Time to evolve

How many generations would link an evolutionist to a very distant ancestor?

Age

14 to 16

Challenge level

Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving

Being curious Being resourceful Being resilient Being collaborative

Problem

An evolutionist suggests that at some distant point 400 million years in the past one of his ancestors was an early form of fish. Try to estimate the number of generations that link the scientist to the fish. To make your estimation, you will need to fill in sensible values for the species in the table below (you will possibly need to research these numbers, and feel free to use a spreadsheet for the calculations. A good place to start is http://en.wikipedia.org/wiki/Timeline_of_human_evolution)

Category	First appearance (million years ago)	Similar modern day example
Category	First appearance (million years ago)	Similar modern day creature	Time from birth to producing first offspring	Lifespan (years)
Bony fishes	400	Coelacanth
Amphibians	350	Lungfish
Reptiles	300	Lizards
Early mammals	200	Small dogs
Mammals	75	Lemurs
Apes	15	Gorillas
Humans	1	Charles Darwin	30	73

Can you produce a sensible estimate for a number that you are confident exceeds the actual number of generations?

Can you produce a sensible estimate for a number that you are confident is definitely less than the actual number of generations?

There will be various estimates and assumptions that you need to make in this question. Can you clearly state the most important factors?

NOTES AND BACKGROUND

Suggested timelines for evolution form fascinating reading.

Interestingly, the bony coelacanth fish was considered extinct by scientists until fishermen caught one alive in 1938. Now they occasionally turn up, caught in deep-water nets.

Teachers' Resources

Why do this problem?

This task will give practice in making sensible estimates, approximations and making a prediction based on a range of possible values. Although the content is relatively simple, answers could be given to this question at a range of levels and the problem would suit both Stage 3 and Stage 5 students as an exercise in thinking.

Possible approach

There are various ways in which approximations can be made and it might be good to let students attempt to make their own approximations before opening up to group discussion. As they work on the problem, various decisions will need to be made and various uncertainties will arise (for example: at what stage between maturity and death of a parent was a particular offspring in the chain of descendants produced?). Students should be encouraged to take notes of these points, as discussion of these forms a key part of the evaluation process.

It is interesting to ask students first to give a guess/estimate of the number of descendants without doing any calculation. Students could then work on the problem in pairs to come up with an estimate and then share their ideas with other groups. Whose estimations seem best? Can students justify clearly their estimations to each other? Do any students wish to revise their estimates in light of such interaction?

Once estimations have been constructed and discussed it would be worth relating the estimates back to the original question: how reliable might we consider our estimates of the number of generations to be? What questions would this raise? What information might lead to better estimates?

Finally, how did the students' initial guesses/estimates fit in with the calculated estimates? This allows students to reflect on the size of the final answers. Were they much larger or smaller than expected?

Key questions

Key questions should be used as appropriate to help students find their way into the question:

Can you make a start to the question by giving a very rough estimate of the numbers that go into the table? How could you use these numbers to work out the number of generations?
When you fill in the table, what sensible range of choices do you have for each entry?
When you calculate the number of descendants from a filled-in table, what uncertainties are there?
How could you use a filled-in table to calculate the maximum or minimum number of descendants?

Possible extension

The fullest solution to this task/main extension involves a careful investigation of the minimum and maximum possible number of descendants. For those with a knowledge of statistics, you might refer them to Time to Evolve 2.

As a very general extension discussion point, it is worth mentioning that the evolution from one species to another occurs through gene mutation. Can students get any sense of the rate at which the genes would have to mutate to account for the required genetic change over the given time period? This activitiy would, of course, be research intensive.

Possible support

Some students might feel uncomfortable that there are no 'right' numbers to fill into the table and no 'right' answer to the estimation question. Encourage them that it is OK to make a rough estimate to begin with and then to refine that estimate later. Give them some concrete estimates of time to maturity/death if necessary.

Creature	Timespan	Time to maturity	Lifespan	Min number	Max number	Average number
Fishes	50,000,000	20	100	500,000	2,500,000	833,333
Amphibians	50,000,000	20	100	500,000	2,500,000	833,333
Reptiles	100,000,000	2	30	3,333,333	50,000,000	6,250,000
Early mammals	125,000,000	2	10	12,500,000	62,500,000	20,833,333
Mammals	60,000,000	2	25	2,400,000	30,000,000	4,444,444
Apes	14,000,000	2	35	400,000	7,000,000	756,757
Humans	1,000,000	13	40	25,000	76,923	37,736

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