I think the main problem is to appropriately account for the correlation structure of unexplained variation in the data (i.e., to avoid pseudoreplication). As long as this issue is sorted out, you should be able to include explanatory variables data on different scales without problems. This is one of the main benefits with mixed effects models.

In your case, I believe including "Year" and "Trap ID" as factor variables with random effects (on the intercept), should do the job. After that you should be able to include trap-specific, year-specific and observation-specific explanatory variables. Naturally, observations which are specific for each combination of trap and year contain more information than those, which are common for all traps or all years.

Cool data.

Are you modeling abundance or biodiversity? There are some good programs for biodiversity. I have used EstimateS.

I would try tow analyses. I would use Julian date, and I would use Growing Degree Days (GDD). I would compare the outcome, even if you only use one approach in the end. The use of GDD will correct your data for year-to-year variability in temperature. You will have to guess at the developmental threshold, but I would try any developmental threshold for any arthropod in your area. A single value is not realistic, but it is a good approximation if you have no other information. The GDD model had a lower variance that using Julian date for moths in NE Ohio.

Past that, there are nonlinear models that can be used to estimate the number of yearly cycles in the data.

With luck you have temperature and rainfall for each trap.

It really depends on what sort of data you have and what your goals are. The other thing is to take time with the data analysis. There are a large number of questions that you can ask.

Can you find a change that would be consistent with the issue of global warming. I couldn't, but I had only 9 years of data.

What is the seasonal profile for the spider species?

Are some spiders more sensitive to environmental change?

Does temperature and rainfall explain the shift in seasonal distribution, or is there an elevation effect that is in addition to the temperature/rainfall differences?

Is there an ecological niche shift in the spider community with location? Fishing spiders in an area with water, or something like that?

How far are your traps?

If you have data from various close meteorological stations you can model climatic data with spatial data (mainly altitude, distance to the sea and X and Y coordinates), obtaining specific climatic data for each trapping point.

Hi, Stacey, you surely can fit a GLMM model to those data, although I would say no simple approach can be used.

On the one hand, you have a longitudinal model, where traps (trap ID as random factor) are measured every year. Certainly, I would model year as a random effect, but you will probably need a covariance matrix with some dependence among years (to account for temporal correlation).

The most tricky issue, however is to model the covariates. You have two scales of analysis, one for the subjects (traps) and one for years. The difficult part is to model the error term for both analysis. The fixed model is easy to model. Some statistical softwares (for example SAS) would detect if the covariate changes with different levels of subjects (or any other factor) and apply the corresponding error term. However, when determining the error term, the semantic of the command is important, as the software uses it to identify the nested effects (which are to be taken into account when defining the error term, and degrees of freedom). For example, if you name all the measures as trap1year1, trap2year2... and input that as an identifying variable, the software won't identifiy the underlying structure of this factor combination (interaction). You need to use the original year and trap factors and model it as trap*year. I'm not sure if this would be an issue for you, probably not, but just to be aware.

To sum up, first of all, I would try to include the covariates in a standard way and run the model. Then, pay attention to the degrees of freedom of each covariate. For trap covariates, they should be close to (number of traps -1); for year covariates, close to (number of years - 1). If this is the case, you can trust the software has identified the correct error term for each covariate. Otherwise, you will need to check the method for calculating the degrees of freedom (often, for partially nested designs, as yours, a BW method is needed). This is a complex issue that depends on the syntax of your software, but If you proceed carefully you can get the correct output.

Best regards,

           Asier

To me it seems a fairly simple mixed model would do the job here:

Spider abundance as a function of Rain + Temp + Geophys data and a random factor Trap ID. You can include interaction between the two types of explanatory variables.

Since each trap is presumably sampled just once in each year, I don't see why Year would need to be a random effect. A year effect would be the same for all traps. It's the traps that really are sampled repeatedly and Trap ID would therefore be included as a random effect. If traps are sampled multiply in each year, you could include Year as a random effect as well, with Trap ID nested within it.

Including a random effect of "Year" as described in my answer above is not only relevant when there are multiple samples for each trap and year, as suggested by René. It simply accounts for the possibility that data from different traps are more similar when sampled in the same year. In other words, the spiders usually have some kind of population dynamics (non-constant population size). The random effect of "Year" is included according to the same principle as the random effect of "Trap ID", which accounts for similarity between years in same trap. My point is that this may be relevant even in cases with only one replicate per site and year. Quite often effects of year are ignored in this kind of situations, but I don't see why. Perhaps just because the site effects are thought to be more important.

If you have multiple observations per trap each year, you have to further modify the model, to account for the dependency of each combination of year and trap. This could be done e.g. by including an interaction between the two random effects and probably also using the method described by René above.

As Asier pointed out, it can further be relevant to consider relevant covariance structures of the random effects, e.g. an autoregressive covariance to the effect of "Year", as two consecutive years are probably not statistically independent. While such an approach would indeed be elegant, it starts to be a bit more advanced than what is usually done. With few years, a simple and fully valid approach is to model the annual variation as a fixed effect of the factor "Year", but in that case you can not include environmental covariates which have only one value per year.

The other issue that you have to account for is the cyclical nature of year. The seasonal component enters in even if you only take a single measure per year because the seasons do not progress at exactly the same rate each year. The easiest way to deal with a single observation each year is to correct all the data using temperature. The only way I have seen of modeling the seasonal component uses nonlinear regression. While modern statistical programs have made nonlinear regression more accessible, it is still seldom used.

Multiple observations from a single trap are dependent on one another, but the relationship is not simple. Depending on how often you sample and environmental factors, it is possible that the dependence of repeated measures is immaterial. If you took measurements from a single location every ten years you probably would not do a repeated measures analysis because environmental change in the intervening time has made the correlation between repeated measures minute relative to other factors. As the time interval gets shorter the environmental change diminishes, and at daily intervals the repeated measures correlation becomes very high. It is not clear to me what interval would be the critical transition from high to not worth considering. In an environment that if fairly static (a desert) the interval might be relatively long compared to a highly active environment (tropical rainforest). If possible I would test for correlation and act accordingly.

Of course, it would be possible to treat each trap date as a "treatment" and treat it as a categorical variable. But simplifying things in this way discards an important biological component to your data.

Here is one approach to modeling seasonality:

https://www.researchgate.net/profile/Thomas_Ebert3/publications

As Timothy said, the autoregressive effect (the carryover effect from year to the next) is usually negligible. Unfortunately, we don't have any way to check it other than modelling it. You can test for it, but the test would to fit a model with this effect and a model without it and then compare them (via AICc, most commonly). But, this is usually not needed. When the temporal effect is low, the estimate obtained for the temporal dependence parameter (whatever it is, as it depends on the particular covariance structure used) would be very low, with little influence on the remaining parameters in the model, and hence, deleting it from the model becomes needless.

It might not be the simpler approach but have a look to gamm models allowing for fitting autoregressive terms, non linerar responses by using smooth terms and in case you have count data to use Poisson or the negative binomial family for the error. If I remember well you can also use random effects in gamms

@Asier,

If I had to guess .....

The data that they have are 20 traps. Each trap was sampled 10 to over 100 times each year for 15 years. The samples/year are probably closer to 10, but there are well known sampling efforts where sampling is every day for the entire season over multiple years. The moth survey conducted at the Rothamstead Experiment Station (now known as Rothamstead Research) is one case with nightly sampling.

This is a question best figured out by yourself, maybe in consultation with a biostatistician. See how we have applied GLM to termite data...

Article Biomass of Macrotermes natalensis in the northern Kruger Nat...

I think Rene has a correct summary, and you can choose whether or not including interaction(s) between the fixed variables makes sense for your questions, however, if you are trying to estimate influences on spider abundance for the forested area then I think a mixed-effects model is unnecessary (I'm bringing this up because it isn't clear to me in your question). As written, the question you are trying to answer seems to be what local geophysical factors affect spider abundances? So, this would make sense for using  mixed-effects (aka hierarchical) modeling approach.

Further related to Rene's response, the reason you may not need to have a year random effect, or why it might not make much of a difference, is because you are including fixed effects in the form of rainfall and temperature that are at the level of the year. Hopefully most of the variation between years is captured in these variables that were measured each year. This doesn't preclude you from putting a random effect for year in your model, but it will likely account a small amount of variance after the fixed effects and the random effect for trap. Similarly, the geophysical variables were measured at the level of the traps, so a random effect of trapID will capture the remaining variation that these fixed effects did not. This is a very likely situation because there are often local factors or processes contributing to the abundances measured at a particular location that go unmeasured. Since your subject is spiders, then it could be travel/migration routes (as an example). 

If you have access to Mixed Effects Models and Extensions in Ecology with R written by Zuur and others in 2009, this book does a great job of laying out why and how.

Thank you all so much for your answers! For some reason I have not been getting notification emails from researchgate, so am only seeing your answers now.  I have proceeded with a GLMM, intially separating the climatic and geophysical variables, but given your suggestions I will include them all in one model, with appropriate interactions.

However I have a follow up question: I am trying to figure out which quantitative measure of rainfall I should use in my model. I have total monthly rainfall values for the total length of the study. However I am unsure whether it would be appropriate to use the value of total rainfall for three months prior to spider sampling, 6 months prior, 12 months prior, the year preceding etc.

So would it be appropriate to fit the full model to each rainfall variable, and choose the one with the lowest AIC to undergo further model selection? I have read that AIC can be used for non-nested models (Although I am aware of some of the limitations of using this critereon with GLMMs)

keep rainfall at the same temporal scale as your sampling.

Watch for time lags.

Regarding your choice of rainfall variable(s), I would base this on what would be the most biologically relevant/what other studies may have found. Model selection with AIC can be a way to compare competing hypotheses if the models are carefully constructed as such (I have seen this argued as the original intent of the information theoretic approach). I think perhaps more commonly it is used in an exploratory fashion. You could take either approach: 1. explore the relationship with rainfall by trying a set of different variables, or 2. select specific rainfall variables that are, or are thought to be, biological meaningful in terms of predicting spider abundance and test these models as competing hypotheses. Either way, I would approach this by fitting the full model with different rainfall variables that you want to examine. Could multiple rainfall variables make sense biologically?

Further model selection may not be necessary, but could be done in an exploratory framework. For model selection with GLMM it is crucial to maintain the same random-effect structure across all models for the estimation algorithms to provide comparable results.