# Determining Sample Size in Natural Populations

#### Clairemarie63

##### New Member
I was wondering how I would determine a sample size for the given scenerio. Please let me know if more information is needed.
There is a natural population in the wild of 3000 individuals and the sex ratio is 1:1. I collect eggs from nests of known females. From the DNA I have a probability of paternal exclusion of P=0.995. What sample size of males in the population and number of eggs would I need to determine X number of fathers to produce a significant relationship between mating relationships of males and females. I will be use size, weight, or age comparisons between the males and females.
Thanks. Any help in leading me to equations for use would be great.

#### JohnM

##### TS Contributor
I'm a bit confused over what your research questions are.

What is "paternal exclusion?"

And I'm a bit confused as to the objective of your study:

What sample size of males in the population and number of eggs would I need to determine X number of fathers to produce a significant relationship between mating relationships of males and females. I will be use size, weight, or age comparisons between the males and females.

What exactly are you trying to determine through egg sampling? Maybe if you word it without using "statistical" language it may be easier for me to point you in the right direction....

#### Clairemarie63

##### New Member
I'm sorry I am very new at this. I've only had one simple course in statistics. In my natural "experiment" I am going to look at a population that is estimated to be of about 3000 individuals. About half are male and half are female. Females lay eggs in the dirt. Thus I can follow the females and once they have laid their clutch of eggs, I will take the eggs and the females. I will retrieve DNA from the females, and incubate the eggs so that I may retrieve DNA from them after they hatch. Then I will capture males in the population and retrieve their DNA. Based on the DNA loci that I am looking at, if I capture a male that has laid eggs that I have, the probability of exclusion of these DNA loci will allow me know that this is almost certainly the father and I can exclude all other males as potential fathers. Meanwhile, I have been collecting data on mother and father sizes, age, and weight. I want to know if there is a relationship between fathers and mothers in any of these measurements. Therefore, I need an estimate of the number of clutches of eggs I will need and potential fathers in order to get enough definite fathers of clutches to provide a significant relationship (if there is actually a relationship...I'm hoping so!)

#### JohnM

##### TS Contributor
OK, thank you for clarifying - I understand what you're after now.

Unfortunately, even if you sampled the entire population, there's no guarantee that you will find a significant relationship, so with correlation/regression type studies, it's difficult to predict the necessary sample size.

If the relationship is in fact strong and reliable, then you won't need very many - but if it's relatively weak, you'll need a big sample size (but then again, what you've shown, with a big sample size is that there is a weak relationship - so a lot of work for very little payoff).

In other words, you kind of need to know what the correlation coefficient is (at least a rough estimate) before you can determine the minimum sample size required to detect such a correlation.

So, my answer, although not what you wanted to hear, is that you need to sample "as many as you can" within your allotted budget and time, and then see how strong or weak the correlation is. Of the references I've been able to locate on the web, they say anywhere between 30 and 60 should be enough in most cases, but more is better.

My question is: Why would there be a relationship (correlation) between male and female physical attributes such as size/age/weight - wouldn't there be a more-or-less random pairing of mates? Why, in nature, would there be a predictable relationship here? Just curious....

#### Clairemarie63

##### New Member
Thanks for your help. The reason why there might be a relationship is sexual selection. In the population that I am looking at males are much smaller than the females. There is a possibility that either females are selecting for small males or males are selecting for large females (may be due to larger egg laying capacity).

#### jerryb

##### New Member
interesting topic, but it makes me recall being a grad student in physics and having to take a class in the philosophy of evolutionary biology

cheers
jerry