Notebooks on plantarum.ca

Rawtherapee Notebook

Sun, 15 Jan 2023 00:00:00 +0000

Default Profile

Notes based on the default profile describe by Andy Astbury on YouTube (posted 9 September 2021).

Andy recommends the following settings as your default RAW processing profile. His video describes his rationale in some detail.

Start From the Built-in “Neutral” profile

Open a raw file in RawTherapee.

Select the (Neutral) profile in the profile selector at the upper right side of the editor window. This will give you a very ‘flat’ (linear) view of the image. This is desireable to allow you to see all of the detail available in your file, in order to better decide how to approach your processing. From this linear beginning you’ll set the exposure etc. to suit your image.

Set the Output Profile

tldr; use RTv4_sRGB for finished photos to be posted online, or for which you don’t control the software used to view them; use ProPhoto (or maybe RTv4_Large) when you are going to further edit your images in Gimp, Photoshop, Lightroom, or edit/print/view with other programs that understand wide gamut profiles.

RTv4_sRGB for the web, ProPhoto for Photoshop/Gimp

If you’re exporting from RawTherapee to Gimp, Photoshop, or Lightroom, Astbury recommends using the ProPhoto colour profile, in order to maintain maximum compatibility with PhotoShop and Lightroom. This is also the default working profile (NB: not the default output profile!) for RawTherapee. However, by default, RawTherapee doesn’t offer ProPhoto as an output profile. In order to use it, you need to install the ProPhoto.icc file.

Download the file ICCProfiles.zip from chromasoft. Unzip the files and copy them to the profile directory for your system. You can find this (and change it if you like) in the Preferences dialog, under Colour Management.

You could also use RTv4_Large, which is provided with RawTherapee and provides a similar extended gamut to ProPhoto.

Note that Astbury’s video includes the aside:

Only do this if you want to use and maintain a fully ProPhotoRGB workflow between RawTherapee, Photoshop, and Lightroom.

This is because the ProPhoto profile is not understood by many programs, so what your audience sees will depend on how they view it. Consequently, regardless of what your workflow is, when you export a ‘finished’ image for display online, you should use a sRGB profile. RawTherapee provides RTv4_sRGB for this purpose. It’s an extended sRGB profile that degrades gracefully to plain sRGB in programs that don’t understand the full RTv4_sRGB profile.

As an example of the potential problems with profiles, on my android phone, Firefox, and also the Flickr app, don’t provide accurate renderings of the ProPhoto or rtv4_Large profiles (shown on the right), but are just fine with sRGB and rtv4_sRGB (shown on the left).

This is hard to anticipate, because the same images, on the same website, may appear differently on different browsers, OS, or other combinations. In this case, my Linux laptop with firefox displays the images properly, as does Chrome on Android. You can see the actual images on my Flickr account to see for yourself.

Set the Demosaicing Algorithm

The default demosaicing algorithm is AMaZE. This is very good for high frequency detail (i.e., areas in sharp focus, detailed subjects), but not so good for low frequency detail (i.e., out of focus areas, soft background). Astbury prefers RCD for sharp detail, and VNG4 for out of focus areas.

You get both together with the setting RCD+VNG4. With this setting, a contrast setting is used to determine which areas of the image have high contrast, and will have RCD applied; and which have low contrast, and will get VNG4 applied. This value is set automatically when the box is checked. Leave the box checked.

Capture Sharpening

Further down in the raw tab, turn on the Capture Sharpening option, and leave it at the default setting (i.e., the automatic check box is ticked). This will address details lost due to in-camera blurring (defraction, anti-aliasing etc). You will usually want Capture Sharpening applied, which will often be combined with either Unsharp Mask or RL Deconvolution.

Auto Chromatic Aberration Correction

Located in the Raw tab: turn on this checkbox, but turn off Avoid colour shift.

Andy discusses Avoid Colour Shift as a “Top Tip” in his video on local adjustments. The issue is that, in some circumstances, Avoid Colour Shift can actually cause a colour shift. That’s counter-intuitive, and you probably wouldn’t think to turn off this feature to reduce colour tinting. So better to leave it off by default, and only apply it intentionally such that you might detect how it improves (or degrades) a particular image.

Turn on Defringe

In the Detail tab. Use default settings.

Turn on Noise Reduction

Also in the Detail tab. Turn it on, set colour space to L*a*b*, mode to Conservative, Luminance to slider, with the actual sliders set to 0 (these should be the default settings).

Uncheck ‘Clip Out of Gamut Colors’

In the exposure tab. Mentioned in the Pinned comment below the video.

Set the Profiled Lens Correction to Auto

Not mentioned by Astbury, this is under the Transform tab. I set it to Automatically selected, which usually sets the correction to the camera at least. I have to select the lens manually, but this at least saves one step.

Don’t turn on Dead Pixels and Hot Pixel Filters

Astbury previously recommended this, but no longer considers it a good default setting. These options are in the Raw tab, in the Preprocessing section.

Specifically, Andy has explained (in the comments below the default profile video):

I no longer class [dead pixels and hot pixel filters] as essential - they only need activating if an individual image needs them. If they are not needed they could prove slightly detrimental.

To which KuruGDI added:

When I take images with small grained details it’s sometimes degrading the image quality for me with these settings. The software thinks that these tiny spots should be fixed while in reality it’s just a small detail. I could see this problem especially in area that were just slightly out of focus.

Save the Profile

Save the profile! Click the disk icon in the profile dialog at the upper right, and give the profile a useful name, like myBase, or AstburyBase or something like that.

Set the Profile as your default

Open the Preferences dialog, open the Image Processing tab, and set the default profile for raw photos to your new profile.

At this point, this neutral++ profile will be applied to every Raw image the first time you open it, providing the base corrections for the image. All additional changes you make for that particular image are stored in the image-specific profile, so that on the second and subsequent times that you open the image, you’ll see everything you’ve added in addition to the base profile.

Lightening an Image

Notes from RawTherapee Basics: 3 Ways to Lighten Images, posted September 15, 2021.

Astbury prefers the third method, as it is most ‘tractable’ - provides you with a great deal of fine-control over brightness, without making a mess of contrast and saturation. However, each of the three have their place, and you may end up using a different one (or a combination) for different images.

Method 1: Exposure Compensation

The exposure slider increases or decreases exposure for the entire image. Getting your midtones where you want may result in blown highlights.

You can correct for this with:

Highlight Reconstruction

Guesses what the best colour for the clipped highlights should be based on adjacent pixels, or data in other channels (i.e., the values in the red and green channel can be used to infer the blue channel, if only the blue channel is blown out). Primarily for details that are clipped (i.e. blown out in the RAW), but also used in combination with Highlight Compression to protect highlights clipped during editing.

Options include:

Luminance Recovery: details will be neutral gray, doesn’t attempt to restore colors.
Color propagation: recovers the luminance of highlights, and also the colors, using adjacent colors.
CIELab: reduces luminance, and then restores colors.
Blend: replaces clipped colors with values from nearby areas.

Highlight Compression

Recovers highlights that present (i.e., not blown out) in the raw file, but have been clipped by editing, such as exposure compensation. Works in conjunction with highlight reconstruction.

A general rule of thumb is the histogram for each colour channel should reach the right and left side of the histogram panel, but should not be clipped at either end. Unless you have a very flat image (e.g. misty/foggy landscape).

The Problem With Exposure Compensation

Exposure compensation works in the RGB space, applying a uniform shift to exposure AND contrast AND saturation to the entire image. This makes it difficult to tweak brightness independent from contrast, and vice versa, and often leads to garrish/glossy images. So Astbury recommends one of the following two options instead.

Method 2: LAB* Adjustments

Turning on the LAB Adjustments tab, you can independently modify brightness, contrast, and chromaticity (saturation), with the three sliders. Or if you want to really fine-tune it, you can use the curves and equalizers below.

Method 3: Abstract Profile

New tool available in RawTherapee 5.9, found in the Colour Management tab, between Working Profile and Output Profile.

Set the Abstract Profile to Custom, and you will be presented with two sliders:

Gamma : Controls the highlights, without modifying the darker tones.
Slope : Controls the darker areas, without modifying the lighter tones.

These sliders interact - moving the Slope up will push some of the midtones up such that they are bright enough to be influenced by Gamma. Meaning you have to play with both sliders in concert to find a balance that works.

Noise Reduction

Details panel -> Noise Reduction -> change slider to curve. Increase the height of the curve to increase noise reduction. Slide the bottom of the noise reduction tone curve to the left to restrict noise reduction to darker tones, or to the right to include lighter tones¹.

Thanks to Wayne Sutton for correcting the previous version! ↩︎

Spatial Ordinations

Fri, 24 Jul 2020 00:00:00 +0000

Spatial Statistics

Moran’s `I`

A univariate measure of global spatial autocorrelation.

From Dray, Saïd, and Débias (2008):

\[I(x) = \frac{n\sum_{(2)}c_{ij}(x_i - \bar{x})(x_j - \bar{x})} {\sum_{(2)}c_{ij}\sum_{i=1}^{n}(x_i - \bar{x})^2}\]

where

\(x_t = [x_1, \dots, x_n]\) is a vector of the variable of interest, which for which spatial coordinates are available
\(C = [c_{i,j}]\) is a spatial connectivity matrix
\(\sum_{(2)} = \sum_{i=1}^{n} \sum_{j=1}^{n}\) with \(i \neq j\)

If we define \(z^t = [z_i] = [x_i = \bar{x}]\), the centered variable values, this becomes:

\[I(x) = \frac{n\sum_{(2)}c_{ij}z_iz_j} {\sum_{(2)}c_{ij}\sum_{i=1}^{n}z_i^2}\]

Alternative definition from Wikipedia:

\[I = \frac{N}{W} \frac{\sum_i \sum_j w_{ij}(x_i-\bar{x}) (x_j-\bar{x})} {\sum_i(x_i-\bar{x})^2}\]

\(N\) is the number of spatial units indexed by \(i\) and \(j\);
\(x\) is the variable of interest;
\(\bar x\) is the mean of \(x\);
\(w_{ij}\) is a matrix of spatial weights with zeroes on the diagonal (i.e., \(w_{ii} = 0\));
\(W\) is the sum of all \(w_{ij}\).

This is a variation of covariance/correlation, where the contributions of individual comparisons are weighted by the spatial weighting/connectivity matrix.

The value ranges from -1 for complete negative autocorrelation (presence in one cell indicates absence in adjacent cells) to 1 for positive autocorrelation (presence in one cell indicates presence in adjacent cells). 0 indicates no spatial autocorrelation (presence in a cell is unrelated to presences in adjacent cells).

Spatial Weighting Matrix

Can take any form deemed appropriate by the investigator. Binary matrices are often used to limit comparisons to spatially contiguous observations. A common transformation is row-standardization, where elements of the matrix are divided by the sum of their row. Using such a matrix, Moran’s I can be simplified to:

\[ I(x) = \frac{\sum_i\sum_j w_{ij}(x_i - \bar{x})(x_j - \bar{x})} {\sum_i(x_i - \bar{x})^2} \]

Thioulouse et al. (2018) describe options in detail, and include walk-throughs of the main steps in R, based on the spdep package:

Create a spatial neighbourhood object (class nb), using criteria of distance (dnearneigh), adjacent polygons (poly2nb), ‘rook’ or ‘queen’ patterns on a grid (cell2nb), or nearest neighbours (knearneigh, which can be asymmetrical). More complex approaches include Delaunay Triangulation (deldir::tri2nb) and Gabriel Graphs (gabrielneigh), which are described in detail by (Legendre and Legendre 2012).
Spatial Neighbourhoods (nb) are converted to Spatial Weighting Matrices (class listw). These allows for binary associations to be weighted by spatial distances, including tranformations such as row or total standardization.

Applying spatial weights to the neighbourhood graphs is not clearly explained in the package. This is how it’s done (after Thioulouse et al. 2018)

## Create a neighbourhood network based on
## point-point distance less than MAXDIST 
nbd <- dnearneigh(coords, d1 = 0.001, d2 = MAXDIST)

## calculate inverse distance between observations
invdist <- lapply(nbdists(nbd, coords), function(x) 1/x)

## Apply inverse distances as weights to the
## neighbourhood network:
swm <- nb2listw(nbd, glist = invdist, style = "W")

Adespatial provides the function listw.explore to interactively examine the alternatives available. It didn’t work when I tried it though. Intuitively, creating a neighbourhood based on distance is the most intuitive approach. Neighbourhoods can be edited directly, which might make sense for distributions that span geographic boundaries (ie., lakes or mountains).

Spatial Lag

The spatial lag is a smoothed estimate of the value of a cell, calculated as the weighted averages of all the cell’s neighbours:

\[ \tilde{x}_i = \sum_jw_{ij}x_j \]

Lee (2001) shows Moran’s I is very similar to the Pearson’s correlation between the values of a cell, and the spatial lag for that cell. i.e.,

\[ I(x) = \frac{\sum_i(x_i - \bar{x})(\tilde{x}_i - \bar{x})} {\sqrt{\sum_i(x_i - \bar{x})^2} \sqrt{\sum_i(x_i - \bar{x})^2}} \]

and

\[ r_{X, \tilde{X}} = \frac{\sum_i(x_i - \bar{x}) (\tilde{x}_i - \bar{\tilde{x}})} {\sqrt{\sum_i(x_i - \bar{x})^2} \sqrt{\sum_i(\tilde{x}_i - \bar{\tilde{x}})^2}} \]

It follows that Moran’s I is the correlation between a variable and its spatial lag, scaled by the root of the ratio between the variance of the spatial lag and the variance of the original variable. (really it does, see Lee (2001) for the math). This ratio is the “spatial smoothing scalar,” aka SSS, or at least it is when the spatial weighting matrix is row-standardized.

SSS thus measures the degree of smoothing of a variable when it is represented by its spatial lag. Spatial clustering produces larger SSS values, because increased clustering reduces the difference between a variable and its spatial lag (i.e., increases correlation). The SSS value can be interpreted as the reduction in variance in the spatial lag relative to the original variable.

Together, this allows us to decompose Moran’s I into a correlation value, and a measure of variance reduction (SSS).

Geary’s `c`

All the papers and books about this stuff mention Geary’s c. It doesn’t appear to be used in any of the analyses, but since everyone else is talking about it, I will too.

\[c(x) = \frac{(n - 1)\sum_{(2)}c_{ij}(x_i - x_j)^2} {2\sum_{(2)}c_{ij}\sum_{i=1}^n(x_i - \bar{x})^2}\]

From Wikipedia, Geary’s c is sensitive to local spatial autocorrelation, capturing relationships among adjacent observations. This contrasts with Moran’s I, which is a measure of global spatial autocorrelation. The two measures are related, but not exactly inverse of each other.

Geary’s c ranges from 0 (positive spatial autocorrelation) to 1 (no spatial autocorrelation) to values larger than 1 (negative autocorrelation).

MULTISPATI Analysis

MULTISPATI analysis is co-inertial analysis of a multivariate data matrix \(X\), and the corresponding lag matrix \(\tilde{X} = WX\). Which means we need to understand what co-intertia analysis does.

Co-inertia Analysis

Co-inertia analysis is a form of symmetrical canonical ordination. It is closely related to Procrustes Analysis, and has some parallels to Canonical Correlation Analysis (Legendre and Legendre 2012).

Legendre and Legendre (2012): “variables of both data sets are projected onto the axes obtained by eigen-analysis of the cross-set covariance matrix.” The total co-inertia is the sum of the squared cross-set covariances. The original objects are projected into the co-inertial space. Since each sample is represented in both data sets, we can then compare their relative location in the co-inertial space. Paired observations that are close to each other in this projection indicate that they have similar relative positions in both data sets (“good agreement between” data sets, Thioulouse et al. 2018). Similarly, points that are close together in one data set, but have diverging arrows, indicate similarities in the first data set are not reflected in similarities in the second.

Full details in (Dray, Chessel, and Thioulouse 2003; Dray, Saïd, and Débias 2008; Thioulouse et al. 2018). Very heavy on matrix algebra, hard to develop an intuitive understanding. For the moment, I shall hum along and pretend it is just CCorA.

Spatial Principal Components Analysis

sPCA is the application of co-inertia analysis to a data matrix and its spatial lag. This is a specific case of MULTISPATI, developed particularly for application in population genetics. adegenet::spca() is a high-level wrapper that handles the details, but also obscures some of the steps.

In the case of a genpop object, it does the following:

## Extract the allel frequences from the genpop object:
X <- tab(obj, freq = TRUE, NA.method = "mean")

## coordinates retrieved from the genpop or nb object, or
## supplied by the user:
xy

## regular pca of allele frequencies, default center = TRUE,
## scale = FALSE:
x_pca <- ade4::dudi.pca(x, center = center, scale = scale,
                       scannf = FALSE) 

## Connection network from user or generated interactively:
resCN

## defaults
## scannf = TRUE, nfposi = 1, nfnega = 1

out <- ade4::multispati(dudi = x_pca, listw = resCN,
                       scannf = scannf, nfposi = nfposi,
                       nfnega = nfnega)

This returns an object of class spca, which contains:

eig:: a numeric vector of eigenvalues.
nfposi:: an integer giving the number of global structures retained.
nfnega:: an integer giving the number of local structures retained.
c1:: a data.frame of alleles loadings for each axis.
li:: a data.frame of row (individuals or populations) coordinates onto the sPCA axes.
ls:: a data.frame of lag vectors of the row coordinates; useful to clarify maps of global scores.
as:: a data.frame giving the coordinates of the PCA axes onto the sPCA axes.
call:: the matched call.
xy:: a matrix of spatial coordinates.
lw:: a list of spatial weights of class listw.
tab:: the original data supplied to the PCA (possibly scaled/centered)

Note that the PCA here is based on allele frequencies, which define a Euclidean distance among populations (T. Jombart et al. 2008).

Example:

library(adegenet)
library(utils)
library(graphics)
data(spcaIllus)
spca2A <- spca(spcaIllus$dat2A,
              xy = spcaIllus$dat2A$other$xy, ask=FALSE,
              type = 1, plot = FALSE, scannf = FALSE,
              nfposi = 2, nfnega = 0)

spca always warns that it is deprecated. The package author says that’s ok, and it should be, since behind the scenes it just calls the function the warning tells you to use anyways.

li contains the observations, projected onto the coinertia space. ls provides the lagged values in the same space. We can compare them using arrows:

plot(spca2A$li, pch = 16, asp = 1)
arrows(x0 = spca2A$li[, 1], x1 = spca2A$ls[, 1],
       y0 = spca2A$li[, 2], y1 = spca2A$ls[, 2],
       length = 0.1)

Here, pairs with short arrows indicate sites where the composition of the site is well-described by the composition of its neighbours; they demonstrate high spatial-autocorrelation. In contrast, long arrows denote sites where the actual composition of the site differs substantially from what you would expect based on its nearest neighbours.

These plots don’t appear to be used for sPCA, as they are for other co-inertia analyses. Instead, the values from the first axis are plotted geographically, to illustrate the spatial component of the data:

s.value(spca2A$xy, spca2A$li[,1], include.origin = FALSE,
        addaxes = FALSE, clegend = 0, csize = 0.6)

This shows us the spatial pattern present in the subset of the original data that is spatially structured (on the first axis). We could plot the lagged data the same way, but I’m not sure what that would show us.

We can also contrast this with a spatial plotting of the standard PCA analysis:

allFreq <- tab(spcaIllus$dat2A, freq = TRUE)

pca <- ade4::dudi.pca(allFreq, center = TRUE, scale = FALSE,
                     scannf = FALSE) 

s.value(spca2A$xy, pca$li[,1], include.origin = FALSE,
        addaxes = FALSE, clegend = 0, csize = 0.6)

The main difference is that the sPCA more clearly shows the spatial pattern; that’s what it does. It isolates the spatial pattern in the data, and discards non-spatial structure. There should be a way to quantify how much of the original variation is spatially structured?

Eigenvalues

From Thibaut Jombart (2008): Regular PCA decomposes total variance into decreasing, orthogonal components. sPCA (and MULTISPATI generally, I think) does something different. The eigenvalues are the product of variance and autocorrelation. Axes with high variance and positive autocorrelation indicate strong global structures. That is, they capture a relatively high proportion of the variation in the data, and it has a relatively high proportion of spatial structure (gradient, clustering etc). Axes with low variance represent only a small amount of the total variation, and so aren’t very interesting.

Axes with high variance but high negative autocorrelation indicate strong local structures in the data. That is, spatial replusion, where neighbouring locations are more likely to have different compositions (alleles, species composition etc).

Deciding which axes are interesting seems to be a bit of an art. In general, we look for a large drop between the first or second (or more) axes and the rest, to indicate which ones are worth examining. And similarly at the negative end. The adegenet package (Thibaut Jombart 2008) provides the function screeplot for jointly visualizing the variance and spatial component. Axes that are separated from the main cloud of points are considered interesting/interpretable:

library(stats)
screeplot(spca2A)

Here, axis 1 is clearly separated, and should be interpreted. Axis 79 is less obvious. And the idea of spatial repulsion is going to be difficult to interpret biologically in most cases I think.

Packaging Oddities & Significance Testing

Note that despite both packages bearing the prefix ade, adespatial and ade4 do NOT use the same implemenatation of co-inertia analysis. ade4 provides the function coinertia() to compute co-inertia on any two data sets. adespatial implements it’s own co-inertia code within the function multispati. The package adegenet provides the wrapper spca, which uses multispati to complete the coinertia analysis it needs. Using the function spca generates a warning, indicating that this function is deprecated and the user ought to use multispati instead. However, spca actually calls multispati itself, so its really just a convenience/wrapper.

The consequence of this is analyses completed via spca and multispati do not return (or contain) an object of class coinertia, and functions in ade4 that process such objects won’t work on their output. Particularly the function ade4::randtest, which might otherwise provide a signficance test for the existence of spatial structure in the data.

But wait! There is a function global.rtest that does provide a randomization test for sPCA objects, and packages the results in a randtest object. It is based on Moran’s Eigenvector Maps. MEMs are part of an alternative approach to spatial ordination from the Legendre group. So, I’m not sure if this is actually testing the significance of the sPCA (i.e., coinertia between the data and its spatial lag matrix), or rather the equivalent in the MEM framework?

Both adespatial and adegenet have their own version of global.rtest, of course. They are nearly identical, but use different code to generate the MEM values. The results are close, but not identical. Can’t say if this is an artifact of them being randomization tests, or if there’s some substantive difference in the implementation.

The co-existence of multiple loosely-loosely linked packages with overlapping/duplicated functions and documentation scattered in books, online tutorials, and, only secondarily, in the package documentation itself, makes figuring this out more work than it needs to be.

References

Dray, Stéphane, Daniel Chessel, and Jean Thioulouse. 2003. “Co-Inertia Analysis and the Linking of Ecological Data Tables.” Ecology 84 (11): 3078–89. https://doi.org/10.1890/03-0178.

Dray, Stéphane, Sonia Saïd, and Françis Débias. 2008. “Spatial Ordination of Vegetation Data Using a Generalization of Wartenberg’s Multivariate Spatial Correlation.” Journal of Vegetation Science 19 (1): 45–56. https://doi.org/10.3170/2007-8-18312.

Jombart, T., S. Devillard, A.-B. Dufour, and D. Pontier. 2008. “Revealing Cryptic Spatial Patterns in Genetic Variability by a New Multivariate Method.” Heredity 101 (1): 92–103. https://doi.org/10.1038/hdy.2008.34.

Jombart, Thibaut. 2008. “Adegenet: A R Package for the Multivariate Analysis of Genetic Markers.” Bioinformatics 24 (11): 1403–5. https://doi.org/10.1093/bioinformatics/btn129.

Lee, Sang-Il. 2001. “Developing a Bivariate Spatial Association Measure: An Integration of Pearson’s r and Moran’s I.” Journal of Geographical Systems 3 (4): 369–85. https://doi.org/10.1007/s101090100064.

Legendre, Pierre, and Louis Legendre. 2012. Numerical Ecology. 3rd Edition. New York: Elsevier.

Thioulouse, Jean, Stéphane Dray, Anne-Béatrice Dufour, Aurélie Siberchicot, Thibaut Jombart, and Sandrine Pavoine. 2018. Multivariate Analysis of Ecological Data with Ade4. New York, NY: Springer New York. https://doi.org/10.1007/978-1-4939-8850-1.

Maxent Best Practices

Mon, 15 Jun 2020 00:00:00 +0000

Key Resources

Merow et al. (2013) provides a very thorough introduction to Maxent modeling, and especially to what the various settings mean and how to set them.

RSpatial is a (nearly complete) set of lessons covering spatial data analysis in R, and including good tutorials for Maxent and other SDM approaches.

Best Practices in Species Distribution Modeling is another set of online notes, including R code.

From the same author (Adam B. Smith), a database of biodiversity databases.

Another workshop, from Lee-Yaw, is available on github. It’s a little old now, and doesn’t appear to be as comprehensive as Smith’s workshop above (maybe?). However, some people may prefer the more condensed format. Both authors have demonstrated expertise in the subject, so I don’t doubt that these are both reliable sources.

Technical Summaries

Phillips et al. (2017) provides a short discussion of recent developments of the Maxent application, and related statisical methods. See papers cited there for (even more) detailed information.

Elith et al. (2011) provides a statistical interpretation of the Maxent process; possibly superceded by Phillips et al. (2017) and the work cited therein, which was done post-2010.

Valavi et al. (2022) reproduce and extend the seminal paper of Elith (2006), showing that 16 years later Maxent remains one of the top performing SDM approaches (although some newer entrants may be slightly better now).

Sampling Bias

Sampling bias in occurrence data is an issue because it means we can’t be sure a species is detected under certain conditions because that’s its preferred habitat, or because those are the conditions in the locations we prefer to search.

The uniform sampling assumption does not require a uniformly random sample from geographic space, but instead that environmental conditions are sampled in proportion to their availability, regardless of their spatial pattern (Merow et al., 2013)

This problem can be addressed by thinning records (also called spatial filtering, Radosavljevic and Anderson, 2014), such that multiple records from within the same area are represented by only one or a few of the total records. This is a bit crude, but should remove the worst biases, such as a particular field station getting preferentially sampled by recurring visits from scientists or students, or general biases towards sampling roadsides and popular trails.

Lee‐Yaw et al. (2018) developed their own method to thin species records, using kernel smoothing estimates to reduce the number of samples from a neighbourhood, and selecting which samples to keep by identifying which occupy novel environments. ~~I don’t think this is widespread, and feels a bit like overkill.~~ 2025-05-05: This still isn’t widespread, but there is evidence to support the importance of environmental filtering in model accuracy (Varela et al., 2014). I need to investigate this further!

Another interesting approach in Atwater et al. (2018), who used a large dataset of gbif records to establish geographic (and presumably also environmental) bias in the full set of records, and used that to correct bias for individual species. Simply put, occurrence records for each species are weighted by the proportion of records for the entire set are found in that location (either geographic or a cell in a climate grid).

Subsampling based on raster grids is a simpler, more intuitive approach provided by Hijmans et al. (2017). It doesn’t account for the possibility that local density may be an accurate reflection of the niche requirements of a species, as the approach of Lee‐Yaw et al. (2018) does.

NB: See my extended discussion of thinning records on a grid

Grid-sampling:

library(terra)
## `occs` is a spatVector object containing the occurrence
## records as points

## wclim is a spatRaster object containing the environmental
## variables

## select one occurrence record per cell in the
## environmental raster layers::
lsOccs <- spatSample(occs, size = 1, strata = wclim)

Aiello‐Lammens et al. (2015) provides an alternative approach based on imposing a minimum permissible nearest-neighbour distance, and then finding the set that retains the most samples through repeated random samples.

Thinning by Nearest-Neighbour:

## thin.par sets minimum distance in km
trichthin <- thin(data.frame(LAT = coordinates(trich)[, "Y"],
                             LONG = coordinates(trich)[, "X"],
                             SPEC = rep("tplan", nrow(trich))),
                  thin.par = 2, reps = 1, write.files = FALSE,
                  locs.thinned.list.return = TRUE)

Radosavljevic and Anderson (2014) show that unfiltered/unthinned data produces elevated assessment of model performance, as a consequence of over-fitting to spatially auto-correlated data. So filtering works.

See also Boria et al. 2014 (unread), Varela et al. (2014)

Merow et al. (2013) provide two more rigorous approaches, depending on whether or not data on search effort is available. When search effort is known, it can be used to construct a biased prior.

When search effort is unknown, we can create a biased background sample to account for bias in presence data, via Target Group Sampling. Under TGS, records that are collected using the same surveys/methods as the focal species are form the background points. i.e., the set of all herbarium records in GBIF may be an appropriately biased background for any one of those plant species. This assumes that the target plant is collected/detected at the same rate as the reference set. It may be appropriate to subset the reference set to increase the likelihood of this being true: use only graminoids as biased background for sedges, or woody plants as background for a tree?

Spatial Bias

Elith et al. (2011) – The area of individual cells in raster layers projected in Lat-Lon coordinates are not equal. This can be corrected by:

project the grids to an equal area projection
create a ‘bias grid’ that can be used to weight background samples
create a background sample with appropriate sampling weights

Study Extent

Discussed extensively in Barve et al. (2011). They identified three general approaches to consider:

Biotic regions (ecozones etc). A good compromise between biological realism and tractability
Niche-model reconstructions: back-project a niche model over the appropriate time period (i.e., previous glacial maximum or interglacial) to identify the area that the species could have occupied over an extended period. Nice idea, but a real risk of circularity?
Detailed simulations. Sounds great, but I think if we had enough data to properly parameterize such a model, we wouldn’t need to resort to sdms in the first place.

If you wanted to improve on biotic regions, things to consider in developing a more rigorous approach should include:

Dispersal characteristics of the species
Crude estimate of the niche (again, circularity?)
Establish relevant time span
Identify relevant environmental changes

Soberón (2010) is often cited together with Barve et al. (2011), but the latter provides more explicit discussion of best practices for SDM model construction. I think the deference to Soberon is probably due to their creation of the BAM model (in earlier publications), which Barve’s system is based on (Biotic, Abiotic, Movement).

Merow et al. (2013) provide a shorter discussion, and emphasize matching the study extent to the biological question of interest. Prioritizing sites for protection within the range of a species should constrain the extent to the existing range of the species; evaluating invasion potential should use an extent large enough to encompass the areas of concern (i.e., global, or continental scale for novel invasives).

Background Points: Number and Bias Grids

The number of background points should be large enough to comprehensively sample (and hence represent) all environments in the region of interest. (Valavi et al., 2022)

If computational resources aren’t limiting, the ‘gold standard’ would be to use every cell in the background extent. When that’s not feasible (i.e., most of the time!), Valavi et al. (2022) recommend using 50,000 points. This is based on empirical tests on a large number of species which showed that model AUC_ROC approaches that of the ‘gold standard’ when 50K background points are used. This comes at a cost of doubling the computation time compared to sampling 10K background locations. They also note that choosing 50K, rather than 35K or 70K, is somewhat arbitrary.

This updates previous work that recommended sampling 10K background points (Phillips and Dudík, 2008; Barbet-Massin et al., 2012).

Note that some reviewers hold the view that the number of background points should be ‘balanced’ (or weighted) against the number of presence records in the model. This idea comes from considering Maxent models to be a form of logistic regression, where the background points take the role of absences. This is flawed, because we don’t know if our species is present or absent at any given background point.

This problem is resolved when we recognize that Maxent is more accurately seen as an approximation of a Poisson Point Process Model. In this framework, the background points serve to estimate the distribution of environmental conditions in the full study area. That is, they aren’t tied to presences or absences at all. The consequence is that, in general, more background points is better, and efforts to match background numbers to presence records is misguided.

The theory underpinning this is explained by Renner et al. (2015), and practical application to distribution models is covered in Valavi et al. (2022).

Variable Selection

Variables == predictors, the spatial layers used as the environmental/dependent variables in the model.

Interesting discussion in Guisan et al. (2017) (section 6.4, page 102+): variables that are measured most accurately often/usually are only indirectly related to a species’ niche; e.g., elevation, slope, aspect. Very precise and accurate spatial layers are available for these.

Variables with a direct relationship to a species niche are referred to as “proximal”. These include temperature, moisture, soil type etc, and are usually created through interpolation from sparse reference points (weather stations). This involves unavoidable error propagation and imprecision.

Over small extents, it may be preferable to use indirect variables, as they offer greater precision in quantifying the local environment. However, as extent increases, the relative value of direct variables increases. The indirect variables are likely not stationary on large scales - a species relationship to slope and elevation are likely different in southern US vs northern Canada, for instance. On the other hand, a species relationship to temperature, however coarsely it is mapped, is likely similar across its geographic range.

Elith et al. (2011) point out that Maxent’s built-in variable selection (via L1-regularization) is reliable, relatively insensitive to correlation among variables, and model performance may actually be degraded by imposing additional model selection procedures prior to running Maxent! They do suggest that sticking to proximal variables is preferable when projecting models to novel contexts.

Worldclim

One of the most common sources of climate data for SDMs is WorldClim. There are actually three distinct data sets available from Worldclim:

Historical climate data
- compiled from a combination of weather stations and databases, and further refined with satellite imagery (Fick and Hijmans, 2017)
- climate normals (30 year averages for the period 1970-2000) including monthly minimum, maximum, average temperature; monthly total precipitation; 19 bioclim variables (biologically meaningful values calculated from monthly temperature and precipitation values).
Historical monthly weather data (1950-2024)
- downscaled from CRU (Harris et al., 2020)
- 10-year averages for monthly minimum, maximum and average temperatures; monthly total precipitation.
Future climate projections
- downscaled & bias corrected data from CMIP6, including a variety of global climate models (GCM) and shared socio-economic pathways (SSP).
- 20-year averages for monthly minimum, maximum and average temperatures; monthly total precipitation; bioclim variables.

Transferability

Petitpierre et al. (2017) explicitly tested different approaches to model selection for use in projecting models in space and time. They recommend modelers should use a small number of proximal variables, or, particularly when very few observations are available for training, the first few PCA axes of a larger set of environmental variables. PCA axes are orthogonal (i.e., not collinear) by construction, but interpretation may be tricky if they incorporate a large number of variables.

Since we rarely have much information on proximal variables (beyond understanding that temperature and moisture are generally important), Petitpierre et al. (2017) recommend a suite of “State of the Art” (SOA) variables that have been shown to be useful for plants. These include:

BIO 01: annual mean temperature
BIO 04: temperature seasonality
BIO 11: mean temperature of coldest quarter
BIO 10: mean temperature of warmest quarter
BIO 15: precipitation seasonality
BIO 16: precipitation of wettest quarter
BIO 23: moisture index seasonality
BIO 28: annual mean moisture index

Note the last two aren’t included in the WorldClim/Bioclim archives, and the numbering above BIO 19 isn’t necessarily consistent (at least between different sources). These variables are available from https://www.climond.org, but that appears to be an outdated source relative to Worldclim? Worldclim currently offers more and more recent climate projections, but only for the first 19 variables. The Climond data is currently is also only available at 10’ and 30’ resolution, while Worldclim provides data (without the moisture indices) down to 30” resolution.

At a global scale, annual mean temperature and temperature of the warmest quarter are (not suprisingly) highly correlated, and the moisture indices are moderately correlated with precip var and precip wet quarter (again, not suprising). So it might be reasonable to use a reduced set of the SOA variables in studies that aim to generate transferable models: BIO 01, BIO 11, BIO 15, BIO 16 (and maybe BIO 23).

Beware temperature/precipitation ratios!

Booth (2022) found some very interesting problems with climate variables that mix temperature and precipitation (e.g., temperature of wettest quarter, precipitation of warmest quarter). In some cases these can generate abrupt gradients that reflect numerical oddities of the ratios rather than any biologically meaningful pattern. If you use the SOA variables this isn’t a concern, but if you are using combination ratios, be sure to check that paper for details.

Filtering Collinear Variables

This section is out of date and needs to be updated and trimmed!

I will need to reconsider whether evaluating collinearity is something I should continue to do. In the meantime, I leave the following notes on how to do it:

Merow et al. (2013) identify two general approaches to selecting variables. The machine learning approach is based on the understanding that the Maxent algorithm will, by design, select the most useful variables and features, so we can include all reasonable variables.

However, this probably only applies when the objective is to provide accurate predictions of occurrences in the same context in which the model is built. Efforts to understand the environmental constraints on that distribution, or projecting it to a new context, will be potentially confounded when the model includes correlated variables.

To minimize this problem, Merow et al. (2013) recommends taking a statistical approach (i.e., treating a Maxent model as a ‘conventional’ statistical model). In this case, they recommend prescreening variables to limit colinearity, and emphasize biologically relevant variables. This should produce more parsimonious and interpretable models.

Pairwise correlations can be used to identify pairs or groups of variables that are highly correlated. ENMTools (Warren et al., 2019) provides several helper functions for this, including raster.cor.matrix, raster.cor.plot.

I prefer using hclust based on 1 - abs(cor) to visualize correlated groups:

## "predictors" is a raster stack

## Calculate correlations:
cors <- raster.cor.matrix(predictors) # from ENMTools

threshold = 0.7  ## the maximum permissible correlation

dists <- as.dist(1 - abs(cors))

clust <- hclust(dists, method = "single")
groups <- cutree(clust, h = 1 - threshold)

## Visualize groups:
plot(clust, hang = -1)
rect.hclust(clust, h = 1 - threshold)

## Print the groups:
groups

##  bio1 bio12 bio16 bio17  bio5  bio6  bio7  bio8 biome 
##     1     1     1     1     1     1     1     1     2

NB I set the method argument to "single". This ensures that all the variables with correlations above the threshold will be captured together in a cluster. The default method, "complete", creates clusters that may include variables with correlations above the specified threshold. See discussion of hierarchical agglomerative clustering (section 8.5) in Legendre and Legendre (2012) for details, if you want to know more.

After running this, groups will identify which cluster each variable belongs to. Keep at most one variable from each group.

This doesn’t absolutely guarantee that variables in different groups will have correlations less than threshold, but in most cases this will be true. When it isn’t, the highest inter-group correlation will still be very close to the threshold. If you’re concerned, double check the correlations of the variables after you’ve picked them.

Alternatively, you can use cutree to select the number of groups you want, then pick a variable from each group. Since this doesn’t use a threshold, you’ll have to make sure the number of groups you pick is equal to or lower than the number of groups generated using the threshold approach.

## "predictors" is a raster stack

## Calculate correlations:
cors <- raster.cor.matrix(predictors) # from ENMTools

groupNum = 3  ## the desired number of groups

dists <- as.dist(1 - abs(cors))

clust <- hclust(dists, method = "single")
groups <- cutree(clust, k = groupNum)

## Visualize groups:
plot(clust, hang = -1)
rect.hclust(clust, k = groupNum)

## Print the groups:
groups

##  bio1 bio12 bio16 bio17  bio5  bio6  bio7  bio8 biome 
##     1     2     2     2     1     1     1     1     3

However, neither of these approaches will address multicollinearity among three or more variables. Guisan et al. (2017) suggest using the function usdm::vif instead, which calculates variable inflation. They recommend keeping the vif values under 10, but different authors will use cutoffs from 5-20.

Feature Selection

Features == the statistical models used to fit the variables to the response variables (presences). i.e., linear, quadratic, product, hinge, threshold, categorical.

Note that hinge is essentially a superset of linear and threshold features, so if you have hinges, the other two are redundant (Elith et al., 2011). As of version 3.4.0, threshold featues are not included by default; experience has shown that this improves model performance, and produces simpler, more realistic models (Phillips et al., 2017). Similarly, product features appear to contribute very little to model performance, given the added complexity.

Merow et al. (2013) recommend selecting features on biological grounds. They provide a short discussion, noting that the fundamental niche is likely quadratic for most variables over a large enough extent, but may be better approximated by a linear function if the study extent is truncated with respect to the species’ tolerance for that variable (a la Whittaker). Interesting ideas, but not much to go on unless you actually do know a fair bit about your species.

Warren and Seifert (2011) describe a process for selecting features to keep/include in the model (linear, quadratic, polynomial, hinge, threshold, categorical). It uses the AIC to identify the optimal combination. Easy and quick to do with the ENMEval package (note that many references cite ENMTools for these tests, but they’ve been moved to ENMEval nowadays).

NB applying different spatial filtering/thinning to your data can produce different ‘optimal’ models (i.e., different retained features and regularization value), as determined by the AIC criterion.

NB The enmeval function only evaluates AIC for models with an appropriate number of parameters. If you have a low number of observations, a low regularization (i.e., permissive approach to including parameters), and complex/high-parameter models (especially hinge features), the AIC values will be reported as NA. These models are overfit, and as such you shouldn’t use them with your data. Explanation on Maxent discussion list.

Regularization

Regularization is used to penalize complexity. Low values will produce models with many predictors and features, with 0 leading to all features and variables being included. This can lead to problems with over-fitting and interpretation. Higher regularization values will lead to ‘smoother’, and hopefully more general and transferable models. There will be a trade-off between over- and under-fitting.

The default values in Maxent are based on empirical tests on a large number of species. These are probably not unreasonable, but it’s pretty standard to mention that they’re a compromise, and we improved them for our the needs of our particular species and context by doing X (for various values of X).

The approach of Warren and Seifert (2011) (see previous) can be used here as well, testing a range of regularization (aka beta) values, and selecting the one that generates the lowest AIC. It may also be worth selecting the simplest model that is within a certain similarity of the ‘best’ model? That’s more to explain to reviewers though.

Warren and Seifert’s simulations demonstrate that models with a similar number of parameters to the true model produce more accurate models, in terms of suitability, variable assessment, and ranking of habitat suitability, both for the training extent and for models projected in space/time. Furthermore, AIC and BIC are the most effective approaches to model tuning to achieve the correct number of parameters.

Radosavljevic and Anderson (2014) also consider the impact of the regularization parameter on over-fitting. They find that the default value often leads to over-fitting, especially when spatial auto-correlation is not accounted for in model fitting. They conclude that regularization should be set deliberately for a study, following the results of experiments exploring a range of potential values.

Note that specifying the regularization is done via the betamultiplier argument, which applies to each of the different feature classes. That is, the actual regularization value will be set by Maxent automatically for each class, subject to the multiplier value specified by the user. We don’t set the regularization values for each class directly (which is possible via the options beta_lqp, beta_threshold etc. (Phillips, 2017), although Radosavljevic and Anderson (2014) suggest experiments to explore this should be done.

Output type

Raw: values are Relative Occurrence Rate (ROR) ~~which will sum to 1 over the extent of the study~~. Merow et al. (2013) considers this to be a reasonable interperetation of the Maxent output, but the actual values can be difficult to interpret; they produce maps that “do not often match ecologists’ intuition about the distribution of their species” (Phillips et al., 2017).

Logistic: attempts to provide an accurate estimate of the probability that the species is present, given the environment. Monotonically related to raw values; site rank is identical for these measures. Based on the assumption that there is a 50% probability that a species will be present at a site with ‘average’ conditions for the species. This assumption is problematic and unrealistic according to Merow et al. (2013). However, Elith et al. (2011) prefer logistic output, and discuss justification for preferring it over raw values.

Cumulative: the sum of all cells with <= to the raw value of the cell. Rescaled to range from 0-100.

Complementary Log-Log (aka CLOGLOG): the standard output from version 3.4.0 onwards. Generally similar to the logistic output, but tending to give slightly higher values. There is a stronger theoretical justification for CLOGLOG than logistic, as summarized in Phillips et al. (2017). CLOGLOG provides an estimate of the probability of presence, but with the caveat that this probability is based on an arbitrary quadrat size (similar to the prevalence assumption made with logistic).

Merow et al. (2013) recommends sticking to Raw whenever possible, which means using the same species in the same extent. Note that the raw values will change for different extents, even for identical models, so they can’t be compared across projections without additional post-processing.

Cumulative is preferable when defining/describing range boundaries, or otherwise dealing with omission rates.

Elith et al. (2011) prefer to use the logistic, which they present as a biologically reasonable estimate. However, it will be a problem in comparisons among species with different prevalence on the landscape, as it assumes identical (and arbitrary) prevalence.

Following (Phillips et al., 2017), CLOGLOG now seems to be the most intuitive output to use in most cases.

Evaluation

AUC

AUC assesses the success of the model in correctly ranking a random background point and a random presence point; that is, it should predict the suitability of the presence point higher than the background point. It is threshold-independent.

Lobo et al. (2008) identified five problems with AUC:

it ignores the predicted probability values and the goodness-of-fit of the model;
it summarises the test performance over regions of the ROC space in which one would rarely operate;
it weights omission and commission errors equally;
it does not give information about the spatial distribution of model errors; and, most importantly,
the total extent to which models are carried out highly influences the rate of well-predicted absences and the AUC scores.

Additionally, Radosavljevic and Anderson (2014) point out that AUC doesn’t assess over-fitting or goodness-of-fit; rather, it is a measure of discrimination capacity.

However, comparing the difference in AUC for the training and testing data does give an estimate of overfitting. If the model fit perfectly, without overfitting, the AUC should be identical. It won’t be, and the difference reflects the degree to which the model is over-fit on the training data. In other words, the extent to which the model is fit to noise in the data, or environmental bias, if geographic masking is used in the k-fold partitions.

Boyce

Boyce et al. (2002) proposed an index that compares the predicted and expected number of occupied sites with the suitability value of those sites:

sites are first sorted from lowest to highest suitability
then they are binned into groups of equal frequency
the number of actual occurrences for each bin are tabulated
the Spearman-rank correlation between bin rank and occurrence number is then calculated; if the model is good, we expect increasing numbers of occurrences for higher-ranked bins

Hirzel et al. (2006) evaluated a variety of SDM evaluation measures; on data sets with more than 50 presences, most evaluators had > 0.70 correlation with each other. Which is a little reassuring I suppose? They used AUC on presence/absence data as the ‘gold standard’, and found that the continuous Boyce index (which uses presence-only data) performed best.

This can be calculated with the function ecospat::boyce(), which takes a raster of suitability values and a matrix or data.frame containing the coordinates of presences. Note that as of 2025-05-06 there is a bug in this function, and the values it produces are not correct! Hopefully this will be fixed soon.

Related discussion in Phillips and Elith (2010), who note that the Boyce index is an example of their presence-only calibration plot (POC plot).

Thresholds

Radosavljevic and Anderson (2014) Threshold-dependent evaluation requires identifying a threshold in values predicted by the model to generate a binary suitable/unsuitable map. Setting the threshold to the lowest predicted value for a presence location may produce undesireable results if the lowest values is associated with an observation from an extreme outlier. More robust is setting the threshold to a particular quantile (10%), to exclude weirdos from establishing what’s suitable.

Again, if the model is perfectly fit, the omission rate in the testing data should be the same as in the training data. That is, setting the threshold at 10% to create the binary suitability map, we expect the omission rate in the test data to be 10%. Higher omission in the testing data reflects over-fitting (noise and/or bias).

For presence-only data commission error is unknown/unknowable. Accordingly, Radosavljevic and Anderson (2014) defined an optimal model as one that “(1) reduced omission rates to the lowest observed value (or near it) and minimized the difference between calibration and evaluation AUC [i.e., minimized over-fitting]; and (2) still led to maximal or near maximal observed values for the evaluation AUC (which assesses discriminatory ability). When more than one regularization multiplier fulfilled these criteria equally well, we chose the lowest one, to promote discriminatory ability (and hence, counter any tendency towards underfitting).”

Cross-validation

Radosavljevic and Anderson (2014) evaluated cross-validation using random k-fold partitions, geographical structuring, and geographic masking of partitions. Random partitions suffer from preserving biases in the training data in the testing data.

Geographic structuring, which uses occurrences from a pre-defined geographic area (rather than a random sample) as the test set, introduces additional spatial bias, and should be avoided. However, geographic structuring combined with masking (which excludes both presences and background from the specified geographic region from the test set) may substantially reduce overfitting, and yields more realistic models than random partitions.

Checkerboard partitions offer a nice compromise - this is geographic structuring and masking on a fine scale, and so should reduce spatial correlation between training and testing data. A version was used by Pearson et al. (2013), without a lot of discussion. Functions to do checkerboard cross validation are provided by Muscarella et al. (2014), but without a lot of discussion. The cited references suggest this might be intended more for species with limited occurrence data? Also, as implemented it looks like they only allow for 2-fold and 4-fold cross-validation. I’m not sure there’s any reason not to use checkerboards to do 9- or 16- fold cross validation?

Spatial Null Models

Not often used, but see Rodríguez-Rey et al. (2013), and discussion of Bahn and McGill (2007).

The dismo package (Hijmans et al., 2017) provides the function geoDist to serve as a spatial null model. Provided a matrix of occurence points, it generates a simple model of occurence based on the distribution of those points (i.e., the likelihood of an occurence at a location is inversely proportional to the distance of that location from known occurences).

geoDist returns a raster of ‘suitability’ values that can be evaluated just as the output from an SDM model projection.

Projection

Complex models, with large numbers of predictors, or that use complex features, are more likely to be overfit. Overfitting sacrifices generality (i.e., capacity to project to different scenarios) in favour of better fit to training data. Consequently, for the purposes of projection, we may want to emphasize smaller, simpler models. See also Petitpierre et al. (2017) for discussion of variable selection.

Guisan et al. (2017): two related issues to consider when comparing the environment in the training region to that in the region into which the model is projected:

availability: are environment ‘types’ similarly abundant and available?
analog: are the environment ‘types’ in the projected range also present in the training range?

The act of projection implicitly assumes environments are fully analagous with equal availability.

This is to a large extent unavoidable, so we have to take measures to reduce it in data preparation, and/or account for it in interpretation of results.

Clamping

Maxent includes the option of “clamping” projections. This constrains the values for environmental values in the projected range to the limit of that variable that is found in the training range. This has the effect of setting the predicted value of all non-analog cells to the value for the most extreme environments that are found in the training region.

This will reduce the occurence of unrealistic patterns emerging from the extension of complex models beyond the range of values they were trained on. It’s probably better than not clamping, but no reason to expect it’s particularly realistic.

Guisan et al. (2017) doesn’t mention clamping at all. Instead, they recommend explicitly identifying non-analog environments and excluding them from the projection (see MESS and exDet below); or at least, identifying them clearly and giving them due consideration in the interpretation of the results.

MESS

Multivariate Environmental Similarity Surfaces, Elith et al. (2010), provide a way to identify non-analog environments, and to quantify the extent to which they differ from environments in the training area. ~~The functions dismo::mess and ecospat::ecospat.mess~~ predicts::mess (as of 2023-10-19) is the main R function for calculating MESS values.

MESS is applied in geographic space, and calculates a single index value for each cell. The value is based on the single environmental variable that is most different from the conditions in the training region. If all variables at a cell are within the range of the training data, the MESS index will be between 0 and 1, with 1 indicating maximum similarity with the training range. Values below 0 indicate locations where at least one variable is outside the range of the training data. The further the departure from the training range, the lower the value will be. Note that this incorporates only the single worse variable: if only one variable is out of range, or all variables are out of range, the index only reflects the worst one.

There is no formal test or strict rule for interpreting MESS maps, other than that we ought to be skeptical of projected results into areas with MESS values < 0.

Extrapolation Detection

Extrapolation Detection, or exDet, was proposed by Mesgaran et al. (2014). It uses the Mahalanobis distance as the basis for an index of novelty. It accomodates covariation among variables, a major improvement over MESS. I’ve put together a tutorial for completing exDet analysis in R with more details.

COUE

Broennimann et al. (2012) presents and approach to contrast environmental conditions between training and projection regions in E-space. E-space and G-space provide complementary views of the niche. E-space shows the environmental distribution of a species in the context of all possible environmental combinations; G-space shows the geographic distribution of the species, constrained to environmental conditions that actually exist in the landscape. This analysis applies the COUE framework (centroid, overlap, underfilling and expansion).

ecospat (Cola et al., 2017) provides all the functions necessary to implement these analyses.

Climate Models

Climate projections are not predictions of future conditions—they are model-derived descriptions of possible future climates under a given set of plausible scenarios of climate forcings. The intention of simulating future climate is not to make accurate predictions regarding the future state of the climate system at any given point in time but to represent the range of plausible futures and establish the envelope that the future climate could conceivably occupy.

– Harris et al. (2014)

Recommendations

From Harris et al. (2014) (originally presented as 9 points):

Include a high and a low emissions scenario, to capture ‘best-case’ and ‘worst-case’ scenarios.

Note that as of 2014 we are trending close to the high emissions RCP8.5 scenario. RCP2.6 represents an increasingly unlikely aggressive mitigation approach.
Time and resources may limit us to one or two emissions scenarios, but more than one GCM should be used.

Different GCMs have different strengths, weaknesses and biases. Some models are known to be ‘wet’ or ‘dry’ or ‘hot’, compared to the mean of all GCMs. These biases are also spatially variable: some GCMs may be ‘hot’ for Africa, and ‘cold’ for North America.

Ostenibly different GCMs may share code and assumptions, and thus share biases in their projections.
Consider the most appropriate way to present the output from multiple climate models;
- If the multi-model mean is presented, report the range or standard deviation;
- best-case and worst-case scenarios can be presented using envelopes/binary maps: envelopes based on locations where any of the models predict suitable habitat show worst case (i.e., all areas identified as being suitable habitat in any model), envelopes based on locations identified by all models show best case (i.e., only areas that all models agree are suitable are identified) [good approach for IAS].
Choose a baseline time period appropriate to the study
- baselines are preferably defined on data amalgamated over 30 years, to account for stochastic inter-annual variation. Shorter time periods may be unacceptably influenced by noisy weather.
- baseline climate should correspond to the time period in which the data (i.e., observations) were collected
- NB: different climate sources use different baseline periods!
- Further discussed in Roubicek et al. (2010). They tested the sensitivity of SDMs trained on a different baseline than the one used to simulate the data, and found those models were signficantly worse than ones trained on the correct baseline.
Be aware of the real resolution of the climate data used;
- GCMs are coarse resolution, and need to be down-scaled for use with SDMs.
Maintain a dialog with climate modelers, to keep up-to-date with developments in climate models.

WorldClim

WorldClim 2.1 has CMIP6 data: 9 GCMs for four SSP, at resolutions down to 2.5 minutes (30 seconds overdue for release in March 2020), projected to 2040, 2060, 2080 and 2100.

WorldClim 1.4 has CMIP5 data: 19 GCMs, four RCP, projected to 2050 and 2070, at resolutions as low as 30 seconds.

Definitions

AR: Assessment Report for the IPCC. AR4 was released in 2007, AR5 in 2014, AR6 is scheduled for 2022
CMIP: Coupled Model Intercomparison Project, IPCC collection of GCMs, Numbered to correspond to the AR (eg. CMIP5 for AR5). “Models are only admitted to the CMIP archive if they meet a suite of rigorous requirements, including consistency with relevant observations, both past and present, and with fundamental physical principles.” IPCC doesn’t judge the models beyond being deemed fit for service. As such, the collection of models represents set of plausible future climates under a given emissions scenario.
GCM: General Circulation Model: 3D numerical representation of the climate system. 50-250km cell size, 10-20 layers in the atmosphere. Includes Atmosphere-Ocean GCM (AOGCM), incorportating interactions between the oceans and atmosphere, and Earth System Models (ESM), GCMs that incorporate biogeochemical cycles (eg. carbon cycle); ESM may also contain dynamic global vegetation models (DGVM)
SRES / RCP / SSP: Special Report on Emissions Scenarios, socioeconomic analysis of future climate emissions under varying conditions, used in AR4. Updated to Representative Concentration Pathways, in AR5. Updated to Shared Socionomic Pathways, in AR6. RCP2.6/ SSP 126 is aggressive mitigation (best case); RCP8.5/SSP 585 is our current trajectory (worst case)

Downscaling

GCMs have a native resolution in the range of 50-250km², much coarser than what is used for SDMs. To use for model projections, they need to be downscaled (i.e., converted to finer resolution) to the required scale. If you are using WorldClim data, it has already been downscaled for you.

Three options:

Dynamic Downscaling: uses the coarse-resolution GCMs as the input for similarly complex fine-scale models for the region of interest. Lots of added value compared to the GCMs, but computationally expensive, requiring expert skill to produce and interpret. Thus availability is limited.
Statistical Downscaling: uses past coars and fine-scale data to establish statistical/numerical models mapping regional data to local data. Then uses the resulting model to create future local data from future projections. Easier to do than Dynamic Downscaling, but less realistic, more implicit assumptions.
Simple Scaling: break coarse pixels up into smaller pixels containing the same value as the parent; doesn’t create any new values, or introduce any error.

Ensembles

TODO

TO-READ

Boria, R. A. et al. 2014. Spatial filtering to reduce sampling bias can improve the performance of ecological niche models. – Ecol. Model. 275: 73–77.

References

Aiello‐Lammens, M. E., R. A. Boria, A. Radosavljevic, B. Vilela, and R. P. Anderson. 2015. spThin: an R package for spatial thinning of species occurrence records for use in ecological niche models. Ecography 38: 541–545.

Atwater, D. Z., C. Ervine, and J. N. Barney. 2018. Climatic niche shifts are common in introduced plants. Nature Ecology & Evolution 2: 34–43.

Bahn, V., and B. J. McGill. 2007. Can niche-based distribution models outperform spatial interpolation? Global Ecology and Biogeography 16: 733–742.

Barbet-Massin, M., F. Jiguet, C. H. Albert, and W. Thuiller. 2012. Selecting pseudo-absences for species distribution models: how, where and how many? Methods in Ecology and Evolution 3: 327–338.

Barve, N., V. Barve, A. Jiménez-Valverde, A. Lira-Noriega, S. P. Maher, A. T. Peterson, J. Soberón, and F. Villalobos. 2011. The crucial role of the accessible area in ecological niche modeling and species distribution modeling. Ecological Modelling 222: 1810–1819.

Booth, T. H. 2022. Checking bioclimatic variables that combine temperature and precipitation data before their use in species distribution models. Austral Ecology 47: 1506–1514.

Boyce, M. S., P. R. Vernier, S. E. Nielsen, and F. K. A. Schmiegelow. 2002. Evaluating resource selection functions. Ecological Modelling 157: 281–300.

Broennimann, O., M. C. Fitzpatrick, P. B. Pearman, B. Petitpierre, L. Pellissier, N. G. Yoccoz, W. Thuiller, et al. 2012. Measuring ecological niche overlap from occurrence and spatial environmental data. Global Ecology and Biogeography 21: 481–497.

Cola, V. D., O. Broennimann, B. Petitpierre, F. T. Breiner, M. D’Amen, C. Randin, R. Engler, et al. 2017. ecospat: an R package to support spatial analyses and modeling of species niches and distributions. Ecography 40: 774–787.

Elith, J., C. H. Graham, R. P. Anderson, M. Dudík, S. Ferrier, A. Guisan, R. J. Hijmans, et al. 2006. Novel methods improve prediction of species’ distributions from occurrence data. Ecography 29: 129–151.

Elith, J., M. Kearney, and S. Phillips. 2010. The art of modelling range-shifting species. Methods in Ecology and Evolution 1: 330–342.

Elith, J., S. J. Phillips, T. Hastie, M. Dudík, Y. E. Chee, and C. J. Yates. 2011. A statistical explanation of MaxEnt for ecologists: Statistical explanation of MaxEnt. Diversity and Distributions 17: 43–57.

Fick, S. E., and R. J. Hijmans. 2017. WorldClim 2: new 1-km spatial resolution climate surfaces for global land areas. International Journal of Climatology 37: 4302–4315.

Guisan, A., W. Thuiller, and N. E. Zimmermann. 2017. Habitat Suitability and Distribution Models: with Applications in R. Cambridge University Press.

Harris, I., T. J. Osborn, P. Jones, and D. Lister. 2020. Version 4 of the CRU TS monthly high-resolution gridded multivariate climate dataset. Scientific Data 7: 109.

Harris, R. M. B., M. R. Grose, G. Lee, N. L. Bindoff, L. L. Porfirio, and P. Fox‐Hughes. 2014. Climate projections for ecologists. WIREs Climate Change 5: 621–637.

Hijmans, R. J., S. Phillips, J. Leathwick, and J. Elith. 2017. dismo R package Version 1.1-4.

Hirzel, A. H., G. Le Lay, V. Helfer, C. Randin, and A. Guisan. 2006. Evaluating the ability of habitat suitability models to predict species presences. Ecological Modelling 199: 142–152.

Lee‐Yaw, J. A., M. Fracassetti, and Y. Willi. 2018. Environmental marginality and geographic range limits: a case study with Arabidopsis lyrata ssp. lyrata. Ecography 41: 622–634.

Legendre, P., and L. Legendre. 2012. Numerical ecology. 3rd Edition. Elsevier, New York.

Lobo, J. M., A. Jiménez‐Valverde, and R. Real. 2008. AUC: a misleading measure of the performance of predictive distribution models. Global Ecology and Biogeography 17: 145–151.

Merow, C., M. J. Smith, and J. A. Silander. 2013. A practical guide to MaxEnt for modeling species’ distributions: what it does, and why inputs and settings matter. Ecography 36: 1058–1069.

Mesgaran, M. B., R. D. Cousens, and B. L. Webber. 2014. Here be dragons: a tool for quantifying novelty due to covariate range and correlation change when projecting species distribution models J. Franklin [ed.],. Diversity and Distributions 20: 1147–1159.

Muscarella, R., P. J. Galante, M. Soley‐Guardia, R. A. Boria, J. M. Kass, M. Uriarte, and R. P. Anderson. 2014. ENMeval: An R package for conducting spatially independent evaluations and estimating optimal model complexity for Maxent ecological niche models. Methods in Ecology and Evolution 5: 1198–1205.

Pearson, R. G., S. J. Phillips, M. M. Loranty, P. S. A. Beck, T. Damoulas, S. J. Knight, and S. J. Goetz. 2013. Shifts in Arctic vegetation and associated feedbacks under climate change. Nature Climate Change 3: 673–677.

Petitpierre, B., O. Broennimann, C. Kueffer, C. Daehler, and A. Guisan. 2017. Selecting predictors to maximize the transferability of species distribution models: lessons from cross-continental plant invasions. Global Ecology and Biogeography 26: 275–287.

Phillips, S. J. 2017. A Brief Tutorial on Maxent. Website http://biodiversityinformatics.amnh.org/open_source/maxent/ [accessed 19 May 2020].

Phillips, S. J., R. P. Anderson, M. Dudík, R. E. Schapire, and M. E. Blair. 2017. Opening the black box: an open-source release of Maxent. Ecography 40: 887–893.

Phillips, S. J., and M. Dudík. 2008. Modeling of species distributions with Maxent: new extensions and a comprehensive evaluation. Ecography 31: 161–175.

Phillips, S. J., and J. Elith. 2010. POC plots: calibrating species distribution models with presence-only data. Ecology 91: 2476–2484.

Radosavljevic, A., and R. P. Anderson. 2014. Making better Maxent models of species distributions: complexity, overfitting and evaluation. Journal of Biogeography 41: 629–643.

Renner, I. W., J. Elith, A. Baddeley, W. Fithian, T. Hastie, S. J. Phillips, G. Popovic, and D. I. Warton. 2015. Point process models for presence-only analysis. Methods in Ecology and Evolution 6: 366–379.

Rodríguez-Rey, M., A. Jiménez-Valverde, and P. Acevedo. 2013. Species distribution models predict range expansion better than chance but not better than a simple dispersal model. Ecological Modelling 256: 1–5.

Roubicek, A. J., J. VanDerWal, L. J. Beaumont, A. J. Pitman, P. Wilson, and L. Hughes. 2010. Does the choice of climate baseline matter in ecological niche modelling? Ecological Modelling 221: 2280–2286.

Soberón, J. M. 2010. Niche and area of distribution modeling: a population ecology perspective. Ecography 33: 159–167.

Valavi, R., G. Guillera-Arroita, J. J. Lahoz-Monfort, and J. Elith. 2022. Predictive performance of presence-only species distribution models: a benchmark study with reproducible code. Ecological Monographs 92: e01486.

Varela, S., R. P. Anderson, R. García-Valdés, and F. Fernández-González. 2014. Environmental filters reduce the effects of sampling bias and improve predictions of ecological niche models. Ecography 37: 1084–1091.

Warren, D. L., N. Matzke, M. Cardillo, J. Baumgartner, L. Beaumont, N. Huron, M. Simões, et al. 2019. ENMTools R Package.

Warren, D. L., and S. N. Seifert. 2011. Ecological niche modeling in Maxent: the importance of model complexity and the performance of model selection criteria. Ecological Applications 21: 335–342.

Notebooks on plantarum.ca

Rawtherapee Notebook

Default Profile

Start From the Built-in “Neutral” profile

Set the Output Profile

RTv4_sRGB for the web, ProPhoto for Photoshop/Gimp

Set the Demosaicing Algorithm

Capture Sharpening

Auto Chromatic Aberration Correction

Turn on Defringe

Turn on Noise Reduction

Uncheck ‘Clip Out of Gamut Colors’

Set the Profiled Lens Correction to Auto

Don’t turn on Dead Pixels and Hot Pixel Filters

Save the Profile

Set the Profile as your default

Lightening an Image

Method 1: Exposure Compensation

Highlight Reconstruction

Highlight Compression

The Problem With Exposure Compensation

Method 2: L*A*B* Adjustments

Method 3: Abstract Profile

Noise Reduction

Spatial Ordinations

Spatial Statistics

Moran’s I

Spatial Weighting Matrix

Spatial Lag

Geary’s c

MULTISPATI Analysis

Co-inertia Analysis

Spatial Principal Components Analysis

Eigenvalues

Packaging Oddities & Significance Testing

References

Maxent Best Practices

Key Resources

Technical Summaries

Sampling Bias

Spatial Bias

Study Extent

Background Points: Number and Bias Grids

Variable Selection

Worldclim

Transferability

Beware temperature/precipitation ratios!

Filtering Collinear Variables

Feature Selection

Regularization

Output type

Evaluation

AUC

Boyce

Thresholds

Cross-validation

Spatial Null Models

Projection

Clamping

MESS

Extrapolation Detection

COUE

Climate Models

Recommendations

WorldClim

Definitions

Downscaling

Ensembles

TO-READ

References

Method 2: LAB* Adjustments

Moran’s `I`

Geary’s `c`