Rehan, we just spent 15 minutes talking about your problem over coffee in our office. Bottom line: 4 population ecologists think the study design is really problematic and we are highly-skeptical of double-observer methods in your case. Jose's suggestion to model these data as coming from a double-observer count is a good suggestion, but you would almost certainly be violating a lot of assumptions and produce bogus answers. These observers are not independent. How could they be? Bob lifts his binocs to look at a heron and Sarah sees Bob raising his binocs so she looks as well and sees the heron. There's no simple way in Mark or unmarked to model this non-independence between observers, and ignoring it will cause your estimates to be overly-precise (b/c the observers' observations will much more similar to each other than if they had been truly counting independently). Did the 4 observers actively share information (i.e., "I've got an osprey over here, it's flying left to right in front of the boat, but don't count it, we've already got it.")? That would be your best-case scenario and then you could use the boat's entire count to produce an index to the population size using any number of simple models. If all 4 people produced "independent" counts then your data are troubling, and you'll need to explicitly acknowledge that in the manuscript and be prepared to defend your use of whatever model you come up with.

Cheers,

Jason

I think it is possible to use data collected this way to look at population trends in relative abundance, but it depends on how the surveys were done. Were the lines/transects a set length and did they record how much time they spent per distance surveyed? Did the observer change? Were the wetland variables recorded the same years the surveys were done?

Do you have spatial or temporal replicas into the same place/season? Maybe you can conduct a N-mix analysis with some covariates:

http://classes.warnercnr.colostate.edu/bayes-workshop/files/2013/04/Royle_Biometrics_2004.pdf

@ Cara Joos

The data was collected after every 15 days in a lake, The route was same every time.So time taken by them is almost same (going from one point and returning to the same). Every time minimum 4 observers (2 recording data at right side and 2 recording at left side of moving boat). All of them have very good knowledge about the identification of waterbirds.

Yes the variables are also from same years.And for some variables we are using RS and Land-use Maps.

You can estimate the densities even using the strip transects. Where the absorber can lay strips of width 50m or say even 100m based on the level of sighting. Also, you can estimate the encounter rates of individual species and how they vary seasonally.

If you have double observer data, you can use this way to calculate p (detection probabilities) and psi (occupancy). The method depends if you have independent or dependent observers. You can make the analysis in R+unmarked (see link).

http://cran.at.r-project.org/web/packages/unmarked/vignettes/unmarked.pdf

Rehan, we just spent 15 minutes talking about your problem over coffee in our office. Bottom line: 4 population ecologists think the study design is really problematic and we are highly-skeptical of double-observer methods in your case. Jose's suggestion to model these data as coming from a double-observer count is a good suggestion, but you would almost certainly be violating a lot of assumptions and produce bogus answers. These observers are not independent. How could they be? Bob lifts his binocs to look at a heron and Sarah sees Bob raising his binocs so she looks as well and sees the heron. There's no simple way in Mark or unmarked to model this non-independence between observers, and ignoring it will cause your estimates to be overly-precise (b/c the observers' observations will much more similar to each other than if they had been truly counting independently). Did the 4 observers actively share information (i.e., "I've got an osprey over here, it's flying left to right in front of the boat, but don't count it, we've already got it.")? That would be your best-case scenario and then you could use the boat's entire count to produce an index to the population size using any number of simple models. If all 4 people produced "independent" counts then your data are troubling, and you'll need to explicitly acknowledge that in the manuscript and be prepared to defend your use of whatever model you come up with.

Cheers,

Jason

I usually make population estimates from boat using double observer. Two people (seated, one of them looking at one side and another on the other side), the pilot (standing) and myself, asking for locations of the birds after every sampling point. The independence, as Jason says, is complicated, but not impossible. But, in this case, I'm suggesting you about the use of unmarked with independent or "dependent" observers using unmarked in R. See the link attached (unmarked forum):

https://groups.google.com/forum/#!searchin/unmarked/simulate$20double/unmarked/XSjOU4Q4Iw0/2ZihdmG-JcUJ

Regards,

Jose

Thankyou so much Jason and Jose, It is a very nice explanation from you side

I am really sorry i didn't explain in detail about this earlier.

Actually every time there are 6 people in the boat, one boat driver (He is only driving)

A team of 2 people looking for birds at right side(Say team A) of the boat and a team of 2 people looking at left side of the boat(Say team B) and the sixth person is to Record the data and tell them if the bird is already counted by any right or left team or if the bird move from right to left and vice versa, And the team of both observers work dependently.and sometimes in any need they convey their message to even other team also.

All of them share information actively.

Rehan - 

This sounds interesting.  It would be nice if you could let us know how this is going now.  

It seems the discussion here was over obtaining a reliable bird count for a given boat trip.  It was noted that models could then be used to estimate the population.  But from a statistical point of view, which would be the point here, yes, measurement error is very important, but no less crucial would be the model used.  In other applications, randomized "area sampling" (see, for example, W.G. Cochran, Sampling Techniques, 3rd ed, 1977, John Wiley & Sons, or other survey sampling books) might be used, but I understand the geographical restrictions here.  So the error made in attempting inference to the population (sampling error) is quite problematic.  (Is there any information on the accuracy of the models noted above?)  

Some of the most reliable information obtained from your bird counts might be your comparative data.  That is, you can look at the ratio of bird counts over time.  That might at least tell you what is changing along the river or lake itself.  But once again, without measures of accuracy (variance, and perhaps bias), results are tenuous.  Still, a ratio of counts is likely more accurate than individual population estimates,  You could easily over- or underestimate a population count.  However, each population estimate is likely biased in the same direction.  If you overestimate both numerator and denominator, or perhaps you underestimate both numerator and denominator, as long as both numerator and denominator are biased in the same direction, the result tends to be more accurate, or at least more accurate than the least accurate of those two population estimates.  (If you want to, you could make up some examples and check it out, to convince yourself.)     

You asked "... if I have such data for 10 years can I use it to relate with wetland variables (water depth, Vegetation, etc)?"  That sounds like a regression problem.  Your dependent variable would be the bird counts, and your predictor-regressor-independent variables would be those you just listed.  Note that for regression, you should look at the "variance of the prediction error."  -  Again, you should caveat that results are for the observable region.  -  You could look at any given period, as a regression for 'prediction' (which is not a time series), and you could also look at time series.  

Cheers -  Jim 

PS  -  Oops. I worked with continuous data, and it has been pointed out that count data requires a different treatment than the usual regression for continuous data, so please bear that in mind. 

The biometrics article that Jose attached to his first response compares results of two population estimation models. That is a good way to get a handle on part of the error. 

To work out population densities as my response variable from this sort of study I would normally favour a distance sampling approach - this unfortunately makes a great deal of assumptions which must be considered before the data is collected in order for these to be accounted for in an analysis, and as the name suggests it also relies on you knowing the distance (and usually angle) from your observation. However, it does sound as though you have enough consistency in your sampling effort and study design to be able to compare your encounter rates relative to one another. Whilst this will not allow you to make any comments on the absolute abundance of the species of interest, it will allow you to comment on any observed trends. For instance if you can statistically prove the encounter rate of herons declines when water turbulence increases, you could conclude that locally, higher water turbulence deters herons. Dealing with count data I would expect to do this sort of analysis with a poisson GLM - which would also allow for you to deal with any spatial and temporal autocorrelation present in your data.

Hope that helps.