Glo-/Glo- +/gol;Glo-/Glo- +/gol;Glo-/GloYFP +/gol;Glo-/GloYFP

    +;Glo- +/gol;Glo-/Glo- +/gol;Glo-/Glo- +/gol;Glo-/GloYFP +/gol;Glo-/GloYFP

    +;Glo- +/gol;Glo-/Glo- +/gol;Glo-/Glo- +/gol;Glo-/GloYFP +/gol;Glo-/GloYFP

    +;Glo- +/gol;Glo-/Glo- +/gol;Glo-/Glo- +/gol;Glo-/GloYFP +/gol;Glo-/GloYFP

    Glo- GloYFP

    Glo-/Glo-Glo-

    Glo-

    genotype phenotypeGlo-/Glo- grey body (WT)Glo-/GloYFP yellow body

    B

    Glo-/GloYFP

    Glo-/Glo- Glo-/GloYFP

    gol gol

    +/gol +/gol+

    +/gol

    genotype phenotype+/gol striped (WT)

    A

    + +/gol

    FIG. 2. Hypothesis for dihybrid GloYFP and gol cross. Thehypothesis for the inheritance pattern of the dihybrid cross ispresented as Punnett squares. The genotypes of the gametesproduced by the female parent are shown in the top row andthe genotypes of the gametes produced by the male parent areshown in the left column. The genotypes of the progeny weregenerated by filling in the appropriate inherited genes fromeach parent, with maternal genes marked in black and paternalgenes marked in gray. The hypothesized relationship of ge-notype to phenotype is listed below the Punnett squares. (A)Hypothesis for striped phenotype considered alone. (B) Hy-pothesis for body color phenotype considered alone. (C) Hy-pothesis for stripe pattern and body color analyzed together ina dihybrid Punnett square. Because there are two loci thatmust be followed at once, there are four possible gamete ge-notypes for each parent. The hypothesis predicts that half ofthe progeny should be normal colored with normal stripes andhalf of the progeny should be yellow with normal stripes.

    FIG. 3. Dihybrid cross of parents heterozygous for GloYFP

    and gol. The parental (P0) generation consisted of a femaleand a male fish heterozygous for the GloYFP transgene andthe gol mutation. Genotypes at the different loci are sepa-rated by semicolons with the genotype at the transgene locuslisted first. The F1 generation was produced through a singlemating of the P0 pair, with one progeny of each phenotypeshown. Images are lateral views, anterior to the left anddorsal to the top. Images of all of the progeny are included inSupplementary Figure 2.

    FIG. 1. Dihybrid cross with fish carrying the GloYFP transgene and gol mutation. The parental (P0) generation consisted of afemale fish heterozygous for the GloYFP transgene and homozygous for the gol mutation and a WT male fish that was notcarrying the transgene or the gol mutation. Genotypes at the different loci are separated by semicolons with the genotype atthe transgene locus listed first. The F1 generation was produced through a single mating of these adult fish, with one progenyof each phenotype shown. Images are lateral views, anterior to the left and dorsal to the top. Images of all of the progeny areincluded in Supplementary Figure 1. WT, wild type.

    44

    http://www.liebertonline.com/action/showImage?doi=10.1089/zeb.2010.0686&iName=master.img-000.jpg&w=237&h=246http://www.liebertonline.com/action/showImage?doi=10.1089/zeb.2010.0686&iName=master.img-001.jpg&w=288&h=203

  • To make the experiment more challenging, students aretypically not told the genotypes or phenotypes of the parents,and have to generate the null hypotheses based only on theirobservations of the progeny. Even when lacking the parentalinformation, generating a correct hypothesis is typically not achallenge for the sophomore level undergraduate students inthis course. For this cross, two null hypotheses fit the dataequally well. The correct one is that the gol mutation is recessiveand the GloYFP transgene is dominant (Fig. 2). Alternatively,students could hypothesize that the GloYFP transgene is reces-sive, with the yellow parent being homozyogous for thetransgene, and the gray parent being heterozygous for thetransgene. Class discussions can be used to generate a next-stepexperiment to determine which of these two null hypotheses iscorrect. Our Dihybrid cross 2 is one such cross (Fig. 3).

    For simplicity, only the correct hypothesis (Fig. 2) is testedhere. From our null hypothesis, we expect that 50% of theprogeny will be yellow and 100% will be striped (Fig. 2, Table2). The p-value from the chi-square analysis falls between 0.6and 0.7, supporting the null hypothesis (Table 2). The numberof progeny for this cross is quite low. This offers a strongopportunity for discussions on what experiments could beused to further support the null hypothesis. One possibility isto repeat the experiment to increase the number of progenyanalyzed. If the null hypothesis is correct, then increasednumbers should cause the p-value to increase. In contrast, if

    the number of fish increases, but the ratio of fish with eachphenotype stays the same, the p-value will decrease. Anotherpossibility is for the students to carry out a chi-square test onthe alternative (incorrect) hypothesis, providing support fortheir hypothesis by disproving the alternative. Perhaps thebest approach would be to design an experiment that will givedifferent outcomes whether the hypothesis is correct or in-correct, such as the experiment in Dihybrid cross 2.

    This cross could also be used for an even more basic start to theexperiment, following only the GloYFP transgene and the bodycolor phenotype as a monohybrid cross. In this case, chi-squareanalysis for body color generates a p-value between 0.6 and 0.7,and in fact is exactly the same as the chi-square analysis whenboth phenotypes are considered (Table 3). Note that chi-squareanalysis cannot be used to analyze the striped/nonstriped phe-notypes alone because there is only one phenotype in the prog-eny, making the degrees of freedom equal to zero.

    Dihybrid cross 2

    Our second cross is designed to distinguish between the twonull hypotheses that fit the data for Dihybrid cross 1. In thiscross, both parents have the same phenotype of a yellow bodyand stripes, and are heterozygous for both GloYFP and gol(Fig. 3). The progeny phenotype ratios are approximately 3:1yellow:gray and 1:1 striped:nonstriped (Supplementary Fig. 2,

    Table 2. Chi-Square Analysis of a Dihybrid Cross Between a Wild-Type Male and a FemaleHeterozygous for the GloYFP Transgene and the GOL Mutation

    (1) (2) (3) (4) (5) (6)Phenotype Observed number (O) Expected number (E) Difference (D)¼O � E D2¼ (O � E)2 w2¼D2/E

    Normal color, 6 7 �1 1 0.1Normal stripes

    Yellow color, 8 7 1 1 0.1Normal stripes

    (7) Total w2¼ 0.2(8) Degrees of freedom (n� 1)¼ 2–1¼ 1(9) 0.6< p< 0.7

    (1) The two phenotypes expected from the hypothesis in Figure 2 were written in the first column.(2) The number of fish observed (O) with each phenotype was recorded in the second column.(3) The expected number of progeny was calculated and recorded in column 3. E (normal color, normal stripes)¼ 0.5�1.0�14¼ 7. E (yellow

    color, normal stripes)¼ 0.5�1.0�14¼ 7.(4–6) For each phenotype, D, D2, and w2 were calculated for each phenotype and recorded in the appropriate column. Numbers were

    rounded to one significant digit, as this is the number of significant digits in column 2.(7) The degrees of freedom were calculated using the number of phenotypes (n) expected by the hypothesis.(8) The w2 value for the experiment was the sum of the w2 values for each phenotype.(9) The range of p-values was calculated by using a w2 table (www.sociology.ohio-state.edu/people/ptv/publications/p%20values/

    chi_table.jpg), the w2 value for the experiment, and the degrees of freedom.

    Table 3. Chi-Square Analysis of a Monohybrid Cross for Fish Carrying the GloYFP Transgene

    (1)a (2) (3) (4) (5) (6)Phenotype Observed number (O) Expected number (E) Difference (D)¼O � E D2¼ (O � E)2 w2¼D2/E

    Normal 6 7 �1 1 0.1body color

    Yellow 8 7 1 1 0.1body color

    (7) Total w2¼ 0.2(8) Degrees of freedom (n� 1)¼ 2–1¼ 1(9) 0.6< p< 0.7

    aCalculations for each column and row carried out as in Table 2. This analysis was done on the same cross as in Table 2, except the pigmentphenotype was ignored.

    STATISTICAL ANALYSIS AND MENDELIAN GENETICS 45

  • Table 4). These ratios should lead students to formulate thenull hypothesis that the gol mutation is recessive and theGloYFP transgene is dominant (Fig. 4). Chi-square analysisyields a p-value between 0.1 and 0.15 (Table 4). This p-valuesupports the null hypothesis, but is close enough to 0.05 toleave some doubt. This low p-value could be used to promptstudent discussions on how to decide when a hypothesis issupported. Questions that can be used to stimulate discussioninclude the following: Does the experiment need to be re-peated to increase the number of fish analyzed? If Dihybridcrosses 1 and 2 are considered together, does this increase thesupport for the hypothesis? Are their alternative hypothesesthat could explain these data? Are these alternative hypoth-eses supported or rejected by chi-square analysis?

    Trihybrid cross 1

    Our next cross, a trihybrid cross, significantly increases thenumber of phenotypes found in the progeny, and thus the

    mathematical complexity of the chi-square analysis. A crossbetween a red, striped female and a yellow, striped maleyields progeny with four different colors: gray, yellow, red,and orange, and because both parents are carrying one copyof the gol mutation, two different pigment patterns, stripedand nonstriped (Fig. 5, Supplementary Fig. 3).

    This cross also brings in a new inheritance pattern. Thepresence of orange fish should lead students to form the nullhypothesis that the GloYFP and GloRFP transgenes are in-completely dominant with each other: blending of yellow andred produces orange fish, and orange is dominant over thenormal gray color. The gol mutation, which causes loss ofstripes, is recessive as in the dihybrid crosses. Together, theseinheritance patterns lead to the expectation that the progenywill be divided equally among each body color, and that 75%of the fish will have stripes and 25% will be non-striped(Fig. 6). The chi-square test yields a p-value greater than 0.9,indicating any deviation from expected distributions is likelydue to chance and the hypothesis is supported (Table 5).

    Trihybrid cross 2

    The second trihybrid cross enables students to practicetheir analysis skills, introduces a new phenotype and muta-tion, and explicitly tests whether orange fish are carrying bothGloYFP and GloRFP transgenes. In this cross, an orange malewith short fins, one of the progeny from Trihybrid cross 1, wasmated with a gray female fish with long fins, producing fishthat were gray, yellow, red, and orange, with either long orshort fins (Fig. 7, Supplementary Fig. 4).

    The presence of red and yellow fish should lead to thehypothesis, as in the first trihybrid cross, that GloYFP andGloRFP are incompletely dominant with each other and indi-vidually dominant over a gray body color (Fig. 8). Presence ofa long-finned phenotype in approximately half of the progenyshould lead to the hypothesis that the lof mutation is domi-nant (Fig. 8). This hypothesis is supported by the chi-squaretest, which yields a p-value between 0.4 and 0.5 (Table 6).

    Laboratory 2: F3 genetic screen

    Genetic screens are one of the most powerful techniquesin biology. They have been used to identify hundreds ofgenes with key roles in development, disease, basic cellularfunctions, and a host of other biological processes and have

    Table 4. Chi-Square Analysis of a Dihybrid Cross of Fish Heterozygous for GloYFP and GOL

    (1)a (2) (3) (4) (5) (6)Phenotype Observed number (O) Expected number (E) Difference (D)¼O � E D2¼ (O � E)2 w2¼D2/E

    Normal color, 5 6 1 1 0.2Normal stripes

    Normal color, 4 2 2 4 2No stripes

    Yellow color, 15 19 �4 16 0.8Normal stripes

    Yellow color, 10 6 �4 16 2.7No stripes

    (7) Total w2¼ 5.7(8) Degrees of freedom (n� 1)¼ 4–1¼ 3(9) 0.1< p< 0.15

    aCalculations for each column and row carried out as in Table 2.

    Glo- GloYFP

    Glo-/Glo-Glo-

    GloYFP

    genotype phenotypeGlo-/Glo- grey bodyGlo-/GloYFP yellow bodyGloYFP/GloYFP yellow body

    B

    Glo-/GloYFP

    GloYFP/Glo- GloYFP/GloYFP

    gol +

    gol/gol gol/+gol

    +/+

    genotype phenotype+/+ striped+/gol stripedgol/gol not striped

    A

    + +/gol

    Calculations: grey, striped phenotype 1/4 grey X 3/4 striped = 3/16 of progeny grey, not striped phenotype 1/4 grey X 1/4 not striped = 1/16 of progeny yellow, striped phenotype 3/4 yellow X 3/4 striped = 9/16 of progeny yellow, not striped phenotype 3/4 yellow X 1/4 not striped = 3/16 of progeny

    C

    FIG. 4. Hypothesis for dihybrid cross of heterozygous fish.The hypothesis for the inheritance pattern of the dihybrid crossis presented as Punnett squares generated as in Figure 2. (A)Hypothesis for striped phenotype considered alone. (B) Hy-pothesis for body color phenotype considered alone. (C) Cal-culations of expected fraction for each phenotype using thePunnett squares in (A) and (B). When the loci being analyzed arenot linked, this method of calculating expected fractions of eachphenotype can be used instead of a dihybrid Punnett square.

    46 LINDEMANN ET AL.

  • FIG. 7. Trihybrid cross with fish carrying Glo transgenesand the lof mutation. The parental (P0) generation consistedof a female not carrying a transgene and heterozygous for thelof mutation and a male fish heterozygous for the GloRFP andGloYFP transgenes. Genotypes at the different loci are sepa-rated by semicolons, the GloYFP locus listed first. The F1generation was produced through a single mating of the P0pair, with one progeny of each phenotype shown. Images arelateral views, anterior to the left and dorsal to the top. Imagesof all of the progeny are included in Supplementary Figure 4.

    FIG. 5. Trihybrid cross with fish carrying Glo transgenesand the gol mutation. The parental (P0) generation consistedof a female fish heterozygous for the GloRFP transgene andheterozygous for the gol mutation and a male fish hetero-zygous for the GloYFP transgene and heterozygous for the golmutation. Genotypes at the different loci are separated bysemicolons with the genotype at the GloYFP transgene locuslisted first. The F1 generation was produced through a singlemating of the P0 pair, with one progeny of each phenotypeshown. Images are lateral views, anterior to the left anddorsal to the top. Images of all of the progeny are included inSupplementary Figure 3.

    gol;Glo-;Glo- gol;Glo-;GloRFP gol;Glo-;Glo- gol;Glo-;GloRFP gol;Glo-;Glo- gol;Glo-;GloRFP gol;Glo-;Glo- gol;Glo-;GloRFP

    +;Glo-;Glo-+ /gol

    Glo-/Glo-

    Glo-/Glo-

    +;GloYFP;Glo-

    +;Glo-;Glo-

    +;GloYFP;Glo-

    + /golGloYFP/Glo-

    Glo-/Glo-

    + /golGlo-/Glo-

    Glo-/Glo-

    gol/golGlo-/Glo-

    Glo-/Glo-

    + /golGloYFP/Glo-

    Glo-/Glo-

    gol/golGloYFP/Glo-

    Glo-/Glo-

    gol/golGloYFP/Glo-

    Glo-/Glo-

    gol/golGlo-/Glo-

    Glo-/Glo-

    gol;Glo-;Glo-

    gol;GloYFP;Glo-

    gol;Glo-;Glo-

    gol;GloYFP;Glo-

    + /golGlo-/Glo-

    Glo-/GloRFP

    + /golGloYFP/Glo-

    Glo-/GloRFP

    + /golGlo-/Glo-

    Glo-/GloRFP

    gol/golGlo-/Glo-

    Glo-/GloRFP

    + /golGloYFP/Glo-

    Glo-/GloRFP

    gol/golGloYFP/Glo-

    Glo-/GloRFP

    gol/golGloYFP/Glo-

    Glo-/GloRFP

    gol/golGlo-/Glo-

    Glo-/GloRFP

    + /golGlo-/Glo-

    Glo-/Glo-

    + /golGloYFP/Glo-

    Glo-/Glo-

    + /golGlo-/Glo-

    Glo-/Glo-

    gol/golGlo-/Glo-

    Glo-/Glo-

    + /golGloYFP/Glo-

    Glo-/Glo-

    gol/golGloYFP/Glo-

    Glo-/Glo-

    gol/golGloYFP/Glo-

    Glo-/Glo-

    gol/golGlo-/Glo-

    Glo-/Glo-

    + /golGlo-/Glo-

    Glo-/GloRFP

    + /golGloYFP/Glo-

    Glo-/GloRFP

    + /golGlo-/Glo-

    Glo-/GloRFP

    gol/golGlo-/Glo-

    Glo-/GloRFP

    + /golGloYFP/Glo-

    Glo-/GloRFP

    gol/golGloYFP/Glo-

    Glo-/GloRFP

    gol/golGloYFP/Glo-

    Glo-/GloRFP

    gol/golGlo-/Glo-

    Glo-/GloRFP

    + /golGlo-/Glo-

    Glo-/Glo-

    + /golGloYFP/Glo-

    Glo-/Glo-

    + /golGlo-/Glo-

    Glo-/Glo-

    gol/golGlo-/Glo-

    Glo-/Glo-

    + /golGloYFP/Glo-

    Glo-/Glo-

    gol/golGloYFP/Glo-

    Glo-/Glo-

    gol/golGloYFP/Glo-

    Glo-/Glo-

    gol/golGlo-/Glo-

    Glo-/Glo-

    + /golGlo-/Glo-

    Glo-/GloRFP

    + /golGloYFP/Glo-

    Glo-/GloRFP

    + /golGlo-/Glo-

    Glo-/GloRFP

    gol/golGlo-/Glo-

    Glo-/GloRFP

    + /golGloYFP/Glo-

    Glo-/GloRFP

    gol/golGloYFP/Glo-

    Glo-/GloRFP

    gol/golGloYFP/Glo-

    Glo-/GloRFP

    gol/golGlo-/Glo-

    Glo-/GloRFP

    + /golGlo-/Glo-

    Glo-/Glo-

    + /golGloYFP/Glo-

    Glo-/Glo-

    + /golGlo-/Glo-

    Glo-/Glo-

    gol/golGlo-/Glo-

    Glo-/Glo-

    + /golGloYFP/Glo-

    Glo-/Glo-

    gol/golGloYFP/Glo-

    Glo-/Glo-

    gol/golGloYFP/Glo-

    Glo-/Glo-

    gol/golGlo-/Glo-

    Glo-/Glo-

    + /golGlo-/Glo-

    Glo-/GloRFP

    + /golGloYFP/Glo-

    Glo-/GloRFP

    + /golGlo-/Glo-

    Glo-/GloRFP

    gol/golGlo-/Glo-

    Glo-/GloRFP

    + /golGloYFP/Glo-

    Glo-/GloRFP

    gol/golGloYFP/Glo-

    Glo-/GloRFP

    gol/golGloYFP/Glo-

    Glo-/GloRFP

    gol/golGlo-/Glo-

    Glo-/GloRFP

    FIG. 6. Hypothesis fortrihybrid GloYFP; GloRFP;gol cross. The hypothesisfor the inheritance patternof the trihybrid cross ispresented as a trihybridPunnett square generatedas in Figure 2. Becausethere are three loci thatmust be followed in thecross, there are eight possi-ble gamete genotypes foreach parent. The hypothesispredicts that one-eighth ofthe progeny should haveeach of the F1 phenotypesshown in Figure 5.

    47

    http://www.liebertonline.com/action/showImage?doi=10.1089/zeb.2010.0686&iName=master.img-002.jpg&w=216&h=360http://www.liebertonline.com/action/showImage?doi=10.1089/zeb.2010.0686&iName=master.img-003.jpg&w=238&h=309

  • been the foundations of many Nobel Prizes (for instance, seehttp://nobelprize.org/nobel_prizes/medicine/laureates/1995/ and http://nobelprize.org/nobel_prizes/medicine/laureates/2002/). This protocol gives students the opportu-nity to gain experience with forward genetic screens by doinga mock screen, biased so that students will successfully findinteresting mutants. Because this F3 screen protocol is longerand requires more skills than the GloFish protocol, it hastypically been done in the middle of the semester. It includesMendelian genetics and the use of chi-square analysis as in theGloFish protocol, but in addition brings in the concepts offorward genetics and the use of model systems. Further, itbuilds skills in embryology, light microscopy, and even fishhusbandry (Supplementary Materials 1, 7–13).

    Zebrafish is a relatively new model system. When the fieldstarted, the first mutations were induced with gamma radia-tion. Gamma radiation causes large deletions or transloca-tions in the genome (for instance, see ref.31). Keeping some of

    these mutant lines going was quite difficult, as chromosomesegregation during meiosis was often disrupted. In the mid-1990s, zebrafish research began its exponential growth withthe completion of two very large forward genetic screens, onein Tubingen, Germany, and the other in Boston.32–34 Thesescreens used the chemical N-ethyl-N-nitrosourea to inducepoint mutations, and then kept every mutant line that had adevelopmental defect (Development Vol. 123, published inDecember 1996).

    The screening methods developed for these large screensare the basis for this protocol (Supplementary Materials 9 and10). The screen is called F3 because it requires three genera-tions of offspring (F1, F2, and F3) from the parental (P) gen-eration. The students carry out the last step of an F3 screen,which takes three laboratory periods. On the first day of theprotocol, students set up several single pair matings, calledblind intercrosses, between fish in a tank that contains amixture of fish heterozygous for a mutation and fish that are

    FIG. 8. Hypothesis for trihybrid GloYFP;GloRFP; lof cross. The hypothesis for the in-heritance pattern of each phenotype in thetrihybrid cross is presented as Punnettsquares generated as in Figure 2. (A) Hy-pothesis for striped phenotype consideredalone. (B) Hypothesis for yellow body colorphenotype considered alone. (C) Hypothesisfor red body color considered alone. (D)Calculations of expected fraction for eachphenotype using the Punnett squares in (A),(B), and (C). This method of calculating theexpected fraction of each progeny can be usedinstead of a trihybrid Punnett square.

    Calculations:

    grey, striped phenotype 1/2 striped X 1/2 not yellow X 1/2 not red = 1/8 of progeny grey, not striped phenotype 1/2 not striped X 1/2 not yellow X 1/2 not red = 1/8 of progeny yellow, striped phenotype 1/2 striped X 1/2 yellow X 1/2 not red = 1/8 of progeny yellow, not striped phenotype 1/2 not striped X 1/2 yellow X 1/2 not red = 1/8 of progeny orange, striped phenotype 1/2 striped X 1/2 yellow X 1/2 red = 1/8 of progeny orange, not striped phenotype 1/2 not striped X 1/2 yellow X 1/2 red = 1/8 of progeny red, striped phenotype 1/2 striped X 1/2 not yellow X 1/2 red = 1/8 of progeny red, not striped phenotype 1/2 not striped X 1/2 not yellow X 1/2 not red = 1/8 of progeny

    D

    Glo- GloYFP

    Glo-/Glo-Glo-

    Glo-

    B

    Glo-/GloYFP

    Glo-/Glo- Glo-/GloYFP

    gol +

    +/gol +/++

    +/+

    A

    + +/gol

    Glo- GloRFP

    Glo-/Glo-Glo-

    Glo-

    C

    Glo-/GloRFP

    Glo-/Glo- Glo-/GloRFP

    Table 5. Chi-Square Analysis of Trihybrid Cross Containing the GloYFP and GloRFP

    Transgenes and GOL Mutation

    (1)a (2) (3) (4) (5) (6)Phenotype Observed number (O) Expected number (E) Difference (D)¼O � E D2¼ (O � E)2 w2¼D2/E

    Normal color, 7 7 0 0 0Normal stripes

    Normal color, 4 2 2 4 2No stripes

    Yellow color, 6 7 �1 1 0.1Normal stripes

    Yellow color, 2 2 0 0 0No stripes

    Orange color, 6 7 �1 1 0.1Normal stripes

    Orange color, 2 2 0 0 0No stripes

    Red color, 7 7 0 0 0Normal stripes

    Red color, 3 2 1 1 0.5No stripes

    (7) Total w2¼ 2.7(8) Degrees of freedom (n� 1)¼ 8–1¼ 7(9) 0.9< p< 0.99

    aCalculations for each column and row carried out as in Table 2.

    48 LINDEMANN ET AL.

  • homozygous WT (Supplementary Materials 8 and 10). Thesegroups of fish are the mock F2 families. Laboratories main-taining strains of zebrafish with recessive lethal mutationswill typically have mixed tanks such as these available, asthey are produced in the process of generating the next gen-eration of fish (Supplementary Material 8).

    On the second day of the protocol, which ideally would bethe following day, students learn how to collect embryos and

    sort out debris and infertile embryos under a dissecting mi-croscope (Supplementary Material 10). On the third day,which can be the next day or several days later, studentsscreen the F3 embryos for phenotypes, count the ratio ofnormal to abnormal embryos, make hypotheses about whatkind of mutation is present (recessive, dominant, etc.) and thegenotype of the parents, and test their hypothesis using chi-square analysis (Supplementary Materials 10 and 11). Theprimary difference between this protocol and a real F3 screenis that we know that our mock F2 families are carrying mu-tations and what phenotypes to expect.

    The example crosses we present here both use mutants inthe Nodal signaling pathway (Figs. 9–12). Zebrafish havethree Nodal signaling proteins: Sqt, Cyc, and Southpaw.Mutations in the genes encoding any of these proteins result in

    Table 6. Chi-Square Analysis of Trihybrid Cross Containingthe GloYFP and GloRFP Transgenes and LOF Mutation

    (1)a (2) (3) (4) (5) (6)Phenotype Observed number (O) Expected number (E) Difference (D)¼O � E D2¼ (O � E)2 w2¼D2/E

    Normal color, 4 2 2 4 2Short fins

    Normal color, 0 2 �2 4 2Long fins

    Yellow color, 1 2 1 1 0.5Short fins

    Yellow color, 1 2 �1 1 0.5Long fins

    Orange color, 2 2 0 0 0Short fins

    Orange color, 4 2 2 4 2Long fins

    Red color, 2 2 0 0 0Short fins

    Red color, 2 2 0 0 0Long fins

    (7) Total w2¼ 7(8) Degrees of freedom (n� 1)¼ 8–1¼ 7(9) 0.4< p< 0.5

    aCalculations for each column and row carried out as in Table 2.

    FIG. 9. Cross of fish carrying the cyc mutation. The parental(P0) generation consisted of a female and a male fish het-erozygous for the cyc mutation. A single natural mating ofthese fish produced progeny, the F1 generation, with twonormal eyes or a single cyclopic eye. The fish with cyclopiceyes also had a severe ventral curvature in the anterior–posterior axis. A typical embryo at 3 days postfertilization isshown for each phenotype. All images are lateral views withanterior to the left and dorsal to the top. Images of allprogeny from this cross are included in SupplementaryFigure 5.

    + cyc

    +/+

    cyc/+

    +/cyc+

    cyc cyc/cyc

    genotype phenotype+/+ two eyes (WT)cyc/+ two eyes (WT)cyc/cyc cyclopic eye

    FIG. 10. Hypothesis for cyc cross. The hypothesis for theinheritance pattern of the cyc cross is presented as a Punnettsquare generated as described for Figure 2. The hypothesizedrelationship of genotype to phenotype and the Punnettsquare together generate the prediction that three quarters ofthe progeny should have normal eyes and one quartershould have cyclopic eyes.

    STATISTICAL ANALYSIS AND MENDELIAN GENETICS 49

    http://www.liebertonline.com/action/showImage?doi=10.1089/zeb.2010.0686&iName=master.img-004.jpg&w=238&h=168

  • severe phenotypic defects and are ultimately lethal.35–38 Themost obvious phenotype in cyc and sqt mutants is cyclopiceyes. At 3 days of development, the eyes are pigmented andvery large, making the difference between the two eyes of theWT embryo and the cyclopic eye of the mutants easily dis-tinguishable even to students who are observing embryos forthe first time (Figs. 9 and 11, Supplementary Figs. 5 and 6).

    As with the GloFish laboratory, students are encouraged towork together throughout the laboratory, but written as-signments are to be completed individually by each student.The written assignments include the completion of a labora-tory notebook entry for each week of the laboratory (Sup-plementary Material 7), and a homework assignment(Supplementary Materials 12 and 13).

    Monohybrid cross using the cyclopsm294 (cyc) mutation

    In this experiment, two adult fish heterozygous for the cycmutation are crossed to produce a clutch of sibling progeny(Fig. 9). The progeny are then scored according to their eyephenotype using light microscopy and the number of progenywith each phenotype is counted. The first cross yields 78%progeny with two WT eyes, and 22% progeny with one cy-clopic eye (Fig. 9, Table 7, Supplementary Fig. 5). After com-bining the progeny from several independent cyc crosses, 74%of the progeny have two normal eyes and 26% of the progenyhave one cyclopic eye (Table 8).

    The ratio of fish with a WT eye phenotype to those with acyclopic eye phenotype is approximately 3:1 (Tables 7 and 8).This ratio should lead the students to pose the null hypothesisthat the cyc mutation is recessive (Fig. 10). Chi-square analysisof the single cross generates a p-value between 0.5 and 0.6 (Table7). The combined data from all the cyc crosses, which included376 embryos, produces a p-value between 0.6 and 0.7 (Table 8).Thus, both chi-square tests support the hypothesis that cyc is arecessive mutation. Further, as expected, the p-value becomeshigher, and the hypothesis more strongly supported, as thenumber of embryos included in the analysis increases.

    Monohybrid cross demonstratingincomplete penetrance

    The Sqt and Cyc proteins are 55% identical, and their genesare expressed in many overlapping domains in the develop-

    ing embryo.39–42 Thus, it is not surprising that sqt mutantsshare many features in common with cyc embryos, includingcyclopic eyes (Fig. 11, Supplementary Fig. 6). However, sqtmutants have some phenotypes that are distinct from cyc. Forinstance, cyc mutants are curved ventrally, whereas sqt mu-tants are straight or curved to the left or right (Figs. 9 and 11,Supplementary Figs. 5 and 6).43

    Also, like cyc, the sqt mutation is homozygous recessive.Therefore, the sqt mutant phenotype is observed only in fishwith two copies of the mutant allele. However, the sqt in-heritance pattern is different from cyc, and thus this crossbrings a new aspect of Mendelian genetics to the classroom.The sqt phenotype is incompletely penetrant. In a cross be-tween two heterozygous carriers of the sqt mutant allele, 0%to 25% of the offspring of fish heterozygous for the sqt mu-tation display the mutant phenotype. The expressivity of themutant phenotype is also variable. Some homozygous mu-tants have severe defects, such as complete cyclopia and acurved body axis, some mutants have mild defects such aseyes that are closer together, and other homozygous mutantsare indistinguishable from their WT siblings.44–46 The pen-etrance of the different aspects of each phenotype can alsovary, with an embryo, for example, having a curved bodyaxis but normal eyes.44–46

    FIG. 11. Cross of fish carrying the sqt muta-tion. The parental (P0) generation consisted of afemale and male fish that were heterozygous forthe sqt mutation. As with the cyc cross, a singlenatural mating of sqt heterozygotes fish pro-duced progeny, the F1 generation, with twonormal eyes or a single cyclopic eye. Adults areshown in lateral views, anterior to the left, em-bryos in ventral views with anterior to the left.Pictures of all of the progeny from this cross areincluded in Supplementary Figure 6.

    + sqt

    +/+

    sqt/+

    +/sqt+

    sqt sqt/sqt

    genotype phenotype+/+ two eyes (WT)sqt/+ two eyes (WT)sqt/sqt cyclopic eyes

    FIG. 12. Hypothesis for sqt cross. The hypothesis for theinheritance pattern of the sqt cross is presented as a Punnettsquare generated as described for Figure 2. As with the cyccross, this hypothesis predicts that three quarters of theprogeny should have normal eyes and one quarter shouldhave cyclopic eyes.

    50 LINDEMANN ET AL.

    http://www.liebertonline.com/action/showImage?doi=10.1089/zeb.2010.0686&iName=master.img-005.jpg&w=288&h=169

  • The percentage of homozygous mutants with an abnormalphenotype can vary greatly from clutch to clutch. Because thecyclopic phenotype is the most common and the easiest toidentify, the embryos in this cross are scored only for their eyephenotype. In a single clutch generated by a single pair mat-ing of adult fish heterozygous for the sqt mutation, 93% em-bryos have normal eyes, and 7% embryos have cyclopic eyes(Fig. 11, Table 9, Supplementary Fig. 6). From several com-bined crosses, there are 98% normal embryos and 2% cyclopicembryos (Table 10).

    Students will likely find it challenging to generate a nullhypothesis for these data, as it does not easily fall into astandard Mendelian ratio. In our class, students typicallychoose to test the hypothesis that sqt, like cyc, is inherited as arecessive allele with a 3:1 WT:sqt ratio expected in the progeny(Fig. 12). Chi-square analysis does not support this hypothe-sis. For the single cross, the p-value is between 0.01 and 0.02and for the combined crosses, p is less than 0.001. The findingthat the p-value decreases when increased numbers of em-bryos are analyzed also indicates that this hypothesis is notcorrect. This analysis of the sqt cross illustrates the ability ofstatistical analysis to disprove a null hypothesis.

    To prompt students to generate possible explanations forthe phenotype ratios in these crosses, they can be given afollow-up homework that challenges them to generate ahypothesis that better fits these data (Supplementary Material13). When this homework is given, we stress that it is meant tobe an ill-structured question with many potentially correctanswers. Students typically do very well with this homework,with the most common answer being that this ratio comesfrom a dihybrid cross, with the parents being heterozygousfor sqt and another recessive gene. Only embryos that arehomozygous for both mutant alleles express the mutantphenotype. A discussion of this homework can serve as an

    excellent springboard for discussions aimed at designing ex-periments to distinguish between this and other possible ex-planations.

    Student feedback and assessment

    One of the key steps in both the GloFish and F3 Screenprotocols is testing student-generated hypotheses using sta-tistical analysis. This step in the protocols enabled students tomake connections between their statistics courses and on-the-ground experimental biology. This seemed to be muchneeded, as informal surveys and our own postlaboratory as-sessment indicate that students find it challenging to match ap-value with a conclusion about the experiment (Fig. 13B). TheGloFish and F3 Screen protocols introduce statistical analysisinto a sophomore level course, offering the opportunity tobuild on this initial exposure in subsequent courses.

    Students reported that the protocols presented here werevaluable for cementing their learning of Mendelian genetics,as they complemented and built upon the concepts theylearned in their genetics lecture course. Because the experi-ments in our protocols use real clutches of progeny, they bringthe real complexity of genetic analysis into the classroom. Forinstance, in some crosses, more than one hypothesis is sup-ported by statistical analysis (eg., GloFish Dihybrid cross 1).In other crosses, the ratios of phenotypes in the progeny donot fit well into any Mendelian ratio, and no hypotheses aresupported (eg., F3 Screen sqt crosses). Many students foundthe lack of a clear outcome frustrating. Instructors could avoidthis frustration by bringing only sibling groups that fit wellinto Mendelian ratios and support only one hypotheses. Al-ternatively, this frustration can be a good learning experiencefor the students as it offers the opportunity to think creatively.For instance, students very much enjoyed designing and

    Table 8. Chi-Square Analysis for Combined CYC Monohybrid Crosses

    (1)a (2) (3) (4) (5) (6)Phenotype Observed number (O) Expected number (E) Difference (D)¼O � E D2¼ (O � E)2 w2¼D2/E

    Wildtype 278 282 �4.00 16.0 0.057(two eyes)

    Cyclopic 98 94 4.0 16 0.17(one eye)

    (7) Total w2¼ 0.23(8) Degrees of freedom (n� 1)¼ 2–1¼ 1(9) 0.6< p< 0.7

    aCalculations for each column and row carried out as in Table 2.

    Table 7. Chi-Square Analysis of a Single CYC Monohybrid Cross

    (1)a (2) (3) (4) (5) (6)Phenotype Observed number (O) Expected number (E) Difference (D)¼O � E D2¼ (O � E)2 w2¼D2/E

    Wildtype 91 88 3.0 9.0 0.10(two eyes)

    Cyclopic 26 29 �3.0 9.0 0.31(one eye)

    (7) Total w2¼ 0.41(8) Degrees of freedom (n� 1)¼ 2–1¼ 1(9) 0.5< p< 0.6

    aCalculations for each column and row carried out as in Table 2.

    STATISTICAL ANALYSIS AND MENDELIAN GENETICS 51

  • carrying out their own GloFish cross (Fig. 13C, Supplemen-tary Materials 5 and 6).

    A voluntary assessment survey completed by students afterfinishing all but the last step of the GloFish laboratory (theyhad not yet observed the progeny from their own crosses) in-dicated a positive experience (Fig. 13). This feedback suggestedthat students found the analysis and thinking parts of thelaboratory most valuable for their understanding of genetics,and the work needed to gather the data the least valuable(Fig. 13C). Most students agreed or strongly agreed that thelaboratory increased their confidence with the concepts used,suggesting that it enhanced student learning (Fig. 13A).

    Discussion

    Building on the GloFish laboratory

    The difficulty of this GloFish protocol can be adapted forstudents carrying out their first experiments in genetics tostudents beginning their graduate studies. For elementaryschool students, the simplest GloFish crosses (such as Dihy-brid cross 1) can be used to illustrate how a single gene candramatically change the phenotype of an organism. Formiddle and high school students, GloFish can be used to ex-plore how genes interact to produce phenotypes. Further,because this protocol includes only pre-algebra mathematics,the use of Mendelian ratios to calculate expected proportionsof progeny phenotypes and statistical testing of hypothesescould be easily introduced into pre-college science courses.

    This protocol could also be expanded by including analysisof traits that are not only influenced by genetics. Rather than thesimple X/X¼ female, X/Y¼male sex determination in mam-mals, sex determination in fish is extremely varied.47 In the caseof zebrafish, there are no sex chromosomes. Whether a fish is

    female or male is determined by multiple genes located onautosomes, although the specific genes are just starting to beisolated.48,49 Environmental factors, such as temperatures out-side of the normal range and addition of hormones, can alsoinfluence gender.49 Because of these many contributing factors,it is quite common for clutches of sibling fish to be mostly maleor mostly female, even when fish are raised in a relativelycontrolled laboratory setting. Thus, comparing the gender ratiosin different clutches can illustrate that the inheritance of evensome major phenotypes, like whether a fish is male or female,may defy analysis by Mendelian genetics (Supplementary Figs.1, 7–9, Supplementary Tables 1 and 2). Uncovering the expla-nation for the variation in gender ratios from clutch to clutch canform a challenging puzzle for upper-level students. Their re-search into this subject could be an entry into the sophisticatedapproaches that have been used to uncover traits and diseasesthat are controlled by multiple genes.

    Finally, our protocol is aimed at early stage college students,but there are many other possibilities for building GloFish intoupper level undergraduate and even graduate courses. Forinstance, the GloFish transgenes encode GFP and other relatedfluorescent proteins (Fig. 14). In 2008, Drs. Osamau Shimomura,Martin Chalfie, and Roger Tsien won the Nobel Prize inChemistry for their research on GFP (http://nobelprize.org/nobel_prizes/chemistry/laureates/2008/). This protocol onGloFish could serve as an introduction to this Nobel Prize–winning research and how transgenic/genetic engineeringapproaches are being used to treat human disease.

    Building on the F3 genetic screen laboratory

    The F3 Genetic Screen protocol can be used to introduce theconcept of model organisms and to teach developmental ge-netics, embryology, and the genetics of human birth defects and

    Table 9. Chi-Square Analysis of a Single SQT Monohybrid Cross

    (1)a (2) (3) (4) (5) (6)Phenotype Observed number (O) Expected number (E) Difference (D)¼O � E D2¼ (O � E)2 w2¼D2/E

    Wildtype 26 21.0 5.0 25 1.2(two eyes)

    Cyclopic 2 7 �5 25 4(one eye)

    (7) Total w2¼ 5(8) Degrees of freedom (n� 1)¼ 2–1¼ 1(9) 0.01< p< 0.02

    aCalculations for each column and row carried out as in Table 2.

    Table 10. Chi-Square Analysis of Combined SQT Clutches

    (1)a (2) (3) (4) (5) (6)Phenotype Observed number (O) Expected number (E) Difference (D)¼O � E D2¼ (O � E)2 w2¼D2/E

    Wildtype 1740 1330 410.0 1.68�105 126(two eyes)

    Cyclopic 35 443 �408 1.66�105 376(one eye)

    (7) Total w2¼ 502(8) Degrees of freedom (n� 1)¼ 2–1¼ 1(9) p< 0.001

    aCalculations for each column and row carried out as in Table 2.

    52 LINDEMANN ET AL.

  • FIG. 13. Student Assessment of the GloFishLaboratory. Students in the spring 2011 semes-ter of Genetics Laboratory were asked to fill outan assessment of the GloFish laboratory ap-proximately 4 weeks after they had completedall but the last step (observation of the progenyfrom their own cross, which does not take placeuntil the end of the semester). (A) Assessment ofvalue of the GloFish laboratory for their ownlearning. (B) Assessment of whether studentswere able to correctly define key concepts in-troduced in this laboratory. (C) Student feed-back on which aspects of the laboratory weremost and least useful for their learning. Al-though students were asked to choose at mosttwo answers under each of the ‘‘most’’ andleast’’ categories, many students missed theseinstructions and checked all of the responsesthat they thought answered the questions. Thedesign of this survey was based in part onthe guidelines at http://tep.uoregon.edu/re-sources/newteach/fifty_cats.pdf

    FIG. 14. GloFish fluorescence. (A) Yel-low GloFish under white light. (B) YellowGloFish under blue light/GFP filter. (C)Head of yellow GloFish under blue light/GFP filter. (D) Red GloFish under whitelight. (E) Red GloFish under green light/RFP filter. (F) Head of red GloFish undergreen light/RFP filter. (G) Orange Glo-Fish under white light. (H) Orange Glo-Fish under blue light/GFP filter. (I)Orange GloFish under green light/RFPfilter. Images are lateral views, anterior tothe left and dorsal to the top. GFP, greenfluorescent protein; RFP, red fluorescentprotein.

    STATISTICAL ANALYSIS AND MENDELIAN GENETICS 53

    http://www.liebertonline.com/action/showImage?doi=10.1089/zeb.2010.0686&iName=master.img-006.jpg&w=288&h=410http://www.liebertonline.com/action/showImage?doi=10.1089/zeb.2010.0686&iName=master.img-007.jpg&w=312&h=198

  • human disease. For instance, many disease genes, like sqt, haveincomplete penetrance. Mutations in the BRCA1 and BRCA1genes are associated with increase risk of breast cancer, but arein no way indications that 100% of the women carrying thesemutations will develop the disease.50 Environmental influencesas well as genetic background influence whether the womencarrying the mutation will go on to develop breast cancer.50

    Likewise, studies by Dr. Ben Feldman and colleagues haveshown that environmental factors and genetic backgroundsimilarly affect the penetrance of the sqt mutant phenotype.46

    The F3 Genetic Screen protocol is used as part of a larger setof laboratories that give students exposure to forward andreverse genetics (Supplementary Material 9). To complementthese experiments in zebrafish, students also carry forwardgenetics experiments on Drosophila. In particular, we havefound that the antennapedia mutant flies available from Car-olina Biological (www.carolina.com) have characteristicssimilar to sqt: the phenotype (antennas are replaced by legs) isincompletely penetrant and has variable expressivity. SinceDrosophila have the advantage of a very fast generation time,students are able to follow the penetrance and expressivityof the phenotype over several generations and generateand test hypotheses about the underlying causes of the vari-ability. Students gain experience in reverse genetics by feed-ing C. elegans worms with bacteria carrying differentconstructs that make double-stranded RNA, and by injectingantisense morpholinos into zebrafish (www.zfic.org/classroom%20experiments/microinjectionindex.html).51–53

    Acknowledgments

    This work was supported in part through University ofMinnesota Undergraduate Research Opportunity (UROP)Awards to S.L. and J.S. Publication costs were supported bythe UROP Program, and the University of Minnesota DuluthSwenson College of Science & Engineering and Department ofBiology. We would like to thank Dr. Paul Bates for his manyexcellent suggestions for improving the article, Tonya Connorfor her expert advice on the student assessment survey for theGloFish protocol, and Adelle Schumann for her technicalsupport. In addition, we would like to thank the teachingassistants and students of the Genetics Laboratory course forpiloting this protocol and for all of their valuable ideas forimprovement, and all of the students who have helped withmaintenance of the fish and fish facility.

    Disclosure Statement

    No competing financial interests exist.

    References

    1. Babcock EB, Collins JL. Genetics Laboratory Manual. NewYork: McGraw-Hill Book Company, Inc., 1918.

    2. Fields MC, Adelfio P, Ahmad D, Brown O, Cox B, Davies M,et al. Danio rerio in K-12 classrooms: sparking interest in thenew generation of scientists. Zebrafish 2009;6:145–160.

    3. D’Costa A, Shepherd IT. Zebrafish development and ge-netics: introducing undergraduates to developmental bi-ology and genetics in a large introductory laboratory class.Zebrafish 2009;6:169–177.

    4. Shuda J, Kearns-Sixsmith D. Outreach: empowering stu-dents and teachers to fish outside the box. Zebrafish 2009;6:133–138.

    5. Schmoldt A, Forecki J, Hammond DR, Udvadia AJ. Ex-ploring differential gene expression in zebrafish to teachbasic molecular biology skills. Zebrafish 2009;6:187–199.

    6. Hutson LD, Liang JO. Making an impact: zebrafish in edu-cation. Zebrafish 2009;6:119–120.

    7. Emran F, Brooks JM, Zimmerman SR, Johnson SL, Lue RA.Zebrafish embryology and cartilage staining protocols forhigh school students. Zebrafish 2009;6:139–143.

    8. Nusslein-Volhard C, Dahm R. Zebrafish: A Practical Ap-proach. Oxford, UK: Oxford University Press, 2002;261.

    9. Fukada Y, Okano T. Circadian clock system in the pinealgland. Mol Neurobiol 2002;25:19–30.

    10. Westerfield M. The Zebrafish Book. Eugene, OR: Universityof Oregon Press, 2000.

    11. Gross LJ. Interdisciplinarity and the undergraduate biologycurriculum: finding a balance. Cell Biol Educ 2004;3:85–87.

    12. Cohen JE. Mathematics is biology’s next microscope, onlybetter; biology is mathematics’ next physics, only better.PLoS Biol 2004;2:e439.

    13. Hoy R. New math for biology is the old new math. Cell BiolEduc 2004;3:90–92.

    14. Brent R. Intuition and innumeracy. Cell Biol Educ 2004;3:88–90.

    15. Bialek W, Botstein D. Introductory science and mathematicseducation for 21st-Century biologists. Science 2004;303:788–790.

    16. Derting, T. L, Ebert-May D. Learner-centered inquiry in un-dergraduate biology: positive relationships with long-termstudent achievement. CBE Life Sci Educ 2010;9:462–472.

    17. Schier AF, Neuhauss SC, Harvey M, Malicki J, Solnica-Krezel L, Stainier DY, et al. Mutations affecting the devel-opment of the embryonic zebrafish brain. Development1996;123:165–178.

    18. Feldman B, Gates MA, Egan ES, Dougan ST, Rennebeck G,Sirotkin HI, et al. Zebrafish organizer development andgerm-layer formation require nodal-related signals. Nature1998;395:181–185.

    19. Gong Z, Wan H, Tay TL, Wang H, Chen M, Yan T. Devel-opment of transgenic fish for ornamental and bioreactor bystrong expression of fluorescent proteins in the skeletalmuscle. Biochem Biophys Res Commun 2003;308:58–63.

    20. Lamason RL, Mohideen MA, Mest JR, Wong AC, NortonHL, Aros MC, et al. SLC24A5, a putative cation exchanger,affects pigmentation in zebrafish and humans. Science2005;310:1782–1786.

    21. Streisinger G, Walker C, Dower N, Knauber D, Singer F.Production of clones of homozygous diploid zebra fish(Brachydanio rerio). Nature 1981;291:293–296.

    22. Tresnake I. The long-finned zebra Danio. Tropical FishHobby 1981;29:43–56.

    23. Johnson SL, Weston JA. Temperature-sensitive mutationsthat cause stage-specific defects in Zebrafish fin regenera-tion. Genetics 1995;141:1583–1595.

    24. Carvalho AP, Araujo L, Santos MM. Rearing zebrafish(Danio rerio) larvae without live food: evaluation of acommercial, a practical, and a purified starter diet on larvalperformance. Aquac Res 2006;37:1107–1111.

    25. Ju B, Chong SW, He J, Wang X, Xu Y, Wan H, et al. Re-capitulation of fast skeletal muscle development in zebrafishby transgenic expression of GFP under the mylz2 promoter.Dev Dyn 2003;227:14–26.

    26. Xu Y, He J, Wang X, Lim TM, Gong Z. Asynchronous acti-vation of 10 muscle-specific protein (MSP) genes duringzebrafish somitogenesis. Dev Dyn 2000;219:201–215.

    54 LINDEMANN ET AL.

  • 27. Goldsmith MI, Fisher S, Waterman R, Johnson SL. Saltatorycontrol of isometric growth in the zebrafish caudal fin isdisrupted in long fin and rapunzel mutants. Dev Biol2003;259:303–317.

    28. Geraudie J, Monnot MJ, Brulfert A, Ferretti P. Caudal finregeneration in wild type and long-fin mutant zebrafish isaffected by retinoic acid. Int J Dev Biol 1995;39:373–381.

    29. van Eeden FJ, Granato M, Schach U, Brand M, Furutani-Seiki M, Haffter P, et al. Genetic analysis of fin formation inthe zebrafish, Danio rerio. Development 1996;123:255–262.

    30. Iovine MK, Johnson SL. A genetic, deletion, physical, andhuman homology map of the long fin region on zebrafishlinkage group 2. Genomics 2002;79:756–759.

    31. Hatta K, Kimmel CB, Ho RK, Walker C. The cyclops mu-tation blocks specification of the floor plate of the zebrafishcentral nervous system. Nature 1991;350:339–341.

    32. Haffter P, Granato M, Brand M, Mullins MC, Hammersch-midt M, Kane DA, et al. The identification of genes withunique and essential functions in the development of thezebrafish, Danio rerio. Development 1996;123:1–36.

    33. Driever W, Solnica-Krezel L, Schier AF, Neuhauss SC,Malicki J, Stemple DL, et al. A genetic screen for mutationsaffecting embryogenesis in zebrafish. Development1996;123:37–46.

    34. Stemple DL, Driever W. Zebrafish: tools for investigatingcellular differentiation. Curr Opin Cell Biol 1996;8:858–864.

    35. Schier AF, Talbot WS. Nodal signaling and the zebrafishorganizer. Int J Dev Biol 2001;45:289–297.

    36. Alexander J, Stainier DY. A molecular pathway leading toendoderm formation in zebrafish. Curr Biol 1999;9:1147–1157.

    37. Liang JO, Rubinstein AL. Patterning of the zebrafish embryoby nodal signals. Curr Top Dev Biol 2003;55:143–171.

    38. Halpern ME, Liang JO, Gamse JT. Leaning to the left: la-terality in the zebrafish forebrain. Trends Neurosci2003;26:308–313.

    39. Erter CE, Solnica-Krezel L, Wright CV. Zebrafish nodal-re-lated 2 encodes an early mesendodermal inducer signalingfrom the extraembryonic yolk syncytial layer. Dev Biol1998;204:361–372.

    40. Sampath K, Rubinstein AL, Cheng AM, Liang JO, Fekany K,Solnica-Krezel L, et al. Induction of the zebrafish ventralbrain and floorplate requires cyclops/nodal signalling.Nature 1998;395:185–189.

    41. Rebagliati MR, Toyama R, Haffter P, Dawid IB. cyclopsencodes a nodal-related factor involved in midline signaling.Proc Natl Acad Sci U S A 1998;95:9932–9937.

    42. Rebagliati MR, Toyama R, Fricke C, Haffter P, Dawid IB.Zebrafish nodal-related genes are implicated in axial pat-

    terning and establishing left-right asymmetry. Dev Biol1998;199:261–272.

    43. Liang JO, Etheridge A, Hantsoo L, Rubinstein AL, NowakSJ, Izpisua Belmonte JC, et al. Asymmetric nodal signaling inthe zebrafish diencephalon positions the pineal organ. De-velopment 2000;127:5101–5112.

    44. Dougan ST, Warga RM, Kane DA, Schier AF, Talbot WS.The role of the zebrafish nodal-related genes squint andcyclops in patterning of mesendoderm. Development2003;130:1837–1851.

    45. Aquilina-Beck A, Ilagan K, Liu Q, Liang JO. Nodal signalingis required for closure of the anterior neural tube in zebra-fish. BMC Dev Biol 2007;7:126.

    46. Pei W, Williams PH, Clark MD, Stemple DL, Feldman B.Environmental and genetic modifiers of squint penetranceduring zebrafish embryogenesis. Dev Biol 2007;308:368–378.

    47. Desjardins JK, Fernald RD. Fish sex: why so diverse? CurrOpin Neurobiol 2009;19:648–653.

    48. Tong SK, Hsu HJ, Chung BC. Zebrafish monosex populationreveals female dominance in sex determination and earliestevents of gonad differentiation. Dev Biol 2010;344:849–856.

    49. Orban L, Sreenivasan R, Olsson PE. Long and windingroads: testis differentiation in zebrafish. Mol Cell Endocrinol2009;312:35–41.

    50. Beckmann MW, Bani MR, Fasching PA, Strick R, Lux MP.Risk and risk assessment for breast cancer: molecular andclinical aspects. Maturitas 2007;57:56–60.

    51. Timmons L, Court DL, Fire A. Ingestion of bacterially ex-pressed dsRNAs can produce specific and potent geneticinterference in Caenorhabditis elegans. Gene 2001;263:103–112.

    52. Kamath RS, Martinez-Campos M, Zipperlen P, Fraser AG,Ahringer J. Effectiveness of specific RNA-mediatedinterference through ingested double-stranded RNA inCaenorhabditis elegans. Genome Biol 2001;2:RESEARCH0002.

    53. Nasevicius A, Ekker SC. Effective targeted gene ‘knock-down’ in zebrafish. Nat Genet 2000;26:216–220.

    Address correspondence to:Jennifer O. Liang, Ph.D.

    Department of BiologyUniversity of Minnesota Duluth

    1035 Kirby Drive, Rm. 207Duluth, MN 55812

    E-mail: [email protected]

    STATISTICAL ANALYSIS AND MENDELIAN GENETICS 55