Survival Estimates from Annual vs. Monthly Capture Histories

questions concerning analysis/theory using program MARK

Survival Estimates from Annual vs. Monthly Capture Histories

Postby Laurel » Thu Mar 30, 2023 10:40 am

Hello all,

I am working on a 5-year walleye project. Beginning in 2017, fish were tagged and released each spring (April-June) and returned via angler reports. We are using a Seber dead recovery analysis to estimate annual survival and explore survival patterns in relation to a number of variables.

We set up monthly capture histories to incorporate a time-varying environmental covariate in our models. To obtain annual estimates with the monthly capture histories, I specified that each monthly interval was equal to 1/12 of a period and binned time intervals to correspond to year in RMark.

We are considering removing the time-varying covariate from our models. I was curious if our annual estimates of survival would be the same with annual capture histories, so I collapsed the monthly capture histories into annual intervals and reran our models. I found that I had significant issues with estimating annual survival for some years. I think that this is related to minimal tagging that occurred in 2020 due to the pandemic. My question is – would it be acceptable to use the annual estimates from the monthly capture histories even if they are no longer necessary to incorporate our time-varying covariate? I am also wondering about the validity of annual survival probabilities estimated from the monthly capture histories given the discrepancy between the results.

I tried to be concise in my explanation, but please let me know if I have left out any important details that would be helpful in answering my questions.

Thank you in advance for any assistance!

Laurel
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Re: Survival Estimates from Annual vs. Monthly Capture Histo

Postby Eurycea » Thu Mar 30, 2023 11:52 am

I will give this a shot even though I am not exactly certain I understand your question.

Let me see if I'm understanding correctly- your data are collected on a monthly basis, from which you entered a time interval correction in MARK to reflect an annual rate of survival. In addition, you modeled survival as a function of a covariate. Now you want to remove the covariate from the model. You ask:

My question is – would it be acceptable to use the annual estimates from the monthly capture histories even if they are no longer necessary to incorporate our time-varying covariate?


If you remove the covariate from the model, this is entirely independent of the scale you report your survival estimates on (annual vs. monthly). That correction is not really part of the model per se. When you are setting up data in MARK, you can put in 1/12 for a time interval or you can put in 1, the resulting model for survival is exactly the same because this has no effect on it. You can check that this is true by running both models and comparing the deviance (should be the same).

However, there may be other things to consider.
1) what are the implications to changing assumptions when you collapse all of the data? This is essentially a different model of the data. This is what gives different estimates of survival.
2) why are you removing the covariate? Did it improve the model at all?

I hope I understood this correctly, but if not, please let me know.
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Re: Survival Estimates from Annual vs. Monthly Capture Histo

Postby Laurel » Thu Mar 30, 2023 1:26 pm

Hi Eurycea,

Thank you for your prompt reply! Regarding the set up of the study, we tagged every spring from 2017-2021. No additional tagging occurred past June and our data are collected basically continuously throughout the 5-year period as anglers report tagged fish. We ask for exact dates of walleye captured from anglers which can be parsed into monthly or annual intervals. I hope that helped with clarifying things. Please let me know if I need to explain anything else.

If you remove the covariate from the model, this is entirely independent of the scale you report your survival estimates on (annual vs. monthly). That correction is not really part of the model per se. When you are setting up data in MARK, you can put in 1/12 for a time interval or you can put in 1, the resulting model for survival is exactly the same because this has no effect on it. You can check that this is true by running both models and comparing the deviance (should be the same).


I think that the time-varying covariate was somewhat of a misdirection. It is not really relevant to this question other than it prompted a comparison between annual survival estimates obtained from monthly or annual capture histories. Thank you for clarifying the time interval scale and the removal of the covariate. I understand that these don’t really change the model, but I included the scaling to explain how I went about the two methods of getting annual survival estimates.

1) what are the implications to changing assumptions when you collapse all of the data? This is essentially a different model of the data. This is what gives different estimates of survival.


I think that this question addresses exactly what I am trying to understand about the survival estimates we get with monthly vs. annual capture histories (if I understand you correctly). I have been questioning if monthly capture histories are appropriate given that we did not mark fish every month.

2) why are you removing the covariate? Did it improve the model at all?


Regarding the time-varying covariate, we are considering removing it from the model(s) because we are uncertain if we can estimate survival well with this variable. I wrote a separate post about this: http://www.phidot.org/forum/viewtopic.php?f=1&t=4412. To summarize, the covariate is a harvest regulation that is in place every month except July and August of each year. We included the regulation in our models as an environmental covariate. Basically, we would like to compare survival between the months with and without the regulation. If I understand direct and indirect recoveries correctly then I am concerned that, because we do not have any direct recoveries during July or August, we cannot obtain survival estimates during this “no regulation period”. This gets back to my larger concern about the monthly intervals being appropriate for the study design.

I hope that this did not confuse you further. Please let me know if I can clarify anything else. Thank you for your help!

Laurel
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Re: Survival Estimates from Annual vs. Monthly Capture Histo

Postby jlaake » Thu Mar 30, 2023 1:46 pm

If you know the recoveries within each month, I don't see any reason to throw away that information and collapse to annual histories. I would expect seasonal variation in recovery rate which you could model with the monthly data and in another post you mention that there are length limits for some months and not others which you would expect to affect the recovery rate as well. Also since you are tagging for 3 months you can have a staggered entry with the monthly histories.

Since you are using 1/12 for time intervals, your survival rates are expressed as annual rates and when you bin within year for a year effect then your monthly estimates within a year should all be the same. I would think you should consider a seasonal covariate as well but I don't know much about your fishery.

In another post which I no longer see, you asked about plotting for a year*length model where length is an individual covariate. All you need to do is to select one of the indices for S within each year to get the annual estimate as a function of year and then supply the values of length in data.

These are the arguments for
covariate.predictions(
model,
data = NULL,
indices = NULL,
drop = TRUE,
revised = TRUE,
mata = FALSE,
normal.lm = FALSE,
residual.dfs = 0,
alpha = 0.025,
...
)

the S indices for each year (get from ddl$S) would be specified as a vector for argument "indices" and data would be a dataframe containing the values for the variable length that you want (e.g., data=data.frame(length=c(1,2,3))). Each length will be used for each S index. So if you gave it 3 values with 5 indices your would get 15 estimates. Presumably you would use more length values to show clearly. You can plot as a set of 5 lines on the same plot or as a line with confidence interval on 5 separate plots. Up to you.
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Re: Survival Estimates from Annual vs. Monthly Capture Histo

Postby Laurel » Thu Mar 30, 2023 3:47 pm

Hi Jeff,

Thank you for all of your help! Regarding the monthly capture histories, we would like to have the additional information from the monthly intervals. I think that the underlying question for this post and my previous post about the harvest regulations environmental covariate is related to how direct and indirect recoveries for our study would work with the monthly intervals. From my understanding, direct recoveries only occur in the time interval following tagging and survival for a particular interval is derived from the relative proportions of direct and indirect recoveries. I was concerned that, with monthly intervals, obtaining survival estimates for months without tagging would be problematic because no direct recoveries would occur during those intervals. By extension, wouldn't this affect survival estimates for the July and August period when no direct recoveries occurred? Does specifying the 1/12 time intervals get around this issue? Or, is it not an issue at all because I am misunderstanding how the direct and indirect recoveries work? Hopefully my explanation and questions were not confusing - please let me know if I need to add any further details.

In another post which I no longer see, you asked about plotting for a year*length model where length is an individual covariate. All you need to do is to select one of the indices for S within each year to get the annual estimate as a function of year and then supply the values of length in data.

These are the arguments for
covariate.predictions(
model,
data = NULL,
indices = NULL,
drop = TRUE,
revised = TRUE,
mata = FALSE,
normal.lm = FALSE,
residual.dfs = 0,
alpha = 0.025,
...
)

the S indices for each year (get from ddl$S) would be specified as a vector for argument "indices" and data would be a dataframe containing the values for the variable length that you want (e.g., data=data.frame(length=c(1,2,3))). Each length will be used for each S index. So if you gave it 3 values with 5 indices your would get 15 estimates. Presumably you would use more length values to show clearly. You can plot as a set of 5 lines on the same plot or as a line with confidence interval on 5 separate plots. Up to you.


Thank you for explaining to me how to graph the length*year model. I suspected that there was a more obvious solution I overlooked.
Laurel
 
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Re: Survival Estimates from Annual vs. Monthly Capture Histo

Postby jlaake » Thu Mar 30, 2023 4:16 pm

I don't know what you mean by indirect recoveries. You can have recoveries in months you don't tag. Hopefully, you will have recoveries many months after they are initially tagged or they aren't surviving well or losing their tags.
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Re: Survival Estimates from Annual vs. Monthly Capture Histo

Postby Laurel » Thu Mar 30, 2023 5:30 pm

Hi Jeff,

Indirect recoveries are those that occur after the interval following their marking. So, for fish marked in April, direct recoveries would be those that occur in April while indirect recoveries would be those that occur during any interval following April. My understanding is that both indirect and direct recoveries are important to the survival estimates. My concern is coming from a section of chapter 8 in Program MARK: A Gentle Introduction where it addresses a situation when no tagging and releases occur in relation to an annual time interval. I’m paraphrasing a bit, but the section states that when you do not release animals in year t, you cannot get separate survival estimates of the year before (St−1) or that year (St). By specifying 1/12 intervals and binning over an annual period, I am not trying to get separate estimates for each month so I may avoid this issue altogether. That said, I am still uncertain as to how this would work with the harvest regulations environmental covariate. I am not sure if I need direct recoveries to occur within those months get those estimates. Hopefully that explained my questions a little better. I appreciate your help.

Laurel
Laurel
 
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Re: Survival Estimates from Annual vs. Monthly Capture Histo

Postby jlaake » Tue Apr 11, 2023 2:52 pm

I don't know if I can fully answer your question because I'm not sure I understand your time covariate and I couldn't find the exact section you referenced in Chapter 8 of Gentle Intro. But if you look at pg 8-27 for seber recovery expectations it should be clear why skipping months with tagging could be problematic because some of the time dependent survivals would not be estimable. But if you are assuming constant survival over some time periods or using an environmental covariate that essentially smooths the survival estimates then I would think this should not be a problem. Have you tried it? If there was an identifiability problem it should show up in the parameter estimates, their std errors and parameter count. Even if your time covariate doesn't work I'd still use monthly intervals but just don't try to fit S(t) model. Hope this helps. Maybe others will have better insights.
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Re: Survival Estimates from Annual vs. Monthly Capture Histo

Postby Laurel » Thu Apr 13, 2023 2:50 pm

Hi Jeff,

Thank you for checking! The section of the book that I was talking about was in one of the sidebars in Chapter 8. However, I think that you have answered what I was concerned about regardless. This section does specifically mention that individual estimates of time intervals aren’t possible without direct recoveries and since we’re not trying to estimate each month it sounds like we should be fine. I have also been running models with this environmental covariate with no indications of a problem. I was just unsure if the lack of direct recoveries during the July-August period were causing issues that were not obvious in the estimates. It sounds like if there was a problem though, we would see it. I appreciate your insight and taking the time to follow up on this!

Laurel
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