So you have different measurements of species numbers at this location in each season, I guess? In this case you should better use a Poisson-regression model (since you have count data) with the categorical predictor "season" and the species number as the outcome. But do'nt you have the problem that the species abundance changes continuously with the time of year rather than changing suddenly with the season? In this case your data could show temporal autocorrelation, which has to be considered within the regression model.
p=0.0132 when paired=TRUE, but when paired=FALSE p=0.09667
So I need to decide whether it's paired or not because thats a big difference! I assumed paired as its the same locations being compared but friends have argued not paired as it will be different individual animals being recorded and the season is differen't. Seems like it should be so simple but I can't get my head around it!!
It looks like paired data to me, assuming that some sites are naturally more abundant than others. Find the site differences and see if the differences look normal. If the differences are more or less normal then I would use the paired t test. otherwise the Wilcoxon test.