Hello Jari,
Thank you so much for your help. Yes, I have used percent data. 
I just know tried with the absolute counts and got, what I guess are right, values of AIC and BIC.

Now coming back to the similar values, how can I discriminate in between the models with so similar AIC and BIC (and Deviance) values.
I apologise if you wrote it in the paragraph below, but I did not understand.

I copy here the new results:

Cluster I
RAD models, family poisson 
No. of species 24, total abundance 166

           par1     par2    par3        				Deviance 	AIC      BIC     
Null                                    		 			91.6634    161.7168 161.7168
Preemption  0.23969                   			53.4299    125.4832 126.6613
Lognormal   0.71216  1.6811     			13.3666      87.4199  89.7761
Zipf        0.42497 -1.4264               			  2.4005      76.4538  78.8100
Mandelbrot  0.42497 -1.4264  2.9057e-06      2.4005      78.4538  81.9880

Cluster II
RAD models, family poisson 
No. of species 35, total abundance 228

           par1     par2    par3   	Deviance 	       AIC     BIC    
Null                               		 	  58.597  	  165.650 165.650
Preemption  0.13664                    45.830           154.884 156.439
Lognormal   1.0417   1.3473       10.898           121.951 125.062
Zipf        0.27724 -1.0959              11.181          122.234 125.344
Mandelbrot  0.3957  -1.221 0.4   10.721          123.774 128.440


Thanks again!
Sol

On Dec 17, 2013, at 1:48 PM, Jari Oksanen <jari.oksanen@oulu.fi> wrote:

> Hello,
> On 17/12/2013, at 17:01 PM, Sol Noetinger wrote:
> 
>> Hello,
>> 
>> Cluster II
>> RAD models, family poisson 
>> No. of species 35, total abundance 100
>> 
>>           par1     par2    par3   Deviance AIC     BIC    
>> Null                               25.7004      Inf     Inf
>> Preemption    0.1                  27.8760      Inf     Inf
>> Lognormal   0.21756  1.3473         4.7797      Inf     Inf
>> Zipf        0.27724 -1.0959         4.9038      Inf     Inf
>> Mandelbrot  0.64175 -1.3825      1  4.9181      Inf     Inf
>> 
>> I read from the manual that to see which models fits better you use the AIC values. 
>> What is the meaning of getting "infinite"?
> 
> It seems you can get infinite AIC and BIC when the distribution you selected is in conflict with the nature of your data. For instance, when you postulate a Poisson model (like in your case), but your data are not integers (counts). Was that the case with you? Distribution families that go along with non-integer (real) data are gaussian and Gamma. You can neither use quasipoisson nor other quasi models, because these do not have AIC. 
> 
>> Can I use the Deviance value to compare the models?
>> And in case I can use the deviance, since there are very close values, should I run a test to see if the differences are significant?� in that case, which  one?.
> 
> The models have different numbers of estimated parameters and they are not nested. Many people claim that you can use neither deviance nor AIC (and they are right). At least you must take into account the number of estimated parameters that varies from zero to three.
> 
> Cheers, Jari Oksanen
> 


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