Multiple year surveys: stratification or covariates?

[Laura]

Hello!

I have distance sampling transect data from two surveys conducted six years apart, following the same transects. My main goals with this dataset are:
a) to estimate the number of animals present, and
b) to build a density surface model (DSM) to understand which environmental variables best explain their distribution.

My study area is naturally divided into two subregions (north and south), so I’ve used a stratified approach when fitting the detection functions. I fitted a detection function for each year separately and then built two DSMs. However, I’m wondering whether it would make more sense to combine both years into a single model and produce one final map, since the environmental variables influencing my species’ distribution should be consistent across years.

My question is: should I use a stratified design that accounts for both subarea and year (e.g., north-2018, north-2024, south-2018, south-2024), or instead include year as a covariate? Alternatively, would it be better not to combine the years at all?

I understand that by using the stratified approach (subarea + year), I would obtain abundance and density estimates per year and per region, whereas using year as a covariate would only give me estimates per region. But is that the only difference between these approaches, or are there other implications I should consider?

Thank you in advance for your time, 

Best

Laura

[Eric Rexstad]

Laura

It is challenging to provide "off the shelf" advice for your questions. If you combine everything into a single spatial model, your estimated abundance will be an average across the six years; is that useful to you?

Likewise, you are making an assumption when you suggest "environmental variables influencing my species’ distribution should be consistent across years", might you want to test that assumption by fitting separate models. Note also, even if the same environmental factors influence animals in both years, if those environmental factors are dynamic, the spatial distribution of the environmental factors (and hence animas) might change between years.

Just some things to consider.

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From: distance...@googlegroups.com <distance...@googlegroups.com> on behalf of Laura <laurabarbe...@gmail.com>
Sent: 14 October 2025 15:08
To: distance-sampling <distance...@googlegroups.com>
Subject: [distance-sampling] Multiple year surveys: stratification or covariates?

 

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[Tiago Marques]

Hi Laura,

Adding to what Eric said, I'm not sure you've given us all the information required to provide the answers you are looking for.

It was unclear to me whether you were referring to the covariates strata end year as having an impact on detectability (ie at the detectionfunctionlevel), having an impact on density (ie at the density surface model) or potentially having an impact on both. It was also unclear to me whether there might be additional covariates, both for the detection function component as well as for the density surface model component.

I am going to pretend that you have a set of covariates A that will influence the dectability, and you have a set of covariates B that will influence density. Let's ignore for now if there are covariates that belong to both sets A and B, which there wouldn't be a problem in principle if there were.

That kind of  goes without saying but, what I would do first would be to fit the best possible model, using the covariates in A, to the detection function component. If year and/or strata are expected to influence detectability, say, because in different years, you used different observers, or in different strata there's different habitats, then include those in the detection function model.

Then I would fit a density surface model that would have year and strata (and anything else avalable that might help predicting animal density) as covariates in the dsm. You could potentially include an interaction term between between year and strata. Perhaps even more interesting you would have an interaction term between any other existing covariates and year so, let's pretend you had say altitude, if you fit  a model with an interaction between year and altitude, that would allow you to say whether the influence of altitude on density has changed across years. If that model has no support from the data, say, using some information criteria like AIC, then that means as Eric suggested that the influence of altitude on density  has not changed across the two years of surveys. 

Using that same model, you could now have two different prediction grids, one with covariate data from the first year (were naturally year value was fixed at 2018) one with data from the second year (year fixed at 2024) and make predictions per year, and or  per region per year, from the same DSM.

Regarding your desire  "to understand which environmental variables best explain their distribution." of course, that is tempting, and we all tend to do it but...I would suggest that you are very careful with the choice of words when discussing the outputs of your model. A dsm is correlative in nature, so it does not allow for causal inferences.  That means that, based on the available data, you do identify the best set of covariates that can be used to predict density, but those might not be the variables that density depends on. Those variables that did end up in your best model might just be usefully available proxies for the variables that truly determine the animal density. So while it might make sense to try to  interpret the smooth functions from the dsm from an ecological point of view, one should always bear in mind that the patterns you are seeing might be driven by other sets of variables that are correlated with the ones you have in your model, but which you had not the luxury to observe.

Anyway, I hope this helps you,

T

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De: 'Eric Rexstad' via distance-sampling <distance...@googlegroups.com>
Enviado: quarta-feira, outubro 15, 2025 9:52:44 AM
Para: Laura <laurabarbe...@gmail.com>; distance-sampling <distance...@googlegroups.com>
Assunto: Re: [distance-sampling] Multiple year surveys: stratification or covariates?

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