📚 Honors Biology Final — Study Hub
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🗂️ Your Resources
Sat / Sun / Mon checklist with interactive checkboxes and progress tracking.
★ Start herePunch in answers, get an instant grade + personalized study plan.
Interactive graderAll 10 topics condensed with reveal-answer self-tests.
Topic summary199 cards. Hide/reveal answers, star cards, filter by topic, shuffle.
Active recallFocused walkthroughs with worked examples and practice problems for every topic. Pick the one you need.
Topic-specific🎯 Top 10 Highest-Yield Facts
If you only have 5 minutes before the exam:
- AUG = start codon; UAA / UAG / UGA = stop
- Transcription → nucleus; Translation → ribosome
- Crossing over happens in Prophase I of meiosis
- Producers = most energy; 10% transfers up each trophic level
- DNA similarity = best evidence for common ancestry
- Mutation = source of new genetic variation
- q² = % showing recessive trait (Hardy-Weinberg starting move)
- Sex-linked recessive = more common in males (only 1 X)
- Carrier = heterozygous (Bb), doesn't show recessive trait
- Bb × Bb = 3:1 dominant:recessive ratio
- 70% of your study time = testing yourself, not rereading
- Spaced over 3 days beats one big cramming session
- Sleep is part of the plan — memory consolidates overnight
- Top 3 weak topics from the practice test = where you spend most of Sunday
- Say flashcard answers OUT LOUD before clicking reveal
📅 3-Day Study Plan
Saturday → Sunday → Monday. Check off tasks as you go.
🎯 Guiding Principles
- Test yourself FIRST, then check.
- Write down what you missed. Build a "weak list."
- Sleep is non-negotiable. Cramming all night → worse on Monday.
- Eat breakfast Monday. Glucose = brain fuel.
- Spaced repetition beats massed practice.
- Take real breaks. 50 min work → 10 min off.
Goal: Find what you know vs. what you think you know.
Goal: Drill your weak spots. Heaviest study day.
Goal: Stay confident, refresh memory, don't burn out.
✅ Practice Test Grader
Interactive grader with personalized study recommendations.
📝 Click your answers
Note: Questions 11, 21, 53, and 58 only have A/B/C.
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🎯 Your Personalized Study Plan
Based on what you missed/skipped, ranked by priority:
📖 Full Answer Key with Explanations
★ = high-frequency concept
Q 1–10
Best evidence of physical changes over geologic time. Homologous structures suggest common ancestry, but fossils literally show change over time.
Replication starts when the double helix unzips. Free nucleotides then pair up.
tRNA anticodon AAA pairs with mRNA codon UUU → phenylalanine. Flip A↔U, C↔G.
Both violate Hardy-Weinberg conditions → gene frequencies change.
Homologous chromosomes during prophase I exchanging segments = crossing over.
Molecular similarity = recent common ancestor. High-frequency concept.
Most stored energy is always at the producer level. 10% rule.
Silent mutation — both code for aspartic acid. Others change the amino acid.
Different structural anatomy = NOT closely related.
10% rule. Energy decreases as it flows up.
Q 11–20
Adenine is in both.
Rr × Rr → 3 round : 1 oval = 75% round.
AB father has no i allele to pass → no ii child possible.
Darwin's survival of the fittest.
Wrens eat grasshoppers — direct food source decreases first.
Energy always decreases moving up trophic levels.
Scorpion hunts (predator), eats meat (carnivore), is heterotroph (consumer).
Translation happens at the ribosome.
DNA similarity = best evidence of common ancestry.
Predators eat visible bright termites → dark survive → classic natural selection.
Q 21–30
mRNA, tRNA, rRNA interact with ribosomes.
Only cross that produces all 4 blood types.
Carrier mom × unaffected dad: 50% of sons get the affected X.
Only crossing over exchanges segments between homologous chromosomes.
Supports Mendel's idea: one factor per gamete.
Fewer mice → more grass → rabbits' food supply increases.
Bat wing + human arm + dolphin flipper = homologous structures.
Natural selection — survivors pass on resistance genes.
Disruptive selection — small and large beaks survive; medium loses out.
Hardy-Weinberg equilibrium = no evolution.
Q 31–40
One cell → 4 cells with half the chromosomes = meiosis.
Biotic (living) factor.
Traits spread if they help survival AND reproduction.
Allele frequencies changed = evolution by definition.
Abiotic = non-living.
Large fish removed → small fish reproduce → distribution shifts smaller.
Ttyy gametes: only Ty and ty possible.
Phe codon UUU → DNA template AAA.
Producers always have the most energy.
Must happen before any cell division.
Q 41–50
Reading the graph: peak height is around 3,000m.
Birth rate > death rate the whole time.
Big fish removed before reproducing → smaller fish dominate.
TT × TT = all TT = all can roll.
mRNA is made in the nucleus (transcription).
mRNA's job: carry code FROM nucleus TO ribosome.
DNA ATG → mRNA UAC. DNA ATC → mRNA UAG (stop codon — nonsense mutation).
Remove rabbits → less food up the chain → fewer of everyone above.
Green offspring of green × yellow cross must be Gg.
Normal male: 46 chromosomes = 22 pairs autosomes + XY.
Q 51–65
tRNA's textbook function.
Mostly males affected, females are carriers — X-linked recessive pattern.
UCG contains U → only RNA.
FF × ff → all Ff = all frizzle.
Foxes, snakes, sparrows eat primary consumers.
Original source of new genetic variation.
Studying homologous structures = comparative anatomy.
tRNA transports amino acids.
Change in DNA base sequence = gene mutation by definition.
Height and color sort independently → Mendel's law.
Vestigial structures lose function with no selection pressure.
Producers → rodents → snakes → hawks/owls (correct order).
Stable population = births equal deaths.
Count only FULLY SHADED squares (affected males). Half-shaded circles are carriers and don't count. X-linked recessive disorders typically affect ~10-25% of a family pedigree, so 3 or 4 is realistic.
Adaptive radiation — Darwin's finches concept.
📘 Cheat Sheet
Condensed notes on all 10 topics. Use the reveal buttons for active recall.
1. Meiosis
- Purpose: produce gametes for sexual reproduction
- Haploid (n): one set of chromosomes; diploid (2n) = two sets
- Includes crossing over (Prophase I) — alleles swap → variation
- Independent assortment (Metaphase I) → more variation
- PMAT happens twice; DNA replicates once
| Mitosis | Meiosis | |
|---|---|---|
| Purpose | Growth/repair | Gamete production |
| # divisions | 1 | 2 |
| Daughter cells | 2 | 4 |
| Chromosome # | Same (2n→2n) | Half (2n→n) |
| Variation | None | Lots |
🎯 Self-Test
2. Protein Synthesis (DNA → RNA → Protein)
| DNA | RNA | |
|---|---|---|
| Sugar | Deoxyribose | Ribose |
| Strands | Double | Single |
| Bases | A, T, C, G | A, U, C, G |
- mRNA — carries code to ribosome
- tRNA — brings amino acids (has anticodon)
- rRNA — makes up ribosomes
- Codon = 3 bases on mRNA = 1 amino acid
- Anticodon = 3 bases on tRNA, complementary to codon
- AUG = start codon (Methionine); UAA, UAG, UGA = stop
Worked example: DNA T-A-C G-G-A C-C-T → mRNA A-U-G C-C-U G-G-A → Met-Pro-Gly
🎯 Self-Test
3. Inheritance & Punnett Squares
- Genotype = genetic makeup (BB, Bb, bb)
- Phenotype = physical trait
- Homozygous = BB or bb; Heterozygous = Bb
- Carrier = heterozygous; doesn't show recessive trait but can pass it
Bb × Bb Punnett square:
| B | b | |
|---|---|---|
| B | BB | Bb |
| b | Bb | bb |
Result: 1 BB : 2 Bb : 1 bb → 75% dominant phenotype
Blood types (codominance): See .
- Iᴬ Iᴬ or Iᴬi = A; Iᴮ Iᴮ or Iᴮi = B; Iᴬ Iᴮ = AB; ii = O
- All 4 types from Iᴬi × Iᴮi
Sex-linked (X-linked): Males (XY) only need 1 recessive allele to show trait. Examples: hemophilia, colorblindness.
Pedigree: Square = male, Circle = female. Shaded = affected. Half-shaded = carrier.
🎯 Self-Test
4. Gene & Chromosomal Mutations
| Gene mutation | What happens |
|---|---|
| Substitution | One base swapped |
| Insertion | Extra base(s) added |
| Deletion | Base(s) removed |
| Frameshift | Reading frame shifts (caused by insertion/deletion, NOT substitution) |
- Silent — no amino acid change
- Missense — one amino acid changes
- Nonsense — creates a stop codon, shortens protein
| Chromosomal mutation | What happens |
|---|---|
| Deletion | Section lost |
| Duplication | Section repeated |
| Inversion | Segment flips |
| Translocation | Piece moves to different chromosome |
| Nondisjunction | Chromosomes fail to separate → Down syndrome (trisomy 21) |
Disorders: Sickle cell (substitution); Down syndrome (nondisjunction).
🎯 Self-Test
5. Natural Selection & Evolution
Darwin's 4 conditions:
- Variation in populations
- Overproduction — more offspring than env can support
- Struggle for existence
- Survival of the fittest — survive AND reproduce
| Type | Effect | Example |
|---|---|---|
| Directional | Favors one extreme | Pesticide-resistant termites |
| Stabilizing | Favors the average | Human birth weight |
| Disruptive | Favors both extremes | Beak sizes with only large/small seeds |
- Mutation = source of new variation
- Adaptive radiation = one ancestor → many species (Darwin's finches)
🎯 Self-Test
6. Evidence for Evolution
| Evidence | What it shows |
|---|---|
| Fossil record | Physical changes over geologic time |
| Homologous structures | Common ancestor (bat wing, human arm, dolphin flipper) |
| Analogous structures | NOT common ancestor (bird vs. insect wings) |
| Vestigial structures | Reduced function (appendix, whale hip bones) |
| Embryology | Similar early embryos = common ancestor |
| Molecular / DNA | Strongest evidence — similar DNA = closer relationship |
🎯 Self-Test
7. Biodiversity & Food Webs
- Biodiversity = variety of life; increases ecosystem stability
- Producers (bottom, autotrophs) → most energy
- Primary consumers (herbivores)
- Secondary consumers
- Tertiary consumers (top) → least energy
- Decomposers recycle nutrients
Biotic = living. Abiotic = non-living (rainfall, temp, sunlight).
🎯 Self-Test
8. Hardy-Weinberg
Full walkthrough in the .
- p + q = 1
- p² + 2pq + q² = 1
- p² = AA; 2pq = Aa; q² = aa (start here when given recessive phenotype %)
5 conditions for equilibrium (no evolution): large pop, no migration, no mutation, random mating, no selection.
9. Mark & Recapture
N = population estimate, M = marked first capture, C = total in second capture, R = recaptured marked.
Examples: 40 marked, 60 caught, 12 marked → N = 200. 25 marked, 50 caught, 5 marked → N = 250. 80 marked, 100 caught, 20 marked → N = 400.
10. Population Growth
| Exponential | Logistic | |
|---|---|---|
| Shape | J-curve | S-curve |
| Resources | Unlimited | Limited |
Carrying capacity (K): max population the environment can sustain.
Stable population: births ≈ deaths.
⚡ Quick Cheat-Sheet Recap
- AUG = start; UAA/UAG/UGA = stop
- Transcription = nucleus; Translation = ribosome
- Crossing over = Prophase I
- 10% rule; producers = most energy
- DNA evidence = strongest for common ancestry
- Mutation = source of new variation
- q² = % showing recessive trait
- N = MC/R for mark-recapture
- Sex-linked recessive = more common in males
- Carrier = heterozygous
🃏 Flashcards
199 cards for active recall. Click reveal only AFTER you've said the answer out loud.
🔬 Topic Deep Dives
Pick any topic for a focused walkthrough with worked examples + practice problems.
🔄 Meiosis
1. The Big Picture
Meiosis takes 1 diploid cell (2n) → 4 haploid cells (n). It does this with:
- 1 DNA replication at the start (S phase before Meiosis I)
- 2 divisions (Meiosis I and Meiosis II)
- Each division goes through PMAT: Prophase → Metaphase → Anaphase → Telophase
2. What Happens in Each Phase
| Phase | What happens |
|---|---|
| Prophase I | Homologous chromosomes pair up. Crossing over happens — alleles exchange. ★ |
| Metaphase I | Homologous pairs line up randomly at the equator. Independent assortment. ★ |
| Anaphase I | Homologous pairs SEPARATE (not sister chromatids yet). |
| Telophase I | Two haploid cells form. Each has chromosomes made of 2 sister chromatids. |
| Prophase II → Telophase II | Like mitosis — sister chromatids separate. Result: 4 haploid cells. |
3. Meiosis vs. Mitosis (KNOW THIS COLD)
| Mitosis | Meiosis | |
|---|---|---|
| Purpose | Growth, repair | Make gametes |
| Divisions | 1 | 2 |
| Daughter cells | 2 (diploid) | 4 (haploid) |
| Identical? | Yes (clones) | No (unique) |
| Crossing over? | No | Yes |
4. Worked Example
Q: A human cell starts meiosis with 46 chromosomes. After Meiosis I, how many chromosomes are in each cell? After Meiosis II?
After Meiosis II: 23 chromosomes per cell (sister chromatids separated). Now there are 4 total cells.
5. Practice Problems
🧬 Protein Synthesis (DNA → mRNA → Protein)
1. Transcription (DNA → mRNA)
- DNA "unzips" along weak hydrogen bonds
- RNA polymerase reads the DNA template strand
- Free RNA nucleotides pair with DNA bases (A→U, T→A, C→G, G→C)
- An mRNA strand is built
- mRNA leaves the nucleus and travels to a ribosome
2. Translation (mRNA → Protein)
- Ribosome reads mRNA 3 bases at a time (each 3-base group = a codon)
- tRNA brings the matching amino acid; its anticodon pairs with the codon
- Amino acids link together via peptide bonds → protein
- Stop codon (UAA, UAG, UGA) → ribosome releases protein
3. The Critical Rules
- AUG = start codon (Methionine)
- UAA, UAG, UGA = stop codons
- DNA → mRNA flips: A→U, T→A, C→G, G→C (T becomes U!)
- mRNA codon ↔ tRNA anticodon flips: A↔U, C↔G (no T in either)
4. Worked Example (Full Pipeline)
DNA template: T-A-C G-G-A C-C-T A-T-T
mRNA:
A-U-G C-C-U G-G-A U-A-ATranslate (read codons): Met — Pro — Gly — STOP
tRNA anticodons (complement of codons):
UAC — GGA — CCU (no anticodon needed for stop)
5. Practice Problems
👨👩👧 Punnett Squares & Inheritance
1. Vocabulary You MUST Know
| Term | Means |
|---|---|
| Allele | Version of a gene (B or b) |
| Genotype | Genetic makeup (BB, Bb, bb) |
| Phenotype | Physical trait expressed (brown vs. blue eyes) |
| Homozygous | Two same alleles (BB or bb) |
| Heterozygous | Two different alleles (Bb) |
| Dominant | Expressed with one copy (capital) |
| Recessive | Only expressed when homozygous (lowercase) |
| Carrier | Heterozygous; has recessive allele but doesn't show trait |
2. Standard Monohybrid Crosses
Bb × Bb (the classic):
| B | b | |
|---|---|---|
| B | BB | Bb |
| b | Bb | bb |
Genotype ratio 1:2:1 | Phenotype ratio 3:1 dominant:recessive → 75% dominant.
Bb × bb (test cross):
| B | b | |
|---|---|---|
| b | Bb | bb |
| b | Bb | bb |
50% dominant : 50% recessive.
3. Sex-Linked (X-linked) Crosses
Carrier mom (Xᴴ Xʰ) × unaffected dad (Xᴴ Y) — for hemophilia or colorblindness:
| Xᴴ | Xʰ | |
|---|---|---|
| Xᴴ | Xᴴ Xᴴ (normal F) | Xᴴ Xʰ (carrier F) |
| Y | Xᴴ Y (normal M) | Xʰ Y (AFFECTED M) |
Result: 50% of sons affected, 50% of daughters are carriers, no daughters affected.
4. Reading Pedigrees
- Square = male, Circle = female
- Shaded = affected, Half-shaded = carrier
- Autosomal recessive: unaffected parents → affected child; skips generations; both sexes
- Autosomal dominant: appears every generation; affected parent → usually affected child
- Sex-linked recessive: mostly males affected; passes from carrier mother to son
5. Practice Problems
1. The Three Alleles
- Iᴬ — codes for A antigen
- Iᴮ — codes for B antigen
- i — codes for NO antigen (recessive)
2. How They Interact
- Iᴬ and Iᴮ are CODOMINANT with each other → both expressed = AB
- Both are DOMINANT over i
i is fully recessive — only shows up if you're ii.
3. Genotype → Phenotype (MEMORIZE)
| Genotype | Blood Type |
|---|---|
| IᴬIᴬ or Iᴬi | A |
| IᴮIᴮ or Iᴮi | B |
| IᴬIᴮ | AB (codominance) |
| ii | O |
4. Key Punnett Squares
Iᴬi × Iᴮi (the famous "all 4 types" cross)
| Iᴮ | i | |
|---|---|---|
| Iᴬ | IᴬIᴮ AB | Iᴬi A |
| i | Iᴮi B | ii O |
25% each: A, B, AB, O.
AB × O
| i | i | |
|---|---|---|
| Iᴬ | Iᴬi A | Iᴬi A |
| Iᴮ | Iᴮi B | Iᴮi B |
50% A, 50% B. NO AB or O possible!
5. Critical Rules
- AB parent cannot pass an i → no O children possible.
- O parent cannot pass Iᴬ or Iᴮ → no AB children possible.
6. Practice Problems
7. Summary
- 3 alleles: Iᴬ, Iᴮ, i
- Iᴬ, Iᴮ codominant. i recessive.
- AB = always heterozygous; O = always homozygous recessive
- AB parent → no O children
- O parent → no AB children
- All 4 types possible: Iᴬi × Iᴮi only
⚠️ Mutations
1. Gene Mutations (Point Mutations)
| Type | What happens | Effect |
|---|---|---|
| Substitution | One base swapped | Changes 1 codon at most |
| Insertion | Base(s) added | Frameshift! Changes every codon after |
| Deletion | Base(s) removed | Frameshift! Changes every codon after |
2. Three Outcomes of Substitution Mutations
| Type | What happens |
|---|---|
| Silent | Base change doesn't change the amino acid (genetic code is redundant) |
| Missense | Changes one amino acid in the protein |
| Nonsense | Creates a stop codon → protein cut short |
3. Frameshift Example
Original mRNA: AUG-CCU-GGA-UAA → Met-Pro-Gly-STOP
New mRNA: AUG-GCC-UGG-AUA-A...
New protein: Met-Ala-Trp-Ile-... (completely different!)
That's why frameshifts are usually devastating — everything downstream is scrambled.
4. Chromosomal Mutations
| Type | What happens |
|---|---|
| Deletion | Section of chromosome lost |
| Duplication | Section repeated |
| Inversion | Segment flips direction |
| Translocation | Piece moves to a different chromosome |
| Nondisjunction | Chromosomes fail to separate in meiosis → wrong # of chromosomes |
5. Disorder Examples (KNOW THESE)
- Sickle cell anemia — substitution mutation (single base change in hemoglobin gene)
- Down syndrome — nondisjunction → trisomy 21 (extra copy of chromosome 21)
6. Practice Problems
🦎 Natural Selection
1. Darwin's Four Conditions
- Variation — individuals differ in traits
- Overproduction — more offspring than environment can support
- Struggle for existence — competition for limited resources
- Differential survival/reproduction — better-suited individuals leave more offspring
2. The Three Types of Selection
| Type | Effect | Example |
|---|---|---|
| Directional | One extreme favored | Pesticide-resistant termites; dark mice on dark rocks |
| Stabilizing | Average favored | Human birth weight (too small or too big = problems) |
| Disruptive | Both extremes favored, average disadvantaged | Drought leaves only small & large seeds — medium beaks lose out |
3. Key Vocab
- Mutation = original source of new genetic variation
- Adaptation = trait that improves survival/reproduction
- Fitness = ability to survive AND reproduce
- Artificial selection = humans breed for traits (dog breeds, crops)
- Speciation = formation of new species
- Adaptive radiation = one ancestor → many species in different niches (Darwin's finches)
- Genetic drift = random changes, especially in small populations
4. Worked Example
Scenario: Termites are sprayed with insecticide. Initially 5% survive. After 6 generations, 80% survive. Why?
The few resistant termites (random pre-existing variation) survived AND reproduced. Their offspring inherited the resistance gene. Over generations, the frequency of resistance alleles increased. This is natural selection — directional selection.
5. Practice Problems
🦕 Evidence for Evolution
1. The Six Lines of Evidence
| Evidence | What it shows |
|---|---|
| Fossil record | Physical changes in species over geologic time |
| Homologous structures | Same underlying structure, different function → common ancestor |
| Analogous structures | Same function, different structure → NOT common ancestor |
| Vestigial structures | Reduced/non-functional remnants → ancestors had different lifestyles |
| Embryology | Similar early embryos → shared developmental genes |
| DNA / molecular | ★ Similar DNA = closer relationship (strongest evidence) |
2. The Big Confusion: Homologous vs. Analogous
Homologous: Look at the BONE STRUCTURE.
- Bat wing, human arm, dolphin flipper — all have the same bones (humerus, radius, ulna, carpals).
- Different FUNCTIONS (flying, grasping, swimming) but same underlying structure.
- → Common ancestor.
Analogous: Look at the FUNCTION.
- Bird wings vs. insect wings — both fly, but the structures are completely different.
- Same FUNCTION but different underlying structure.
- → NOT common ancestor. Evolved independently (convergent evolution).
3. Vestigial Structures
- Whale hip bones — whales' ancestors walked on land
- Human appendix — ancestors processed cellulose-heavy diets
- Snake leg remnants — ancestors had legs
Why do they lose function? No selection pressure to keep them once they're no longer useful.
4. Practice Problems
🌳 Ecology & Food Webs
1. The Trophic Levels
| Level | What | Energy |
|---|---|---|
| 4. Tertiary consumers | Top predators | LEAST (top of pyramid) |
| 3. Secondary consumers | Eat herbivores | |
| 2. Primary consumers | Herbivores | |
| 1. Producers (autotrophs) | Plants, algae — make own food | MOST (bottom) |
| Decomposers | Bacteria, fungi — recycle nutrients | Side path |
2. The 10% Rule
Each level up, ~90% of energy is lost as heat (metabolism). Only ~10% transfers. That's why:
- Pyramids narrow at the top
- Top predators are rare
- Energy/food chain are short (4-5 levels max)
3. Vocabulary You Need
| Term | Definition |
|---|---|
| Autotroph | Makes own food (producer) |
| Heterotroph | Eats other organisms (consumer) |
| Herbivore | Eats plants |
| Carnivore | Eats meat |
| Omnivore | Eats both |
| Predator | Hunts/kills prey |
| Decomposer | Breaks down dead matter |
| Biotic | Living component (predators, prey, disease) |
| Abiotic | Non-living component (rainfall, temperature, soil) |
4. Worked Example: Food Web Cascade
Scenario: A pesticide kills off the mouse population. Mice eat grass; snakes eat mice and rabbits; rabbits eat grass.
And: Less grass eaten by mice → more grass available → rabbits' food supply increases.
Removing one species ripples through the whole web — that's why biodiversity matters for stability.
5. Practice Problems
📐 Hardy-Weinberg
Master the math, the conditions, and what the equations mean.
1. What It Measures
H-W tells us frequencies of alleles and genotypes:
- p = probability of grabbing the dominant allele (A)
- q = probability of grabbing the recessive allele (a)
2. The Two Equations
| Variable | What it represents | Genotype |
|---|---|---|
| p | Dominant allele freq | — |
| q | Recessive allele freq | — |
| p² | Homozygous dominant freq | AA |
| 2pq | Heterozygous freq | Aa |
| q² | Homozygous recessive freq | aa |
3. The 3-Step Solver
For number of individuals: multiply the frequency by total population size.
4. Zooming In: How to Find 2pq
Where the "2" Comes From
When two parents have a baby, the heterozygous combination (Aa) can happen TWO ways:
- A from mom × a from dad = p × q
- a from mom × A from dad = q × p
Adding both: p×q + q×p = 2pq. That's why it's doubled. (Same logic as Bb appearing twice in a Bb × Bb Punnett square.)
How to Calculate It — Three Sub-Steps
Worked Example
Q: 16% of the population shows the recessive trait. What % is heterozygous?
| Step | Math | Result |
|---|---|---|
| 1. Find q | q² = 0.16 → q = √0.16 | q = 0.4 |
| 2. Find p | p = 1 − 0.4 | p = 0.6 |
| 3. Find 2pq | 2 × 0.6 × 0.4 | 2pq = 0.48 = 48% |
Sanity check: p² + 2pq + q² = 0.36 + 0.48 + 0.16 = 1.00 ✓
So 48% of the population is heterozygous (Aa) — they carry the recessive allele but don't show the trait.
Finding the NUMBER (not just %) of Heterozygotes
Q: A population has 1,000 people; 9% show the recessive phenotype. How many are heterozygous?
p = 1 − 0.3 = 0.7
2pq = 2 × 0.7 × 0.3 = 0.42
Number of heterozygotes = 0.42 × 1,000 = 420 people
Fun Fact: 2pq Has a Maximum
2pq can never exceed 0.5. The maximum happens when p = q = 0.5 (a perfectly balanced gene pool). As one allele becomes more common than the other, 2pq shrinks. That's why "half the population is heterozygous" is the upper limit — heterozygotes can never make up more than 50% of a population in H-W equilibrium.
5. Worked Examples
Example 1: q² = 0.25
Example 2: 9% show recessive phenotype
Example 3: p = 0.8
Example 4: Population 500, q² = 0.16. How many homo recessive?
6. The 5 Conditions for Equilibrium
All 5 must hold or the population is evolving:
- Large population (otherwise genetic drift)
- No migration
- No mutation
- Random mating
- No natural selection
7. Practice Problems
8. Summary
Equations: p + q = 1 | p² + 2pq + q² = 1
3-step solver:
- q = √(% showing recessive phenotype)
- p = 1 − q
- Plug into p², 2pq, q²
5 conditions: large pop, no migration, no mutation, random mating, no selection.
🐢 Mark & Recapture
1. The Formula
- N = population estimate
- M = number marked in FIRST capture
- C = total CAUGHT in SECOND capture
- R = RECAPTURED marked individuals (the ones with marks in the second catch)
2. The Intuition
The ratio of marked-to-total in your second sample should equal the ratio of marked-to-total in the whole population:
R/C = M/N
Rearrange: N = (M × C) / R
3. Why Marked Organisms Must Mix Back In
Between captures, the marked individuals need to randomly redistribute among the whole population. If they don't, your second sample won't be representative — you'll get a bad estimate.
4. Limitations (Often Asked!)
- Marks can fall off (under-counts recaptures → overestimates population)
- Assumes no births, deaths, immigration, or emigration between captures
- Marked organisms might behave differently (trap-shy or trap-happy)
- Marking might affect survival
5. Practice Problems
📈 Population Growth
1. Exponential Growth (J-Curve)
Population doubles in a fixed time. The graph is a J-shape. Only happens when resources are unlimited — usually in:
- Newly introduced species in a new habitat
- Bacteria in fresh nutrient medium
- Small populations with no competition or predation
Can't continue forever — eventually something limits it.
2. Logistic Growth (S-Curve)
Population starts exponential but slows as it approaches the environment's limits, then levels off. The graph is an S-shape.
The level-off point = carrying capacity (K) — the max population the environment can sustain.
3. What Causes Growth to Slow
| Density-dependent (more impact when crowded) | Density-independent (no relation to crowding) |
|---|---|
| Competition for food, water, space | Weather (drought, frost) |
| Predation | Natural disasters (fire, flood) |
| Disease (spreads faster when crowded) | Climate |
| Waste accumulation |
4. Stable Populations
When a population is stable (at the top of the S-curve), births + immigration ≈ deaths + emigration. The population isn't growing or shrinking — it's at carrying capacity.
5. Human Impact
- Habitat destruction reduces carrying capacity
- Pollution adds to density-independent stress
- Climate change shifts which species can thrive where
- Overharvesting (fishing, hunting) acts like extra predation