📚 Year 13 AQA Biology Quick Reference: Formulas and Principles | Year 13 AQA 生物：公式定理速查手册
This compact handbook gathers every key equation, formula and principle you are expected to use in Year 13 AQA Biology. It covers population genetics, statistical tests, ecological sampling, energy budgets, physiological calculations and more—so you can quickly check the relationships, symbols and applications before your exams.
这本简洁的手册汇集了 Year 13 AQA 生物中所有你需要掌握的关键方程、公式和原理。内容涵盖群体遗传学、统计检验、生态采样、能量收支、生理计算等方面，让你在考前可以快速查阅各关系式、符号和实际应用。
1. Hardy-Weinberg Principle and Equations | 哈迪-温伯格原理与方程
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 evolutionary influences.
哈迪-温伯格原理指出，在一个不受进化因素影响的大群体中，如果随机交配，等位基因频率和基因型频率将在世代间保持恒定。
The two fundamental equations are:
两个基本方程为：
p + q = 1
where p is the frequency of the dominant allele, and q is the frequency of the recessive allele.
其中 p 为显性等位基因的频率，q 为隐性等位基因的频率。
p² + 2pq + q² = 1
where p² is the frequency of the homozygous dominant genotype, 2pq is the frequency of the heterozygous genotype, and q² is the frequency of the homozygous recessive genotype.
其中 p² 为纯合显性基因型频率，2pq 为杂合基因型频率，q² 为纯合隐性基因型频率。
The gene pool must satisfy five conditions for the principle to hold: no mutation, random mating, no gene flow, large population size (to avoid genetic drift) and no natural selection.
基因库必须满足五个条件才能使原理成立：无突变、随机交配、无基因流动、大群体（避免遗传漂变）以及无自然选择。
If any condition is violated, evolution may occur, and the Hardy-Weinberg equations can be used to test whether a population is evolving at a particular locus.
如果任一条件被打破，就可能发生进化；我们可以用哈迪-温伯格方程检验群体在某个基因座上是否正在进化。
2. Chi-squared Test (χ²) | 卡方检验 (χ²)
The chi-squared test is used to determine whether there is a significant difference between observed and expected frequencies in categorical data, such as phenotypic ratios in genetic crosses.
卡方检验用于判断分类数据（如遗传杂交中的表型比例）的观察值与期望值之间是否存在显著差异。
The test statistic is calculated as:
检验统计量按下式计算：
χ² = Σ (O − E)² / E
where O is the observed frequency, E is the expected frequency, and the sum is taken over all categories.
其中 O 为观察频率，E 为期望频率，求和遍及所有类别。
The number of degrees of freedom is (number of categories − 1), or, for a genetic cross with expected ratios, the number of phenotypic classes minus one.
自由度为 (类别数 − 1)，对于具有期望比例的遗传杂交，即为表型类别数减一。
The null hypothesis states that there is no significant difference between observed and expected results. The calculated χ² is compared with a critical value at a chosen probability (usually p = 0.05).
零假设为观察值与期望值之间无显著差异。计算得到的 χ² 值与选定概率（通常 p = 0.05）下的临界值进行比较。
If χ² exceeds the critical value, the null hypothesis is rejected and the difference is considered significant.
若 χ² 大于临界值，则拒绝零假设，认为差异显著。
3. Student’s t-test | 学生 t 检验
The Student’s t-test compares the means of two independent samples to decide whether they came from the same population (null hypothesis) or whether there is a significant difference between them.
学生 t 检验用于比较两个独立样本的平均值，以判断它们是否来自同一总体（零假设），还是存在显著差异。
For unpaired data, the t-statistic is given by:
对于非配对数据，t 统计量由下式给出：
t = (mean₁ − mean₂) / √(s₁²/n₁ + s₂²/n₂)
where mean₁ and mean₂ are the sample means, s₁² and s₂² are the sample variances, and n₁ and n₂ are the sample sizes.
其中 mean₁ 和 mean₂ 为样本均值，s₁² 和 s₂² 为样本方差，n₁ 和 n₂ 为样本量。
The degrees of freedom are (n₁ + n₂ − 2). The calculated t is compared with the critical t-value at a 5% significance level.
自由度为 (n₁ + n₂ − 2)。计算得到的 t 值与 5% 显著性水平下的临界 t 值比较。
If the calculated t exceeds the critical value, the null hypothesis is rejected and the means are significantly different.
如果计算的 t 值超过临界值，则拒绝零假设，认为两均值存在显著差异。
4. Mark-Release-Recapture | 标记-释放-重捕法
The mark-release-recapture method estimates the size of a mobile animal population. It assumes that marked individuals mix randomly and that no significant births, deaths or migrations occur between samples.
标记-释放-重捕法用于估计移动动物种群的大小。其假设为标记个体随机混合，且在两次取样之间没有显著的出生、死亡或迁入迁出。
The population estimate (N) is calculated as:
种群数量估计值 (N) 按下式计算：
N = (M × C) / R
where M is the number of individuals caught and marked in the first sample, C is the total number caught in the second sample, and R is the number of marked individuals recaptured in the second sample.
其中 M 为第一次捕捉并标记的个体数，C 为第二次捕捉的总个体数，R 为第二次捕捉中重捕到的标记个体数。
The technique is most reliable when the population is closed and the marks are not lost or overlooked.
当种群为封闭种群且标记不会丢失或不被遗漏时，该方法最为可靠。
5. Simpson’s Index of Diversity | 辛普森多样性指数
Simpson’s Index of Diversity (D) quantifies the biodiversity of a habitat, taking into account both the number of species (species richness) and the evenness of their abundances.
辛普森多样性指数 (D) 量化一个栖息地的生物多样性，同时考虑物种数（物种丰富度）和各物种个体数的均匀度。
The index is calculated using the formula:
该指数用下列公式计算：
D = N(N − 1) / Σ n(n − 1)
where N is the total number of organisms of all species, and n is the total number of organisms of a particular species. The summation runs over every species present.
其中 N 为所有物种的个体总数，n 为某一特定物种的个体数。求和遍及所有现存物种。
A higher value of D indicates greater diversity. The index can be used to compare habitats or to monitor the impact of environmental change.
D 值越高代表多样性越大。该指数可用于比较不同栖息地，或监测环境变化的影响。
Complementary measures such as species richness and percentage cover give a fuller picture of community structure.
物种丰富度、百分比覆盖度等补充指标可以更全面地反映群落结构。
6. Net Primary Production and Energy Efficiency | 净初级生产量与能量效率
In a plant community, gross primary production (GPP) is the total chemical energy fixed by photosynthesis per unit area per unit time.
在植物群落中，总初级生产量 (GPP) 是单位时间、单位面积内光合作用固定的总化学能量。
Net primary production (NPP) is the energy that remains after plants have met their own respiratory needs:
净初级生产量 (NPP) 是植物满足自身呼吸消耗后剩余的能量：
NPP = GPP − R
where R represents respiratory losses. NPP is the energy available to the next trophic level (primary consumers).
其中 R 代表呼吸消耗。NPP 是可供下一营养级（初级消费者）利用的能量。
For consumers, net production (N) is given by:
对于消费者，净生产量 (N) 表示为：
N = I − (F + R)
where I is the ingested chemical energy, F is the energy lost in faeces, and R is the respiratory loss.
其中 I 为摄入的化学能量，F 为粪便中丢失的能量，R 为呼吸消耗。
The efficiency of energy transfer between trophic levels is calculated as:
营养级间能量传递效率按下式计算：
Efficiency (%) = (energy available after transfer / energy available before transfer) × 100
Typically, efficiencies are low (often around 10%) because much energy is lost as heat through respiration, uneaten parts and excretion.
通常传输效率很低（经常在 10% 左右），因为大量能量通过呼吸作用以热的形式散失，或以未食用部分和排泄物的形式损失。
7. Respiratory Quotient (RQ) | 呼吸商 (RQ)
The respiratory quotient is the ratio of the volume of carbon dioxide produced to the volume of oxygen consumed during respiration. It provides information about the respiratory substrate being used.
呼吸商是呼吸作用中产生二氧化碳体积与消耗氧气体积的比值。它能提供所用呼吸底物的信息。
RQ = CO₂ produced / O₂ consumed
For glucose, the complete oxidation gives RQ = 1.0; for lipids the RQ is around 0.7; for proteins it is approximately 0.9.
葡萄糖完全氧化的 RQ = 1.0；脂类的 RQ 约为 0.7；蛋白质的 RQ 约为 0.9。
RQ values can be determined using a respirometer. When the value deviates from the expected range for a pure substrate, it suggests a mixture of substrates is being respired.
RQ 值可用呼吸计测定。若数值偏离单一底物的预期范围，则表明有混合底物在被氧化。
Knowing the RQ also helps calculate metabolic rate and interpret energy expenditure in organisms under different conditions.
了解 RQ 还有助于计算机体的代谢率并解释不同条件下能量消耗的差异。
8. Cardiac Output | 心输出量
Cardiac output is the volume of blood pumped by one ventricle of the heart per minute. It is a key indicator of the
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