Biology IA · D · Continuity and change · topic 25 of 25

Natural selection vs chance: will a helpful allele win? · IB Biology IA idea: guide, sample graph and step-by-step plan

sounds easy. it isn't. but it's SO good.

A mutation makes an organism fitter, and it still vanishes more often than not. Build a population and watch how often chance beats selection.

Difficulty●●● Stretch
KitComputer only: a spreadsheet with random numbers, or a short script
TimeAbout 10 hours
FitsSL and HL (allele frequencies and gene pools are HL content)
  • ✓ you like models and a bit of code or spreadsheet logic
  • ✓ you are curious about luck in evolution
  • ✓ you want an IA with no lab and no mess

The big idea

← check against a known result

In a small population, allele frequencies change by chance (genetic drift) as well as by selection. A new advantageous allele starts as one copy, so it is easily lost in the first few generations even when it helps. You build a model in which a selection coefficient raises the allele's chance of being passed on and chance does the rest, then run it many times at each setting. The proportion of runs in which the allele takes over is your dependent variable. Check the model against a known result before you trust it, and say which assumptions you made.

Make it yours: pick one twist

Copying a classic won't show your choices. Pick one of these (or invent your own) and your IA becomes yours.

Swipe for more twists →

Change the population size

Repeat for populations of 50, 100 and 500 (HL link: gene pools and allele frequencies).

→ Drift becomes weaker in large populations; you compare how fixation probability depends on population size as well as selection.
Start with a higher frequency

Start the allele at 10% instead of a single copy.

→ Your neutral baseline changes (it should be about the starting frequency); you need far fewer runs, and you discuss what real situations look like this.
A recessive allele

Make the allele advantageous only in homozygotes.

→ Selection is much weaker while the allele is rare; you need a model with genotype fitnesses and a bigger comparison with the additive case.
Follow the time to fixation

Record how many generations it takes for each run that ends in fixation.

→ You get a second dependent variable, with a distribution that is skewed; you must choose between mean and median.
Add a bottleneck

Shrink the population for a few generations and then restore it.

→ Your model needs a time-varying size; you can discuss real bottlenecks, and compare the result with a constant population.
Change the context

Link it to antibiotic resistance, a conservation story or pesticide resistance in an insect.

→ Gives the introduction a real purpose; the model and the graph stay the same.

Your Biology IA research question: run the check

Write your own question first. Then make sure it ticks every box:

  • Names the independent variable (the selection coefficient), its range and the values you will test.
  • Names the dependent variable as the proportion of runs reaching fixation, and says what counts as fixation.
  • States the model: population size, starting frequency, how selection and random sampling are applied each generation.
  • Says the number of runs at each setting and justifies it with the size of the effect you are looking for.
  • Says which known result you will use to test the model, and why it applies to your set-up.
  • Is small enough to run in your software on the computer you have, in the time you have.

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The set-up

No apparatus here, so the picture is the model. This is one possible design. Draw yours, with your own rules for selection and sampling.

start: one copy ofthe new allele in 2Nselection reweightsp′ = p(1+s) / (1+sp)drift: draw 2N copiesat random, chance p′p = 0 or 1?record:fixed or lostnoyescheck s = 0 first:expect about 1/(2N)repeat for MANYruns: 100 is abare minimumchance = drift

How your Biology IA could be laid out

The usual order for a topic like this, what each part needs to show, and roughly how much of your 3,000 words it takes. The words are all yours.

Research question and context~250
Your question; why chance matters for new mutations; what you predict about selection coefficient and fixation.
Background biology~450
Allele frequency, selection coefficient, genetic drift, fixation and loss; a published formula or result you will compare with, with its assumptions; HL: gene pools and allele frequencies.
Variablestable
Independent, dependent and controlled variables (population size, starting frequency, number of runs, generations allowed).
Method~550
The model, step by step; how selection is applied; how random sampling is done; software; how a run ends; number of runs; how the model was checked against a known result.
Safety, ethics, environment~40
Short: screen use, and a sentence on the assumptions of a computer model.
Raw datatable
For each setting: number of runs, number of fixations, number lost. A short extract in the report.
Processing~300
Proportion fixed and its uncertainty (it comes from the number of runs); one worked example; the check against the known result.
Graphs and analysis~400
Proportion fixed against selection coefficient with SE error bars; the known result drawn on the same axes; whether the theory lies within about 2 SE of each point, or a chi-squared test of fixed and lost counts against the theory.
Conclusion~350
Answer with values and uncertainty; say how close the model is to theory and whether the gap is bigger than the uncertainty; limit the claim to your population size.
Evaluation~550, the biggest part!
Weaknesses ranked by their effect on the fixation proportion: number of runs, model assumptions, random number quality, run length, simplifications of real populations.
Referencesnot counted
Theory, formula source and software.

What your Biology IA graph could look like

bars come from the NUMBER OF RUNS

Made-up data, to show you the form of a strong graph, not the answer. The theory curve is one standard prediction: check which model it assumes before you copy it. example only

0.000.020.040.060.080.100.000.020.040.060.080.100.120.140.160.180.200.22Selection coefficient, s (set in the model)Proportion of runs reaching fixation (± SE from n = 500 runs)diffusion theory, N = 100, one starting copysimple 2s approximationsimulation, with standard errorat s = 0 the theory says1/(2N), only 0.005ILLUSTRATIVE · MADE-UP DATA
  • The bars come from the number of runs: a proportion estimated from n runs has a standard error of about the square root of p(1−p)/n.
  • Both theory lines drawn so the reader can see which one the simulation follows.
  • Starting from one copy, even a strong advantage gives a fixation chance well below 1. Say why.
  • Test s = 0 as a separate check, and put it on the graph.
  • Another graph to consider: how the fixation proportion changes as the number of runs grows, to show where it settles.

How many runs do you need?

how many runs? decide with numbers

A proportion from n runs has a standard error of about the square root of p(1−p)/n. This chart is for a made-up setting where 18% of runs reach fixation. For the neutral case, where the chance is about 0.5%, you need far more runs still.

100 runs3.8 pp500 runs1.7 pp1000 runs1.2 pp5000 runs0.5 pp20000 runs0.3 pp100 runs is too few!standard error of the fixation proportion, in percentage points (pp)ILLUSTRATIVE · MADE-UP NUMBERS

Your game plan

Tick steps off as you go. We'll remember on this device.

0 of 10 done

  1. Read and predictLearn drift, selection coefficient and fixation. Find the known result for the chance of fixation of a new neutral allele, and write down what you predict for a helpful one.
  2. Design the model on paperWrite down the population size, how each generation is formed, how selection acts and what ends a run. Check each rule is something you can code.
  3. Build and test (the trial run)Build it. Run it with s = 0 and check it against the known result. If your answer is off, find out why before moving on.
  4. Decide settings and runsChoose at least five values of s across your range, and a number of runs at each. Use the size of the effect and the standard error to justify it.
  5. Run itRun all settings. Save the raw results (fixed or lost for each run) and the exact version of your sheet or script.
  6. ProcessProportion fixed for each setting with its standard error. One worked example. Check that fixed plus lost equals runs.
  7. Graph and comparePlot proportion against s with error bars, with the theory on the same axes. Decide how you judge agreement and say how you will check it.
  8. ConcludeAnswer with values and uncertainty; say whether the model supports the theory; limit your claim to your population size and your model.
  9. EvaluateRank weaknesses by their effect on the proportion. Tie each improvement to a problem you found.
  10. Check before your teacher's draftRun the checklist below, then get your RQ or draft checked. Your teacher reads one draft only, so make it count.

Biology you'll need

Traps to avoid in this Biology IA

  • Too few runs: with a single starting copy, only about one run in 200 fixes a neutral allele, so 100 runs may show none.
  • Never checking the model against a known result, so a coding error goes unnoticed.
  • Copying a theory formula without checking that its definition of s matches your model.
  • Stopping runs after a fixed number of generations, so that unfinished runs are counted as lost.
  • Using the random number generator badly, such as reusing the same seed for every run.
  • Treating 'fixation proportion' as certain when it is an estimate with a standard error.
  • Making claims about real populations from a model with constant size and no mating structure.

More Biology IA ideas like this

Make sure it's yours

This guide shows how a topic like this is usually approached. It is not an IA. Your question, choices, data, analysis and words must be your own: change something, tell your teacher where the idea came from, and follow your school's rules on outside help.

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