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Mixed modelling and Species Area Relationship (SAR)

4 messages · Gitu wa Mbui, Thierry Onkelinx, Ben Bolker

Original
Gitu wa Mbui
# 
How does one account for the species area relationship in a mixed model of
predicting species richness?

Sampling was carried out using different methods - photoquadrats, transects
etc ( five different methods).

The area of the sampled plots differed and there were hundreds of plots. I
am constructing a glmm for predicting the species richness, overall, and
have configured the Method of sampling as a random intercept in the model.
I am wondering how I should construct the model such the influence of SAR
is taken into account - considering that SAR can not be a random factor.

~Gitu
Thierry Onkelinx
# 
Dear Gitu,

If the area is constant within each method, then the random effect of
method will model the area effect. If not you can add area to the fixed
effects of the model. You have several options: as an offset, as a
(log)linear trend, as a smoother, ... Much will depend on your assumption
on the relation between species richness and sample area.

Best regards,

ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium

To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to say
what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey

2015-11-26 15:09 GMT+01:00 Gitu wa Mbui <gitumbui at gmail.com>:

  
  


  


      

    

    

      
      

        


  

        

      Ben Bolker
    

    

      
      #
    

  


  

      
On 15-11-26 09:09 AM, Gitu wa Mbui wrote:

            

      
      
      
    

        
This is probably a little bit too vague for most of the people on the
list (who are not ecologists).

   Supposing that you're using a log link for the response (which would
make sense if you plan to treat species richness as Poisson or negative
binomial), try incorporating log(Area) as a covariate.  Then (ignoring
all the other stuff in your model for the moment)

  log(mu) = b0 + b1*log(area)

or

  mu = exp(b0)*exp(b1*log(area)) = C*area^b1

 which looks like a pretty respectable model for the species-area
relationship.

  Ben Bolker

  
  


  


      

    

    

      
      

        


  

        

      Gitu wa Mbui
    

    

      
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Thanks @TO and @BB. Sounds like there is a consensus that adding area as a
covariate (log area) is the way to go, considering a variable area among
methods. A few clarifications:

1. @TO - under what circumstances would you add area 'as an offset, as a
(log)linear trend, as a smoother'? please clarify

2. Would it make a difference if the model is smoothed spline? (i.e such
that: gamm4(response ~ s(Area) + s(b1, k..) +...)

~Gitu







On Fri, Nov 27, 2015 at 12:21 AM, Thierry Onkelinx <thierry.onkelinx at inbo.be