I am looking for some advice (possible articles) on the number of sampling points one would need to establish a level of significance to confirm a species is absent?
To what degree of confidence (95/99/100%) do you wish to confirm the species is absent? Remember that proof of a negative is a difficult proposition on many occasions.
Formally, a significance of data can be calculated only for a defined hypothesis. If you your sampling is like placing a trap for a given period of time in a possible habitat and then check whether there is at least one individual caught, the response is binary (yes/no) and an appropriate probability model to calculate the significance is the binomial distribution with the parameter p as the expected proportion of traps with caught individuals. Now you can test your data under any chosen value of p. Chosing p=0 is not particularily helpful here; observing only empty traps is not something that would become unexpected under that hypothesis, no matter how many traps you have. And observing even a single non-empty trap will be completely impossible under that hypothesis (the P-value in that case will thus be 0.000). That's an evident result that would be crystal clear even without testing: as soon as you observe at least one individual, it is impossible that there don't exist any such individuals at all.
What you can do is to define some lower limit for p (call it L) that is larger than 0 (L>0) and test your data under this hypothesis. A small P-value and an observed p
To add to Jochen's very helpful reply, you have to consider other ways of testing your hypothesis than trapping. If a species is present, what should you observe? Not just the creatures you can trap – can you leverage data from multiple sources (what do they eat? how about fecal samples? tracks?) to build a case that they are absent.
And, as Jochen says, the naive definition of absent isn't provable. You have to define absent as fewer than a certain density. In the case of water quality, which I know something about, you define absent as no colony-forming units of bacteria from a sample of 100 mL. This doesn't mean the water is sterile, just that with no CFU in 100 mL, the upper Poisson confidence interval is roughly 3/100 CFU, which is good enough to drink anyday.
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