Dear Romina, alternatively, you could divide the treeline (755m) into different segments and evaluate the time spent on each segment by comparing it against chance level. For example, if segment1 is 75,5m long, it will represent 10% of the total length of the treeline. Hence the chance level for the time spent on segment1 will be 10%. You can then compare, for each segment, the mean percentages of your group of 15 birds versus chance level through a one-sample t-test against a target value. Of course, this is a group analysis, you should then try to check the percentages of the single individuals to understand if there are any particular individual preferences, that could be related for instance to social hierarchy. Clearly, the segmentation will be a crucial part for this type of analysis. You could for example classify the segments within a same treeline as higher altitude vs lower altitude, distant or adjacent to a lake, etc...

I hope I helped somehow,

Raffaele

Perhaps as an alternative framework or hypothesis to that which is based on the Monte Carlo methods, a flocking model that is proximity-triggered instead of one based on memory.

Article Large-Scale Patterns in a Minimal Cognitive Flocking Model: ...

Hi Romina. I am a researcher currently working on Agent-based modeling (ABM) of social systems.

 I think there are two approaches to answer your question, statistical analysis of the actual data and a simulation to reproduce the real phenomenon.

To know if birds show any preference for locations, statistical analysis of the actual data of birds’ locations would be the priority to do. Next, we can try to reproduce the obtained result by a simulation model, in which birds' activity space would be divided into many small segments and behavioral rules of birds to move to any of the adjacent segments would be assumed. The behavioral rules include a random movement, but we can also assume more complex behavior including individual’s preference. By comparing the simulated locations with the actual data, we can get more understanding about the behavioral rules which might be likely to occur.

  I hope this would be some help to you

Shigeaki

I agree with the other respondents that there are 2 approaches: either statistical analysis of the observations (data) or Monte Carlo simulations to determine whether a process with some randomization thrown in can reproduce the observations.

For me, the analysis of the actual data is preferable. However, I believe using t-tests are not to be recommended. For several reasons (Prosecutor's Fallacy, for one) but primarily because looking at means does not look at enough of the signal you have obtained. Rather, why not use ML (maximum likelihood) estimators of the distribution parameters and compare these? The most likely distribution tells you more about the behavior of the birds than does a mean (most notably: whether the distribution is symmetric). And: don't consider the normal distribution, as your line of trees does not go from negative infinity to positive infinity. Simplest would be, in my opinion: to scale the positions from 0 to 755 m to 0 to 1 (by dividing positions by 755) and then modeling using a Beta Distribution. In so doing, you can look at the likelihoods where there birds congregate. You can also use bootstrapping to determine uncertainties in the ML estimators of the parameters.

Hi Romina, Curious as to the identity of the species. Looks like you are breaking this down into a linear problem; i.e. a point along a line. Is this a linear row of trees? Seems like it may actually be a 3 dimensional problem is you are indeed looking to test if birds prefer certain "spots" Can you break down the "tree line" (which is a three-dimensional space) into boxes and identify each box by x,y,z coordinates. I bird may choose location 650 along your line but be actually going to different altitudes and depths at 650.

Thank you all for the answers and ideas. I attach a figure showing the data for the 15 individuals, which may help to think the problem. 

Hermann, I'm quite interested in what you suggest, but I have never done that kind of modeling, could you suggest me some reading or pointers to start? Thanks a lot.

 Hi Romina, this type of distrubution is very interesting. It s evident that single individuals have some preferred locations. You could do many different analyses on these results.

To start, you could for example divide the treeline in zones of 100 m each and calculate the percentage of nights spent in that zone on the total period of observation. Most individuals will have a high percentage in few zones and low or null percentages in the rest of the treeline.

Another interesting point you could consider is the duration of the preference for a certain zone. You could for instance, for each night, calculate the probability that a bird will remain at a distance of ± 50 m (or ± 25 m) from the location of the previous night. Maybe the probability of change of location will be low in the first nights but high at a certain point. Is there a constant in the duration of the preference for a location (for example high probability of change every 4 days)? To answer to this question, you could also calculate for each individual, the number of nights without changing area from the chosen location (i.e. remaining in the ± 50 m or ± 25 m zone). Once you find a change of preference, for the subsequent night you should consider the new position for this type of calculation. You could find that birds tend to spend x days in a preferred location and then change, hence calculating the mean duration of the preference for a chosen location.

Just a couple of ideas,

Raffaele

Dear Romina,

Thank you for supplying a *.pdf with a graph of the raw data. I can answer some of your queries, therefore:

(1) Clearly, each individual bird's roosting position is beta-distributed. You need not subdivide into intervals, or similar artificial constructs (not bird thinks in 10-m intervals).

(2) There is, I believe, other information to be extracted from the roosting pattern. Do you know further attributes (age, sex, plumage features, etc.) of these birds?

(3) As I program all my ML methodology myself, I cannot give you literature quotes (vz. textbooks) about the use of Beta distributions in biological contexts (other than my own stuff).

I do not know whether there are any rules about offering collaboration via ResearchGate. If I am not violating any rules, I offer to collaborate with you and we publish our findings together. You send me the raw data (and other precautionary information) and I write the programs and analyze the data for you. You may take up my offer, if you wish. If I am not allowed to make this offer (because of ResearchGate regulations), I offer apologies for having made the offer.

My email address: [email protected]

Cheers, Hermann