Dale Fort Blog Number 14

16 01 2013

This article concerns itself with the problem of how to estimate the size of a population when you can’t count them directly





The Lincoln Index

P = AN/r

P = Population    A = Total in the first sample (i.e. marked)  

N = Total in the second sample      r = Number recaptured


As I mentioned in the video, there are several assumptions that the Lincoln Index makes about the population and what you do to it.  Here they are:

1) The size of the population doesn’t change during the experiment. 

What might happen if it did?  If there were a lot of births (or immigration which is much the same in terms of population numbers) what would that do to the estimate?

Answer: You’ll be diluting the marked animals among more unmarked individuals so the estimate will go up

If there were a lot of deaths (or emigration which is much the same in terms of population numbers) what would that do to the estimate?

Answer: Assuming the marked animals die or emigrate at the same rate as the unmarked, the ratio of marked to unmarked will stay the same.  So your estimate will remain unchanged even though the population has actually gone down (an over-estimate).

The key is to work out what the assumptions are likely to do to the number of recaptures and hence the population estimate.

2) The mark should last for the duration of the experiment

If it doesn’t, what does that do to the number of recaptures?

Answer:  It reduces it leading to an over-estimate

What if wet paint or dye rubbed off on to unmarked animals?

3) The marking procedure should not harm the animals

If the animals were impeded by the procedure are they going to mix up OK?  If the marking material was toxic are they going to feel like socialising with their chums?  What about predators?  Will a predator find the marked animals more easily, or might the mark put a predator off?

4) The population has to have boundaries and inhabit an area which you can define

This might be OK if you’ve got a small pond with some goldfish but it’s likely to be problematical in lots of situations.  How could you define the boundaries of a woodlouse population for example?

5) The individuals in the population (including the marked ones) should mix at random

Apart from drunken people staggering out the pub what population mixes at random?  Motile creatures are going to move in response to stimulation e.g. towards food or shade or moisture.

I think this is one of the biggest problems with mark/recapture.

6) There should be no trap-happy or trap-shy individuals in the population

Often this technique is used in small mammal surveys.  To catch and mark a small mammal you use a baited trap with nesting material in it (a Longworth trap, look it up).  Mammals are good at learning and some quickly realise that getting trapped means free bed and breakfast, no predators and the enticing prospect of escaping into the huge beard of the bloke who opens the trap and there building a cosy nest.  Such individuals are called trap-happy because they actively seek out traps.  The opposite extreme is where individuals find the prospect of being trapped and meeting the ecologist with his vile smelly beard appalling.  These individuals actively avoid the traps and are known as trap-shy animals.  If you have individuals of either persuasion (or both) in the population then your estimate is unlikely to be correct.

Other Points

Sample size

It’s reckoned that you should sample until you get 10% of the marked animals back in the second sample.  So, if you marked 50 in the first sample you should keep sampling in the second sample until you get at least 5 recaptures.

Why do this if it’s got so many problems?

The Lincoln Index is loved by A-Level Exam setters because it allows them to give you a simple calculation to do and then ask you what might have gone wrong.  It’s worth knowing about because the basic idea is easy and it can score you marks.

The Blog will return when I get time to write another one.






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