孤独的天才（中英文2023修改版）

【《孤独的天才》是《生物学概念与途径》第一章。雏形起源于2000年在中国科学院上海生命科学研究院和北大、清华开始BIO2000的研究生课程第一讲的一部分。2008年后成为我在北大给大一本科生的《生物学概念与途径》第一讲。‍

2022年，孟德尔诞生两百周年，国际学术刊物出现一些新材料。加上有读者反馈（例如我多年把豆荚性状的黄和绿哪一个为显性写反了）。‍‍‍

2022年修改好中文版。2023年春节修改好英文版】‍‍

1    孤独的天才

为坚持智力追求，不惜放弃其天伦之乐；

在学术群体外围，做出科学的核心发现；

用数学分析生物，成功地进行学科交叉；

十年一系列实验，一篇论文开创新学科。

他孤立于当时的科学界，做出奠基性突破却终生未被学界承认；他的工作几十年后尚不为同一学科的诺贝尔奖得主所理解；他发现的貌似简单的理论，大多数学过其结论的人，都没意识到其智力高度；他不是为利益做研究的纯粹科学家，身后却被疑造假，遭遇不公。

这位孤独的天才，就是自称为“实验物理学教师”的遗传学之父：孟德尔（Johann Gregor Mendel，1822-1884）。

我认为，生物学有两座智力高峰：第一次是1854年至1866年孟德尔独自一人；第二次是1951年至1965年克里克(Francis Crick)及其合作者们。两个高峰碰巧相隔一百年。

今天重读孟德尔的论文，追寻孟德尔的思路，思考孟德尔的环境，仍然很有意义。

1.1    孟德尔的论文和思路

由于同时代理解孟德尔科学工作重要性的人极少，他的遗物保留下来的很少。孟德尔最重要的遗物是一篇遗传学论文。与此相关，他曾有两篇与遗传学无关的作物害虫的论文、一篇遗传学论文、以及给一位植物学家解释其遗传学研究的10封信。

孟德尔的主要论文显示了清晰的思路，有助于我们追踪科学是如何在一个头脑中诞生的。

孟德尔的时代，人们对遗传的认识还很粗浅，基本认同“混合遗传”（blending inheritance）学说：遗传是“黑+白=灰”，父母的黑和白简单融合得到子代的灰。此学说虽未被正式提出和论证，却是一个普遍接受的、朴素的、以为不证自明的规律。

而孟德尔不以为然，他设计实验，通过锲而不舍的研究，发现了与此不同的学说。从1854年开始，孟德尔用豌豆做了一系列遗传学实验，时间长达十年。他于1865年公布所发现的遗传学规律，并于次年以德文在《布鲁恩自然史学会杂志》发表了论文《植物杂交的实验》（Versuche über die Pflanzen-Hybriden）。

从孟德尔的文章，我们可以体会他如何做研究：发现重要问题，提出解决问题的途径；设计实验思路，进行实验研究；得到结果，分析结果，提出前人没有想到的理论；进一步实验，得到更多可以分析的结果；进而推广理论， 证明理论。

孟德尔的论文由十一部分组成。

在“引言”部分，孟德尔简要回顾以往研究，指出Josef Gottlieb Kölreuter (1733-1806）和Carl Friedrich von Gärtner (1772-1850)等坚持做过大量杂交之后，立即明确提出问题：无人成功地提出过对杂交体形成和发生普遍适用的规律。

他指出前人做过不少杂交实验，但未得到普遍规律是因为所需的工作不仅量大，而且较难。孟德尔认为需要考虑到：规模要相当大；具有不同型的杂交后代要定量分析；在不同代间要准确地知道不同型之间的关系；要确切地分析它们之间的相对数量关系。

他写道：需要勇气花力气做大量实验，这是唯一正确的道路，才能最终解决重要的问题。..本文就是仔细研究的结果，进行了八年的工作得出的结论。

孟德尔说的八年，是他收集论文所用数据的八年。其实，此前，他做了两年实验，摸索条件选择最佳材料。所以实际上，论文工作进行了十年。十年实验后，又隔两年才发表论文。论文发表后，他还用其他植物做过几年研究。

在“实验植物选择”部分，孟德尔指出：“任何实验的价值和用处取决于所用材料是否符合其目的，所以选什么植物和怎么做实验并非不重要…必须特别小心地选择植物，从开始就避免获得有疑问的结果。”

他选的植物首先具有恒定的分化特征；其次，在进行杂交的时候不会受到外来花粉的污染；另外，每一代杂交后代生殖力不能变。

孟德尔所谓“分化特征”现在称为“性状”（如高矮、颜色）；他的“恒定”是指同一性状在不同代之间不变；他注意避免外来花粉污染，怕不确切知道父本，研究结果无从分析；他还注意代间生殖力无变化，减少在性状数量分析时的干扰。

后人认为，为了选择到合适的实验材料，孟德尔有可能考虑过二十多种植物。孟德尔说他因为花形状的奇异而试了豆科（Leguminosae），后决定用豌豆（Pisum）。对所用豌豆的确切生物学分类，孟德尔并不是很确定，说“专家意见”说大多数是Pisum sativum，还有几种，不过他明确指出分类对其研究并不重要。

用豌豆还有论文中没说明的、实验操作的优点：既能自花授粉，又能异花授粉，较易人为控制。1854年和1855年，孟德尔试过34种不同的豌豆。在孟德尔为数不多的遗物中，有一张1856年购买豌豆的订单。

在“实验分工和安排”中，孟德尔对所研究的性状进行了选择：他选择成对的性状，研究他们在代间的传递规律。这些性状可以在代间稳定遗传，且易于识别和区分。

在“杂交体的外形”部分，他进一步说明了对性状的选用。他专门选择子代性状一定相同于父本或母本的性状，而不是介于父母之间、或其他变异。孟德尔知道豌豆有些性状居于父母本之间，而不等同于父本、或母本，例如，在论文第八部分，他发现杂交体的开花时间介于父母本之间，但孟德尔没有研究介于父母本性状之间的性状。他研究的7对性状，一定是与父本或母本相同，每对中必定有一种传到下代，而一对性状的两种在后代不会变化，也不会永远消失。孟德尔明确这样选择的重要性。

孟德尔的选择简化了分析从而可以得出有意义的结论。比如到2017年知道，有八百多个基因决定人的高矮，子代高矮是父母这些基因及其含有的更多多态性综合结果，另外还有环境因素（如食物）等。如果谁在十九世纪研究人身高的遗传，就很难得出简单的规律，这并非人类高矮不符合孟德尔遗传规律，而是很难进行分析。

他选了7对性状：种子形状（平滑或皱褶）、种子颜色（黄或绿）、种皮颜色（紫或白）、豆荚形状（鼓或狭）、豆荚颜色（紫或白）、花的位置（顶或侧）、茎的高度（长或短）。

对应于7对性状，孟德尔安排了7个实验。实验一用15株植物做了60次授粉；实验二用10株植物做了58次授粉；实验三用10株植物做了35次授粉；实验四用10株植物做了40次授粉；实验五用5株植物做了23次授粉；实验六用10株植物做了34次授粉；实验七用10株植物做了37次授粉。

所有实验，孟德尔都进行了双向杂交：一对性状中，如种子颜色的黄和绿，既做过父本黄、母本绿，也做过父本绿、母本黄，他发现亲本来源不影响这些性状的传代。

他认识到性状有显隐之分，发明了“显性”（dominant）和“隐性”（recessive）两个词。当父本母本分别是不同性状（如黄和绿），而他们杂交子代只显现一种性状（黄）时，孟德尔称显现的一种（黄）为显性、没有显现的（绿）为隐性。他指出，隐性在杂交体（以后称为F1代）看不见，但在以后可以完全不变地重新显现。进一步的实验表明：显性隐性与父本母本来源也无关。

他确定了7对性状的显隐性：种子形状平滑为显而皱褶为隐、种子颜色黄为显而绿为隐、豆荚颜色绿为显而黄为隐、豆荚形状鼓为显而狭为隐、花色紫为显而白为隐、花的位置侧为显而顶为隐、茎的高度长为显而短为隐。“任何实验中都没有过渡型式”。

我们现在知道，其实在两年的预实验中，孟德尔实际上得到了纯合子。虽然当时并无纯合子和杂合子的概念，他本人也未明确这样说，但如果不以纯合子开始实验，分析结果会很复杂。

在孟德尔所谓“杂交体来的第一代”实验结果部分，我们稍需改变他的称呼，以方便叙述。他用的第一代，我们现在称为F0代。他所谓“杂交体”，我们现在称F1代。他称“杂交体来的第一代”，现称F2代。

我们可以看到，他用不同表型的两种F0代亲本间授粉得到的F1代均表现显性的性状，比如，豌豆种子分别为平滑和皱褶的F0代父母本授粉得到的F1代的豌豆种子都是平滑的，没有皱褶的。

接着，他让F1代自花授粉，得到F2代，发现隐性（如皱褶）没有因为在F1代不表现而永远消失，它重新出现在F2代。进一步数量分析表明，在F2代，显性对隐性呈3:1的比例。孟德尔强调，3:1比例毫无例外地适用于所有（7对）性状。其中，实验一发现：从253株F1代杂交体得到7324颗F2代种子，其中5474颗平滑，1850颗皱褶，比例为2.96:1。实验二发现：258株F1代植物产生了8023颗F2代种子，其中6022颗种子黄色，2001颗绿色，比例为3.01:1。

孟德尔还分析每个豆荚内种子形状和颜色是否有关，不同植物是否有关，结果认为都无关。他指出如果算的植物少了，比例漂移很大；如果昆虫损害了种子，也会影响对性状的确定。

从实验三到实验七，他列出了其他5对性状的传代结果，发现7对性状平均显隐比例为2.98:1。他看到了规律：F1代100%为显性；F2代隐性重现，而且有规律，显隐比例3:1。

孟德尔知道隐性没有在F1代不表现而消失，所以知道混合学说不对。至此，他已经超出一般人，而他还继续迈出了后面三步，发现3：1的比例、探究对比例的解释、用实验验证解释，从而获得了新的理解，远远超过了同时代的其他生物学家，包括所有时代最伟大的科学家之一。

孟德尔在看到3:1的比例后，他分析在F2代显性的性状可以有两种意义，它可以是F0一样（自交后保持与亲代的显性性状），或是F1代（自交后既有显性性状的后代、也有隐性性状的后代）。只能用F2代再做一代实验来检验是哪种状况。他预计，如果F2和F0一样，那么其后代性状就应该不变，而如果F2代类似F1杂交体状态，那么其行为与F1相同。

由此，引出孟德尔下一年的实验，即他所谓“杂合体来的第二代”（我们现称F3代）部分结果。他发现，表现隐性性状的F2代，传F3代后其性状不再变化（总是隐性表型）。而表现显性的F2代，其F3代结果表明：2/3的F2代是杂交体（其F3代出现3:1的显性和隐性），而另外1/3的F2代其F3代都是显性表型。

实验一：F2代565棵平滑豌豆植株，193株F2代只产生平滑的F3种子，372株F2代生平滑和皱褶的F3种子（F3的平:皱比例为3:1）。也就是说，F2代中显性的其实含类似F0和类似F1的比例为1.93:1。

实验二：F2代519棵黄色种子的豌豆植株自交后，166株只生黄色种子的F3代，353株生黄和绿种子（黄:绿为3:1），F2代中表现显性的植株含类似F0和类似F1的比例为2.13:1。

从实验三到实验七算其他五种性状时，孟德尔没有每次都算全部后代性状，而只分析100株植物的后代，结果有漂移但大体相似。他说计算数量大的实验一和实验二更有意义。实验五漂移最大，他重复了一次，数字更趋接近预计比例。

这样，孟德尔将F2的3:1中的3，进一步分成2和1。3:1就被分解成1:2:1（显性恒定:杂交体:隐性恒定)。

在F3代后，他还做了几代“杂交体后几代”，发现结果都符合F3代前所发现的规律，“没有察觉任何偏移”。到发表论文时，实验一和二做了六代，实验三和七做了五代，实验四、五、六做了六代。可以算出，他用豌豆做了17610次授粉。

孟德尔再迈进了一步：数学模型。

生物学研究用数学的较少。即使是今天，虽然有些生物学家非常需要定量，但绝大多数生物学研究者关心数量只在乎升高、降低和不变。孟德尔以数量分析、定量不同表型的植物，从而发现3:1的规律，继而推出和验证1:2:1的规律，已经使他成为在生物学领域成功运用数学的先驱。

在以上基础上，孟德尔进一步用了数学模型。这就超出不仅那时、甚至包括今天绝大多数生物学研究者。他提出，用A表示恒定的显性，a表示恒定的隐性，Aa表示杂合体。那么F2代就是：A+2Aa+a。

他观察到的F2代1:2:1就符合这个数量关系（杂合性状为2，显性和隐性恒定性状皆为1）。

分别分析单个性状传代情况后，孟德尔研究了不同对的性状间是否有关系。在“几个分化性状相关联杂交体的后代”部分，孟德尔发现7对性状之间完全独立。比如种子是平滑还是皱褶，与种子是黄色还是绿色毫无关联。总结这部分实验结果，孟德尔说：每对不同性状之间的关系独立于亲本其他不同（性状）。

后人好奇，为什么孟德尔做的7对性状都无关？如果有些基因在染色体较近位置的话，会有一定关联。现在知道，他做的7对性状，其基因分别在4条染色体上，而在同一染色体上的三个正好分别在染色体上相距很远的位置。

孟德尔在发现各对性状独立传代后，他在文章中可能考虑了自己的发现与进化论的关系。我们现在知道，他读过第二版《物种起源》德译本，在书的边缘做了评注。可能由于自己在修道院吃饭，他不能公开说接受进化论，所以在论文中完全没提进化论。但是，他文章故意讨论了性状独立遗传的意义。他指出：如果一个植物有7种不同的性状，产出后代就有2的7次方（128）种不同的组合。孟德尔的这个算法其实解决了 “混合学说”给达尔文进化论造成的矛盾。混合学说导致每一代比上一代更少样（黑加白得到灰，灰加灰得此灰，以此类推），而不是多样，可供选择的越来越少，生物应该退化。而孟德尔推出不同组合的数量很多，每代的多样性在增加，进化就有很多可以选择。

行文至此，孟德尔简要总结了结果：分化性状在杂交组合中行为完全一模一样。每对分化性状杂交体的后代，一半又是杂交体，另外一半中含同等比例的亲本恒定分化性状。（这等于是他用文字复述1:2:1的发现）。如果不同分化性状在杂交时组合起来，每对分化性状成为组合系列。

孟德尔也认为通过研究他选择的性状所得到的规律，也适用于其他的性状。

在从外观的性状上推出规律后，孟德尔推断外观的差别实际是由生殖细胞的组成的差别所造成。原因在于雄性的花粉细胞，雌性的卵细胞。

他推理：因为总是当卵细胞和花粉细胞具有同样的恒定性状（显性纯合子或隐性纯合子）时，其后代得到同样的恒定性状（显性或隐性纯合子），所以此时两种细胞都有创造同样个体的物质。我们必须认为在杂交体（显性和隐性杂合子）授粉后出现恒定性状（显性或隐性纯合子）时，也是这样。“杂交体的卵巢中卵细胞的种类，或杂交体雄蕊中花粉细胞数量，与可能的恒定组合型式相同，卵细胞和花粉细胞的内在组分与其不同外形相符”（斜体为本文所加）。

如果F0代是恒定的显性，其生殖细胞应该内含A的花粉细胞和内含A的卵细胞。如果F0代表型是恒定隐性，其生殖细胞应该内含a的花粉细胞和内含a的卵细胞。F0代花粉细胞和卵细胞交配后，得到F1代。F1代的花粉细胞有A和a两种、且数量相等，卵细胞也有数量相等的A和a两种。在F1代自交时，各自含A或a的两类花粉细胞与各自含A或a的卵细胞交配后，不同花粉细胞有同等机会与不同的卵细胞组合，那么得到的下代就有：A/A, A/a,a/A, a/a等四种。其中Aa和aA个体不同只在于其显性隐性来源不同，一个来源卵细胞，一个来源花粉细胞，但最后表型相同，可以归为Aa。这样，F2就应该是A+2Aa+a。

F1代产生F2代可以表示为：

A/A+A/a+a/A+a/a= A+2Aa+a。

孟德尔这个等式很重要。他将等式左边性细胞内的成分和右边得到植物后代的表型连起来。左边是我们现在说的基因型，右边是表型。孟德尔从表型的1:2:1推导出生殖细胞遗传物质的组成。他依据的是观察到的表型，推测生殖细胞的情形。

孟德尔说明这是平均的结果，具体每个后代有多种可能，而且随机，所以分开的实验肯定有漂移，只有大量收集数据，才能得到真实的比例。在这里，我们可以猜想孟德尔意识到了纯合子A/A，a/a和杂合子A/a 和a/A，可惜没有明确提出名词。

至此，他把理论深入到生殖细胞，而且可以用数学模型表示遗传学的规律，虽然其数学虽然简单，是很基本的组合。数学分析结合生物学实验，产生很重要的意义，揭示了遗传的规律。

因为孟德尔希望找到普遍适用的规律，所以，他论文最后一部分实验是“其他种属植物杂交体的实验”，检验他从豌豆发现的规律是否适用于其他植物。在论文发表时，他说开始用了几种其他植物，其中用大豆做的两个实验已经做完。用Phaseolus vulgaris和Phaseolus nanus（两者都是菜豆）做的杂交结果, 发现后代好几个性状的传代完全吻合符合他从豌豆得到的规律。但是，用Ph nanus和Ph multiflorus做杂交时，其花色有较多变异。孟德尔觉得花色仍符合他发现的遗传规律，提出要假设花色是两个或更多独立颜色的组合，花色A由单个性状A₁+A₂+…..的组合而成。他实际上提出了多基因遗传，而通常误解导致“孟德尔遗传学”被误认为单基因遗传学。

孟德尔经过新颖的、严谨的、长期的实验和定量分析，终于找到了杂交发育的普适规律。后人将孟德尔发现的规律表述成为两个定律：第一个是分离律，决定同一性状的成对遗传因子彼此分离，遗传给后代，也可以表述为颗粒遗传，以区别于以前流行的混合学说，说明因子没有消失；第二个是自由组合律，确定不同遗传性状的遗传因子间可以自由组合（本章省略了孟德尔原文研究不同性状A、B、C之间的关系部分）。虽然这些内容在原文中都有叙述，孟德尔本人并不认为自己发现了两个分开的规律，而是一个普遍的规律。

在“结语”部分，孟德尔介绍前人杂交实验的结果和前人有关植物受精过程的论述。他指出：根据著名生理学家的意见，植物繁殖时，一个花粉细胞和一个卵细胞结合成为单个细胞，同化和形成多个新细胞，长成植物个体。

然后孟德尔提出：（杂交体）发育遵循一个恒定的定律，其基础就是细胞中生动地结合的“因子的物质组分和安排(material composition and arrangement of elements)”。…豌豆的胚胎毫无疑问是亲本两种生殖细胞中因子的结合。…如果生殖细胞是同类的，那么新个体就像亲本植物…如果杂交后代不同，必需假设卵细胞和花粉细胞的分化因子间出现妥协，形成作为杂交体基础的细胞，但矛盾因子的安排只是暂时的，…分化的因子在生殖细胞形成时可以自我解放。在生殖细胞形成时，所有存在的因子完全自由和平等地参与，分化的因子互相排斥地分开。这样，产生卵细胞和花粉细胞的种类在数量上相同于形成因子可能的组合数量。

将孟德尔原文的“因子”换成现代的“基因”，就可以几乎原封不动地以他的文字理解遗传。对于喜欢直观的人来说，还有一个总结孟德尔的简单方法是：A/A+A/a+a/A+a/a。

孟德尔文中六次复述相似的内容：豌豆杂交形成生发细胞和花粉细胞，其中的组成数量相同于通过授粉将性状组合起来的所有恒定型式。这也表明他知道遗传的基础在于生殖细胞中存在数量相应于性状的物质。

在1870年9月27日，孟德尔给植物学家Nägeli的信中明确用anlage（德文“原基”）描述遗传因子，也说明他对基因的理解与现在很接近。

孟德尔早年研究过老鼠毛发颜色的遗传，被要求停止：修道院不宜做动物交配。他自己做道长后，1871年在花园建蜂房，用蜜蜂做过实验，但未见报道蜜蜂遗传结果，所以没有将植物中发现的规律推广到动物。

1.2    其他科学家对遗传学的理解

孟德尔之前有没有人做过豌豆杂交实验？孟德尔时代的科学家如何理解遗传？孟德尔时代的科学家如何理解孟德尔？孟德尔之后第二伟大遗传学家如何理解孟德尔？

我们可以讨论12位科学家：孟德尔之前做过植物杂交实验的六位（包括做豌豆杂交的五位）、孟德尔同代独立做过豌豆杂交的三位、孟德尔与其交流过杂交结果的Nägeli、自己独立做过杂交实验并得到同样结果的达尔文、和四十年后的摩尔根。

孟德尔之前科学家认识到植物有性别，用植物做杂交的实验也在孟德尔出生一百多年前就开始了。德国的Josef Gottlieb Kölreuter (1733-1806）和Carl Friedrich von Gärtner (1772-1850)系统地做过大量植物杂交实验。而孟德尔之前，至少有五位做过豌豆的杂交、一位做过获得类似结果的香瓜杂交实验。独立于孟德尔但发表时间稍后还有三位科学家做过豌豆的杂交实验。

1729年，英国神父Thomas Henchman （1666-1746?）的豌豆实验观察到同一个豆荚可以含有蓝色和白色的豌豆。

英国的Thomas Andrew Knight (1759-1838)，曾任皇家园艺学会主席，与达尔文有长期交流，杂交实验为达尔文的《物种起源》所引用。Knight主要目的是改良品种，特别是苹果。因为用苹果做实验慢，自1787年他就开始用过豌豆做杂交实验。他选豌豆的原因是其不同形态、大小、颜色，而且是开花模式不容易被昆虫和外来花粉所污染。1799年就发表了他的实验方法，去除雄的部分几天后引进另外的花粉。断断续续到孟德尔出生的第二年（1823年），Knight还发表了豌豆杂交的实验结果。1799年他报道观察到的结果：白色豌豆的后代都是白的；而如果花粉来自有颜色（灰或紫）父本，即使母本为白色，后代也都有颜色（灰或紫）；灰色总是可以传后代，即使母本为白色。

1822年8月20日，皇家园艺学会宣读了苏格兰的Alexander Anderson Seton（1769-1850）的研究结果。他观察到绿豌豆和白豌豆杂交的后代为绿豌豆。

1822年10月15日，皇家园艺学会宣读了英国农民John Goss（1787-1833）投寄的研究结果。他报道：1820年夏杂交白色豌豆（西班牙矮）与蓝色豌豆（普鲁士蓝）杂交，后代为白色豌豆；杂交以上豌豆，得到的豌豆，在同一个豆荚里，可以全部是蓝色，全部白色，或者蓝和白都有；以上蓝色的豌豆与蓝色的豌豆杂交，后代全部是蓝色，而以上白色的与白色杂交，后代可以豆荚里面都是白色，或者白色和蓝色都有。

Seton和Goss的结果都刊出在1824年集结出版的第五卷《皇家园艺学会会志》。紧接着他们刊出的是1822年11月15日宣读的Thomas Andrew Knight有关培育西瓜方法的改进。同一卷杂志，还在后面刊出1823年6月3日Knight的实验结果。他发现，灰色豌豆与白色豌豆杂交后代为灰色，灰色再与“恒定习惯种类的白色”杂交后代有灰色，但也重新出现了白色。

法国植物学家Augustin Sageret（1763-1851）于1826年发表甜瓜与香瓜杂交的实验结果。他用的甜瓜种子是黄色的、瓜皮不平，而香瓜种子白色、瓜皮平滑。杂交后代的种子为白色、瓜皮不平。杂交后代瓜子是白色、瓜皮不平。

德国植物学家Carl Friedrich von Gärtner（1772-1850）在1849年发表的书里面，有较多植物杂交的实验结果。其中，他观察到，黄色豌豆与绿色豌豆杂交的后代为黄色。

法国植物学家Charles Naudin（1815-1899）与孟德尔开始杂交实验是同一年（1854）。他开始是杂交报春花，发明了回交。1856年，他发表文章，观察到了杂交性状的自动回复，也观察到了性状的分离。1861年，他给法国科学院的报告（1863年刊出），提到后代的性状有些完全如父本、有些完全如母本，而不是中间状态。

十九世纪还有两位科学家的文章在孟德尔后面发表，但估计并不知道孟德尔的研究。Thomas Laxton（1830-1893）对英国豌豆品种改进有重要贡献，有以他命名的豌豆。1866年在国际园艺展和植物大会上，1872年在皇家园艺学会杂志上，他介绍了研究结果：白色的豌豆杂交紫色的豌豆，后代为紫色；白色的杂交棕色后代为棕色。1893年，荷兰的E Giltay（1858-1935）发表其豌豆杂交的实验结果：黄的与绿的后代为黄的。

孟德尔寄出40份论文单行本给不同科学家.

其中，只有瑞士著名植物学家、慕尼黑大学教授Nägeli回了信。所以，40人中Nägeli算最重视孟德尔。

孟德尔不仅给Nägeli寄了论文，而且他们还交换了植物种子。孟德尔自己提出用山柳菊做实验验证豌豆中发现的规律，得到研究山柳菊的专家Nägeli的鼓励。孟德尔信中说过种子少、不容易授粉、自己时间少。1867年11月6日他给Nägeli的信还说“老天让我过度肥胖，使我不再适合做植物园户外工作”。 他得到结果有点慢，不知情的会以为他在找借口、磨洋工。等他把山柳菊实验做完后，发现不符合豌豆里面得出的规律。孟德尔在信中告诉Nägeli，山柳菊的结果和豌豆的矛盾，但自己还做了其他植物，紫罗兰、茯苓、玉米和紫茉莉，发现结论和豌豆一样，所以山柳菊比较特殊，而自己发现的规律适用于多数植物。Nägeli不为所动，尽管孟德尔写过很多信告诉他辛辛苦苦做的实验，Nägeli发表植物学重要著作时，一字不提孟德尔的工作。正确地解释山柳菊结果要等到1904年，山柳菊是单性繁殖（所谓孤雌生殖），所以不能父本母本杂交，而遗传规律其实和豌豆相同。

仅以Nägeli的例子，还不能说孟德尔是超越时代的天才，而比较达尔文更说明问题。

1859年，达尔文发表《物种起源》提出了进化论，其核心是：“如果出现对生物生存有利的变异, 有此特性的个体就一定会有最佳的机会在生存斗争中保存下来；这些个体在强大的遗传原理中倾向于产生有类似特性的下一代。我把这一保存原理，或适者生存，称为自然选择。”如何遗传是达尔文自然选择进化论的必要支柱，达尔文非常希望了解遗传学。

神学对达尔文的攻击虽然猛烈，但非理性。而有人提出了严厉而富有逻辑的理性批评：自然选择进化论违背当时人们理解的遗传规律共识。根据“混合学说”，生物的性状黑加白得到后代灰，灰加灰出现的后代次灰，依此类推，性状越来越单调，不存在很多可供选择的性状，因此没有物竞天择的物质基础。所以，达尔文急需遗传学说为进化论提供解释和支持。但是，遗传规律在他眼皮底下溜过去了。

达尔文从Thomas Laxton那里知道豌豆杂交实验的结果。1868年，达尔文引用Laxton的结果，称白色的与有色的豌豆杂交后代失去白色种类的特征，无论父母本何者为白色。1876年，达尔文引用Laxton的新结果，豌豆杂交后代的活力。

与一般人印象不同，达尔文不仅依赖观察来推导理论，引用其他人的实验观察，他自己也做过实验。达尔文用花做了十一年的实验，部分结果先于孟德尔于1862年以论文形式发表，主要结果发表于1876年和1877年的两本书中，也散在于其他书中。

1868年，达尔文发表《动植物在家养情况下的变异》。此书记录了达尔文用金鱼草做的实验。常见金鱼草的花是双侧对称（达尔文称common型式，我们表为大写C），但偶尔也会出现一些怪怪的金鱼草变种，其花呈现辐射对称（达尔文称peloric型式，我们表为小写p）。达尔文把具有p性状的父本与具有C性状母本进行杂交，发现所得后代（F1代）全部呈现C性状。进一步授粉得到127株F2代金鱼草中，88株具有C性状，37株具有p性状，2株介于两种性状之间。他的实验到此结束。

观察到实验结果后，达尔文的结论是：同种植物里有两种相反的潜在倾向，…第一代是正常的占主要，…隔一代怪的倾向增加。

这样的结论没有太大意义，远不如孟德尔深刻，即使不做实验的人们也能通过生活经验得到直观的“常识”。

达尔文不止一次失去机会。在1877年的《同种植物不同花型》一书中，从他总结的报春花研究结果的表格中，我们可以看到，他用杂合体授粉时，得到显性后代为75%，隐性为25%，一个完美的3:1。不过，达尔文还是没有意识到其重要性，再次与现代遗传学失之交臂。

在《动植物在家养情况下的变异》中，达尔文提出了错误的泛生论（pangenesis）。他提出生物体全身体细胞都产生泛子gemmules（后人亦称pangenes），进入性细胞中，这些gemmules组合决定了性细胞内含，形成不同的性细胞，再产生不同的后代。在强调体细胞产生泛子的重要性时，达尔文说生殖能力要么不全在于生殖细胞，要么生殖细胞没有生殖能力，而是收集和选择泛子。他论述此假说时，将代间遗传、植物嫁接、发育、再生等多种现象混在一起谈，认为有同样机理。他的讨论相当于混淆了我们现在知道的细胞全能性（很多细胞本身含有整套遗传物质）、与代间遗传两个不同层次的问题。他在讨论中接受拉马克主义的“用进废退”，而认为泛生假说能解释用进废退，受外界影响的体细胞性状可以获得并通过gemmules进入性细胞而传代。现代科学表明，生物体中无泛子。后人从pangenesis这个词中抽出了gene来表示基因。

对比孟德尔的实验和推理，可以看到达尔文的问题：1）达尔文没有意识到样本量太小，实验设计有问题，没有做到孟德尔论文很前面就提到的“从开始就避免获得有疑问的结果”；2）达尔文在获得F1代的结果看到都是C性状时，和其他做杂交实验观察到同样现象的人一样，没有提出显性和隐性的概念；3）F2代重新出现F1代不见了的p性状，达尔文也仅看到现象，提出所谓“回复原理”（Principle of Reversion）复述现象，并无原理；4）在F2得到数量时，他没算两种性状的比例（2.38:1），也不知道比例蕴含的意义；5）没有推测而发现下一步的1:2:1；6）没有数学模型；7）没有从实验结果中发现规律，提出错误的遗传理论。

我们不知道达尔文是否读过孟德尔的文章。有些人认为，假如达尔文读了，也读不懂，或者不能接受孟德尔的理论。我们知道孟德尔在达尔文1860年第二版《物种起源》的德译本上有批注。孟德尔1866年的论文有时好像是他希望给达尔文的进化论提供遗传基础。孟德尔从自己发现的多个性状自由组合规律，推算如果有7对不同性状的两种植物间授粉，可以产生很多不同的组合，从而解释了多样性。孟德尔很可能在1866年就想到了自己发现的规律对于进化论的意义。当然，孟德尔当时的实验没有考虑进化论还需要的一部分：变异如何出现。要等七十年后，到1930年代后，英国的费舍尔（Ronald A Fisher，1890-1962）和霍尔丹(JBS Haldane，1892-1964)、美国的莱特(Sewall Wright，1889-1988)和杜布赞斯基(Theodosius Dobzhansky，1900-1975)等才成功地将孟德尔遗传学和达尔文进化论结合起来。

一般教科书说三位科学家1900年重新发现孟德尔：德国的Carl Correns (1864-1933)、荷兰的Hugo de Vries (1848-1935) 和奥地利的Erich von Tschermak (1871-1962)，虽然von Tschermak已被遗传史学家排除在重新发现者之外。这几位所谓重新发现孟德尔的人，理解程度当时都还低于孟德尔。de Vries重新写数学公式不如35年前孟德尔的公式。三人的工作量加起来也远不如孟德尔一人。Correns是Nägeli的学生和亲戚，推动了对孟德尔的认识。英国的William Bateson (1861-1926) 对孟德尔学说的推广起了很大作用。

第二伟大的遗传学家，无疑是美国的摩尔根（Thomas H. Morgan，1866-1945）。但是，直到1909年，摩尔根还发表文章称孟德尔的方法是玩数字的高级杂耍（superior jugglery）。事实上，摩尔根当年不仅不信孟德尔，也不信遗传的染色体学说。是1910年他自己发现了白眼突变果蝇的事实后，他也做了和孟德尔一样的交配实验，取得数据和比例。为了解释事实，摩尔根不得不沿着孟德尔的思路，也提出因子，也进行拼凑数字的“高级杂耍”，最后奠定了遗传学的现代基础。在事实面前，摩尔根不得不“出尔反尔”，因为科学真理高于个人偏见，也不会败于俏皮话的讥笑挖苦。

Nägeli的狭隘、达尔文的缺憾、摩尔根的态度，给孟德尔的超前程度提供了绝佳的注释。

1.3    孟德尔的生平

孟德尔出生地德文称Heinzendorf，捷克称Hyncice，现在捷克境内，当时属于奥匈帝国。孟德尔的父亲是佃农，每周四天料理自家的田地，三天给一位女伯爵干农活。命运似乎注定了孟德尔不得不子承父业，终其一生在农田中度过，但当地的神父Johann A.E. Schreiber （1769-1850）鼓励孟德尔的父母让他多受教育。孟德尔自己也要与命运抗争，并得妹妹的支持。孟德尔后来为报答妹妹的支持，资助了她的孩子读书。

1850年4月17日，他为了考教师证以第三人称写过一个自我简介，清楚地说明了他的情况、心境和决心，信的大意是：

…小学后，1834年他上中学。4年后，接连不断的灾难[译注：一次是他父亲事故受伤]，使他父母完全不能支持他学业所需的费用。因此，16岁的他落入不得不完全自己支持自己的可悲境地。所以，他一边给人做家教，一边上学。1840年中学毕业时，首要问题是取得必要的生活来源。因此，他曾多次试图做家庭教师，由于没有朋友和推荐，未果。失去希望和焦虑的痛苦、未来前景的悲观，彼时对他有强烈影响，导致生病，被迫和父母待了一年。次年，他努力后得以做私人教师，以支持学业。通过极大努力后，他成功地修完两年的哲学。他意识到无法这样继续下去，所以在学完哲学后，他觉得非得进入一个生命驿站，能让自己脱离痛苦的生存挣扎。他的境况决定了他的职业选择。

1843年，他要求并得以进入布鲁诺的圣汤玛斯修道院。从此，他的物质境况彻底改变。有物质生活的舒适后，他重新获得勇气和力量。他满心欢喜和集中精力学习经典。空余时间忙于修道院一个小型植物和矿物收藏。有机会接触后，他对自然科学的特别爱好更加深化。…虽然缺乏口头教育，而且当时教学方法特别困难，从此他却更依附于自然研究。他努力通过自学和接受有经验者的教诲，来弥补自己的缺陷。1845年，他到布鲁诺哲学学院听了农业、园艺和葡萄种植课程。…他很乐意代课，倾力以容易理解的方式教学生，并非无成效…

孟德尔手书自传

孟德尔坦陈入修道院不是为了宗教信仰，而是经济原因。这一重要的人生选择中他权衡的不是神圣与世俗，而是智力追求与成家育子的权利。为了头脑，他舍弃了生殖权。对于血气方刚的青年，并非容易，而需要很大的决心。孟德尔的决定也和中国传统的一种说法（也是当代相当一部分华人的想法）不同：这些人读书是为了颜如玉，而孟德尔为了智力追求放弃颜如玉。

1843年，不满21岁的孟德尔进入布鲁恩（Brünn，现称Brno）的圣汤玛斯修道院（the Abbey of St. Thomas），并于1847年25岁成为神父。孟德尔原名Johann，入修道院后加教名Gregor。

到修道院后，他同时做过代课老师。那时，中学老师已需要证书。孟德尔第一次教师资格考试没通过，被送到维也纳大学去学习，这加强了他的科学背景。孟德尔曾再考教师资格，还是没能通过，而且，估计两次都是没过生物学，所以后来只能做代课老师，在当地的实科中学（Brünn Realschule）教了14年低年级物理学和自然史。他一直以实验物理学教师自称，而不说是生物学家。

‍

孟德尔积极参与学术活动。他长期研究气象，曾任国家气象和地磁研究所布鲁恩站长，1862年提交布鲁恩地区15年气象总结。他一生中参与了八个科学学会、二十六个非科学协会。1861年，孟德尔在任课的中学和一百多人共同创立当地的自然史学会。1865年2月8号和3月8号两个星期三的晚上，在布鲁恩自然科学学会，孟德尔宣读了豌豆研究结果。当地小报对孟德尔演讲有报道，但未能引起国际科学界的注意。

1866年论文发表后，孟德尔将40份抽印本寄给国际上的科学家，后人找到了13份的下落，传说达尔文处有，并未证实。发表文章的杂志有120本在世界主要图书馆。

1868年，修道院道长去世后，孟德尔经过两轮选举后当选道长。他不用教书后，但还有其他工作繁重，他还是尽量做了研究。他用了多种植物做遗传实验。留下的纸片表明在去世前三年，他还在想有关豌豆的遗传问题。1865年到1878年，他记录了14年的地下水位。1870年，他加入养蜂协会，1877年报告对蜜蜂飞行和产蜜量的四年观察。他曾研究苹果和梨的抗病性。在一些协会刊物中，他以M和GM笔名写过一些短篇。

孟德尔生活丰富。他的政治观点偏自由派，与自己的教会背景矛盾。而他支持的自由派掌政时，出台的税收政策却对他的修道院很不利。政府为缓和与他争论曾安排他任银行副董事长和董事长。但他持续十年坚决反对税收，造成他晚年生活很大的苦恼。他在政治上左右碰壁。

1884年1月6日，孟德尔去世。他生前要求尸检，结果表明他肾炎并发心脏病。有位年轻的神父将其诗化，称孟德尔是心给伤了。孟德尔自己是乐天派，年纪大的时候回顾自己一生满意多于不满意。

园艺协会刊物讣告称：“他的植物杂交实验开创了新时代”。 猜想讣告作者是刊物主编Josef Auspitz（1812-1889），他曾任实科中学校长，支持孟德尔无证代课14年，是孟德尔的重要支持者和欣赏者之一。 但是，讣告的溢美之辞远非共识。

据他的朋友Gustav von Niessl (1839-1919)说，孟德尔生前相信“我的时代会到来”。确实如此。但是，要等他去世16年、理论公布34年以后。

1900年声称重新发现孟德尔的三位科学家。其中de Vries的第一篇论文没有提孟德尔，后来可能因为隐瞒不住曾借鉴孟德尔的事实（包括难以解释如果他没有读过孟德尔，为什么他第一篇文章用了孟德尔的dominant和recessive两个词），在第二篇论文中说是重新发现孟德尔。von Tschermak可能不懂孟德尔也说自己重新发现了孟德尔，所以史学家认为不能算。有趣的是，von Tschermak的外公 Eduard Fenzl（1808-1879）是维也纳大学教孟德尔的生物老师之一，不仅教学保守，也可能是没让孟德尔第二次考到教师证书的考官之一。

1.4    孟德尔“造假”案

除了有人说孟德尔不懂自己发现了什么以外，对于孟德尔最大的冤枉是说他编造了实验结果。英国统计学家和遗传学家费舍尔于1936年首先发难，他对孟德尔的实验数据进行统计分析后，断定孟德尔的数据过于接近理想数据。轻一点说，孟德尔可能有我们不知道的助手，在做了前两年实验导致孟德尔有理论后，助手为了满足孟德尔的理论而在后面几年给孟德尔提供他喜欢的数据。重一点说就很难听：“多数—如果不是所有—的实验结果都伪造了，以期贴切地符合孟德尔的预期”。以后每过一些年，就有人小聪明又发现孟德尔的“问题”。

反击孟德尔造假说法的文章也不断。最近一篇较好的反击是2007年哈佛大学Hartl 和Fairbanks 发表于《遗传》杂志的文章。

我认为，给孟德尔伸冤的首要理由是：他无需造假。科学对于他来说不能带来利益。他如果造假，最对不起的是放弃生育人权、十几年如一日做研究的他自己。

其次，孟德尔时代没有统计学。统计学是几十年以后发明的。孟德尔只需分析数量关系，无需检验统计显著性。那时不知道应该做多少次实验、收集多少数据后才应该停止实验。可能是孟德尔收集到觉得差不多的就时候停止，所以数据会接近预计。孟德尔也在论文中明确说过，有一次实验漂移较远，他重复了实验后，数据更接近预计。

孟德尔的行为证明他不是造假和隐瞒不利结果的人。他曾努力使怀疑自己工作重要性的Nägeli相信自己发现的规律。但即使这种情况下，他也没隐瞒自己发现了有悖于自己理论的现象。他把自己的豌豆种子给了Nägeli和其他人，希望他们验证自己的结果。孟德尔致Nägeli信说：我观察到山柳菊的杂交行为与豌豆的正好相反。孟德尔用另外四种植物（紫罗兰、茯苓、玉米和紫茉莉）做的实验观察到其杂交行为都与豌豆一样。

孟德尔不仅在给Nägeli的信说明了山柳菊的结果，而且将结果在1869年发表了。后来多年认为，有两种遗传方式，一种是“豌豆式”（符合经典孟德尔学说），一种是“山柳菊式”（不符合孟德尔学说）。虽然以后也发现这些生物其实都符合孟德尔学说，造成困惑是因为山柳菊是单性遗传，但当时孟德尔以为山柳菊与豌豆不同。如果孟德尔造假，或选择只符合自己理论的结果，那么他就无需在已经公开自己的理论后，将只有他自己知道的山柳菊的结果直接告诉一位不愿接受自己理论的人，而且发表第二篇生物学论文，公布与第一篇的矛盾。

1.5    孟德尔的精神遗产

孟德尔以天生的才能、青年的果断和壮年的坚持，在困难中成长，以放弃获得条件，在失败中得机遇，最终在有限的环境做出了超越时代的发现。

孟德尔的成就，一百多年来催生了多个现代科学学科。首先是直接导致遗传学诞生，而对于同时期诞生的进化论，孟德尔可能隐约知道自己工作的意义，虽然遗传学和进化论结合于1930年代。二十世纪遗传学与生物化学结合，并与微生物、生物物理学交叉，在1940年代又催生了分子生物学。1970年代诞生的重组DNA技术，全面改观了生命科学：分子生物学深入到从医学到农业各个领域，带来多个学科的变革，人类遗传学、基因组学、生物信息学是其直接传承。

在应用上，遗传学带来了二十世纪绿色革命，对于解决全人类食物起了很大作用。遗传学、分子生物学和重组DNA技术奠定了现代生物技术、产生了生物技术产业。现代遗传学和基因组学为个体化医学奠定了必不可少的基础，虽然我们今天还远未达到个体化医学的远景。

孟德尔的发现，对于科学和人类，今后长期还将有深远影响。

最后的问题是：既然孟德尔不受科学家重视，不为科学界所认同，那么，他怎么能获得做研究的条件？

这个问题，背后有一个更加鲜为人知的故事：欲知后事如何，请听下回分解……

注1：孟德尔用“杂交”一词，是现代意义的cross（动物可译成“交配”、植物“授粉”），而非后来科学家重新定义的“杂交”，即 不同种或不同品系之间的交配。孟德尔文章中多半都是同种植物的交配，并非物种或品系间的交配。“杂交”一词今天在中国学生和老师中仍未严格使用，部分原因可能是学孟德尔理论时听惯了杂交一词。

注2：本文中斜体都是孟德尔原文的着重强调。

注3：孟德尔的论文中用了“对照实验”（control）一词。每个在野外做的实验，他都在暖房中也做了，证明野外实验未因昆虫或外源花粉等环境因素所干扰，结果可信，他才采用。

注4：孟德尔用花粉细胞来表示精细胞。现在知道花粉中包含2或3个细胞。参与受精的是其中的两个精细胞。

注5：孟德尔在结语中说花粉细胞和卵细胞结合成单个细胞后，“同化和形成多个新细胞”。现在看来“同化”是错误的，限于当时对发育的误解。全部细胞都来源于受精卵分裂、增值，并不发生同化母体细胞参与子代发育。

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阅读

Mendel G (1866)Versuche über Pflanzen-Hybriden. Verhandlungen des naturforschenden Vereines, Abhandlungen, Brünn 4:3-47，英译本Experiments in Plant Hybridization in Genetics: readings from Scientific American pp. 8-17. W.H. Freeman and Company, San Francisco-USA.

饶毅 (2008) 一意孤行的伯乐

饶毅 (2008) 达尔文的泛生论

Chapter 1 A Lonely Genius

Abandoning natural rights for intellectual pursuits;

Making core discoveries outside the inner circle of science;

Succeeding in applying mathematics to biology;

Ushering in an entirely novel science with a single paper from 10 years of work;

Standing lonely with his theory never accepted by peers in his life time;

Being ridiculed by the second greatest scientist in the discipline he created;

Being underestimated for intellectual height partly because of apparent simplicity of his conclusions;

Being suspected of misconduct though the purpose of research was for curiosity not for personal gains.

The lonely genius was disguised as“a teacher of experimental physics” in his self description, but in truth, the founding father of genetics: Johan Gregor Mendel (1822-1884).

There were two intellectual peaks in biology: the first was Mendel alone from 1854 to 1866, and the second was Francis Crick and his collaborators from 1951 to 1965, separated by exactly 100 years.

It is meaningful today for us to read Mendel (1866), tracing the origin of genetics.

1.1Mendel’s Paper 

Because few contemporaries understood the importance of Mendel’s research, little was preserved of him. The most important of Mendel’s legacy was a paper on genetics. In addition, he had two papers on insects unrelated to genetics, another paper on genetics and ten letters to a botanist explaining his genetic studies.

Mendel’s major paper was written lucidly, showing his line of reasoning, helpful for tracing the birth of a concept.

In Mendel’s time, there was little understanding of genetics and “blending inheritance”, while never validated, was tacitly accepted for its simplicity: that black and white gave rise to the gray, with contributions of parents blended in the progeny. 

Mendel did not take it for granted. He designed experiments, working on them for 10 years, and proposed a novel theory. Beginning in 1854, Mendel used the garden pea to do a series of experiments, announced the general law in 1865, and published his paper Versucheüber die Pflanzen-Hybriden in the Journal of the Society of Natural History, Brünn in 1866.

Mendel’s paper informed us how he did research: finding an important question, propose an approach to solve the problem; designing experiments, carrying out experiments; obtaining results, analyzing results, proposing a theory that no one has proposed before; further experiments, more results to analysis; expanding the theory, proving the theory.

Mendel’s paper consists of 11 parts.

In introduction, Mendel briefly summarized the background and previous results,credited Josef Gottlieb Kölreuter (1733-1806) and Carl Friedrich von Gärtner (1772-1850) for a large amount of hybrid experiments before pointing out immediately: “no generally applicable law governing the formation and development of hybrids has been successfully formulated.” 

He pointed out that, while previous researchers had carried out many hybridization experiments, but did not formulate laws because of considerable amount of work required and difficulties involved. Mendel carefully considered what were required: a fairly large scale, quantitative analysis of progenies of different types, certainties regarding types in different generations, statistical relations.

He recognized that much work needs to be done, but he called his efforts “detailed” experiments, while Mendel (1866) was far beyond details. He said that this paper was the results of “eight years’ pursuit”, excluding the first two years when he collected peas and examined their characters (and unconsciously obtained genetically homozygote peas). His research on peas began in 1854 and ended in 1864.

In“Selection of the Experimental Plants”, Mendel pointed out the importance of selecting the appropriate experimental materials, and “to avoid from the outset every risk of questionable results”.

He selected plants with three criteria: 1) it should possess constant differentiating characteristics (or phenotypes in modern terms); 2) results should not be affected by foreign influences; 3) fertility should not be disturbed in successive generations.

“Differentiating characteristics” in Mendel’s paper are now known as traits or phenotypes (such as tall or short, red or green). His “constant” means that the same traits remain the same in different generations. He was careful about foreign pollen contamination, if one does not know the father of the hybrid, then it was not possible to analyze. He was also careful about fertility.

Mendel may have considered more than twenty species of plants. Mendel chose Leguminosae or the bean family because their“peculiar floral structure”. He used Pisum or the garden pea, but he was not quite certain, and relied on “the opinion of experts” that what he used were Pisum sativum (and others). He quickly noted that the classification was not important.

He did not mention that the garden pea had experimental advantages: it could either self-fertilize, or cross-fertilize and easily controlled by human intervention. In 1854 and 1855, Mendel tried 34 varieties of garden peas. An order for peas in 1956 was among the few physical leftovers from Mendel.

In“Division and Arrangement of the Experiments”, Mendel chose characters (or traits in current terminology) for his research: he chose pairs of traits, studied their transmission between generations. These traits are stable and easily recognizable. The seven pairs of traits were: seed shapes (smooth or wrinkled), seed colors (yellow or green), seed-coat colors (white or gray), pod forms (inflated or constricted), pod colors (green or yellow), flower positions (axial or terminal), stem length (long or short).

In“Forms of the Hybrids”, Mendel further explained his selections. He chose traits that were identical between the progenies and the parents. He noticed traits in progenies that were different from those in parents. For example, he described that flowering times in progenies were inbetween that of the paternal and the maternal traits in Section 8 of the paper. But he did not study such traits. Mendel was clear about the significance of such selections. Mendel’s selections vastly simplified the analysis and helped him to reach general conclusions. For example, by 2017, we know that more than eight hundred genes are involved in the single trait of human height. The height of an individual is determined by these genes and their functionally significant polymorphisms, in addition to environment factors (such as food). If one were studying the genetics of human height, it would have been extremely difficult, not because human height did not obey Mendelian laws but because it was simply difficult to study when the number of genes involved was large. 

Mendel designed seven experiments corresponding to the seven pairs of traits. Experiment 1 involved 60 fertilizations on 15 plants, Expt 2 with 58 fertilizations on 10 plants, Expt 3 with 35 fertilization on 10 plants, Expt 4 with 40 fertilizations on 10 plants, Expt 5 with 23 fertilizations on 5 plants, Expt 6 with 34 fertilizations on 10 plants, Expt 7 with 37 fertilizations on 10 plants. For each experiment, he did crosses in both ways: e.g., green father to yellow mother and yellow father to green mother. The results were not influenced.

During his experiments, Mendel realized that traits could be“dominant” or “recessive” (terms invented by him). When parental traits were different (yellow or green), but their progenies showed only one (such as yellow) but not the other (such as green), Mendel referred the trait showing up in the progenies as dominant (yellow) and the other recessive (green). He pointed out that, while the recessive was not visible in the hybrids (F1 generation), it reappeared in “the first generation from the hybrids” (the F2 generation). He showed that smooth was dominant in seed form to wrinkled, yellow in seed color dominant to green, green in pod color dominant to yellow, inflated in pod form dominant to constricted, purple in flower color dominant to white, axial in flower position dominant to terminal, and long in stem length dominant to short. 

In retrospect, we know that, during those two years of preparation, Mendel actually obtained homozygotes, though there was no such concept as homozygosity and he did not explain as such. But if the starting materials were not homozygous, the analysis would have been more complicated.

We should change to terminology here and used the later convention: Mendel’s firs generation should be called the F0 generation, his “hybrids” the F1 generation and his “first generation from the hybrids” the F2 generation.

Mendel used two different F0 parents for fertilizations and obtained F1 with dominant traits. For example, when parents with smooth and wrinkled seed forms were crossed, F1 progenies all had smooth seeds, no wrinkled seeds. This happened regardless whether the father or the mother carried the dominant traits.

Mendel then crossed F1 to F1 to obtain F2, finding that recessive traits (such as wrinkled seeds), though not showing up in F1, reappeared in F2. Further analysis revealed that the ratio of the dominant to the recessive in F2 was on the average 3 to 1. Mendel emphasized that 3:1 was the ratio for all 7 pairs of traits: Expt 1 showed that, from 253 plants in the F1 generation, 7324 seeds in the F2 generation were obtained and 5474 were smooth and 1850 wrinkled (smooth/wrinkled=2.96:1); Expt 2 began with 258 F1 plants and yielded 8023 seeds with 6022 yellow and 2001 green (yellow/green=3.01:1).

Mendel analyzed whether the shapes of seeds were related to their colors and concluded that they were not related. He also pointed that if the number of plants counted were too small, ratios could drift, and that if insects had damaged seeds, determination of traits would be comprised.

From Expt 3 to Expt 7, he obtained ratios of the other 5 pairs of traits and found the average of all 7 pairs of traits to be 2.98:1.

Mendel observed the rules: 100% of the F1 generation were dominant, whereas the recessive reappeared in F2, with a ratio of dominant to recessive at 3:1.

By observing the reappearance of the recessive trait in F2, Mendel knew that the recessive trait did not disappear in F1 and thus the idea of blending inheritance could not be correct. At that point, he was ahead of others. But he took further steps of finding the 3:1 ratio, tried to explain the ratio and validated the explanation by experimental results, far exceeding his contemporary scientists, including one of the greatest scientists of all times.

After finding the 3:1 ratio, Mendel analyzed two possibilities for the dominant trait in F2: that either the dominant trait in F2 was similar to the dominant trait in F0 and thus passes to the next generation without change, or that the dominant trait in F2 was similar to the dominant trait in F1 and thus, if self-crossed, F2 with dominant traits will give rise to both the dominant and the recessive trait.

Next year, Mendel carried out experiments described in the section“the Second Generation from the Hybrids” (or F3 in current terminology). He found that F2 plants with recessive, when crossed to F2 recessive plants, gave rise to only F3 plants with recessive traits. By contrast, 1/3 of F2 plants with dominant traits gave rise to only to F3 plants with dominant traits, whereas 2/3 of F2 plants with dominant traits gave rise to F3 plants with either dominant or recessive traits: the ratio of the dominant to the recessive was again 3:1 in F3 progenies from such dominant F2 crosses. 

Thus, in Expt 1, among 565 F2 plants with smooth seeds, 193 gave rise to F3 progenies with smooth seeds and 372 to F3 with both smooth and wrinkled seeds (3:1 ratio of smooth to wrinkled). In F2 plants showing the dominant traits, 1.93 was the ratio of F0 like F2 plants to F1 like F2 plants.

In Expt 2, among 519 F2 plants with yellow seeds, 166 plants gave rise to F3 plants with only yellow seeds, 353 gave rise to F3 plants with both yellow and green seeds (yellow to green at 3:1). 2.13:1 was the ratio of F0 like F2 plants to F1 like F2 plants.

From Expt 3 to Expt 7, Mendel did not count all progenies, but only 100 plants for each of the other five pairs of traits. Some results fit the same ratio, some drifted. He mentioned that Expts 1 and 2 were more meaningful because he counted more plants. In Expt 5, the drift was considerable, and he counted another hundred and obtained a result closer to his expected ratio.

Thus, Mendel further separated the 3 in 3:1 in F 2 into 2 and 1. The 3:1 ratio on F2 was thus 1:2:1 (constant dominant or F0 dominant like: hybrid or F1 like: constant recessive or F0 recessive like).

After F3, Mendel carried out a few“successive generations” of crosses, and found that all results agreed with previous findings. By the time he wrote the paper, he had carried out Expts 1 and 2 for six generations, Expts 3 and 7 for five generations, and Expts 4, 5 and 6 for six generations. In all, he had carried out at least 17610 fertilizations with garden peas.

Mendel took a big step: mathematical modeling.

Few biologists had proper mathematical training at that time, and many became biologists because they were not weak in mathematics. Even today, although some biologists require quantitative analysis, most biologists pay attention only to more, less or the same. Mendel quantitatively analyzed plants of different traits, finding the 3:1 ratio, and further found 1:2:1, making him one of the pioneers of biologists who had successfully used mathematics.

On the basis of the above, Mendel went far beyond biologists not only by then, but even by now. He used A to denote the constant dominant, and a to denote the constant recessive, and Aa to denote the hybrid. He derived A+2Aa+a for the F2 generation. His observations of the F2 generation of 1:2:1 precisely fit this quantitative relationship (with the dominant and recessive as 1, and the hybrid as 2).

After analyzing single pairs of traits, Mendel analyzed whether different pairs of traits were related. In “the Offspring of Hybrids in Which Several Differentiating Characters Are Associated”, Mendel found that all seven pairs of traits were completely independent. For example, the smoothness/wrinkledness of seeds were unrelated to their colors (yellow/green). He concluded that “the relation of each pair of different characters in hybrid union is independent of the other differences in the two original parental stocks”.

We only know much later that the 7 pairs of traits studied by Mendel happened to be determined by 7 genes on 5 chromosomes. Of the 3 genes on the same chromosomes, they happened to be far from each other. Thus, all 7 traits appeared to be independent.

After discovering the independence of 7 traits, Mendel might have considered the relation of his own findings to evolution. We now know that Mendel read the German translation of the second edition of the Origin of Species by Charles Darwin (1809-1882) and made notes on its margin. Perhaps because he worked in a monastery, Mendel could not openly accept evolution, and thus did not mention evolution at all in his paper. He did discuss the implications of independent inheritance of different traits. He pointed out that, if a plant had 7 different traits, its progenies would have 2⁷(128) kinds of combinations. This calculation solved the problem created by “blending inheritance” for Darwinian evolution. In blending inheritance, black and white gave rise to the gray. Gray plus gray begets sub-gray, and so on and so forth. With each generation, there would be decreasing diversity and not increasing diversity. Organisms should degenerate over generations. Mendel showed that different combinations of different traits would increase diversity, providing a basis for natural selection to work.

Mendel summarized: “the offspring of the hybrids of each pair of differentiating characters are, one–half, hybrid again, while the other half are constant in equal proportions having the characters of the seed and pollen parents respectively. If several differentiating characters are combined by cross–fertilization in a hybrid, the resulting offspring form the terms of a combination series in which the combination series for each pair of differentiating characters are united”.

Mendel believed that the principle he discovered applied to other traits (such as peduncles of different lengths).

After analyzing the outward characters (or phenotypic traits in our terminology), Mendel inferred that the differences in appearances resulted from differences in reproductive cells, the male pollens and female eggs.

He reasoned: because only when the egg and the pollen had the same constant traits (both homozygous for either the dominant or the recessive), could the progeny had identical phenotype as that of the parental reproductive cells, “similar factors must be at work” when the constant dominant (homozygous dominant) or the constant recessive (homozygous recessive) was observed in the progeny. “In the ovaries of the hybrids there are formed as many sorts of egg cells, and in the anthers as many sorts of pollen cells, as there are possible constant combination forms, and that these egg and pollen cells agree in their internal compositions with those of the separate forms” (my emphasis in italic).

If F0 shows constant dominant (i.e., homozygous dominantA), its reproductive cells should consist of pollens with Aforming internal composition and eggs with A forming internal composition. If F0 shows constant recessive (i.e., homozygous recessive a), its reproductive cells should consist of pollens with a forming internal composition and eggs with a forming internal composition. Crosses of pollen and eggs in the F0 generation gave rise to F1 generation. Each F1 pollen contains either A or a forming internal composition, and in equal numbers. The same for F1 eggs. When an F1 plant self-fertilizes, its eggs and pollens of A or a genotype has an equal chance of being crossed to pollens or eggs of either genotype.

Therefore, F1 and F2 can be described as:

A/A+A/a+a/A+a/a= A+2Aa+a

This is very important. Mendel linked the internal composition of reproductive cells on the left with the traits of next generation of plants on the right. We now call the left the genotype and the right the phenotype.

From the genotype of 1:2:1, Mendel deduced the genetic composition of reproductive cells. He relied on observed phenotype and deduced the composition of reproductive cells.

Mendel explained that these were average results, and each progeny had multiple possibilities, with random distribution. There would certainly be shifts in separate experiments which could only be ameliorated by collections of a large amount of data to reach a reliable ratio. Here we can guess that Mendel might be aware of homozygousA/A or a/aand heterozygous A/a or a/A, but he did not coin the terms.

By now, Mendel advanced his theory to the level of composition of reproductive cells and used mathematical model to express genetic rules. His math was simple combination, but it was effective in revealing genetic rules behind experimental results, with profound implications in biology.

Because Mendel wanted to find “generally applicable law”, the last part of his paper was to test in “other species of plants” whether the law he discovered from the garden pea was applicable to other plants. He showed completed experiments with two species of beans: Phasseolus vulgaris and Phaseolus nanus. He obtained results with several traits which were “in perfect agreement” with those from the peas. Furthermore, in his experiments with Ph vulgaris and Ph nanus, he found the flower colors varied. Mendel felt that the genetic transmission of flower colors still obeyed his law (“the law governing Pisum”) with the additional proposal that each flower color was a combination of two or more independent colors. For example, flower colorA was a combination of A₁+A₂+……. Thus, Mendel had proposed multi-gene transmission, defying the conventional definition of Mendelian genetics as single gene genetics.

After innovative, rigorous and persistent experimentation and quantitative analysis, Mendel had finally found a generally applicable law governing the formation of hybrids. Later scientists took two statements from his paper as two Mendelian laws: the first being the law of dissociation which states that a pair of genetic factors controlling the same trait dissociate from each other and transmit to progenies; the second being free combination of factors controlling different traits (the results of this part were omitted from this chapter but can be found in Mendel’s 1866 paper). Mendel did not believe that he had discovered two laws, but only one generally applicable law, although both statements can be found in Mendel’s paper: “we must further assume that it is only possible for the differentiating elements to liberate themselves from the enforced union when the fertilizing cells are developed. In the formation of these cells all existing elements participate in an entirely free and equal arrangement, by which it is only the differentiating ones which mutually separate themselves. In this way the production would be rendered possible of as many sorts of egg and pollen cells as there are combinations possible of the formative elements.”; “There is therefore no doubt that for the whole of the characters involved in the experiments the principle applies thatthe offspring of the hybrids in which several essentially different characters are combined exhibit the terms of a series of combinations, in which the developmental series for each pair of differentiating characters are united. It is demonstrated at the same time that the relation of each pair of different characters in hybrid union is independent of the other differences in the two original parental stocks.”  

In “Concluding Remarks”, Mendel summarized hybrid experiments of previous researchers and statements about plant fertilization by others. He pointed out that: “in the opinion of renowned physiologists, for the purpose of propagation one pollen cell and one egg cells unite…into a single cell, which is capable by assimilation and formation of new cells to become an independent organism.”

Mendel then proposed: “this development follows a constant law, which is founded on the material composition and arrangement of the elements which meet in the cell in a vivifying union. If the reproductive cells be of the same kind and agree with the foundation cell of the mother plant, then the development of the new individual will follow the same law which rules the mother plant. If it chance that an egg cell unites with a dissimilar pollen cell, we must assume that between those elements of both cells, which determine opposite characters some sort of comprise is effected. The resulting compound cell becomes the foundation of the hybrid organism the development of which necessarily follows a different scheme from the obtaining in each of the two original species…the arrangement between the conflicting elements is only temporary…it is only possible for the differentiating elements to liberate themselves from the enforced union when the fertilizing cells are developed. In the formation of these cells, all existing elements participate in an entirely free and equal arrangement, by which it is only the differentiating ones which mutually separate themselves. In this way the production would be rendered possible of as many sorts of egg and pollen cells as there are combinations possible of the formative elements.”

If we change Mendel’s “elements” into “genes”, we could understand genetics by almost verbatim recitation of his words in 1866. For those who prefer simple expressions, another way to summarize Mendel’s conclusion would be:A/A+A/a+a/A+a/a.

Mendel repeated 6 times that in the development of hybrids of the garden peas, pollen cells and egg cells had the same number of compositions as those which will form, in combination, constant characters (traits). It was further evidence that he knew the basis for genetic transmission lied in corresponding elements in reproductive cells. In his September 27 1870 letter to the botanist KarlNägeli, Mendel used the term anlage in German to describe the genetic factor, again showing that his understanding of the elements is the same as our understanding of the gene.

Mendel did research on the genetic transmission of the fur color of mice, but was asked to stop: animal breeding was not a good sight in a monastery. Once he became the abbot, Mendel built a bee house in 1871 and used honey bees for experimentation, but no results of genetics could be found. Thus, his findings in plants were not extended to animals.

1.2Genetics as Understood by Other Scientists

Have others carried out hybrid experiments with peas?How did scientists in Mendel’s time understand genetics? How did they understand Mendel? And how the second greatest geneticist understood Mendel?

We can discusstwelves scientists: 6 before Mendel (including 5 analyzing pea hybrids), 3 contemporaries of Mendel who worked on peas, Karl Nägeli (1817-1891) with whom Mendel communicated his results from pea experiments, Charles Darwin (1809-1882) who independently carried out hybrid experiments and obtained similar results, and Thomas Morgan (1866-1945), a scientist who carried out genetic studies 40 years after Mendel’s paper.

Before Mendel, scientists have recognized sex in plants, and hybrid experiments of plants have been carried out more than a hundred years before Mendel’s birth.Josef Gottlieb Kölreuter (1733-1806）and Carl Friedrich von Gärtner (1772-1850) of Germany had systematically carried out a large amount of hybrid experiments with plants. Before Mendel, at least 5 scientists had used peas in hybrid experiments and one had used muskmelon and obtained similar results. Independent of Mendel, but publications slightly after Mendel, 3 scientists had used peas for hybrid experiments.

In 1729, British priest Thomas Henchman (1666-1746?) crossed varieties of peas and observed the presence of both blue and white seeds in the same pea pod.

Thomas Andrew Knight (1759-1838) was the president of the Royal Horticultural Society and had long term communication with Darwin, and his hybrid experiments were cited inThe Origin of Species by Darwin. The purpose of Knight was to improve fruits, especially apples. Because it was slow to use apples for experimentation, he began in 1787 to use pea. He chose peas “not only because I could obtain many varieties of this plant of different forms, sizes, and colours’ but also, because the structure of its blossoms, by preventing the ingress of insects and adventitious farina, has rendered its varieties remarkably permanent”. In 1799, Knight published his experimental method of destroying the male parts a few days before introducing the pollen of other peas. On and off, Knight continued to publish on peas, with the last one on hybrid experiment published in 1823, the second year after Mendel’s birth. Knight’s 1799 paper reported his results: that the offsprings of white peas were all white. If the pollens from the father were colored (gray or purple), even if the mother was white, all offsprings were colored (gray or purple). Gray could be passed onto offsprings, even if the mother was white. 

On August 20th, 1822, the results ofAlexander Anderson Seton（1769-1850）from Scotland were read at the Royal Horticultural Society. He observed that crosses between green peas and white peas gave rise to green peas.

On October 15^thof 1822, results submitted by the British farmer John Goss (1787-1833) were read at the Royal Horticultural Society. He had observed: that all progenies from the crosses in the summer of 1820 of yellowish white peas (dwarf peas, or Dwarf Spanish) and deep blue peas (prolific blue, or Blue Prussian) to be yellowish white, that crossing of these peas gave rise to all blue or all white or blue and white peas in the same pod, that crossing blue with blue progenies from the above gave all blue peas, and crossing white with white progenies from the above gave rise to either all white peas, or white and blue in the same pod.

The results of Seton and Goss were all published in 1824 in the 5^thvolume of the Proceedings of the Royal Horticultural Society. Following their papers were the improvement of melon culture method by Thomas Andrew Knight read to the society on November 15^th, 1822. In the same volume, results of Knight read on June 3^rd 1823 was published. He reported that the progenies of gray peas crossed with white peas to be gray, and that crosses of these gray peas with white peas (of “permanent habits”) gave progenies of gray, but also white, peas.

In 1826, Augustin Sageret (176301851) of France published results of crosses between cantaloupe and muskmelon. He used cantaloupe with yellow seeds and netted skin, muskmelon with white sees and smooth skin. The progenies had white seeds and netted skin.

In 1849,Carl Friedrich von Gärtner (1772-1850) of Germany published more plant hybrid experiments in his book. Among which, he observed that the progenies of yellow peas and green peas were all yellow. 

In 1854, Charles Naudin (1815-1899) of France began in the same year as Mendel. Naudin first used primula, and he invented back-crossing in genetic studies. In 1856, he observed spontaneous reversion and segregation of traits. In 1861, he submitted a report to the French Academy of Sciences (and published in 1863), that the traits of progenies were either the same as those of the father, or those of the mother, with no intermediates.

Two scientists published after Mendel, but might not be aware of Mendel’s results. Thomas Laxton (1830-1893) of Britain made important contributions to the improvement of peas, with one species named after him. In the 1866 International Horticultural Exhibitions and Botany Congress, and the 1872 Journal of the Royal Horticultural Society, Laxton presented his results: that crosses of white and purple peas gave rise to purple peas, while crosses of white and brown peas gave rise to brown peas. In 1893, E. Giltay (1858-1935) of the Netherlands reported that the progenies of yellow peas crossed with green peas were yellow.

Among those who received the 40 reprints sent by Mendel, only the Swiss botanistNägeli, working then at the University of Munich, is known to have replied. Therefore, Nägeli can be considered as the one among those 40 who treated Mendel most seriously. Mendel also exchanged seeds with Nägeli. Without prompting, Mendel proposed to use hawkweed (Hieracium) to validate the law he found with the pea, which was encouraged by the world expert on hawkweed: Nägeli. Mendel complaint about paucity of seeds, difficulties in pollination and lack of time on his own part (due to promotion to the position of the abbot). In his November 6, 1867 letter to Nägeli, Mendel also explained that he was growing too much in weight to be able to work easily in the garden. He was slow in obtaining results with hawkweed, and those who did not know might think that he was finding excuses or dragging on his feet. Once his experiments with hawkweed were finished, it was clear that the law from the peas could not explain results from the hawkweed: the law did not seem generally applicable. Mendel faithfully informed Nägeli so. But he also added that he had carried out experiments with Matthiola annua, glabra, Zea and Mirabilis, their results did agree with the law from the peas. Mendel believed that the law was right, only that hawkweed was special. Although Mendel wrote to Nägeli repeatedly, informing him the many experimental results, Nägeli never mentioned Mendel or his results once when publishing. The correct explanation for hawkweed would have to wait until 1904: parthenogenesis, or asexual reproduction without contribution from the sperms. 

The only example of Nägeli may not be sufficient to show how far-sighted Mendel was. Darwin would be more convincing.

In 1859, Darwin published his “On the Origin of Species by Means of Natural Selection”, in which he stated: “if variations useful to any organic being ever do occur, assuredly individuals thus characterized will have the best chance of being preserved in the struggle for life; and from the strong principle of inheritance, these will tend to produce offspring similarly characterized. This principle of preservation, or the survival of the fittest, I have called Natural Selection”. Thus, principle of inheritance, or genetics, is a pillar of Darwin’s natural selection theory of evolution. Darwin was motivated to understand “principle of inheritance” or genetics.

Religiously based attacks on Darwin were fierce, but not rational. A reasonable criticism at that time was logical and rational: natural selection during evolution was against the commonly accepted knowledge of inheritance. According to the blending theory of inheritance, black and white would give rise to the gray. Gray and gray would give rise to the sub-gray, and so on and so forth. Traits will become simpler and simpler, with less and less for selection. Darwinian selection required genetics for explanations and support. However, genetic rules escaped Darwin even though he tried hard to find them.

Darwin had learnt the results of pea hybrid experiments from Thomas Laxton. In 1868, Darwin cited Laxton that“whenever a cross has been effected between a white-blossomed and a purple- blossomed pea, or between a white-seeded and a purple-spotted, brown or maple- seeded pea, the offspring seems to lose nearly all the characteristics of the white-flowered and white-seeded varieties; and this result follows whether these varieties have been used as the pollen-bearing or seed-producing parents”. In 1876, Darwin cited Laxton’s new results for “the rigour and luxuriance of the new varies (from numerous crosses)”.

Contrary to the general assumption, Darwin not only relied on observations to deduce theoriesor citing results of others, but he also carried out experiments. He experimented with flowers for 11 years, part of his results was published before Mendel in 1862, and major results in two books published in 1876 ad 1877, and the rest scattered in other publications.

In 1868, Darwin publishedThe Variation of Animals and Plants under Domestication. It reported his experiments with snapdragon. The flowers of most snapdragon were bilaterally symmetric and were referred to the common type by Darwin (and noted as C here). Occasionally, a mutant form was observed, with radially symmetric flowers (referred to as the peloric form, and noted as p here). When he crossed p type fathers to C type mothers, their progenies (F1) were all of the C phenotype. Further fertilizations among F1 plants gave rise to F2 progenies. Darwin counted 127 F2 progenies, 88 were of the C phenotype and 37 of the p phenotype, 2 with a phenotype in-between C and p. Darwin’s snapdragon experiments ended there. 

After obtaining these experimental results, Darwin concluded:“we have two opposed latent tendencies in the same plants. Now, with the crossed Antirrhinums the tendency to produce normal or irregular flowers, like those of the common Snapdragon, prevailed in the first generation; whilst the tendency to pelorism, appearing to gain strength by the intermission of a generation, prevailed to a large extent in the second set of seedlings”. This conclusion was not as deep as those of Mendel, and can be reached by non-biologists who observe traits in real life.

Darwin missed his chance more than once. In his 1877 book titledThe Different Forms of Flowers on Plants of the Same Species, he included a table showing results of his experiments with Primula auricula. In his F2 results, he obtained 75% with the dominant trait and 25% with the recessive trait, a perfect 3:1 if only he had noted. However, Darwin did not realize its importance and missed modern genetics again.

InThe Variation of Animals and Plants under Domestication, Darwin proposed the erroneous pangenesis hypothesis. He proposed that all somatic cells in an organism contained gemmules (also called pangenes later). They entered the germline cells. The combination of gemmules determine the contents of the germline cells, leading to the formation of distinct reproductive cells and different progenies. In emphasizing the significance of gemmules from somatic cells, Darwin stated that either the reproductive ability was not entirely in germline cells or that germline cells collected gemmules. In his pangenesis hypothesis, Darwin merged transmission between generations, plant grafting, development and regeneration and tried to explain all of them, with much confusion. He even embraced the idea of acquired inheritance by use and disuse, which was exactly the Lamarckian evolution theory overthrown by Darwinian natural selection theory of evolution. He believed that environmental influences could affect gemmules in somatic cells and passed onto germline cells to change traits in the progenies. The pangenesis hypothesis was wrong, but the word gene came from this term.

Comparison with Mendel shows Darwin’s problems: 1) Darwin did not realize that the sample size was important and that the observation of 88C:37p with F2 snapdragon would have been 2.38:1, drifting far away from 3:1, resulting from his mistake in his experimental design with snapdragon. By contrast, Mendel knew that he should “undertake a labor of such far-reaching extent, and counted thousands of plants with multiple traits and multiple generations over eight years; 2) when Darwin found all F1 showed the C phenotype, he did not proposed the concept of dominant-recessive phenotypes; 3) when he observed the p phenotype in F2 after it did not show up in F1 progenies, Darwin noted the phenomenon, proposed the “Principle of Reversion” which was a restatement of the phenomenon, not an understanding of the mechanism; 4) When counting F2 progenies, he did not calculate the ratio of C:p; 5) even when he observed 3:1 ratio in the F2 of Primula auricular, Darwin did not notice its significance and did not try to explain, and deduce further 1:2:1; 6) Darwin did not use mathematical modeling; 7) Darwin did not extract rules or laws from experimental results, and proposed a wrong hypothesis of pangenesis.

It is not known whether Darwin read Mendel’s 1866 paper or not. It is also unclear whether Darwin could have understood or accepted Mendel’s law even if he had read it. We know that Mendel made notes on the German translation of the second edition ofOn the Origin of Species published by Darwin in 1860. The 1866 paper of Mendel could be read as if it was trying to provide a genetic basis for Darwinian evolution. From his findings of free association of multiple phenotypes, he could deduce that crossing of plants with 7 pairs of phenotypes would lead to multiple combinations, explaining diversity. Mendel might well have thought about the implications of his law for evolution. He did not consider the other part of evolution: how variations occur. It would take another seven decades, till the 1930s, before Ronald Fisher (1890-1962) and JBS Haldane (1892-1964) of Britain, Sewall Wright (1889-1988) and Theodosius Dobzhansky (1900-1975) were able to integrate Mendelian genetics and Darwinian evolution.

It is generally stated that Mendelian genetics was rediscovered in 1900 by three scientists: CarlCorrens (1864-1933) of Germany、Hugo de Vries (1848-1935) of the Netherlands and Erich von Tschermak (1871-1962) of Austria, though von Tschermak has been ruled out by historians of genetics. Their understanding did not reach the level of Mendel. The mathematical formula of de Vries was not as good as that of Mendel 35 years ago. The combined workload of all three was not more than that of Mendel alone. Correns was a student of Nägeli and was instrumental in driving later understanding of Mendel. Willian Bateson (1861-1926) played an important role in propagating Mendelian genetics.

The second greatest geneticist was undoubtedly Thoman Morgan (1866-1945) of the US. But, as late as 1909, Morgan was still ridiculing the Mendelian approach as superior jugglery of numbers. After his discovery of white eyed mutants of Drosophila in 1910, Morgan did crosses and analysis exactly according to Mendel, counting numbers and analyzing ratios. To explain his findings, Morgan followed Mendelian genetics, and enriched it. Facing facts, Morgan had to abandon his opinions and switch his positions. In science, truth and logic are far above personal biases.

The narrow-mindedness of Nägeli, the missed chances of Darwin and the biased opinions of Morgan provided excellent foodnotes to highlight the foresight and greatness of Mendel.

1.3 Mendel’s Life

Johann Mendel was born to Anton and Rosine Mendel in a city called Heinzendorf in German and Hyncice in Czech, located then in the Austrian Empire and now the Czech Republic. His father was a farmer who worked on his own field 4 days a week and on the field of Countess Maria Walburga (1753-1817). It seemed that the fate of Mendel was to be a farmer like his father, but the local priest Johann Schreiber (1769-1850) encouraged his parents to allow more education for Mendel. Mendel fought for his own fate and was supported by his sisters. To reciprocate his younger sister’s support, he later supported her children’s education.

On April 17, 1850, Mendel wrote an autobiography to take a teacher’s qualification examination（translated by Hugo Iltis, 1882-1952）: 

“…After he had received elementary instruction …, he was admitted in the year 1834 to (middle school). Four years later, due to several successive disasters, his parents were completely unable to meet the expenses necessary to continue his studies, and it therefore happened that the respectfully undersigned, then only sixteen years old, was in the sad position of having to provide for himself entirely.


…When he graduated from the Gymnasium in the year 1840, his first care was to secure for himself the necessary means for the continuation of his studies. …but all his efforts remained unsuccessful because of lack of friends and recommendations. The sorrow over these disappointed hopes and the anxious, sad outlook which the future offered him, affected him so powerfully at that time, that he fell sick and was compelled to spend a year with his parents to recover. 

…In the following year the respectfully undersigned found himself finally placed in the desired position of being able to satisfy at least his most necessary wants by private teaching in Olmütz, and thus to continue his studies. By a mighty effort, he succeeded in completing the two years of philosophy... The respectfully undersigned realized that it was impossible for him to endure such exertions any further. Therefore, after having finished his philosophical studies, he felt himself compelled to step into a station of life, which would free him from the bitter struggle for existence. His circumstances decided his vocational choice. He requested and received in the year 1843 admission to the Augustinian Monastery St. Thomas in Altbrünn.

Through this step, his material circumstances changed completely. With the comfortableness of his physical existence, so beneficial to any kind of study, the respectfully undersigned regained his courage and strength and he studied the classical subjects prescribed for the year of probation with much liking and devotion. In the spare hours, he occupied himself with the small botanical- mineralogical collection which was placed at his disposal in the monastery. His special liking for the field of natural science deepened the more he had the opportunity to become familiar with it. Despite his lack of any oral guidance in these studies, plus the fact that the autodidactic method here, as perhaps in no other science, is extremely difficult and leads to the goal only slowly, he became so attached to the study of nature from this time on that he will not spare any effort to fill the gaps that are still present through self instruction and the advice of experienced men. In the year 1846, he also attended courses in agriculture, pomiculture, and wine-growing at the Philosophical Academy in Brünn...

After completing the theological studies in 1848, the respectfully undersigned received permission from his prelate to prepare himself for the philosophical rigorosum [examination for the Doctor of Philosophy degree]. In the following year at the time when he was about to undergo his examination, he was asked to accept the position of a substitute teacher at the Imperial Royal Gymnasium in Znaim, and he followed this call with pleasure. From the beginning of his substitute teaching, he made all efforts to present his assigned subjects to the students in an easily comprehensible manner. He hopes his endeavor was not quite without success since, during that private tutoring to which he owed his bread for four years, he found sufficient opportunity to collect experiences regarding the possible accomplishments of the students and the different grades of their mental capacity.

The respectfully undersigned believes to have rendered with this a short summary of his life's history. His sorrowful youth taught him early the serious aspects of life, and taught him also to work. Even while he enjoyed the fruits of a secure economic position, the wish remained alive within him to be permitted to earn his living. The respectfully undersigned would consider himself happy if he could conform with the expectations of the praiseworthy Board of Examiners and gain the fulYillment of his wish. He would certainly then shun no effort and sacrifice to comply with his duties most punctually. ”

Mendel was straightforward that he did not join the monastery for religious belif but for economic necessacity. In this important juncture of his life, he did not have to resolve any conflict between religion vs atheism, but had to choose between intellectual pursuit vs the natural rights of having a family with children. For his brain, he gave up reproduction. This is not easy for a young man. Mendel’s decision was also different from some Chinese who believe that studying is for the purpose of getting a good marriage.

In 1843, short of his 21^st birthday, Mendel joined the Abbey of St. Thomas of Brünn (now known as Brno) and became a priest in 1847 when he was 25. To his original name of Johann was added Gregor once joining the monastery.

Mendel was also a substitute teacher. But even then, certificates were required for middle school teachers. Mendel failed his first examination. Because of the failure, he was sent to Vienna University, which provided him with highly significant education, which also turned out to be relevant for his later research. After college, he might have tried the examination again and failed again. It was possible that he failed biology in both examinations. He could only be a substitute teacher, teaching lower class physics and natural history atBrünn Realschule for 14 years. He called himself a teacher of experimental physics, not a biologist.

Mendel was active in academic activities. He published more papers on meteorology than genetics. He participated in eight scientific societies and twenty-six - associations outside science. In 1861, Mendel joined more than a hundred others in establishing the Natural History Society ofBrünn, physically located at the middle school in which he taught. On two Wednesdays, February 8^th and March 8^th of 1865, Mendel announced his results from the pea experiments to the Natural History Society. His lectures were reported by the local media, but not noticed by the international science community.

Mendel sent 40 copies of the reprints to scientists internationally, of which 13 has been located. The rumor that Darwin received a copy was never proven. 120 copies of the journal which published his article was found in major libraries of the world.

In 1868, after the death of the abbot of the St. Thomas Abbey, Mendel was elected its abbot after two rounds of votes. He no longer had to teach, but was heavily involved in other work. He tried more experiments, especially with more plants to replicate his genetic results. A note left three years before his death showed that he was still thinking about genetic questions related to the garden pea. In 1870, he joined the local apiculture association and reported his observations of bee navigation and honey production in 1877. He published under the pseudonyms of M and GM in local societies.

Mendel had a rich life. His political views were those of a liberal, conflicting with his church. When the liberals were running the government, its tax policies were not favorable to his monastery. The government appointed him to the board of directors of banks to alleviate their conflicts. His insistence on fighting the taxes was a major source of displeasure in his late years.

On January 6^th, 1884, Mendel died. He asked to be autopsied and the results showed that he had nephritis and heart problems. A young priest made it poetic, saying that Mendel was heart broken. Mendel was an optimist and felt more satisfied than unsatisfied when reminiscing about his own life in old age.

The local horticulture society stated that“his plant hybridization experiments have opened a new era”. The guess is that the chief editor of the horticulture society Josef Auspitz (1812-1889) wrote the obituary. He was once the principal of the Brünn Realschule where Mendel taught for 14 years without a certificate. The view of Auspitz as an important supporter expressed in the obituary was unlikely to be generally shared at the time.

According to Mendel’s friend Gustav von Niessl (1839-1919), Mendel believed that “my time will come”. That turned out to be true, although it would take 34 years after the publication of his paper and 16 years after the death of Mendel.

It is usually described that Mendel was rediscovered by three scientists in 1900. de Vries did not mention Mendel in his first paper, which enraged Correns who questioned why de Vries used dominant and recessive had he not read Mendel before. de Vries credited Mendel in his second paper. von Tschermak did not understand Mendel and was ruled out as a co-discoverer of Mendel by historians. von Tschermak was a grandson of Eduard Fenzl (1808-1879) who taught Mendel biology at Vienna and might be one of the examiners who failed Mendel in his second attempt to obtain the teacher’s certificate. 

1.4 Mendel’s “Scandal”

There were some who claimed that Mendel was only doing crosses, and not knowing what he actually discovered. But Mendel’s letters to Carl Nägeli and his usage of the term anlage clearly showed that he knew that he was uncovering the basis of genetic transmission.

The biggest scandal was the persistent suspicion that Mendel or his assistant fabricated experimental results.

It was first in 1936 raised by the British statistician and geneticist Fisher. He analysed Mendel’s data statistically, and concluded that the data were too close to the expected results to be true. To put it lightly, Fisher suggested that Mendel could have had an assistant not known to us. After Mendel had a theory with two years of data, the assistant fed Mendel with data he liked. To put it more bluntly, Fisher said that “the data of most, if not all, of the experiment have been falsified so as to agree closely with Mendel’s expectations”.

Since then, questions about Mendel were raised every once in a while.

There has been no lack of counter-arguments. A good one is that by Daniel Hartl and Daniel Fairbanks of Harvard in 2007.

In my view, first of all, there was no reason for Mendel to fabricate. Science is his hobby, not profession, and can not bring him any tangible benefit. Had he fabricated, the biggest damage would be done on himself who gave up his natural rights to marry and reproduce for the non-natural privilege of carrying our research for more than ten years.

Secondly, in Mendel’s time, there was no statistics, which was invented decades later. Mendel only needed to analyze relationship between numbers, without having to test for statistic significance. It was not known at the time how many experiments should be done and when to stop counting the peas of certain phenotype. It is possible that Mendel stopped counting when it felt right, thus making the numbers close to expectations. Mendel’s paper stated that the number drifted from the 3 to 1 ratio and he repeated the experiment and obtained a result closer to expectation.

Thirdly, Mendel’s behavior has proven that he was not a liar or one to hide unfavorable results. He tried to convince Nägeli the importance of his genetic studies. But he did not hide findings known only to him. He sent pea seeds to Nägeli and hoping that his results could be confirmed. In his letters to Nägeli, Mendel told Nägeli that “At this point, I cannot hold back remarking that it must be noticed that the hybrids of Hieracium show an almost opposite behavior when compared with those of Pisum. We are here, obviously, confronted with only isolated phenomena”. Mendel pointed out that “those dealing with Mattiola annua and glabra, Zea, and Mirabilis…their hybrids behave exactly like those of Pisum”. Not only had Mendel informed Nägeli his hawkweed results, but he also published it in 1869. This puzzle was not resolved until 1904 when hawkweed was found to be parthenogenetic, breeding without the participation of the father. It showed that Mendel did not hide results contradicting his theory.

1.5 Mendel’ Legacy

Born with natural talent, decisive in youth and persistent in adulthood, Mendel, though growing up with socioeconomic disadvantages, traded his reproductive rights for education, scholarship and intellectual pursuits, run into opportunities during failures and finally made epoch-breaking discoveries, with limited conditions.

Over more than a century, the achievement of Mendel has facilitated the birth of multiple disciplines in science. It first gave birth to genetics directly. For the natural selection theory of evolution, Mendel might not have completely missed the implications, although genetics and evolution would not be successfully until the 1930s. The integration of genetics and biochemistry, with inputs from microbiology and biophysics, gave birth to molecular biology in the 1940s. The invention of recombination DNA technology in the 1970s changed life sciences on a large scale: molecule biology has been brought to many areas of medicine and agriculture., revolutionizing many disciplines, with human genetics, genomics and bioinformatics as direct descendants.

In applications, genetics brought about the green revolution of the twentieth century and played a major role in providing food to the humankind. Genetics, molecular biology and recombinant DNA technology shaped modern biotechnology and gave birth to the biotech industry. Genetics and genomics have provided a foundation to personalized medicine, whose goals are yet to be fully realized.

Discoveries of Mendel will still impact sciences and humans for a long time.

Now, because Mendel was not recognized by scientists, not supported by the scientific community, a natural question is: how did he obtain conditions for research?

A more obscure history was behind this question……

Notes

1)“hybridizing” in Mendel’s paper is similar to “crossing”, not the stricter modern term of hybrid.

2) Italics in this chapter were those in the original Mendel paper.

3) Mendel used“control” in the paper. For every experiment he conducted in the field, he also did it in the green house, to rule out interferences such as insects or pollen contamination.

4) Mendel used pollen cells as sperms. It is now known that each pollen contains 2 to 3 sperms, of which 2 participates in fertilization.

5) In his concluding part, Mendel stated that, after a pollen cell and an egg formed a single cell, it“assimilated and formed many new cells). Assimilation is wrong, due to limited understanding of development. All cells in an embryo result from proliferations and divisions of the fertilized egg, no other cells in the mother are assimilated into the embryo.

REFERENCES

http://www.mendelweb.org/

Corcos A and Monaghan F (1985) Role of de Vries in the recovery of Mendel's work. I. Was de Vries really an independent discoverer of Mendel? Journal of Heredity 76:187-90.

Corcos AF and Monaghan FV (1987) Correns, an independent discoverer of Mendelism? I. An historical/critical note. Journal of Heredity 78: 330.

Corcos AF, Monaghan FV and Weber MC (1993) Gregor Mendel's Experiments on Plant Hybrids: A Guided Study, Rutgers University Press.

Correns C (1905) Gregor Mendel's Briefe an Carl Nägeli 1866-1873. Ein Nachtrag zu den veröffentlichten Bastardierungsversuchen Mendels. Abh. Math.-Phys. Classe Kgl. Sächs. Ges. Wiss. 29:189-265.

Darwin C (1859) On the Origin of Species by Means of Natural Selection. John Murray, London, England.

Darwin CR (1862) On the two forms, or dimorphic condition, in the species of Primula, and on their remarkable sexual relations. Journal of the Proceedings of the Linnean Society of London (Botany) 6:77-96.

Darwin C (1868) The variation of animals and plants under domestication. John Murray, London.

Darwin CR (1876)The effects of cross and self fertilisation in the vegetable kingdom. John Murray, London.

Darwin CR (1877)The different forms of flowers on plants of the same species. John Murray, London.

Dunn LC (1965) Mendel, his work and his place in history. Proceedings of the American Philosophical Society 109:189-198.

Ellis THN, Hofer JMI, Swain MT and Van Dijk, PJ (2019) Mendel’s peacrosses: varieties, traits and statistics. Hereditas 156:33.

Fairbanks DJ (2020) Mendel and Darwin: untangling a persistent enigma. Heredity 124:263-273.

Fisher RA (1936) Has Mendel’s work been rediscovered? Annals of Science 1: 115-137.

Galton D（2009） Did Darwin read Mendel? Quarterly Journal of Medicine 102:587-589.

Gärtner CF (1849) Versuche und Beobachtungen über die Bastarderzeugung im Pflanzenreiche. K.F. Herring, Stuttgart, Germany.

Gasking EB (1959) Why was Mendel’s work ignored? Journal of Historical Ideas 20:60-84.

Giltay E (1893)Über den directen Einfluss des Pollens auf Frucht und Samenbildung. 

Goss J (1824) On the variation in the colour of peas, occasioned by cross-impregnation. Transactions of the Horticultural Society of London 5:234-236.

Hartl DL and Fairbanks DJ (2007) On the alleged falsification of Mendel’s data. Genetics 175: 975–979.

Howard JC (2009) Why didn't Darwin discover Mendel's laws? Journal of Biology 8:15.

Iltis H (1924) Gregor Johann Mendel. Leben, Werk und Wirkung. Springer, Berlin. English translation by Eden and Cedar Paul (1932), W.W. Norton & Company, Inc. New York.

Iltis A (1954) Gregor Mendel’s autobiography. Journal of Heredity 45:231-231.

Knight TA (1799) An account of some experiments on the fecundation of vegetables. Philosophical Transactions of the Royal Society 89:195-204.

Knight TA (1823) Some remarks on the supposed influence of the pollen, in cross breeding, upon the colour of the seed-coats of plants, and the qualities of their fruits. Transactions of the Horticultural Society of London 5:377-204.

Mawer S (2006) Gregor Mendel: planting the seeds of genetics. Abrams NY, Fields Museum, Chicago.

Laxton T (1866) Observations on the variations effected by crossing in the color and character of the seed of peas. Report of the International Horticultural Exhibition and Botanical Congress 156. 

Laxton T (1872) Notes on some changes and variations in the offspring of cross-fertilized peas. Journal of the Royal Horticultural Society 3:10-14.

Mendel G (1853)Über Verwüstung im Gartenrettich durch Raupen (Botys margaritalis). Verhandlungen des Zoologisch-Botanischen Vereines in Wien 2:116-118.

Mendel G (1854)Über Bruchus pisi, mitgeteilt von V. Kollar. Verhandlungen des Zoologisch-Botanischen Vereines in Wien 4:27-28.

Mendel G (1866)Versuche über Pflanzen-Hybriden. Verhandlungen des naturforschenden Vereines, Abhandlungen, Brünn 4:3-47，English translation: Experiments in Plant Hybridization in Genetics: readings from Scientific American pp. 8-17. W.H. Freeman and Company, San Francisco-USA.

Mendel G (1869)Über einige aus künstlichen Befruchtung gewonnenen Hieracium-Bastarde. Verhandlungen des Naturforschenden Vereines, Abhandlungen, Brünn 8:26–31. (English translation: ‘‘On Hieracium hybrids obtained by artificial fertilisation.’’, Bateson, W., 1902 Mendel’s Principles of Heredity: A Defense. Cambridge University Press, Cambridge, UK)

Mendel G (1950) Gregor Mendel’s Letters to Carl Nägeli. Genetics 35: 1–29. 见Gregor Mendel’s letters to Carl Nägeli (1866-1873) (Translated by Leonie Kellen Piternick and George Piternick)

http://www.esp.org/foundations/genetics/classical/holdings/m/gm-let.pdf

Monaghan F and Corcos A (1986) Tschermak: a non-discoverer of Mendelism. I. An historical note.Journal of Heredity77:468-9.

Morgan TH (1909) What are “factors” in Mendelian explanations? American Breeders Association Reports 5:365-369.

Naudin C (1856) Constatation du retour spontané des plantes hybrides du genre Primula aux types des espèces productrices.Comptes Rendus de l’Académie des Sciences 42:625.  

Naudin C (1863) Nouvelles recherches sur l’hybridité dans les végétaux. Annales des Sciences Naturelles; Botanique Fourth Series 19:180-203.

Nogler GA (2006)The lesser-known Mendel: his experiments on Hieracium. Genetics 172:1-6.

Orel V (1996)Gregor Mendel the first geneticist. Oxford University Press.

Sageret A (1826) Considérations sur la production des hybrides et des variétés en général et sur celles des Cucurbitacées en particulier. Annales des Sciences Naturelles First Seiesr 8:294-313.

Seton A (1824) On the variation in the colour of peas from cross-impregnation. Transactions of the Horticultural Society of London 5:236-238.

Van Dijk PJ and Ellis THN (2020) Mendel’s journey to Paris and London: contextand significance for the origin of genetics. Folia Mendeliana 56:5-33.

Van Dijk PJ and Ellis THN (2022) Mendel’s reaction to Darwin’s provisional hypothesis of pangenesis and the experiment that could not wait. Heredity 129:12-16.

Van Dijk PJ, Jessop AP and Ellis THN (2022) How did Mendel arrive at his discoveries? Nature Genetics 54:926-933.

Van Dijk PJ, Weissing FJ and Ellis THN (2018) How Mendel’s interest ininheritance grew out of plant improvement. Genetics 210:347-355.

Weiling F (1991) Historical study: Johan Gregor Mendel (1822-1884). American Journal of Medical Genetics 40:1-25.

Zirkle C (1934) More records of plant hybridization before Koelreuter. Journal Heredity 25:3-18.

Required Pre-Class Reading Materials：

Mendel G (1866).Versuche über Pflanzen-Hybriden. Verhandlungen des naturforschenden Vereines, Abhandlungen, Brünn 4:3-47，English translation: Experiments in Plant Hybridization in Genetics: readings from Scientific American pp. 8-17. W.H. Freeman and Company, San Francisco-USA.