Colony fitness increases in the honey bee at queen mating frequencies higher than genetic diversity asymptote

Queens and inseminations We performed an experiment near Athens, Georgia consisting of four treatments in a 2x2 factorial arrangement with two levels of genetic Varroa resistance (semen from VSH-selected drones or non-selected wild type drones) and two levels of polyandry (high or low). There was one dedicated research apiary in which all treatments were represented. Each colony consisted of a 5-frame Langstroth nucleus hive and was started with one 2-lb (0.9-kg) package of worker bees from one supplier practicing a common V. destructor treatment regimen, thus normalizing incipient parasite levels across the experiment. Colonies were arranged in one large circle at the apiary to minimize effects of bee and parasite drift (Dynes et al. 2019a). The experiment was set up in Apr 2018 and ran until Nov 2018. The year before, we made up two sets of dedicated drone-source colonies for future inseminations, one set headed by wild type unselected queens and the other headed by queens from the VSH line. In spring of 2018, we reared one wild type virgin queen and inseminated her with one wild type male. This single-drone inseminated queen was used to rear supersister virgin daughters who were subsequently inseminated and used in the experiment. This procedure minimizes maternal variation in experimental colonies (Harbo 1985). Supersister virgins were each randomly assigned one of four treatments in the 2x2 design: (1) VSH semen/low polyandry, (2) VSH semen/high polyandry, (3) wild type semen/low polyandry, or (4) wild type semen/high polyandry. We had nine strong VSH drone-source colonies come out of winter, a number that dictated the multiples for our polyandry ranges. For our low polyandry treatment, we inseminated each supersister virgin with one male from each of the VSH drone source colonies (mo=9), and for our high polyandry treatment each queen was inseminated with 6 males from each VSH drone source colony (mo=54). Supersister virgins in the wild type treatments similarly received one drone from each of 9 wild type drone source colonies (mo=9) or 6 from each wild type source colony (mo=54). Each virgin queen was emerged and housed in her 5-frame nucleus colony before and after the artificial insemination (AI) procedure, following methods of Cobey et al. (2013). Semen from 9 or 54 males, as per protocol, was collected into one common capillary tube. A different tube was used for each prescribed polyandry/genetic line; no contamination across treatments was possible. However, more than one queen was inseminated from any given tube. The volume of semen in each tube was increased by 15% with physiological saline (recipe 2.2.1 in Cobey et al. (2013)), thoroughly mixed in an Eppendorf tube to encourage a homogeneous drone representation per batch, re-drawn into the capillary tube, then used to inseminate 2-20 queens at an average dose of 4 μL mixed semen each, thus removing effects of semen volume (Niño et al. 2012). Queens were narcotized three times with CO2 – once on the day of insemination and once on each of two successive days thereafter; CO2 narcosis stimulates egg laying (Mackensen and Roberts 1948). Experimental queens were housed in their home 5-frame nuclei and observed until all competent egg layers were identified. We waited six weeks thereafter to allow worker populations to turn over to progeny of the experimental queens. Dependent variables Colonies were sampled at each of four time points (Jul, Aug, Sep, Nov). We sampled colonies to determine brood production, brood survival, Varroa mite levels, and adult bee populations. Brood production and worker bee population were derived by visually summing proportions of whole deep frames covered by brood or workers (Delaplane et al. 2013), converting frames of brood to cm2 by the observation that one deep Langstroth comb (both sides) = 1760 cm2, and converting frames of adult bees to bee populations with the regression model of Burgett and Burikam (1985). When necessary, we converted cm2 brood to cells of brood with the conversion of 3.8 cells per cm2 (Delaplane et al. 2013). Brood survival was measured by removing a comb of open brood, laying over it a sheet of transparent acetate, using a felt-tip permanent marker to mark the location of 100 brood cells each containing a 1st or 2nd instar larva, then returning the comb to the hive; three days later the comb was retrieved, the same acetate laid on top of it, and the number of surviving brood cells recorded. Relative Varroa mite numbers are derived by inserting sticky sampling sheets into bottom board hive inserts and recording the number of Varroa mites trapped after 24 hours (Dietemann et al. 2013). Patriline determination As a check on our success at creating two discrete classes of polyandry with AI, we were able to genotype workers from 18 colonies to determine effective realized paternity (me) in both polyandry classes. A 50-worker sample was taken from each of 8 colonies in the mo=9 polyandry class and 10 colonies in the mo=54 polyandry class. DNA was extracted from the right hind leg for all honey bee specimens using a Qiagen DNeasy Blood & Tissue Kit. Hind legs were thoroughly pulverized with micro-scissors and digested with proteinase K in a 56°C water bath for 3 hours with sample agitation every hour. Extracted DNA was stored at -80°C until microsatellite amplification. Ten variable microsatellite loci were screened for all samples using two multiplexes: Plex 1 and Plex 2. Plex 1 included loci A107, A113, AP043, A024, and A006; Plex 2 included loci A28, A88, AP66, AP81, and B124 (Shaibi et al. 2008; Delaney et al. 2009). Both plexes were amplified for one cycle at 95°C for 7 min, 30 cycles of 95°C for 30 sec, 54°C for 30 sec, 72°C for 30 sec, and a final extension at 72°C for 60 min. A 10 μL final reaction volume containing 5 μL of PCR Master Mix (Promega, Madison, WI), 1.0-2.5 μL of fluorescent dye-labeled primer, 0.9 μL of nuclease-free water, and 2 μL of DNA extract per sample was analyzed at the University of Delaware Sequencing and Genotyping Center at the Delaware Biotechnology Institute with an Applied Biosystems 3130 XL Genetic Analyzer via capillary electrophoresis. Microsatellite repeat sizes were scored using Geneious Prime® 2020.0.5 software (Biomatters Ltd). The number (N0) and frequency (pi) of full sibling patrilines was determined using raw microsatellite data in the software program COLONY 2.0.6.5 (Jones and Wang 2010). The observed patriline number (N0), proportion of each patriline within each sample (pi), and number of worker bees in each respective sample (n) were used to calculate me after (Nielsen et al. 2003; Tarpy et al. 2015): m_e=((〖n-1)〗^2)/(∑_(i=1)^(N_0)▒〖p_i^2 (n+1)(n-2)+3-n〗)

蜂王与人工授精
本实验于佐治亚州雅典附近开展，采用2×2因子设计设置4种处理，包含两个因素：瓦螨抗性遗传水平（VSH<瓦螨敏感卫生，Varroa Sensitive Hygiene>选育雄蜂的精液，或未选育的野生型雄蜂精液）与一妻多夫程度（高水平或低水平）。实验依托一处专用养蜂场开展，场内设置全部处理组。每个实验蜂群为5框朗氏核群（Langstroth nucleus hive），由单一供应商提供的2磅（0.9kg）工蜂蜂包组建，该供应商采用统一的瓦螨（Varroa destructor）防治方案，以此标准化实验初始寄生螨水平。所有蜂群在养蜂场内按大型圆周排列，以降低蜜蜂与寄生螨的漂移效应（Dynes et al. 2019a）。实验于2018年4月启动，持续至同年11月。

实验前一年（2017年），我们构建了两组专用雄蜂种群以用于后续人工授精：一组由未选育的野生型蜂王主导，另一组由VSH品系蜂王主导。2018年春季，我们培育1只野生型处女王，并以1只野生型雄蜂对其实施单雄人工授精。该单雄授精蜂王用于繁育超同胞处女王，后续这些超同胞处女王均接受人工授精并用于本实验，该操作可最小化实验蜂群的母本变异（Harbo 1985）。

超同胞处女王被随机分配至2×2设计的4种处理组中：(1) VSH精液/低一妻多夫，(2) VSH精液/高一妻多夫，(3) 野生型精液/低一妻多夫，(4) 野生型精液/高一妻多夫。越冬后共有9群健壮的VSH雄蜂源蜂群，该数量决定了一妻多夫分组的倍数。低一妻多夫处理组中，每只超同胞处女王接受来自每个VSH雄蜂源群的1只雄蜂精液（总雄蜂数mo=9）；高一妻多夫处理组中，每只蜂王接受来自每个VSH雄蜂源群的6只雄蜂精液（总雄蜂数mo=54）。野生型处理组同理：低一妻多夫组接受来自9个野生型雄蜂源群的各1只雄蜂（mo=9），高一妻多夫组接受来自每个野生型雄蜂源群的6只雄蜂（mo=54）。

在人工授精（AI）操作前后，每只处女王均饲养于其所属的5框核群中，实验方法参考Cobey等（2013）的规程。按实验规程，将9或54只雄蜂的精液收集至同一毛细管中，不同处理组使用不同的毛细管，以避免交叉污染，但同一毛细管可用于授精多只蜂王。使用生理盐水将每份精液的体积增加15%（配方见Cobey等2013的2.2.1节），在微量离心管中充分混匀以确保每批精液中雄蜂的代表性均一，随后将混匀后的精液重新吸入毛细管，以每只蜂王平均4μL混合精液的剂量进行授精，以此消除精液体积带来的影响（Niño et al. 2012）。

使用二氧化碳对蜂王实施三次麻醉：授精当日1次，术后连续两日各1次；二氧化碳麻醉可刺激蜂王产卵（Mackensen and Roberts 1948）。实验蜂王饲养于其所属的5框核群中，直至确认所有可正常产卵的蜂王均已建立种群。随后我们等待6周，以使工蜂种群完全更替为实验蜂王的后代。

### 因变量测量
我们于4个时间点（7月、8月、9月、11月）对蜂群进行采样，以检测幼虫繁育量、幼虫存活率、瓦螨数量与成蜂种群数量。
幼虫繁育量与工蜂种群数量通过目测估算满框幼虫或工蜂所占比例（Delaplane et al. 2013）：将朗氏深框幼虫面积转换为平方厘米，已知1个朗氏深框（两面）的面积为1760 cm²；将成蜂框数转换为蜂群种群数量则采用Burgett与Burikam（1985）的回归模型。必要时，可通过每平方厘米3.8个巢房的换算系数，将幼虫面积转换为幼虫巢房数（Delaplane et al. 2013）。
幼虫存活率的测量方法为：取出1块开放式幼虫巢脾，覆盖透明醋酸纤维膜，使用油性记号笔标记100个包含1龄或2龄幼虫的巢房，随后将巢脾放回蜂箱；3天后取回巢脾，再次覆盖醋酸纤维膜，记录存活的幼虫巢房数量。
相对瓦螨数量通过以下方法获得：在蜂箱底板插入粘虫采样板，24小时后记录捕获的瓦螨数量（Dietemann et al. 2013）。

### 父系确定
为验证我们通过人工授精构建两类离散一妻多夫组的成功率，我们对18个蜂群的工蜂进行基因分型，以计算两类一妻多夫组的有效实际父系数（me）。我们从mo=9一妻多夫组的8个蜂群与mo=54一妻多夫组的10个蜂群中各采集50只工蜂样本。
使用Qiagen DNeasy血液与组织试剂盒从所有蜜蜂样本的右后足提取DNA：将后足用显微剪刀充分剪碎，加入蛋白酶K后于56℃水浴消化3小时，期间每小时振摇样本一次。提取得到的DNA保存于-80℃，直至微卫星扩增步骤。
使用两个多重PCR（聚合酶链式反应）扩增体系对所有样本的10个多态微卫星（microsatellite）位点进行筛选：Plex 1包含位点A107、A113、AP043、A024与A006；Plex 2包含位点A28、A88、AP66、AP81与B124（Shaibi et al. 2008; Delaney et al. 2009）。
扩增程序为：95℃预变性7分钟，30个循环（95℃变性30秒、54℃退火30秒、72℃延伸30秒），最后于72℃终延伸60分钟。反应体系总体积为10μL，包含5μL PCR预混液（Promega，威斯康星州麦迪逊市）、1.0~2.5μL荧光标记引物、0.9μL无核酸酶水与2μL DNA提取物。样本在特拉华大学生物技术研究所的测序与基因分型中心，通过Applied Biosystems 3130 XL遗传分析仪进行毛细管电泳检测。
使用Geneious Prime® 2020.0.5软件（Biomatters Ltd）对微卫星重复片段的大小进行评分。使用软件COLONY 2.0.6.5（Jones and Wang 2010）的原始微卫星数据，计算全同胞父系的数量（N0）与频率（pi）。
基于Nielsen等（2003）与Tarpy等（2015）的方法，利用观测得到的父系数量（N0）、每个父系在样本中的占比（pi）以及每个样本的工蜂数量（n），计算有效实际父系数me：
$$m_e = frac{(n-1)^2}{sum_{i=1}^{N_0} p_i^2 (n+1)(n-2) + 3 - n}$$