Biology IA · B · Form and function · topic 12 of 25

Does metabolic rate really scale with mass^0.75? · IB Biology IA idea: guide, sample graph and step-by-step plan

no lab, so the thinking must be sharp

An elephant is 10,000 times heavier than a mouse, but uses nowhere near 10,000 times the energy. You're going to check the famous three-quarters rule for yourself.

Difficulty●○○ Gentle
KitComputer and spreadsheet only
TimeAbout 10 hours
FitsSL and HL
  • ✓ you like patterns in big data
  • ✓ you can use a spreadsheet
  • ✓ you want an investigation with no apparatus

The big idea

← this is your RQ hook!

A big animal has less surface per kilogram to lose heat through, and each kilogram of its tissue runs more slowly, so metabolic rate rises more slowly than mass. A power law, rate = a × mass^b, is a straight line once you take logs, and the gradient is the exponent b. Theory suggests b is somewhere around two-thirds to three-quarters. Your job: choose and filter the data so the comparison is fair, fit the line, and give the exponent with its uncertainty. No lab, but the same discipline.

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 →

One order of mammals

Use only rodents, or only carnivores, instead of all mammals.

→ A narrower mass range and less scatter; the exponent may differ, and you can ask why.
Two groups, one question

Compare mammals with birds, or with reptiles at a stated temperature.

→ Two lines to compare; the difference in intercept is as interesting as the gradient. Only valid with comparable measurement conditions.
Test the range

Fit the small animals and the large animals separately.

→ Tests whether one exponent fits everything; the residuals become part of your analysis.
Compare two sources

Repeat the analysis with a second published data set.

→ You can judge how much the answer depends on the data source.
A different 'rate'

Use heart rate or lifespan against mass instead.

→ Same log-log method, with a different expected exponent that you must find from published sources.
Change the context

Link to drug dosing by body size, zoo animal diets or the cost of being small in cold climates.

→ Gives the investigation a purpose; the analysis stays the same.

Your Biology IA research question: run the check

write it FIRST, then check it

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

  • Names the group of animals and the range of body mass you will use (and where the data come from).
  • Names body mass and metabolic rate with units, and says how they are processed (logarithms).
  • Says what you will filter out, and why (measurement conditions, group, missing values), so someone else could repeat it.
  • Says what you will compare the result with (the exponents proposed in published work), and how.
  • Is narrow enough to finish in about 10 hours, with a sample large enough to give a useful gradient.

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The method

A database investigation has no apparatus. Instead, draw the path your data takes: source, filter, transformation, fit. Redraw it with your real columns and rules.

speciesmass (kg)BMR (W)log₁₀ (mass)log₁₀ (BMR)one group, one source:record how you filteredtake log₁₀ of both columns firstgradient = the exponent(give its uncertainty)

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 scaling with body size matters (drug doses, zoo diets, heat loss), and what you expect.
Background biology~450
Why metabolic rate and mass might not rise together; what a power law is; the exponents proposed in published work, with citations; what your graph should look like if your prediction holds.
Variablestable
What counts as independent and dependent here, and what you held constant by filtering (group, source, measurement conditions).
Method~450
The database, the version and date, the exact filters and sampling rules, why that sample answers your question, how you handled missing data and duplicates, and what you did in the spreadsheet.
Safety, ethics, environment~40
Short and honest: no experiment, but state data source and licence, and that no animals were involved.
Raw datatable
A clear table of the species and values you used (or a trimmed version with the full list in an appendix), with units and the source in the header.
Processing~250
The logarithm step, what base you used, how you fitted the line and one worked example of each calculation.
Graphs and analysis~400
The log-log plot, the fitted line, the exponent with its uncertainty, a measure of fit and the residuals, and what any statistics can say.
Conclusion~400
Answer the question with the exponent and its uncertainty, and compare with published exponents. State what the data can and cannot say.
Evaluation~600, the biggest part!
Weaknesses of the data and the analysis (mixed conditions, species not independent, gaps), ranked by their effect on the exponent, and improvements.
Referencesnot counted
The database and every paper you compared against.

What your Biology IA graph could look like

the gradient IS your result ✓

Made-up data, to show you the form of a strong graph, not the answer. Your database, species and numbers will differ. example only

-3-2-101234-2-101234log₁₀ (body mass / kg)log₁₀ (basal metabolic rate / W)your fitted linereference line, gradient 0.75one species per point (database entries)scatter around the line is yourresidual spread: report itILLUSTRATIVE · MADE-UP DATA
  • Take the logarithm of both quantities and label the axes as logs with units inside the bracket. The log of a quantity with units needs the unit stated.
  • No error bars here, because the points are database entries, not your measurements. Spread around the line, and the uncertainty of the gradient, take their place.
  • Give the gradient with its uncertainty (the standard error from your spreadsheet's linear regression, or a 95% interval) and see whether the reference value lies inside it.
  • A straight line on this plot means a power law on the raw scales. A straight line fitted to the raw data would force the wrong shape.
  • Another graph to consider: plot the residuals (data minus fitted line) against log mass. A pattern, such as a curve, means a single exponent may not describe the whole range.

How many species is enough?

more data helps, but how much?

Not an uncertainty of measurement, but a sampling question: the uncertainty of your gradient shrinks as you add species. These numbers assume a scatter of 0.15 in log units and a spread of log mass of 1.8; calculate yours from your own data.

10 species0.02830 species0.015100 species0.008more species, smaller uncertaintystandard error of the gradient (assumed scatter)ILLUSTRATIVE · MADE-UP NUMBERS

Your game plan

don't skip the trial run! it saves you weeks

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

0 of 10 done

  1. Read and predictFind out what the proposed exponents are and where they come from. Write down your prediction and the reasoning behind it before opening any data.
  2. Choose a data sourceLook for a database with body mass and metabolic rate for many species, with its measurement conditions recorded. Read how the values were collected, since that decides what you can compare.
  3. Trial run (1 lesson)Take a small slice, such as 20 species, and do the full analysis end to end: filter, log, plot, fit. Where does your spreadsheet struggle? Are there blanks or duplicates? Fix the process now.
  4. Decide filters and sampleWrite down your inclusion and exclusion rules, and why each exists. Decide how you will handle species with several entries.
  5. Build the clean data setKeep a copy of the original and work on a second sheet. Record every row you removed and why.
  6. Transform and plotTake logs of both columns, plot, and check that the pattern looks straight. If it curves, ask why before fitting.
  7. Fit and quantifyFind the gradient with its uncertainty and a measure of fit. Look at the residuals. Decide whether one exponent describes the whole range.
  8. Compare with theoryDoes the published exponent lie within your uncertainty? Be careful what that does and does not show.
  9. EvaluateWhich weakness changes the exponent most? Test it: refit without the largest animals, or with a different filter, and report the change.
  10. Write, then checkWrite in the order of the layout. Run the checklist below before your teacher's draft.

Biology you'll need

Traps to avoid in this Biology IA

  • Fitting a straight line to the raw data instead of the logarithms, so the exponent is meaningless.
  • Mixing warm-blooded and cold-blooded animals, or measurements at different temperatures, in one fit.
  • Quoting the exponent with no uncertainty, then saying it 'matches' a published value.
  • No record of how the data were filtered, so the sample cannot be repeated.
  • Deleting outliers that do not suit the theory, rather than checking them.
  • Treating related species as independent. Say what that does to your confidence.
  • Copying values from a table without checking that mass and rate use the units you assume.

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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