📚 Year 13 Edexcel Biology: Formula & Theorem Quick Reference Handbook | A2 生物公式定理速查手册
This quick reference handbook compiles the essential formulas, equations, and key theorems required for Year 13 Edexcel Biology (A Level). From population genetics to ecosystem energetics, these quantitative tools are vital for interpreting data, solving problems, and achieving high marks in examinations. Each entry presents the formula, defines its components, and describes the context in which it is applied.
本速查手册汇编了 Year 13 爱德思 A Level 生物学所需的核心公式、方程和关键定理。从群体遗传学到生态系统能量学，这些定量工具对于解读数据、解决问题以及在考试中获得高分至关重要。每个条目都给出了公式、定义了组成部分，并说明了其应用场景。
1. Hardy-Weinberg Equilibrium | 哈迪-温伯格平衡
The Hardy-Weinberg principle states that allele and genotype frequencies in a large, randomly mating population remain constant from generation to generation in the absence of mutation, gene flow, genetic drift, and natural selection. It provides a null model against which evolutionary change can be detected.
哈迪-温伯格定律指出，在没有突变、基因流动、遗传漂变和自然选择的大群体中，等位基因和基因型频率会世代保持恒定。它提供了一个零模型，用于检测进化是否发生。
p + q = 1
p2 + 2pq + q2 = 1
p = frequency of the dominant allele; q = frequency of the recessive allele. p2 = frequency of homozygous dominant genotype; 2pq = frequency of heterozygous genotype; q2 = frequency of homozygous recessive genotype. These equations are used to calculate allele frequencies from genotype counts or to predict genotype frequencies in a population assumed to be in equilibrium.
p = 显性等位基因的频率；q = 隐性等位基因的频率。p² = 显性纯合子基因型频率；2pq = 杂合子基因型频率；q² = 隐性纯合子基因型频率。这些公式用于从基因型个体数推算等位基因频率，或预测处于平衡状态的群体的基因型频率。
2. Chi-squared (χ2) Test for Goodness of Fit | 卡方（χ²）适合度检验
The chi-squared test compares observed results with expected theoretical outcomes to determine whether any deviation is due to chance or a significant effect. It is widely used in genetics (e.g., Mendelian ratios) and ecology.
卡方检验将观测结果与理论预期值进行比较，以判断偏差是由偶然因素造成还是存在显著效应。它广泛应用于遗传学（如孟德尔比例）和生态学。
χ2 = Σ (O − E)2 ÷ E
O = observed frequency; E = expected frequency. The sum is taken over all categories. The calculated χ2 value is compared to a critical value from a chi-squared distribution table at a given probability (usually p = 0.05) and degrees of freedom (number of categories – 1). If χ2 > critical value, the null hypothesis is rejected, suggesting the difference is statistically significant.
O = 观测频数；E = 期望频数。对所有类别求和。计算出的 χ² 值与卡方分布表中给定概率（通常为 p = 0.05）和自由度（类别数 – 1）下的临界值进行比较。若 χ² > 临界值，则拒绝零假设，表明差异有统计学意义。
3. Exponential Population Growth Model | 指数种群增长模型
In an unlimited environment, a population grows exponentially. This model describes the increase in population size over time under ideal conditions with abundant resources and no limiting factors.
在无限环境中，种群呈指数增长。该模型描述了在资源充足、无限制因素的理想条件下，种群数量随时间增加的过程。
Nt = N0 ert
Nt = population size at time t; N0 = initial population size; r = intrinsic rate of natural increase (per capita growth rate); t = time; e ≈ 2.718. The differential form is dN/dt = rN. Exponential growth produces a J-shaped curve. In reality, growth becomes logistic as resources become limited and carrying capacity (K) is approached.
Nt = t 时刻种群数量；N0 = 初始种群数量；r = 内禀自然增长率（每个体的增长率）；t = 时间；e ≈ 2.718。微分形式为 dN/dt = rN。指数增长形成 J 形曲线。现实中，随着资源受限并接近环境容纳量（K），增长将转变为逻辑斯蒂增长。
4. Respiratory Quotient (RQ) | 呼吸商（RQ）
The respiratory quotient is the ratio of carbon dioxide produced to oxygen consumed during respiration. It indicates the type of respiratory substrate being metabolised.
呼吸商是呼吸过程中产生的二氧化碳与消耗的氧气的比值，可指示正在代谢的呼吸底物类型。
RQ = CO2 produced ÷ O2 consumed
Typical RQ values: carbohydrate = 1.0; lipid ≈ 0.7; protein ≈ 0.9. These values arise from the stoichiometry of full oxidation. RQ can be measured using a respirometer. A value below 1.0 suggests lipid or protein utilisation, while a value above 1.0 implies anaerobic respiration or synthesis of fat from carbohydrate.
典型的 RQ 值：碳水化合物 = 1.0；脂类 ≈ 0.7；蛋白质 ≈ 0.9。这些值源自完全氧化的化学计量比。可使用呼吸计测定 RQ。RQ 低于 1.0 表明利用脂类或蛋白质，高于 1.0 则意味着进行了无氧呼吸或由碳水化合物合成脂肪。
5. Net Primary Productivity (NPP) | 净初级生产力（NPP）
Net primary productivity represents the chemical energy stored in plant biomass after accounting for the energy used in respiration. It is the energy available to the next trophic level in a food chain.
净初级生产力表示扣除呼吸消耗的能量后，植物生物量中储存的化学能。它是食物链中可用于下一营养级的能量。
NPP = GPP − R
GPP = gross primary productivity (total energy fixed by photosynthesis); R = respiratory losses. NPP is usually expressed in units of energy per area per time (kJ m⁻² yr⁻¹) or biomass (g m⁻² yr⁻¹). Understanding NPP is fundamental to studying energy flow and efficiency in ecosystems.
GPP = 总初级生产力（光合作用固定的总能量）；R = 呼吸消耗。NPP 通常以单位面积单位时间的能量（kJ m⁻² yr⁻¹）或生物量（g m⁻² yr⁻¹）表示。理解 NPP 是研究生态系统能量流动与效率的基础。
6. Energy Transfer Efficiency Between Trophic Levels | 营养级间能量传递效率
Ecological efficiency quantifies the proportion of energy transferred from one trophic level to the next. In Edexcel specifications, efficiency is often calculated as the percentage of energy in biomass at the higher level relative to the lower level.
生态效率量化了从一个营养级传递到下一营养级的能量比例。在爱德思大纲中，效率通常计算为较高营养级生物量中的能量占较低营养级能量的百分比。
Efficiency (%) = (Energy in biomass of higher trophic level ÷ Energy in biomass of lower trophic level) × 100
Typical efficiencies range from about 5% to 20%, with much energy lost as heat through respiration, uneaten parts, and excretion. Calculating efficiency helps explain why food chains are usually short and why the biomass pyramid narrows at higher levels.
典型的传递效率介于 5% 至 20% 之间，大量能量通过呼吸、未食部分和排泄以热的形式散失。计算效率有助于解释为何食物链通常较短，以及为何生物量金字塔在高营养级收窄。
7. Cardiac Output | 心输出量
Cardiac output is the volume of blood pumped by one ventricle per minute. It is a key measure of heart performance and is regulated to meet the body’s metabolic demands.
心输出量是一个心室每分钟泵出的血液量，是衡量心脏功能的关键指标，并受到调控以满足身体的代谢需求。
Cardiac Output (CO) = Heart Rate (HR) × Stroke Volume (SV)
HR = number of heartbeats per minute; SV = volume of blood ejected per beat (typically about 70 ml at rest). Units for CO are litres per minute (L min⁻¹). During exercise, both HR and SV increase, raising cardiac output to deliver more oxygen to muscles.
HR = 每分钟心跳次数；SV = 每搏输出量（静息时通常约 70 ml）。CO 的单位为升每分钟（L min⁻¹）。运动时，心率和每搏输出量均增加，从而提高心输出量以向肌肉输送更多氧气。
8. Body Mass Index (BMI) | 身体质量指数（BMI）
BMI is a simple anthropometric measure used to classify underweight, healthy weight, overweight, and obesity in adults. It is a screening tool rather than a direct measure of body fat.
BMI 是一种简单的人体测量指标，用于将成人体重分为偏瘦、健康、超重和肥胖。它是一种筛查工具，而非直接测量体脂。
BMI = body mass (kg) ÷ height2 (m2)
For example, a person weighing 70 kg and 1.75 m tall has a BMI of 70 ÷ (1.75)2 ≈ 22.9 kg m⁻². Standard classifications: < 18.5 underweight, 18.5–24.9 normal, 25–29.9 overweight, ≥ 30 obese. Limitations include not distinguishing between muscle and fat mass.
例如，体重 70 kg、身高 1.75 m 的人 BMI = 70 ÷ (1.75)² ≈ 22.9 kg m⁻²。标准分类：< 18.5 偏瘦，18.5–24.9 正常，25–29.9 超重，≥ 30 肥胖。其局限性包括无法区分肌肉与脂肪质量。
9. Lung Volumes and Capacities | 肺容积与肺容量
Static lung volumes and capacities are measured by spirometry and describe the amount of air moved during different phases of breathing. The vital capacity is a particularly important measure of respiratory function.
静态肺容积和肺容量通过肺活量计测量，描述呼吸不同阶段移动的空气量。肺活量是衡量呼吸功能的一个特别重要的指标。
Vital Capacity (VC) = Tidal Volume (TV) + Inspiratory Reserve Volume (IRV) + Expiratory Reserve Volume (ERV)
Tidal Volume = volume of air inhaled or exhaled in a normal breath at rest. Inspiratory Reserve Volume = extra air that can be forcibly inhaled beyond tidal inhalation. Expiratory Reserve Volume = extra air that can be forcibly exhaled after tidal exhalation. Residual Volume (RV) remains in the lungs after maximal exhalation and cannot be measured by simple spirometry. Total Lung Capacity = VC + RV.
潮气量 = 静息时每次正常呼吸吸入或呼出的气体容积。补吸气量 = 在正常吸气后继续用力吸气所能吸入的额外气体容积。补呼气量 = 在正常呼气后继续用力呼气所能呼出的额外气体容积。余气量（RV）在最大呼气后仍残留于肺内，无法用简易肺活量计测出。肺总容量 = VC + RV。
10. Simpson’s Index of Diversity | 辛普森多样性指数
Simpson’s Diversity Index quantifies the biodiversity of a habitat, taking into account both species richness and evenness. A higher value indicates greater diversity and a more stable ecosystem.
辛普森多样性指数用于量化栖息地的生物多样性，同时考虑了物种丰富度和均匀度。数值越高表明多样性越高，生态系统越稳定。
D = 1 − Σ (n ÷ N)2
n = total number of organisms of a particular species; N = total number of organisms of all species. The index ranges from 0 (no diversity) to a maximum approaching 1. An alternative formulation is D = N(N − 1) / Σ n(n − 1), but the complementary form D = 1 − Σ(n/N)2 is most common in Edexcel practicals. It is used to compare different habitats or to monitor changes over time.
n = 某一物种个体总数；N = 所有物种个体总数。指数范围从 0（无多样性）到接近 1 的最大值。另一种形式为 D = N(N − 1) / Σ n(n − 1)，但互补形式 D = 1 − Σ(n/N)² 在爱德思实验中最为常用。该指数用于比较不同栖息地或监测时间变化。
11. Lincoln Index (Mark-Release-Recapture) | 林肯指数（标记-释放-重捕法）
The Lincoln Index estimates the population size of mobile organisms. It relies on capturing, marking, releasing, and then recapturing a sample and assuming that the proportion of marked individuals in the second sample reflects the proportion in the entire population.
林肯指数用于估计移动生物种群的大小。它通过捕捉、标记、释放，然后再次捕获样本，并假设第二批样本中标记个体的比例与整个群体中的比例相同来进行估算。
N = (M × C) ÷ R
N = estimated total population size; M = number of individuals captured and marked in the first sample; C = total number captured in the second sample; R = number of marked individuals recaptured in the second sample. Assumptions include: marks are not lost, marked individuals mix randomly, no immigration/emigration or births/deaths between samples, and capture probability remains equal. This method is widely used for estimating animal populations like woodlice or snails.
N = 估计的总种群数量；M = 第一次捕获并标记的个体数；C = 第二次捕获的总个体数；R = 第二次捕获中带有标记的个体数。假设条件包括：标记不脱落、标记个体随机混入、两次采样期间无迁入迁出或生死变化、且捕获概率保持均等。该方法广泛用于估计鼠妇或蜗牛等动物种群。
12. Magnification Formula | 放大率公式
Magnification relates the size of an image to the actual size of the object. It is fundamental in microscopy and biological drawings to express the degree of enlargement.
放大率将图像大小与物体的实际大小联系起来。它是显微技术和生物绘图中的基础概念，用于表达放大的程度。
Magnification = Image size ÷ Actual size
Both image size and actual size must be in the same units. For example, if a cell’s actual diameter is 50 μm and its image under a microscope measures 5 mm (5000 μm), the magnification is 5000 ÷ 50 = 100×. Rearranging the formula allows calculation of any unknown component. It is essential to convert all measurements to the same unit (often μm or mm) before applying the formula.
图像大小和实际大小必须使用相同单位。例如，某细胞的实际直径为 50 μm，显微镜下图像直径为 5 mm（5000 μm），则放大率为 5000 ÷ 50 = 100×。通过重新排列公式，可计算任意未知量。务必先将所有测量值换算为相同单位（通常为 μm 或 mm），再代入公式。
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