Time to evolve
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  

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 deepwater nets.
Getting Started
Estimate lifespan and time to first offspring from those for the modern day equivalent creature.
Think about the point in the lifespan of a descendant at which the next descendant might have been produced.
Don't forget that this is an exercise in estimation and approximation: there is no 'right' answer, so try to put sensible guesses in the table.
Student Solutions
We had an interesting anonymous solution to this problem, giving rise to some sensible numbers. We think that similar investigations would make for interesting datahandling project work.
We used the internet to research lifespans. We were surprised to see that fishes and reptiles live for a very long time. A modern day bony fish is the sturgeon, from which caviar is taken. Lizards seem to have quite a wide range of lifespans (between 10 and 50), so we picked 30 as an average. The numbers for dingos and lemurs seemed typical for these sorts of creatures. We also changed the human numbers because in the past both would be smaller. Our table became
@
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 
To get the minimum number of ancestors for each row we divided the time in years by the lifespan. To get the largest numbers of ancestors we divded the time in years by the time to maturity.
This gave grand totals of between $19,658,333$ and $154,576,923$ ancestors.
To get the average age of an ancestor when giving birth we found an average age = (Lifespan + time to maturity)/2 and timesed this by the timespan.
Assuming that ancestors were born at an average point in their parents' lives, we get $33,988,937$ ancestors.
Rounding up to sensible values, we think that there were at most $150$ million ancestors, at least $20$ million ancestors and probably about $35$ million ancestors.
Teachers' Resources
Why do this problem?
Possible approach
Key questions
 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 filledin table, what uncertainties are there?
 How could you use a filledin table to calculate the maximum or minimum number of descendants?