If you are wanting to undertake multivariate analysis, such as CCA or MDS, you will want to remove rare species that may have been sampled by chance. These species simply produce noise in the data, making it more difficult to interpret. As a rule of thumb, you don't want to end up with too many more species than you have number of samples. There is no hard and fast rule for determining the criteria for species removal - largely it is common sense based on your data. As a first step it is worth removing any species found in less than (or equal to) 3 sites.  Depending on how many species you have left, the next step is to remove species that are always in low abundance; typically you would remove species that never comprise >3 or 4% of the total abundance in any sample. Again, these species simply produce noise - they may just have easily been collected in sites where you found none. 

Probably the mean values with confidence intervals highlight the dominant one. I would calculate it over all stations (by rows). There is a post-hoc test called Duncan's multiple range test, which shows how species differ/similar. It may happen that more dominant species compete. On chart, the error bar type presents the same.

Given that you've got approximately 100 species, some with very low counts, calculating means and reporting confidence intervals may not be valid (e.g. you'll end up with CIs outside the range [0, 1]).

An appropriate statistical technique would be to fit a multinomial regression model (an extension of the Binomial model) so that the concentration y of species i at site j is modelled as y_ij ~ Multinomial(p_i, n_j) where n_j is the sum of all the y_ij at site j. This pools all the proportions of the species (p_i) across each site, rather than taking means of proportions (which is a Bad Idea) or ignoring the differences in the total number of individuals at each site.

This isn't trivially easy, though.

thank you all,

Dewar Dr. Samuel, is the multinomial regression model  is the same as Multinomial Logistic Regression? thanks

Yes, the multinomial is a logistic regression model.

Well, actually, fitting a distribution to few data points may also fail. The CIs were not expected to be in [0,1] since data is already outside of this. The dominant one, what was the question, will pop up among others. On the other hand, I agree that negative lower CI limit warns to the uncertainty of such decision. Similar approach might be the LSD (least significant difference) calculation as a distance function between species.

Anyway, it was only a suggestion.

Just a note, if location of sites was also recorded, the spatial pattern can answer whether randomly scattered species were found or they have a growing pattern.

thanks. now this question for you Dr. Laszlo, lets suggest that i want to do LSD as described at  https://www.youtube.com/watch?v=ZRX4lFtMboo, how can i know which species is dominant? the example method tests groups and i have bunch of species?

If you are wanting to undertake multivariate analysis, such as CCA or MDS, you will want to remove rare species that may have been sampled by chance. These species simply produce noise in the data, making it more difficult to interpret. As a rule of thumb, you don't want to end up with too many more species than you have number of samples. There is no hard and fast rule for determining the criteria for species removal - largely it is common sense based on your data. As a first step it is worth removing any species found in less than (or equal to) 3 sites.  Depending on how many species you have left, the next step is to remove species that are always in low abundance; typically you would remove species that never comprise >3 or 4% of the total abundance in any sample. Again, these species simply produce noise - they may just have easily been collected in sites where you found none. 

WaW, Dr. Duggan... this sounds dead easy!thank you so much

i sampled 8 sites still the concept of removing species that not presented in 3 sites adequate? what if i sampled 50 sites?  

Hi Sama,

Looking at your data, you have 24 sampling stations in your dataset. For a CCA to make much sense of the data (if that is what you are doing), it is best to have any species in several samples - CCA works out the weighted average for each species for each environmental variable, and if the species is sampled only once or twice, these species can disproportionately affect the ordination. If you only had 8 sites in a dataset, I would be concerned that any patterns found were not simply random (i.e., the dataset would be getting too small to be confident of any patterns you are seeing). If you did 50, you might tighten your criteria a little, but by adding more sites you may not actually add many more species. You just need to have some confidence that the species you have in the dataset are reflecting the relationships with the environment, and not in samples due to randomness.

I have had a quick play with your data, removing any species that was found in less than 4 samples, and never in an abundance >100 (see attached). This left 23 species, so I might have been a little harsh in my criteria. However, on the ordination, that is probably about the maximum number of species you will be able to make sense of. Most samples still have >80% of all their counts in the dataset. meaning they wont have lost much information (and noise will have been reduced). I would only be worried about samples 12, 17 and 20. It takes a bit of time and consideration to find the best criteria. However, try this reduced dataset and see if the patterns are useful.

You can use the Chandler score (Chandler (1970) :

No. of species in specimen    Level             Symbol

1-2                                              present                P

3-10                                           frequent                F

11-50                                         Common              C

51-100                                      Abundant               A

100- above                               Very abundant         V

Dear Dr. Sama, in my opinion, the criterion of being "dominant" is to have significantly higher presence. Yes, LSD can be used as post-hoc test in comparison of mean values. I proposed mean because species may not be considered dominant with e.g. outstandingly high amount on one site but missing from all others. Your dominant evaluation may be simple if mean values for species are compared using LSD. The other approach might be a more robust one if dominant species are identified for each site as outliers and finally summarize how many times species were found dominant. This latter one is similar to that of suggested by Dr. Samuel Clifford, without distribution fitting.

Dear Sama,

I put some colours in your table for better view. You can see what is the dominant species in your stations and in the group of species. In your interpetations you can also interpreted your data based on ecological preferences of some dominante/monofloral/very abundant species in the group at some stations.

Best wishes.

I concur with the answers above. Removing the rare taxa and dealing with ambiguities will make the analyses more clear.  You should however, determine what your definition of dominant is though. You can base it solely on abundance or biomass or incorporate both. You could look at bloom producing, colonial, or toxic taxa. Because not all phytoplankton is created equal, dominance need to be defined before it can be identified.

I suggest a few papers relating to dominance plots. 

http://www.sciencedirect.com/science/article/pii/002209819090181B

http://cmep.ca/jcullen/publications/2002/CiottiEtAl2002LandO.pdf

Your data set looks huge and many of them are  rare species. Environmental variabilities  and  physical features  among the sites are not given. First,  compartmentalize into  presence or absence of  species in different sites. Eliminate the rare species considering appropriate number of sites  as a percentage.  I think , better to  calculate the  species dominance for  each genera  to get a clear picture  since environmental requirements of different species may  different. . 

Dear Sama,

it depends on what you want to do with your data. If you are interested in trophodynamics you should fisrt of all use biovolumes and not density (number of cells per liter). Methods to calculate biovolume are available in every paper dealing with phytoplankton. Then you can decide to maintain those species which contribute at least a certain percentage to total biovolume (e.g. 1% or 5% depending on your purposes, data, etc..). You can eventually decide to eliminate those species which appear just once even if they show higher percentage... but again this depends on your purposes.

Good luck! :D

Dear Sama, for my opinion, the best way is to calculate the rate of each species (in %) in the total and take the border of dominance. We take this border as 5%. You will have the dominant species in abundance and in biomass. For trohpic conditions the biomass is better index.

Best regads

Dear Sama

I usually order the species based on two criteria. The first is the total abudance, that is the sum of all their abudances in the data set, which may seem meaningless for ecological interpretation but helps for the task you want to perform. The second criterion is their frequency, that is, in how many samples each species was observed. Then I order the whole data set based on this two criteria. It is easy to do in a spreadsheet. Then you can apply any of the cutting methods just mentioned above. But as a rule of  thomb, the number of species employed in a CCA analysis shuold not be greater than the number of sites or samples.

Another issue is to review those species that show peak abundances in a fea samples. Those might be outliers or may well be a response to a particular condition in those samples.

Dear

Please see the text and the quoted references about the dominant species 

The dominant species (common and numerically abundant species)

 was analyzed based on standard procedures (Yang et al., 1999; Lee et al., 2009; Lin et al., 2011) Yi = (Ni/N) *fi

where Yi is the dominance of species i, Ni is the number of individuals

of species i in all locations, N is the number of individuals of all species in all locations, and fi is the frequency of locations at which species i occurs.

Species with a Yi value of more than or equal to 0.02 were defined as dominant species (Yang et al., 1999; Lee et al., 2009; Lin et al., 2011).

i hope this index is good for demarcation of the dominant forms from the rare forms especially planktonic organisms .

This index considering both the  density as well as the frequency of the occurrences

See the further details 

Ocean currents structuring the mesozooplankton in the Gulf of Mannar

and the Palk Bay, southeast coast of India

Dear 

If u are interested i am ready to collaborate to your works

My email Id : [email protected]

Dear Sama,

It is of utmost importance to be careful when applying any statistics (and/or mathematics) in regard to biological (or ecological) phenomena. Nature does not "play" by the numbers, but rather by many interconnected laws and influences. It of course depends on what you are about to investigate, but in many instances the marginal values or results (in your case algal taxa presence) are those which explain many things in the ecosystem. Many useful things can be deduced just by looking to your algal counts, even if you take care about the forms which are not plankton species (tihoplanktonic ones like many diatoms from your list). Best wishes with your taxonomy as well.  

Sama --

What is the unit for the data in the spreadsheet? Are they cell counts or densities (#/vol)? Are they biovolumes or bv densities (um3/vol)?

Looking at the data -- one of the things that pops out, looking at the taxa, is the large variation in size of the organisms. Looking at just cell densities may give a very different answer than taking into account relative cell sizes when asking which taxa are dominant. It's like having a data set with mice and elephants.

you are absolutely correct Dr. David, the data set contains different sizes of phytoplankton species. this sheet i posted as a samples actually it is only a third of the original data set i have. the units is 10^3 Cell/L so what do you think the answer to  my question will be?

.

sama

if you concentrate about the size then the representation of phytoplankton in terms of  density (cells/lit )  is not the  correct way of presentation but in that cases u can convert density into volume or bio-volume based on the shape of the phytoplankton species and later you can find the which species more contributed to the total biovolume.

Sama ---

i think that the questions of whether to use cell densities or biomass density (e.g. biovolumes) depends on what your top-level question is and what your concept of "dominance" is for this project. For instance if I was looking at biodiversity/ genomic diversity in the environment, I would probably go with individual cell densities as regardless of how large each cell is, they each carry single genome (excluding those of mitochondria and chloroplast genomes). If on the other hand I was interested in questions related to biomass/energetics/food webs then I would most likely look at biovolume (as a proxy for biomass).