Interesting question, not sure as you also include time as a predictor (I think?). I am also not sure what your target variable is, present/absent (binomial), counts (Poisson/negative binomial) or continues (e.g. an diversity estimate for different amphibian species). Also the predictors (I like this term more than independent variable) are seemingly different. For ponds this would seem 3 groups, but for fish it could be count or biomass, but also time which could be regarded as predictor or random effect?

If your study exploratory or hypothesis driven? If hypothesis driven then it would be wise to select an test before, possibly GLMM or ANOVA? For estimating an appropriate sample size of an ANOVA you would need some estimate on the variability of a target value. An online tool would then give some estimation, what an appropriate sample size would be to obtain with a certain power and alpha level (e.g. see this post https://www.researchgate.net/post/What-is-the-best-way-to-determine-the-necessary-sample-size-for-a-two-way-ANOVA-in-a-psychological-study). However, under field conditions it becomes extremely problematic to exclude specific effects of other miscellaneous factors so personally I am always a bit warry of tests.

If exploratory, as much as seem feasible. However, know that with a small sample size the observed "effect-size", for example captured variation in a CCA, might be an extreme over estimation.

I am curious what a real statistician would say.

Check https://www.researchgate.net/publication/339495309_Multi-species_occupancy_models_review_roadmap_and_recommendations

Also check https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0240989

Make sure you have four sitestr for sample collection in each Pond and that gives you 48 samples for the parameters you want to study or investigate

Yes, because the ponds are replicates. As long as they are distant from each other, that's enough. There are no rules :)

I think your research design is perfect, just go ahead and implement it. What is not seen now can be treated as you go along.

Perfect n value has been taken

Variation in pond size can be important - big ponds hold more species than small ones. It seems likely that ponds that dry out will be smaller? You may need a size range of each pond type to check this.

In my day, statistics was handled by a separate government department. Their advice was always "You are ecologists; collect as much data as you can; it still won't be enough". Good luck.

John Flux

I fully agree on collecting as much data as possible, but when a certain number of species have been found - it will be time to move on to the next pond for a study like this.

In my case it's actually the medium size ones that dry out, they're located on karst terrain though - meaning the spring water eventually go down into underground reservoirs.

As for the OP, it depend on what you intend to accomplish with the study. But offhand I do think you have chosen a good number of ponds to be able to do an in depth study. My own problem, is that I am quite lost on the identification of most species of algae but also many insects. So I work on hundreds of localities, though ones where hardly none have done any previous survey.

But that's an approach I would not recommend for anyone else - and I will still have to leave many tens of thousands lakes and ponds without a single visit, so from an ecological viewpoint my work is indeed as shallow as many ponds. =)

(The image show one area that will not be surveyed in my lifetime, even though it's within 1 hour of driving and two lakes use a local name that suggest the presence of T. cristatus.)

Thanks for the explanation, and map. It looks a marvelous place to study.

All the best, John

excellent question