Lion survival between groups, age-cohort model

[maralions]

Hello,

I am new to MARK and am struggling to build a model using the design matrix. Ultimately, I am not sure if what I want to do is possible. I have read the manual, but am as yet unable to apply the relatively basic examples to my quite complex problem.

I am interested in the drivers of lion survival between prides. For each pride I have a capture history of individuals that were marked at different age classes. Recapture was constant over time and thus I have separated presence/absence into 6 month blocks. There are therefore no intervals. I expect survival to vary between prides, and between age classes both within and between prides, but not as a result of time of initial capture. I would like to incorporate covariates into the model which are constant over time for each pride, e.g. the amount of human settlements in a pride area and the amount of a particular habitat. I would like to see how, for example, human settlements affects survival between prides to answer the question of whether anthropogenic factors are limiting lion survival. The between pride comparison is the most fundamental element and I need estimates to be pride specific. I have 8 prides, 3 age groups (1 year, 2-4 years, 4+ years) and at least 7 blocks per pride (some more). Unfortunately it was not possible to monitor all prides at the same time.

Therefore I need to build a model that:
- takes into account that not all prides were monitored at the same time
- considers survival as different for age classes
- considers different marking ages
- allows for comparison of survival between age classes within each pride (e.g. do cubs experience higher survival in pride A than pride B?)
- allows the use of simple covariates that are constant over time and for each pride (i.e. one constant measure that varies by pride area)

I am starting to think that what I want to do is not possible. And very, very complicated. I am considering using RMark as combining the different applications of linear constraints and age/sex cohorts is something I do not seem to be able to do.

If anyone can offer some advice, I would be extremely grateful. Apologies for the long post.

[bacollier]

Hello,

I am new to MARK and am struggling to build a model using the design matrix. Ultimately, I am not sure if what I want to do is possible. I have read the manual, but am as yet unable to apply the relatively basic examples to my quite complex problem.

What you may see as basic examples is what leads you to complex analysis...there is a wide array of relative complex problems folks are working on that you can find out there in the literature.

I am interested in the drivers of lion survival between prides. For each pride I have a capture history of individuals that were marked at different age classes. Recapture was constant over time and thus I have separated presence/absence into 6 month blocks. There are therefore no intervals.

So, were these tagged lion's, radio's, or what type of unique mark (or does it matter?). How many individuals are you talking about (10s or 100s of individuals)? It seems that your study element is the individual lion, nested within a pride? If so, then you are probably going to treat pride as grouping variable in your analysis (see Cp 6 and 7 in the MARKBOOK).

What does presence/absence into blocks mean? Do you mean individuals were captured and resighted every 6 months? How long (in 6 month sampling occasions) was your study? What do you mean 'there are no intervals'?

I expect survival to vary between prides, and between age classes both within and between prides, but not as a result of time of initial capture.

As an aside, why not?

I would like to incorporate covariates into the model which are constant over time for each pride, e.g. the amount of human settlements in a pride area and the amount of a particular habitat. I would like to see how, for example, human settlements affects survival between prides to answer the question of whether anthropogenic factors are limiting lion survival. The between pride comparison is the most fundamental element and I need estimates to be pride specific.

How to do this is detailed in Ch 6.

I have 8 prides, 3 age groups (1 year, 2-4 years, 4+ years) and at least 7 blocks per pride (some more). Unfortunately it was not possible to monitor all prides at the same time.

So, you have >=7 sampling occasions per pride, so 3.5 years of capture/recapture data, is that correct? That seems to be a pretty short set of encounter occasions for a species that lives probably 10+ years (thanks google scholar) in the wild? Do you have significant mortality in your study groups, or do you have a suite of sampling occasions where no one dies as that could cause modeling issues (e.g., you cannot estimate survival if everyone lives).

Therefore I need to build a model that:
- takes into account that not all prides were monitored at the same time
- considers survival as different for age classes
- considers different marking ages
- allows for comparison of survival between age classes within each pride (e.g. do cubs experience higher survival in pride A than pride B?)
- allows the use of simple covariates that are constant over time and for each pride (i.e. one constant measure that varies by pride area)

All of these are outlined in the MARKBOOK in one manner or another. Also, what is 'marking age' you state here, would that not be encompassed in age class (or perhaps time since marking?)

I am starting to think that what I want to do is not possible. And very, very complicated. I am considering using RMark as combining the different applications of linear constraints and age/sex cohorts is something I do not seem to be able to do.

RMark is not a panacea for not being able to figure out how to work the DM in MARK and you can get in significantly more difficulties with RMark if you don't understand what is going on under the hood, so this is a bad idea.

If anyone can offer some advice, I would be extremely grateful. Apologies for the long post.

In general, you have groups (MARKBOOK 6.9) and individual covariates (MARKBOOK chapter 11) and age/cohort models (Chapter 7). Unless I am missing some weird intricacy that you did not describe, there is nothing here not detailed in those 3 chapters, with examples of how to do it as well as examples in the MARK helpfiles you can download from the MARKBOOK download tab (its at the bottom).

\bret

[markmiller]

My initial impression is that what you want to do probably is possible. Based on the information you have provided I cannot give a definitive answer. However, here are some initial thoughts:

1. I am unclear whether you are trying to estimate the effect of true age on survival.

2. Do you know the true age of the lions in the 2-4 year group? In other words, within a given sample period do you know whether each individual is 2-years old or 3-years old or 4-years old? Or do you just know the animal is > 1 year old and < 5 years old?

3. Within each sample period do you know the true age of lions that are 5-or-more years old?

4. I am not sure what you mean by 'considers different marking ages'.

5. I am unclear how you know that 'recapture was constant over time'. Do you mean recapture effort was constant over time? Probably not since you wrote 'it was not possible to monitor all prides at the same time'.

6. If a pride was not monitored in a given sample period then capture probability can be constrained to zero for pride for that period and survival can be estimated for the entire interval between the two consecutive periods when the pride was monitored. If you are estimating 6-month survival and do not monitor a pride for a year, skipping one sample period, then perhaps you can constrain the two 6-month survivals constant between sample periods, or perhaps you can estimate survival for the missing period as a function of covariates.

When I write that you can constrain capture probability to zero, I am pretty sure you would actually constrain that capture probability to one (for mathematical reasons) which would have the effect of removing that capture probability from the model. Using zero instead of one for that capture probability might have the inadvertent effect of telling MARK all of your lions just died.

7. When you write that you 'have separated presence/absence into 6 month blocks. There are therefore no intervals', I assume you mean you have two six-month capture periods per year. This makes me a little uncomfortable. My initial thought might be to have two one-month sample periods per year with a 5-month gap between sample periods or two two-month sample periods per year with a 4-month gap between sample periods. In other words, for example, January and July might be sample periods.

8. I cannot tell you what your design matrix will be, but if I knew the answers to the above questions I could conceivably work out a design matrix. The way I would do it is I would assign a true value to every parameter I wanted to estimate. Then I would create a fake data set using the model structure I wanted and the aforementioned true parameter values. Then I would create a design matrix using my best guess for what that design matrix should be and I would play around with the design matrix until it returned parameter estimates that matched the known true values. To do this process without error I would probably need to use SURVIV or R. Although, you could do it with MARK and probably get parameter estimates that are almost the same as their true values if you use large sample sizes of lions in your fake data set.

I almost always use this process when creating complex models because I want to be sure I get the design matrix correct. However, the process can take several days. If you have never tried this process yourself and think you might want to use it I suggest starting with the simplest possible model and very gradually adding complexity.

Hopefully at least some of this helps.


EDIT:

Regarding No. 6, after a little more thought, perhaps in MARK I really would constrain that p to zero instead of one. If I really were attempting to create your design matrix that is the kind of thing I would look up in the MARK manual and I would eventually figure it out when I went through the process of analyzing the fake data. In SURVIV I would probably constrain the p to 1 or simply remove that p entirely. But with MARK I am now thinking perhaps that p should be constrained to zero.

[maralions]

Dear both,

Thanks very much for getting back to me. I will attempt to answer some of your questions, and will answer the above questions in another post to keep it relatively (!) short. I appreciate that I didn't give too much information in my original post but I was trying to avoid a huge chunk of text!

1. I am unclear whether you are trying to estimate the effect of true age on survival.

Yes, to some extent. However, my main focus is on the effect of pride membership on survival. I don't really 'care' about the effect of age, but I do know that survival will be different across age groups, and this cannot be ignored in my model. Perhaps most important is to identify differences in adult survival. One alternative approach would be to remove all cubs from the model and start monitoring from sub-adulthood (and thus only 2 age classes). Cub mortality is due mostly to inexperienced motherhood and infanticide effects, and my main focus is on anthropogenic drivers of mortality.

2. Do you know the true age of the lions in the 2-4 year group? In other words, within a given sample period do you know whether each individual is 2-years old or 3-years old or 4-years old? Or do you just know the animal is > 1 year old and < 5 years old?

Yes, I know the exact age of all the individuals, apart from individuals that I started to monitor from adults; for these, I have a good estimate. For animals under 6, I have a reliable estimate within a year.

3. Within each sample period do you know the true age of lions that are 5-or-more years old?

The reliability of age estimates decreases with age, so it is difficult to estimate to within a 6 month interval for, say, 9 year olds. That said, I am concerned mostly with survival within age groups and specific ages over, say, 6.

4. I am not sure what you mean by 'considers different marking ages'.

I mean individuals that I have started to monitor as subs or adults, i.e. all those that I first sight that are not within their first interval of life. This is something I am struggling with. My age classes at the moment are: cubs for 2 intervals, sub adults for another 6 intervals, and then adults. I initially wanted to have small cubs (1 interval), large cubs (1 interval), dependent subs (4 intervals), independent subs (2 intervals) and then adults, but I believe this is too complex. I am unsure how to proceed with age at marking - if I divide them into groups of age classes, how do I ensure that a 'new' sub adult remains a sub adult for another three intervals, and an 'old' sub adult progresses to adulthood at the next interval?

5. I am unclear how you know that 'recapture was constant over time'. Do you mean recapture effort was constant over time? Probably not since you wrote 'it was not possible to monitor all prides at the same time'.

You're right, this is wrong. What I mean is for prides where monitoring was occurring, I expect that encounter probability will be very high within a 6 month interval. Usually if a lion is in an area, it is seen pretty quickly - it is a tourist region and they're pretty 'tame'. But this is obviously an assumption I cannot make!

6. If a pride was not monitored in a given sample period then capture probability can be constrained to zero for pride for that period and survival can be estimated for the entire interval between the two consecutive periods when the pride was monitored. If you are estimating 6-month survival and do not monitor a pride for a year, skipping one sample period, then perhaps you can constrain the two 6-month survivals constant between sample periods, or perhaps you can estimate survival for the missing period as a function of covariates.

My concern here is only for those prides that I stopped monitoring. For example, if I monitor pride A from survey year 1 to year 5, and then pride B from year 3 to year 8, I need to discount years 6-8 for pride A. I was going to do that by fixing the parameter values for both Phi and p for pride A (either to 0 or 1 based on your comments below). Would that be a suitable approach?

7. When you write that you 'have separated presence/absence into 6 month blocks. There are therefore no intervals', I assume you mean you have two six-month capture periods per year. This makes me a little uncomfortable. My initial thought might be to have two one-month sample periods per year with a 5-month gap between sample periods or two two-month sample periods per year with a 4-month gap between sample periods. In other words, for example, January and July might be sample periods.

I am also concerned about this. This is my #2 concern after the overlap concern detailed above. Does anyone have any comments on this? Is this approach suitable? In any case, i cannot state that sampling is instantaneous.

8. I cannot tell you what your design matrix will be, but if I knew the answers to the above questions I could conceivably work out a design matrix. The way I would do it is I would assign a true value to every parameter I wanted to estimate. Then I would create a fake data set using the model structure I wanted and the aforementioned true parameter values. Then I would create a design matrix using my best guess for what that design matrix should be and I would play around with the design matrix until it returned parameter estimates that matched the known true values. To do this process without error I would probably need to use SURVIV or R. Although, you could do it with MARK and probably get parameter estimates that are almost the same as their true values if you use large sample sizes of lions in your fake data set.

This sounds very sensible. Unfortunately with the time that I have (analysis and write up before end Aug) I am very limited in terms of how much I can learn and apply. I am sure that if I had more time to do this, I could tackle some of these issues confidently myself. But it is very much a learning process at this point.

Thanks again.

[maralions]

So, were these tagged lion's, radio's, or what type of unique mark (or does it matter?). How many individuals are you talking about (10s or 100s of individuals)? It seems that your study element is the individual lion, nested within a pride? If so, then you are probably going to treat pride as grouping variable in your analysis (see Cp 6 and 7 in the MARKBOOK).

Each lion is identified by its whisker spots so it's a non-invasive process. The spots remain the same throughout its life so it's possible to identify a cub as an adult later. I have only included sightings where I am 100% sure of the identity (e.g. through photographs). Yes I have individual histories for each lion, and want to use pride as a grouping variable. My problem is that all survey periods were not at the same time, and I have several age classes, and I am having trouble with the complexity of the matrix. I understand the basic concepts, but actually writing the whole thing out with possible interactions (i.e. obtaining a global model) is proving very difficult for me in this early stage.

What does presence/absence into blocks mean? Do you mean individuals were captured and resighted every 6 months? How long (in 6 month sampling occasions) was your study? What do you mean 'there are no intervals'?

Recapture was constant, i.e. there were no capture occasions. This was simply due to the resources needed to monitor the amount of lions in the study, and also because they're quite cryptic. However, within a 6 month interval, if a lion is in the area, it WILL be seen (it is a tourist region). Therefore instead of the usual pattern:

-----p--------p-------p-------p-------p-------p--
Phi-----phi-----phi-----phi-----phi-----phi-----

I have:

p--------p-------p--------p-------p--------p-----
Phi-----phi-----phi-----phi-----phi-----phi-----

Does that make sense?

I expect survival to vary between prides, and between age classes both within and between prides, but not as a result of time of initial capture.

To elaborate, I mean that I don't expect 'marking' or 'capture' events to influence survival or recapture, as may be seen with trapping.

How to do this is detailed in Ch 6.

Yes, I think I am relatively comfortable with this.

So, you have >=7 sampling occasions per pride, so 3.5 years of capture/recapture data, is that correct? That seems to be a pretty short set of encounter occasions for a species that lives probably 10+ years (thanks google scholar) in the wild? Do you have significant mortality in your study groups, or do you have a suite of sampling occasions where no one dies as that could cause modelling issues (e.g., you cannot estimate survival if everyone lives).

I have a decent number of individuals spanning all life stages, as I began monitoring for lions within all age groups. Yes, I do have mortality within all age groups.

All of these are outlined in the MARKBOOK in one manner or another. Also, what is 'marking age' you state here, would that not be encompassed in age class (or perhaps time since marking?)

Yes, I know that most/all of what I want to do is outlined in the book. My problem, being very new to MARK, I am having trouble expanding on these concepts. For example, I can see how interactions with age classes work when you have two or three age classes whereby all but the last class are one interval in duration, but I am unsure how to proceed when intermediate/initial age classes span more than one interval. Similarly, for 'marking age' (whereby I mean monitoring starting AFTER interval 1) - I understand how to do this if I have two age classes, with the first age class being one interval and then immediate progression to the next age class. But again, I am unsure how to approach it when I have an intermediate/initial age class that spans more than one interval. For example, if I create a dummy variable saying that an individual was first captured as a first interval sub adult (and thus remains in that age class for another 3 intervals), how do I differentiate that between an individual that is a late sub adult and needs to progress to the adult class at the next interval?

RMark is not a panacea for not being able to figure out how to work the DM in MARK and you can get in significantly more difficulties with RMark if you don't understand what is going on under the hood, so this is a bad idea.

I appreciate and understand this fully. It appears that RMark is easier for dealing with age categories spanning several years and for setting parameters. I do know that I must understand the DM once it has been constructed.

In general, you have groups (MARKBOOK 6.9) and individual covariates (MARKBOOK chapter 11) and age/cohort models (Chapter 7). Unless I am missing some weird intricacy that you did not describe, there is nothing here not detailed in those 3 chapters, with examples of how to do it as well as examples in the MARK helpfiles you can download from the MARKBOOK download tab (its at the bottom).

I know all of what I want to do is detailed in the book at a simpler level. I just cannot seem to 'boost' it to more complex situations, which is extremely frustrating. Particularly given the time!

Thanks again.

[markmiller]

I probably could write one or two design matrices that would do most, if not all, of what you want. However, I will not have time to work on it for several weeks. If mid-July rolls around and you still have questions then check back here or send me an email:

mmiller21@alaska.edu
mark.wayne.miller@gmail.com

[maralions]

Hi Mark,

Many many thanks for the offer of help. Let's see where I get! Certainly if I'm not there by mid-July then it will be panic stations.

Sara