📚 AQA Year 13 Biology Formula & Theorem Quick Reference | AQA Year 13 生物：公式定理速查手册
Welcome to the ultimate quick-reference guide for AQA Year 13 Biology. This handbook compiles the essential formulae, statistical tests, and physiological equations that you must master for examinations. Each entry provides a clear statement of the principle, its formula in Unicode symbols, the conditions for use, and worked application tips. Keep this printable resource at hand when tackling data-handling questions, required practicals, and synoptic essays.
欢迎使用 AQA Year 13 生物终极速查手册。本手册汇集了考试必须掌握的核心公式、统计检验和生理学方程。每个条目都清晰给出了原理陈述、使用 Unicode 符号书写的公式、使用条件以及应用技巧。在处理数据分析题、必修实验和综合性论述时，请将这份可打印资源放在手边。
1. Hardy-Weinberg Principle | 哈迪-温伯格定律
The Hardy-Weinberg principle predicts the allele and genotype frequencies in a large, randomly mating population when no evolutionary forces are acting. It provides a null model for detecting evolutionary change. If observed genotype frequencies deviate significantly from expectations, one or more assumptions are likely violated.
哈迪-温伯格定律可预测一个大型、随机交配且无进化力作用的种群中的等位基因和基因型频率。它提供了检测进化变化的零假设模型。如果观察到的基因型频率与预期显著偏离，则很可能违反了一个或多个假设。
p + q = 1
p² + 2pq + q² = 1
Here p is the frequency of the dominant allele, q is the frequency of the recessive allele. The genotype frequencies are: homozygous dominant (p²), heterozygous (2pq), and homozygous recessive (q²). The five assumptions are: no mutation, random mating, no gene flow (migration), infinite population size (no genetic drift), and no natural selection.
其中 p 是显性等位基因的频率，q 是隐性等位基因的频率。基因型频率为：纯合显性 (p²)、杂合 (2pq) 和纯合隐性 (q²)。五个假设为：无突变、随机交配、无基因流动 (迁移)、无限大种群 (无遗传漂变) 以及无自然选择。
To calculate allele frequencies from observable phenotypes, first find q² from the frequency of homozygous recessives, then take q = √(q²). From p = 1 – q you can determine the frequency of carriers (2pq). This is widely used in screening for genetic disorders such as cystic fibrosis.
要根据可观察的表型计算等位基因频率，先从纯合隐性的频率中得出 q²，然后取 q = √(q²)。通过 p = 1 – q 即可确定携带者频率 (2pq)。这被广泛用于囊性纤维化等遗传疾病的筛查中。
2. Chi-squared Test | 卡方检验
The chi-squared (χ²) test is used to determine whether there is a significant association between categorical variables (tests of independence) or whether observed frequency data fit a theoretical distribution (goodness-of-fit). In AQA Biology, it is commonly applied to genetics crosses and ecological quadrat data.
卡方 (χ²) 检验用于确定类别变量之间是否存在显著关联 (独立性检验)，或者观察到的频率数据是否符合理论分布 (适合度检验)。在 AQA 生物中，它通常应用于遗传杂交和生态样方数据。
χ² = ∑ (O − E)² / E
O is the observed frequency, E is the expected frequency, and ∑ denotes summation over all categories. The expected values are calculated based on the null hypothesis (e.g. Mendelian ratios or equal distribution). The degrees of freedom (df) for goodness-of-fit is (number of categories – 1); for contingency tables it is (rows – 1) × (columns – 1).
O 为观察频率，E 为预期频率，∑ 表示对所有类别求和。预期值基于零假设计算 (例如孟德尔比率或均匀分布)。适合度检验的自由度 (df) 为 (类别数 – 1)；对于列联表，为 (行数 – 1) × (列数 – 1)。
Compare the calculated χ² value with the critical value from a χ² table at a chosen significance level (usually p = 0.05) and the appropriate degrees of freedom. If χ² is larger than the critical value, reject the null hypothesis; the difference is statistically significant and not due to chance alone.
将计算出的 χ² 值与 χ² 表中的临界值进行比较，需指定显著性水平 (通常为 p = 0.05) 和相应的自由度。如果 χ² 大于临界值，则拒绝零假设；差异具有统计学意义，并非仅由偶然因素导致。
3. Student’s t-test | 学生 t 检验
The independent (unpaired) Student’s t-test is used to compare the means of two sets of continuous, normally distributed data to determine if they are significantly different from each other. It is ideal for analysing practical results such as the effect of a treatment on plant growth or enzyme activity.
独立 (非配对) 学生 t 检验用于比较两组连续、正态分布数据的均值，判断它们之间是否存在显著差异。它非常适合于分析实验结果，例如某种处理对植物生长或酶活性的影响。
t = (x̄₁ − x̄₂) / √(s₁²/n₁ + s₂²/n₂)
x̄₁ and x̄₂ are the sample means, s₁² and s₂² are the sample variances, and n₁ and n₂ are the sample sizes. The denominator represents the standard error of the difference between means. The number of degrees of freedom is approximately (n₁ + n₂ − 2).
x̄₁ 和 x̄₂ 为样本均值，s₁² 和 s₂² 为样本方差，n₁ 和 n₂ 为样本量。分母表示均值差的标准误。自由度近似为 (n₁ + n₂ − 2)。
Assumptions: data must be normally distributed, variance should be roughly equal (homoscedasticity), and measurements must be independent. In AQA papers, you are often asked to give a null hypothesis, calculate t, and interpret the result using a t-table. If calculated |t| exceeds the critical value, the difference between means is statistically significant at that confidence level.
假设条件：数据必须呈正态分布，方差应大致相等 (方差齐性)，且测量值相互独立。在 AQA 试卷中，常要求你给出零假设、计算 t 值，并使用 t 表解释结果。若计算出的 |t| 超过临界值，则均值间的差异在该置信水平上具有统计学意义。
4. Spearman’s Rank Correlation Coefficient | 斯皮尔曼等级相关系数
Spearman’s rank correlation (rₛ) tests the strength and direction of the association between two variables when data are not normally distributed or are ordinal. It is frequently used in ecology to examine relationships, e.g. light intensity and daisy abundance.
斯皮尔曼等级相关系数 (rₛ) 用于检验两个变量之间关联的强度和方向，适用于数据不呈正态分布或为顺序数据的情况。它在生态学中常用来研究关系，例如光照强度与雏菊丰度的关系。
rₛ = 1 − (6∑d²) / (n (n² − 1))
Here d is the difference between the ranks of each pair of observations, and n is the number of paired data points. The value of rₛ ranges from –1 (perfect negative correlation) to +1 (perfect positive correlation). A value near 0 indicates no correlation.
其中 d 为每对观测值的秩次差，n 为成对数据点的数量。rₛ 的范围从 –1 (完全负相关) 到 +1 (完全正相关)。接近 0 的值表示无相关性。
Proceed by ranking each variable separately, calculating the difference in ranks d, squaring them, and summing. The critical value of rₛ for a given n is obtained from a Spearman’s rank table at a chosen probability level. If your calculated rₛ is greater than or equal to the critical value, the correlation is statistically significant.
计算步骤为：分别对每个变量排序，计算秩次差 d，求平方并求和。在给定 n 下，rₛ 的临界值可从斯皮尔曼等级相关系数表中查得，指定概率水平。若你计算的 rₛ 大于或等于临界值，则该相关具有统计学意义。
5. Mark-Release-Recapture (Lincoln Index) | 标记重捕法 (林肯指数)
The mark-release-recapture method estimates the population size of mobile animals. A sample is caught, marked harmlessly, and released. After time has elapsed for mixing, a second sample is captured and the proportion of marked individuals is recorded.
标记重捕法用于估算可移动动物的种群大小。先捕获一批个体，进行无害标记并释放。待标记个体充分混合后，再捕获第二批样本，记录其中已标记个体的比例。
N = (M × C) / R
N is the estimated total population size, M is the number of individuals marked and released in the first sample, C is the total number captured in the second sample, and R is the number of marked individuals recaptured in the second sample.
N 为估计种群总量，M 为第一次样本中标记并释放的个体数，C 为第二次样本中捕获的总数，R 为第二次样本中重捕到的标记个体数。
Assumptions include: marks are not lost, marking does not affect survival or behaviour, marked individuals mix randomly with the rest of the population, and no births, deaths, immigration, or emigration occur between samples. In AQA investigations, this technique often links to data evaluation and limitations of the Lincoln Index.
假设条件包括：标记不脱落，标记不影响生存或行为，标记个体与种群其余个体随机混合，且在两次取样之间没有出生、死亡、迁入或迁出。在 AQA 探究活动中，该技术常与数据评估及林肯指数的局限性相联系。
6. Net Primary Productivity (NPP) | 净初级生产力 (NPP)
Net primary productivity is the rate at which energy is incorporated into biomass by producers (plants) and is available to the next trophic level. It accounts for the energy lost through plant respiration.
净初级生产力是生产者 (植物) 将能量固定在生物量中，并可供下一营养级利用的速率。它扣除了植物呼吸作用损失的能量。
NPP = GPP − R
GPP is gross primary productivity (the total rate of photosynthesis), and R is the rate of respiratory losses. NPP is typically expressed in energy per unit area per year (kJ m⁻² yr⁻¹) or in terms of dry biomass. This equation is central to energy flow diagrams and productivity calculations in AQA topic 5 (Energy transfers).
GPP 为总初级生产力 (光合作用总速率)，R 为呼吸损失速率。NPP 通常以单位面积年能量 (kJ m⁻² yr⁻¹) 或干生物量表示。该方程是 AQA 专题 5 (能量传递) 中能量流图和生产力计算的核心。
When solving problems, ensure you convert units consistently. For example, if GPP and R are given in kJ m⁻² day⁻¹, NPP is their difference in the same units. NPP represents the energy truly available to herbivores and decomposers.
解题时，确保单位转换一致。例如，若 GPP 和 R 以 kJ m⁻² day⁻¹ 给出，NPP 则为两者的差值 (单位相同)。NPP 代表着真正可供食草动物和分解者利用的能量。
7. Ecological Efficiency | 生态效率
Ecological efficiency describes the percentage of energy transferred from one trophic level to the next. In most ecosystems, this efficiency is around 10%, which explains why food chains rarely exceed four or five trophic levels.
生态效率描述了能量从一个营养级传递到下一营养级的百分比。在大多数生态系统中，该效率约为 10%，这解释了食物链很少超过四到五个营养级的原因。
Efficiency (%) = (Energy available after transfer / Energy available before transfer) × 100
Alternatively, you can use biomass (dry mass) per given area or volume. Energy is lost between trophic levels because of respiration, excretion, egestion, and uneaten parts. Calculations often require you to extract numbers from food webs or pyramids of energy.
或者，你可以使用单位面积或体积内的生物量 (干质量)。能量在营养级之间会因呼吸、排泄、排遗以及未被取食的部分而损失。计算时常需要你从食物网或能量金字塔中提取数据。
Working systematically: identify the energy input and output for the target trophic levels, apply the formula, and express the answer to an appropriate number of significant figures. Less efficient transfers result in lower biomass at higher levels.
系统性地解题：确定目标营养级的能量输入和输出，应用公式，并以合适有效数字给出答案。效率越低，较高营养级的生物量就越小。
8. Respiratory Quotient (RQ) | 呼吸商 (RQ)
The respiratory quotient indicates the type of respiratory substrate being oxidised. It is the ratio of the volume of carbon dioxide produced to the volume of oxygen consumed during respiration over a given time.
呼吸商指示了被氧化的呼吸底物类型。它是一定时间内呼吸作用产生二氧化碳的体积与消耗氧气的体积之比。
RQ = CO₂ produced / O₂ consumed
Typical RQ values: carbohydrates = 1.0, lipids ≈ 0.7, proteins ≈ 0.9. A value above 1.0 may indicate anaerobic respiration. Respiration of organic acids can also yield RQ > 1.0. This is often measured using a respirometer in practical 9 (Investigation into respiration rates).
典型 RQ 值：碳水化合物 = 1.0，脂类 ≈ 0.7，蛋白质 ≈ 0.9。高于 1.0 的值可能指示无氧呼吸。有机酸的呼吸作用也可使 RQ > 1.0。这常用呼吸计在实验 9 (探究呼吸速率) 中测量。
To calculate RQ, the respirometer must be set up to measure the change in volume due to CO₂ and O₂. By using a CO₂ absorbent (e.g. potassium hydroxide), you can determine O₂ consumption. Subtracting runs with and without absorbant provides the CO₂ produced and RQ.
要计算 RQ，需设置呼吸计来测量由 CO₂ 和 O₂ 引起的体积变化。通过使用 CO₂ 吸收剂 (如氢氧化钾)，可测定 O₂ 消耗量。将有无吸收剂的实验数据相减，即可得到 CO₂ 生成量和 RQ。
9. Magnification and Actual Size
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