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For my ecological research on the impacts of intensity of space-use on vegetation structure I need to quantify temporal variation in the intensity of space-use across years (resulting in a single value for each pixel of my research area).

So for example if I have the following space-use data:

Pixel 2017 2018 2019 2020
1. 5 5 4 5
2. 3 5 1 4
3. 1 0 1 1

I'm looking for a summary value for each column that quantifies the variation but also the magnitude of the space-use. I originally was looking into using a coefficient of variation but ran into the problem that high constant space-use and low constant space-use generates the same CV value. So is there a statistic out there similar to the CV that can still account for the total intensity of space-use as well?

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    $\begingroup$ If I understand correctly, you want a single number that represents both magnitude and variation. This sounds to me to be impossible for informational reasons; if you want to represent two values with one value, you have to lose information unless the two are strictly related in which case there is no information to lose. What isn't clear to me, though, is why you want/need to do this. Why can't you use the data in the form you have? What is the specific research question you are testing? $\endgroup$
    – Bryan Krause ♦
    Commented Apr 4, 2022 at 15:33
  • $\begingroup$ Yes correct - and fair point, something I'll take into consideration. Because I'm looking at responses in vegetation it is important for me to capture both the magnitude and variation. My research relates to elephants and their impact on vegetation. So for example if in 2018 they utilize a certain pixel heavily but leave it alone until 2021 that patch can recover. However, if they keep coming back to that patch the continuous utilization in theory leads to more vegetation damage. If I use a standard utilization distribution value this won't take into account that annual variation. $\endgroup$
    – EmmaE
    Commented Apr 4, 2022 at 17:27
  • $\begingroup$ So I'm looking for a way - if possible- to quantify that annual variation whilst also taking into account the total impact $\endgroup$
    – EmmaE
    Commented Apr 4, 2022 at 17:28
  • $\begingroup$ That sounds like quite a complex nonlinear relationship, where you would need some way to model patch recovery. You are not going to be able to use some standard summary statistic to capture that, it will need to be something very specific to your domain, and which may not even exist. What are the other variables in your study? Is it actually necessary to do this to test your hypothesis/es? Alternatives may be to use a simpler measure, or separate "use" from "rest". $\endgroup$
    – Bryan Krause ♦
    Commented Apr 4, 2022 at 17:35
  • $\begingroup$ I will be able to use metrics such as NDVI, EVI and percentage canopy cover to monitor the vegetation response, it is just quantifying the temporal variation of elephant space-use that is the last piece of the puzzle I am trying to solve. In the modelling I have already done I can see that there is a lot of annual variation in their space-use so I'd like to try and accomodate that, but have no idea if that is possible because I have not been able to find any other research on it. The values I am using are about as simple as I can make them without losing too much information. $\endgroup$
    – EmmaE
    Commented Apr 4, 2022 at 17:56

1 Answer 1

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I do not think you will find a general answer outside your research domain.

There is no general way to express both magnitude and variation as one number without losing information; unless you have a strict relationship between the two, such that the two numbers do not provide separate information (an example would be data with a Poisson distribution, where mean and variance are equal), this is simply not possible.

I'm answering from just a general statistics perspective, as I have little to no domain-knowledge in your area, but if you haven't encountered a measure already in the papers you generally read in your field, then I think it probably doesn't exist.

If you want to test whether "high and consistent elephant utilization will lead to higher vegetation damage", some options I can see are:

  1. Test "high" and "consistent" separately; "high" could be from averaging/summing usage and regressing on your measure of damage, "consistent" could be from measuring the standard deviation, or using a measure like "years of high usage" with some threshold.

  2. Fit a model with both your separate measures of "high" and "consistent", and look for a significant interaction. That is, a model of the form Damage ~ High * Consistency. There are certainly theoretical issues with this type of model, especially given the expected covariance between the two predictors, but I think it could still be practically useful, and in particular could be used to motivate not using measures of magnitude or consistency alone.

  3. Use or modify an ecological model. I don't know much about this area, and it would probably take you quite a bit of reading to find something applicable, but cumulative damage seems to be a recurring issue in ecology, and though you may not find a model used in your specific domain you might find similar ones with parameters you can adjust and fit to your data. I'd expect a differential equation where the current year's vegetation quality predicts the next year's growth with some saturating characteristic (i.e., logistic growth), with elephant presence having a separate additive or multiplicative impact on vegetation quality, growth, or both. One paper I found quickly is this one:

Owen-Smith, N. (2002). Credible models for herbivore-vegetation systems: towards an ecology of equations: Starfield Festschrift. South African Journal of Science, 98(9), 445-449.

which seems like it could be useful, and it cites an older book chapter:

Caughley, G. (1976). Plant-herbivore systems. Theoretical ecology: principles and applications, 94-113.

The approach would be to fit the parameters of a model like this one to predict your observations of the vegetation based on elephant presence.

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