Species-Presence exercise 5 - Multi-season example

This exercise is designed to show how to run programs PRESENCE to compute species presence, detectability, extinction and colonization estimates from 'presence-absence' data which includes covariates.

Input data consists of 'detection-histories' of individual species at 'stops' along bbs survey routes. Site covariates, which place the species in groups according to migration properties have also been included.

Running the program

Start a new project in program PRESENCE.

You can view the data by:

After viewing, close the data window, and enter the title.

You're now presented with a 'Results Browser' window where a summary of each model will be saved. To run our first model:

When the 'Setup Numerical Estimation Run' window appears, a design matrix window will appear. By default, a model with one parameter for occupancy (psi) will appear in the occupancy tab, and one parameter (column) will appear for all 25 p's. Also, 4 parameters will be estimated for extinction (eps), and 4 parameters for colonization(gam). Before running this model, change the model name to 'psi(.),eps(.),gam(.),p(.)'. Click 'OK to Run' to run this model.

After the analysis is complete, click 'yes' to append the output to the results browser.

Next, let's run a model where occupancy (psi) is a different for each covariate group (psi(short migrators) not= psi(residents) not= psi(neotropical migrants)). We'll name it psi(migr),gam(.),eps(.),p(.). Start by adding 2 columns to the Occupancy design matrix.

psi is now different for each covariate group.

Run this model.

Look at the output for this model.

Part 1 of output - Title, model name, filenames, etc.

PRESENCE - Presence/Absence-Site Occupancy data analysis
Mon Mar 24 15:06:41 2008,       Version 2.080310
- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
==>i=C:\x\workshops\france2008\bbs_example\bbsmd.pao
==>l=C:\x\workshops\france2008\bbs_example\bbsmd.pa2.out
==>name=psi(migr),gamma(),eps(),p()
==>model=2000
==>j=C:\x\workshops\france2008\bbs_example\bbsmd.dm
==>lmt=200
model=2000 N,T-->85,25
modtype-->2 Multi-Season data Model selected

Data checksum = 14209
NSi-->3
site_covname[0]=SHORT   
site_covname[1]=RESIDENT
site_covname[2]=NEOTROP 
NSa-->0
Primary periods=5 Secondary periods: 5 5 5 5 5
- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 BBS data from WI, 1970-1990 (every 5th year)
- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
modtype=2 N=85 T=25 Groups=1 bootstraps=0

-->0

5 Primary periods
  Secondary periods: 5 5 5 5 5

Part 2 of output - Model design matrices

Model(1):psi(migr),gamma(),eps(),p()

psi covariates:

Matrix 1: rows=2, cols=4
-,a1,a2,a3,
psi1  SHORT    RESIDENT NEOTROP 
**** logit(psi) = SHORT*β1 + RESIDENT*β2 + NEOTROP*β3
So, for short distance migrating species (SHORT=1, RESIDENT=0, NEOTROP=0), logit(psi) = β1
for resident species (SHORT=0, RESIDENT=1, NEOTROP=0), logit(psi) = β2
and, for neotropical migrating species (SHORT=0, RESIDENT=0, NEOTROP=1), logit(psi) = β3
========================
gam covariates:

Matrix 2: rows=5, cols=2
-,b1,
gam1  1
gam2  1
gam3  1
gam4  1
========================
eps covariates:

Matrix 3: rows=5, cols=2
-,c1,
eps1  1
eps2  1
eps3  1
eps4  1
========================

detection covariates:

Matrix 4: rows=26, cols=2
-,d1,
P[1-1]  1
P[1-2]  1
P[1-3]  1
P[1-4]  1
P[1-5]  1
P[2-1]  1
P[2-2]  1
P[2-3]  1
P[2-4]  1
P[2-5]  1
P[3-1]  1
P[3-2]  1
P[3-3]  1
P[3-4]  1
P[3-5]  1
P[4-1]  1
P[4-2]  1
P[4-3]  1
P[4-4]  1
P[4-5]  1
P[5-1]  1
P[5-2]  1
P[5-3]  1
P[5-4]  1
P[5-5]  1
========================

Part 3 of output - log-likelihood and Beta estimates

Open Population Model:

Number of sites                    = 85
Total number of sampling occasions = 25
Number of primary sampling periods = 5
Number of missing observations     = 0

Number of parameters               = 6
-2log(likelihood)                  = 2272.742322
AIC                                = 2284.742322
Model has been fit using the logistic link.

Untransformed Estimates of coefficients for covariates (Beta's)
==============================================================================
                                                          estimate   std.error
A1     :occupancy        psi1SHORT                          0.575387 (0.370320)
A2     :occupancy        psi1RESIDENT                       1.216880 (0.669897)
A3     :occupancy        psi1NEOTROP                        1.828188 (0.471918)
B1     :colonization     gam1                              -1.626977 (0.284866)
C1     :local extinction eps1                              -1.858940 (0.215355)
D1     :detection        P[1-1]                             0.209428 (0.057745)

Variance-Covariance Matrix of Untransformed estimates:
              A1         A2         A3         B1         C1         D1  
     A1    0.137137   0.001030   0.000664  -0.003782  -0.001047  -0.000635
     A2    0.001030   0.448762   0.000040  -0.000340   0.000436  -0.000119
     A3    0.000664   0.000040   0.222707  -0.003727  -0.000712  -0.000729
     B1   -0.003782  -0.000340  -0.003727   0.081149   0.010409   0.002177
     C1   -0.001047   0.000436  -0.000712   0.010409   0.046378   0.001854
     D1   -0.000635  -0.000119  -0.000729   0.002177   0.001854   0.003335
------------------------------

Part 4 of output - Real parameter estimates (psi,gam,eps,p)

   Individual Site estimates of Psi:

        Site         Survey         Psi     Std.err     95% conf. interval
     1   site_1    1    survey_1:  0.8615   0.0563     0.7116 - 0.9401 
     2   site_2    1    survey_1:  0.6400   0.0853     0.4625 - 0.7860 
     3   site_3    1    survey_1:  0.6400   0.0853     0.4625 - 0.7860 
     4   site_4    1    survey_1:  0.7715   0.1181     0.4760 - 0.9262 
     5   site_5    1    survey_1:  0.6400   0.0853     0.4625 - 0.7860 
     6   site_6    1    survey_1:  0.8615   0.0563     0.7116 - 0.9401 
     :     :
            
Distribution of Psi's:
  0.00     0:
  0.03     0:
  0.05     0:
  0.07     0:
  0.10     0:
  0.13     0:
  0.15     0:
  0.17     0:
  0.20     0:
  0.23     0:
  0.25     0:
  0.28     0:
  0.30     0:
  0.33     0:
  0.35     0:
  0.38     0:
  0.40     0:
  0.42     0:
  0.45     0:
  0.47     0:
  0.50     0:
  0.53     0:
  0.55     0:
  0.57     0:
  0.60     0:
  0.63    32:****************************************
  0.65     0:
  0.68     0:
  0.70     0:
  0.72     0:
  0.75    13:****************
  0.78     0:
  0.80     0:
  0.82     0:
  0.85    40:**************************************************
  0.88     0:
  0.90     0:
  0.93     0:
  0.95     0:
  0.97     0:
  1.00     0:

   Individual Site estimates of Gamma:

        Site         Survey       Gamma     Std.err     95% conf. interval
     1   site_1    1    survey_1:  0.1642   0.0391     0.1011 - 0.2557 

   Individual Site estimates of Eps:

        Site         Survey         Eps     Std.err     95% conf. interval
     1   site_1    1    survey_1:  0.1348   0.0251     0.0927 - 0.1920 

   Individual Site estimates of p:

        Site         Survey           p     Std.err     95% conf. interval
     1   site_1    1    survey_1:  0.5522   0.0143     0.5240 - 0.5800 

================================================================================

 DERIVED parameters - psi2,psi3,psi4,...
These parameters can be computed from the others (psi,gam,eps)
psi(2) = psi(1)*(1-eps(1)) + (1-psi(1))*gam(1)
psi(3) = psi(2)*(1-eps(2)) + (1-psi(2))*gam(2)...
        Site                        psi(t)  Std.err     95% conf. interval
     1   site_1      psi( 2):       0.7681  0.0449     0.6801 - 0.8561 
     1   site_1      psi( 3):       0.7026  0.0443     0.6158 - 0.7895 
     1   site_1      psi( 4):       0.6567  0.0474     0.5638 - 0.7497 
     1   site_1      psi( 5):       0.6246  0.0511     0.5243 - 0.7248 
     2   site_2      psi( 2):       0.6128  0.0626     0.4901 - 0.7356 
     :     :
    85  site_85      psi( 5):       0.5711  0.0540     0.4653 - 0.6769 


 DERIVED parameters - lam2,lam3,lam4,...

        Site                        lam(t)  Std.err     95% conf. interval
     1   site_1      lam( 2):       0.8916  0.0278     0.8371 - 0.9460
     1   site_1      lam( 3):       0.9148  0.0230     0.8698 - 0.9597
     :     :
    81  site_81      lam( 4):       0.9347  0.0192     0.8970 - 0.9724
    81  site_81      lam( 5):       0.9510  0.0161     0.9194 - 0.9826
Next, let's run a model where extinction (eps) and colonization (gam) are also different for each covariate group. We'll name it psi(migr),gam(migr),eps(migr),p(.). Start by retrieving the last model run. Next add 2 more columns to the extinction and colonization design matrices. psi, gam, and eps are now different for each covariate group.

Run this model.