# An Ecological Definition and Objective Threshold for Differentiating Small Fragments

## TL;DR

This paper introduces a new method to objectively define the threshold size for small ecological fragments using species representation data.

## Contribution

The paper proposes an objective threshold called AUSR to differentiate small and large ecological fragments based on species incidence.

## Key findings

- The AUSR threshold was estimated in over 90% of 138 datasets, showing broad applicability.
- Regression slopes revealed consistent trends in species representation across most study systems.
- The method requires minimal data and can be implemented using standard ecological data.

## Abstract

In an increasingly fragmented natural world, understanding how different ecological phenomena vary with patch size has many motivations. Examples include the assembly of biodiversity, ecosystem service provision and the suitability of fragments for habitat specialist species. A common approach to such questions divides fragments into small and large size classes for separate analysis. However, lack of an objective definition and means to differentiate ‘small’ from ‘large’ patches limits our ability to compare findings across studies, arguably impeding progress toward any unified views. Because larger and smaller fragments tend, on average, to respectively over‐represent narrow‐ and wide‐range species, an ‘area for unbiased species representation’ (AUSR) can be defined at some intermediate fragment size predicted to contain species at incidence frequencies approximating that of the overall landscape. A central tendency for AUSR has previously been estimated for patchy habitats (islands, habitat islands and fragments), providing a benchmark to compare this threshold of small fragment size between studies. However, if AUSR can be readily determined within individual study systems, it would also provide an objective threshold to separate small and large fragments under the AUSR definition. Here we assess this potential for 138 published datasets from various fragmented landscapes using an index comparing species incidence frequencies in each fragment with that of the overall landscape. Regressing this index on fragment area yielded an estimate for AUSR in over 90% of cases, suggesting broad applicability as an objective way to separate fragments into two size classes. Regression slopes provide further information on the relative representation of narrow‐ vs. wide‐range species, with ~80% being numerically consistent with the overall negative trend. Requiring only the same data as the island species‐area relationship, AUSR can provide useful insights on the relative importance of narrow‐ vs. wide‐ranging species for studies of patch‐size dependence in ecological phenomena.

Many ecological phenomena vary with fragment size. To quantify the impacts of small fragments on ecological pattern and process, one must differentiate them, but there is no agreed way to achieve this. We present an objective definition and method to identify a threshold size for small fragments that requires minimal data and can be readily calculated using the R code provided.