Lesson 1.6 · Unit 1 · NGSS practice 2
Models in biology: what they are for, and where each one breaks
A food chain is not a claim that foxes eat only rabbits. A Punnett square is not a claim that exactly three of four offspring will be tall. Both are models: deliberate simplifications kept because they make something predictable. A model you cannot criticize is a model you do not understand.
- A model is a simplification built for a purpose. It keeps the features that matter for one question and discards the rest, which is what makes it useful rather than what makes it wrong.
- Physical models are things you can handle: a cell made of gelatin, a plastic DNA helix, a beaker standing for a lake.
- Mathematical models use equations or arithmetic to predict a quantity: exponential growth, the ten percent rule, the Lincoln index.
- Conceptual models are diagrams and schemes: food webs, the carbon cycle, a phylogenetic tree.
- Every model carries assumptions, and naming them is part of using it. Exponential growth assumes unlimited resources; the biological species concept assumes sexual reproduction.
- A model is judged by whether it predicts well enough for the purpose, not by whether it is realistic. A perfectly realistic model of an ecosystem would be the ecosystem.
Where students lose marks: treating a model's simplification as an error to be pointed out for credit. Saying "a food chain is unrealistic" earns nothing. Saying "a food chain cannot show that a fox also eats beetles, so it understates how a fox population would survive losing rabbits" is the answer.
The model. The food chain: grass → rabbit → fox. Examine it as a model rather than as a fact.
Step one: state what it is for. It shows the direction of energy transfer through a sequence of organisms, and it makes the trophic position of each one explicit. That is a narrow purpose, and for that purpose it works.
Step two: state what it predicts. Remove the grass and both other populations must fall. Energy entering the fox is a small fraction of that entering the rabbit. Both predictions are correct and neither is obvious without the model.
Step three: name the assumptions. That each organism occupies one trophic level, that each eats only the organism below it, and that no energy enters or leaves except along the arrows.
Step four: find a case the model handles badly. A fox that also eats beetles and berries occupies more than one trophic level at once. The chain cannot represent this, so it will overstate how badly a fox population suffers when rabbits decline.
Step five: find a second failure. The chain has no decomposers, so matter appears to leave the system at the fox and never return. As a model of energy flow that is acceptable; as a model of matter cycling it is simply wrong, which is why unit 4 needs different diagrams.
Step six: choose the repair that suits the purpose. For the question "what happens to foxes if rabbits decline", replace the chain with a food web, which keeps alternative prey. For "how much energy reaches the top", keep the chain, because the extra links would obscure the arithmetic.
Step seven: state the general rule. The right question about a model is never "is it true" but "is it adequate for this purpose, and where does it fail". Every model in this course will be introduced with that pair of questions.
Questions 1 to 5 are recall. Questions 6 to 10 ask for reasoning.
- Name the three kinds of model and give an example of each.
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Physical (a gelatin cell), mathematical (exponential growth), conceptual (a food web)
- What assumption does exponential growth make?
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That resources are unlimited
- By what standard is a model judged?
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Whether it predicts well enough for its purpose, not whether it is realistic
- Give one thing the grass to rabbit to fox chain cannot represent.
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An organism feeding at more than one trophic level, or the decomposers
- Why is "this model is unrealistic" not an answer?
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All models simplify; the answer must name the specific prediction the simplification gets wrong
- Explain why a more realistic model is not automatically a better model.
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Adding detail costs clarity and usually costs predictive power that can actually be used. A food web including every species in a meadow would be more realistic than a four-link chain and far less useful for calculating how much energy reaches the top consumer, because the arithmetic would be buried in hundreds of arrows whose values nobody has measured. A model earns its detail only when that detail changes the answer to the question being asked, which is why the purpose has to be fixed first. Detail that does not change the answer costs clarity for nothing
- A Punnett square predicts a 3 to 1 ratio, but a cross produces 26 tall and 14
short. Explain whether the model has failed.
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No. The square models probability per offspring, not a guaranteed tally, so the prediction is that each offspring has a three in four chance of being tall, and departures from the exact ratio are expected in small samples. Forty offspring predicts thirty tall and ten short; twenty six and fourteen is a plausible outcome of chance around that expectation, in the same way that forty coin tosses rarely give exactly twenty heads. The model would be in trouble if large samples consistently departed from three to one, which is how non-Mendelian patterns were discovered. It predicts probabilities, and small samples vary around them
- Why must the assumptions of a model be stated when the model is used?
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Because the assumptions define the conditions under which the model's predictions can be trusted, and a reader cannot judge a conclusion without them. Exponential growth predicts a population will double indefinitely, which is correct only while resources remain unlimited, so applying it to a population near its carrying capacity produces a confident and wildly wrong forecast. Stating the assumption tells the reader where the boundary is and signals when a different model is needed. They set the conditions under which the prediction is valid
- Suggest a case the biological species concept handles badly, and say why that
does not make it useless.
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It defines a species by the ability to interbreed and produce fertile offspring, so it cannot be applied to bacteria, which reproduce asexually, or to organisms known only as fossils, where no breeding test is possible. That does not make it useless: for sexually reproducing living animals it captures exactly the boundary that matters, because populations that exchange genes evolve together and populations that do not diverge. A tool with a stated domain is useful inside it. It fails for asexual and fossil organisms but works where gene flow is the relevant boundary
- You want to know how quickly a disease will spread through a school. What kind
of model would you use, and what would you have to assume?
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A mathematical model, since the question asks for a rate and a number infected over time rather than a description. It would have to assume something about how many people each infected person contacts per day, the probability that a contact transmits, how long a person stays infectious, and that mixing is reasonably even across the school. Each assumption is a place the prediction could fail, particularly even mixing, since friendship groups and year groups make contact far from random. A mathematical model, assuming contact rate, transmission probability, infectious period and even mixing