Hi Sean,

it depends on many aspect of your research questions, organisms under study, genetic markers used, population size and so on.... There are quite a few fisheries papers studying genetic diversity over time.... It also depends on the generation time of your subject.... For long living organisms not under "human pressure" (fisheries or hunting) then you might want to try to capture different generation....

Some useful references, sorry it's mainly on fish so far:

1. Therkildsen NO, Nielsen EE, Swain DP, Pedersen JS (2011) Large effective population size and temporal genetic stability in Atlantic cod (Gadus morhua) in the southern Gulf of St. Lawrence. Canadian Journal of Fisheries and Aquatic Sciences 67: 1585-1595.

2. Jakobsdóttir KB, Pardoe H, Magnússon A, Björnsson H, Pampoulie C, et al. (2011) Historical changes in genotypic frequencies at the Pantophysin locus in the Atlantic cod (Gadus morhua) in Icelandic waters: Evidence of fisheries-induced selection? Evolutionary Applications 4: 562-573.

3. Hare MP, Nunney L, Schwartz MK, Ruzzante DE, Burford M, et al. (2011) Understanding and estimating effective population size for practical application in marine species management. Conservation Biology 25: 438-449.

4. Ruzzante DE, Taggart CT, Doyle RW, Cook D (2001) Stability in the historical pattern of genetic structure of Newfoundland cod (Gadus morhua) despite the catastrophic decline in population size from 1964 to 1994. Conservation Genetics 2: 257-269.

5. Poulsen NA, Nielsen EE, Schierup MH, Loeschcke V, Gronkjaer P (2006) Long-term stability and effective population size in North Sea and Baltic Sea cod (Gadus morhua). Molecular Ecology 15: 321-331.

You have the option to use various software package (i.e. Nestimator or LDNE). These will based on the variance of you measured allele frequencies and the generation number between the samples, determine the effective population size. Quite obviously you can not assume that you data are fully independent, after all the generations are connected forward and backwards due to the genes being carried over. However, if you can avoid sampling related individuals, which will depend very much on the population you study, you may assume independency of your samples. For very small populations, it becomes difficult to avoid relatives. The effective population size is a measure of genetic drift, and will thus provide you a direct indication of declining genetic diversity.

Hi Sean,

it depends on many aspect of your research questions, organisms under study, genetic markers used, population size and so on.... There are quite a few fisheries papers studying genetic diversity over time.... It also depends on the generation time of your subject.... For long living organisms not under "human pressure" (fisheries or hunting) then you might want to try to capture different generation....

Some useful references, sorry it's mainly on fish so far:

1. Therkildsen NO, Nielsen EE, Swain DP, Pedersen JS (2011) Large effective population size and temporal genetic stability in Atlantic cod (Gadus morhua) in the southern Gulf of St. Lawrence. Canadian Journal of Fisheries and Aquatic Sciences 67: 1585-1595.

2. Jakobsdóttir KB, Pardoe H, Magnússon A, Björnsson H, Pampoulie C, et al. (2011) Historical changes in genotypic frequencies at the Pantophysin locus in the Atlantic cod (Gadus morhua) in Icelandic waters: Evidence of fisheries-induced selection? Evolutionary Applications 4: 562-573.

3. Hare MP, Nunney L, Schwartz MK, Ruzzante DE, Burford M, et al. (2011) Understanding and estimating effective population size for practical application in marine species management. Conservation Biology 25: 438-449.

4. Ruzzante DE, Taggart CT, Doyle RW, Cook D (2001) Stability in the historical pattern of genetic structure of Newfoundland cod (Gadus morhua) despite the catastrophic decline in population size from 1964 to 1994. Conservation Genetics 2: 257-269.

5. Poulsen NA, Nielsen EE, Schierup MH, Loeschcke V, Gronkjaer P (2006) Long-term stability and effective population size in North Sea and Baltic Sea cod (Gadus morhua). Molecular Ecology 15: 321-331.

To test genetic diversity on the same populations across time you can use the Wilcoxon Signed-Rank Test http://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test

For example in Charbonnel N, Quesnoit M, Razatavonjizay R, Bremond P, Janrne P. 2002. A spatial and temporal approach to microevolutionary forces affecting population biology in the freshwater snail Biomphalaria pfeifferi. Am Nat. 160:741–755.

Do not use a two-way ANOVA with repeated measures to test for this type of data, this is essentially stochastic data and the ANCOVA is the proper statistical test to apply.

Thanks all for the advice thus far. Indeed Ne would be a good method to show whether diversity is likely declining (as in Antao et al 2011- citation below). However, I am interested to directly demonstrate a decline in diversity at neutral microsatellites, SNPs or DNA sequences, e.g. a decline in heterozygosity from 0.8 to 0.7 or a loss in allelic diversity of 10%. In other words, to quantify how much diversity has declined over a given time period and whether this is statistically significant. Therefore I would like to perform something like the Wilcoxon test as David suggests, but I was primarily worried about the assumption of independence. Assume the individuals are short lived (one generation per year) so we are not sampling the same individuals. Still, if its a conservation situation (say 50 to 100 individuals), as Per notes, we might not be able to be sure that the samples are not related individuals (offspring, grandchildren..), therefore there is not complete independence. What I might do is use the Wilcoxon test and note that samples might not be completely independent.

Further, say we have a considerable number of temporal samples, six or eight consecutive years (generations) of sampling, would a linear regression be possible?

Thanks again for the insights and useful references to follow up on. Please add further comments if you think of any.

Antao, T., Pérez-Figueroa, A., & Luikart, G. (2011). Early detection of population declines: high power of genetic monitoring using effective population size estimators. Evolutionary Applications, 4(1), 144–154. doi:10.1111/j.1752-4571.2010.00150.x

statistically dealing with such a data first of all you have to check whether there is a trend in both the samples or not (check with the help of some graphical method)

if there is not any trend then after checking Normality can apply standard procedure.

if there is a trend, then detect the type of trend, detrend the data and then apply standard procedure for testing.

You might be interested in perMANOVA (see http://www.stat.auckland.ac.nz/~mja/prog/PERMANOVA_UserNotes.pdf ), which you could use to estimate changes in betadispersion of genetic diversity among your temporal groups.

Be careful on the MANOVA, it was developed to supplant ANCOVA; but, there is truly no substitute for ANCOVA. The data is a time series; therefore, you must not treat stochastic data as homogeneous in time, hence, use the ANCOVA testing method.

Thanks Luisiana, Alena, and Raja. I appreciate the input. If possible at a later date I will share some of the data generated so everyone can have a look. All the best.