Strategies

This text about available strategies uses several terms one might be unfamiliar with. The Glossary should be able to explain those terms.

To analyse the influence of grain and extent on perceived biodiversity, it is necessary to simulate the existence of quadrats of different size (grain) with different spacing (extent) in the data. seal does so using three different strategies.

Before starting an analysis, it must be specified in the taskfile what strategy should be used. Striped transect merging is the default.

Warning

Strategies have certain constraints regarding the shape of study grid they can be applied to. adjust-grid subcommand may be used to make input data fit these constraints at a cost of some precision.

The following diagrams show manipulation of a hypothetical, 9×9 quadrat study grid throughout the entire analysis process. It is shown adjusted to allow for analysis of 3 levels for every available strategy. Quadrats (for nested quadrats strategy) or transects (for the two transect-centric strategies) are merged and assigned new coordinates accordingly in the process of analysis.

Three strategies are available. The following legend applies to all figures in the strategies description.

• quadrat/transect participating in the current sub-analysis, possibly with newly assigned coordinates during adjustments

• quadrat in the original data/quadrat not participating in the current sub-analysis

• quadrat discarded—either manually or using adjust-grid—to make analysis with given parameters possible

• quadrat coordinate in the original study grid

• quadrat coordinate (transect + zone) in the transformed grid

• quadrat coordinate discarded to make analysis with given parameters possible

While reading the following sections, it is recommended to consults the Glossary about various symbols used throughout the text.

Nested quadrats

Note

This strategy is the most similar to the one used by Palmer & White.^1,4 However, it works best with grids where \(t = z\) (square-shaped with regards to coordinates, not necessarily area). While it can be used for rectangular grids, the results are skewed, with the bias being worse with more disproportional rectangles.

The grid design forms an observational experiment that allows the influence of grain and extent to be assessed. Level 1 quadrats represent the smallest observational units and are nested in the corners of higher-level quadrat. This structure implies that analyzing the same area using lower-level quadrats requires a greater number of them, spaced farther apart, thus covering a larger extent. The two-dimensional layout of the grid enables extent to be examined in both spatial dimensions.

In this strategy, quadrats are incrementally merged along transects (x-axis) and zones (y-axis) both. The grid is divided into square sections with side length equal to \(2^{\max{L} - 1}\) transects.

For each level, a merged quadrat is placed on the bottom left corner of its section, with side length equal to \(2^{l - 1}\) quadrat(s). The remaining quadrats of the original grid in the section are omitted from the analysis.

For \(l = \max{L}\), all quadrats are analysed (but merged). Analogous to Palmer & White.^1,4

Constraints:

• \(t \mod 2^{\max{L}-1} = 0\)

  (number of transects in the original study grid must be divisible by 2 to the power of maximum requested level, lowered by 1)

• \(z \mod 2^{\max{L}-1} = 0\)

  (number of zones in the original study grid must be divisible by 2 to the power of maximum requested level, lowered by 1)

Example:

my-taskfile.toml

levels = [ 1, 2, 3 ]
level-strategy = "nested-quadrats"

Used notation: L, l, t, z

Striped transect merging

Note

This is the default strategy. We recommend using it for highly rectangular grids.

This strategy is similar in nature to nested quadrats strategy, but it operates solely on the x-axis. While this approach loses some of the influence captured by two-dimensional extent, it provides a practical option for analyzing data collected along transects (e.g., using the transect-intercept method) or from quadrats arranged in elongated, rectangular layouts.

In this strategy, the entire study grid is divided into \(\max{L}\) sections, “stripes”, consisting of original transects. Each stripe starts with a transect \(l\) quadrats wide, with the remaining transects being omitted from analysis. Omitted quadrats are depicted as white squares in the following figures. The number of transects remains constant for every level: \(t'=\frac{t}{\max{L}}\). In the maximum level grid, every transect of the original grid is included, though not in its original form.

Constraints:

• \(t \mod \max{L} = 0\)

  (number of transects in the original study grid must be divisible by the maximum analysed level)

Example:

my-taskfile.toml

levels = [ 1, 2, 3 ]
level-strategy = "striped-transect-merging"

Used notation: L, l, t, t’

Repeated transect merging

Warning

This strategy does not examine the influence of grain and extent completely.

This strategy always covers the entire grid and does not account for the influence of extent. Quadrats in any level cover the entirety of original grid, hence the same cumulative number of species is reached in every level. It serves as a supporting strategy, capturing the effect of grain—which is typically more significant than that of extent.

This strategy merges \(l\) adjacent transects into one. This process is done across the entire study grid, resulting in new grid with transects \(l\) quadrats wide (and containing \(t' = \frac{t}{l}\) transects in total). Encounter at \(q_{x,y}\) would become encounter at \(q_{\lfloor{x / l} \rfloor, y}\).

Simply put, the study grid is “tiled” by transects with width being a multiple of the original width and the analysed level.

This strategy does not result in any original transects being omitted from the analysis. The transects are indexed left to right, and the merging always starts with the lowest coordinates (leftmost).

Constraints:

• \(\forall l\in L: t\mod l = 0\)

  (number of transects in the original study grid must be divisible by every analysed level)

Example:

my-taskfile.toml

levels = [ 1, 2, 3 ]
level-strategy = "repeated-transect-merging"

Used notation: L, l, t, t’