# Species Distribution Models

#### Gilles Colling

#### 2026-07-30

## What vectra does for a distribution model

A species distribution model relates occurrence records to environmental predictors. The predictors usually arrive as raster layers (climate, terrain, land cover), and the records as point coordinates. The first step of almost every workflow is the same: sample each raster at the occurrence coordinates to build a table of predictor values, then fit a model to that table.

vectra covers two parts of this pipeline directly. It reads `GeoTIFF` rasters (including tiled and `BigTIFF` layouts) and samples them at point coordinates with `tiff_extract_points()`, reading only the strips that contain query points, so a sparse point set over a continental raster touches a small fraction of the file. And it consumes a query one batch at a time, so a model matrix that exceeds memory can still be fitted: `chunk_feeder()` streams the data through `biglm::bigglm()` one chunk per iteration.

The rest of this article assumes two things are handled before extraction:

- Vector geometry. vectra streams the vector verbs (`spatial_join()`, `spatial_filter()`, `spatial_clip()`, `spatial_overlay()`, `rasterize()`, …) around `sf`, one batch at a time – see Streaming spatial operations. It carries no geometry type of its own, so the topology comes from `sf` and GEOS. This article stays on the raster-sampling path and assumes any range-map intersection or study-region buffer is prepared before extraction.
- Reprojection. vectra reads the coordinate reference system of a `GeoTIFF` with `tiff_crs()` but does not transform coordinates. Occurrence points must already be in the raster’s CRS when they reach `tiff_extract_points()`.

## Align coordinates before extracting

`tiff_extract_points()` maps each coordinate to a pixel through the raster’s affine geotransform. It does this in the raster’s own CRS, so points recorded in a different CRS must be reprojected first. Read the raster CRS with `tiff_crs()`, then transform the points to match:

    # Occurrences recorded in lon/lat (EPSG:4326), raster in a projected CRS.
    target <- tiff_crs("predictors.tif")$epsg          # e.g. 3035 (LAEA Europe)

    pts <- sf::st_as_sf(occ, coords = c("lon", "lat"), crs = 4326)
    pts <- sf::st_transform(pts, target)
    xy  <- sf::st_coordinates(pts)

    env <- tiff_extract_points("predictors.tif", x = xy[, 1], y = xy[, 2])

When the points and the raster already share a CRS this step is unnecessary. The examples below work in lon/lat throughout.

## Build a predictor table

We synthesize a small two-layer climate raster over Central Europe and write it to a `GeoTIFF` with an EPSG:4326 GeoKey. Layer `band1` stands in for mean annual temperature and `band2` for annual precipitation.

    nx <- 80; ny <- 50
    xmin <- 5; xmax <- 17; ymin <- 45; ymax <- 55
    xres <- (xmax - xmin) / nx
    yres <- (ymax - ymin) / ny

    g <- expand.grid(col = 0:(nx - 1), row = 0:(ny - 1))
    g$x <- xmin + (g$col + 0.5) * xres          # pixel centres
    g$y <- ymax - (g$row + 0.5) * yres          # row 1 is the northern edge
    g$band1 <- 14 - 0.6 * (g$y - 50) + 0.2 * (g$x - 11) + rnorm(nrow(g), 0, 0.3)
    g$band2 <- 750 + 25 * (g$y - 50) - 8 * (g$x - 11) + rnorm(nrow(g), 0, 10)

    tif <- tempfile(fileext = ".tif")
    write_tiff(g[, c("x", "y", "band1", "band2")], tif, crs = 4326L)

    tiff_crs(tif)
    #> $epsg
    #> [1] 4326
    #>
    #> $citation
    #> [1] NA

Now we sample the raster at a set of survey sites. `tiff_extract_points()` returns one row per point with the input coordinates and one column per band. Points outside the raster come back as `NA`.

    N <- 1500
    sites <- data.frame(
      x = runif(N, xmin + 0.3, xmax - 0.3),
      y = runif(N, ymin + 0.3, ymax - 0.3)
    )

    env <- tiff_extract_points(tif, sites)
    head(env)
    #>           x        y    band1    band2
    #> 1 12.185552 51.38240 13.48465 767.0959
    #> 2 16.404559 46.80544 16.52226 624.3277
    #> 3  7.619038 51.65444 12.43874 817.2647
    #> 4  5.534852 53.85685 10.44774 896.6918
    #> 5  6.119896 47.56621 14.34668 730.9303
    #> 6 11.790835 52.69071 12.26763 796.8652

We standardize the two predictors once and store the prepared columns, then draw a presence/absence outcome from them. Standardizing before the data reaches the model lets every streaming batch share the same transform, which the out-of-core fit below relies on. With the generating coefficients known, each fit can be checked against them.

    occ <- data.frame(
      bio1  = as.numeric(scale(env$band1)),   # standardized once, then stored
      bio12 = as.numeric(scale(env$band2))
    )
    eta <- -0.2 + 1.3 * occ$bio1 - 0.9 * occ$bio12
    occ$presence <- rbinom(N, 1, plogis(eta))
    table(occ$presence)
    #>
    #>   0   1
    #> 790 710

## Fit in memory when the table fits

For most studies the extracted table has thousands to a few million rows and a handful of predictors, which fits in memory comfortably even when the source rasters are enormous. The ordinary path is to extract, then fit with `glm()`:

    fit <- glm(presence ~ bio1 + bio12, data = occ, family = binomial())
    round(coef(fit), 3)
    #> (Intercept)        bio1       bio12
    #>      -0.182       1.156      -1.099

The recovered coefficients sit close to the values used to generate the data (intercept -0.2, `bio1` 1.3, `bio12` -0.9).

## Stream when the table is larger than memory

Dense background sampling, many predictors, or a model fitted across a whole continent can push the predictor table past available RAM. Here vectra streams the table through the model in bounded pieces. We write the modelling frame to a `.vtr` file to stand in for a table too large to hold in memory.

    vtr <- tempfile(fileext = ".vtr")
    write_vtr(occ, vtr)

### A single pass with collect_chunked()

`collect_chunked()` folds a function over the query one batch at a time. It is the right tool for any summary that accumulates in bounded space across the data. Here we compute the class balance and per-class predictor means in a single streaming pass, never holding more than one batch:

    acc <- collect_chunked(
      tbl(vtr),
      function(acc, chunk) {
        p <- chunk$presence == 1
        acc$n      <- acc$n      + nrow(chunk)
        acc$n_pres <- acc$n_pres + sum(p)
        acc$sum1   <- acc$sum1   + tapply(chunk$bio1, p, sum)[c("FALSE", "TRUE")]
        acc
      },
      .init = list(n = 0L, n_pres = 0L, sum1 = c("FALSE" = 0, "TRUE" = 0))
    )
    acc$n_pres / acc$n                      # prevalence
    #> [1] 0.4733333

The same pattern accumulates the cross-products `X'X` and `X'y` behind a linear model, giving an exact least-squares fit in one pass. A generalized linear model needs more: each iteratively reweighted step reweights the rows by the current coefficient estimate, so the data must be read once per iteration.

### An out-of-core GLM with chunk_feeder()

`chunk_feeder()` exposes the query as a resettable generator that `biglm::bigglm()` drives itself, re-reading the stream on every iteration. Because a vectra node is consumed as it streams, the feeder takes a factory: a function that returns a fresh node each time the stream is rewound.

    src <- function() tbl(vtr) |> select(presence, bio1, bio12)

    fit_stream <- biglm::bigglm(
      presence ~ bio1 + bio12,
      data = chunk_feeder(src),
      family = binomial()
    )
    round(coef(fit_stream), 3)
    #> (Intercept)        bio1       bio12
    #>      -0.182       1.156      -1.099

The streamed fit matches the in-memory `glm()` to within its convergence tolerance, while the engine never holds more than one batch of the predictor table at a time. The same call scales to a `.vtr` or CSV far larger than RAM: only the factory and the formula change.

`bigglm()` rebuilds the model matrix from each batch as it arrives. A formula term whose definition is estimated from the data, such as `scale()`, `poly()`, `ns()`, or `bs()`, is recomputed on every batch and takes a different value on each one. Prepare these terms before writing the table: standardize predictors as we did above, set explicit `Boundary.knots` on splines, and make sure every factor level appears in the stream. The formula then names prepared columns and each batch yields the same transform.

## Transferability: is a projection environment novel?

A model calibrated in one region and projected to another (a different area, or the same area under a future climate) is only trustworthy where the projection environment resembles the calibration environment. Mobility-oriented parity (MOP; Owens et al. 2013) measures that resemblance directly. For each projection site it reports the mean distance, in predictor space, to the nearest fraction of the calibration cloud: small where the site sits inside the training conditions, larger where it is environmentally novel and the model would be extrapolating.

`feature_knn()` computes that distance while streaming the projection side, so a continental projection grid never has to be held in memory. The calibration cloud is the resident reference; each projection batch is scored against it. The predictors here are already standardized, so a plain Euclidean distance is meaningful; `metric = "mahalanobis"` whitens by the calibration covariance when the predictors are correlated.

    calib <- occ[, c("bio1", "bio12")]          # the standardized training cloud

    # Two sites inside the training conditions and one well outside them.
    proj <- data.frame(
      bio1  = c(0.0, 0.5, 4.0),
      bio12 = c(0.0, -0.5, -4.0)
    )
    pv <- tempfile(fileext = ".vtr")
    write_vtr(proj, pv)

    tbl(pv) |>
      feature_knn(calib, percentage = 5) |>
      collect()
    #>   bio1 bio12 knn_distance
    #> 1  0.0   0.0    0.1105930
    #> 2  0.5  -0.5    0.1318012
    #> 3  4.0  -4.0    3.0039278
    unlink(pv)

The third site, far from any training condition, is scored with a much larger distance than the two that sit within the cloud.

When the projection is itself a stack of environmental rasters, `rast_feature_distance()` folds the same distance over the projection grid, reading the reference raster once and walking the projection one tile-row strip at a time, so the surface is written aligned to the grid and computed out-of-core. The strict-extrapolation half of a novelty diagnostic such as MOP, the count of predictors whose value falls outside the range each takes over the calibration cloud, is already native: it is a per-band `min`/`max` reduce over the calibration raster followed by a `rast_calc()` expression on the projection raster, so the distance surface and the extrapolation count compose without a dedicated verb.

## Choosing a path

Extract with `tiff_extract_points()` in every case. After that:

- If the predictor table fits in memory, `collect()` it and fit with `glm()`, `mgcv::gam()`, or any modelling function. This is the common case.
- If a single-pass summary is all you need (class balance, sufficient statistics, an online mean), use `collect_chunked()`.
- If the table itself exceeds memory and you need a full GLM, feed it to `biglm::bigglm()` through `chunk_feeder()`.
- To judge whether a projection is within the calibrated conditions, score it with `feature_knn()`, or `rast_feature_distance()` for a streaming raster novelty surface. ```