Testing the Mantel statistic with a spatially‐constrained permutation procedure

Abstract

Mantel tests are widely used in ecology to assess the significance of the relationship between two distance matrices computed between pairs of samples. However, recent studies demonstrated that the presence of spatial autocorrelation in both distance matrices induced inflations of parameter estimates and type I error rates. These results also hold for partial Mantel test which is supposed to control for the spatial structures. To address the issue of spatial autocorrelation in testing the Mantel statistic, we developed a new procedure based on spatially constrained randomizations using Moran spectral randomization. A simulation study was conducted to assess the performance of this new procedure. Different scenarios were considered by manipulating the number of variables, the number of samples, the regularity of the sampling design and the level of spatial autocorrelation. As identified by previous studies, we found that Mantel statistic and its associated type I error rate are inflated in simple and partial Mantel tests when both distances matrices are spatially structured. We showed that these biases increased with the number of variables, decreased with the number of samples and were slightly lower for regular than irregular sampling. The new procedure succeeded in correcting the spurious inflations of the parameter estimates and type I error rates in any of the presented scenarios. Our results suggest that studies from several fields (e.g. genetic or community ecology) could have been overestimating the relationship between two distances matrices when both presented spatial autocorrelation. We proposed an alternative solution applicable in every field to correctly compute Mantel statistic with a fair type I error rate.

Fragmentation promotes the role of dispersal in determining 10 intermittent headwater stream metacommunities

“…resistant species), notably for stream invertebrates (e.g. Aspin et al, 2018;Crabot, Clappe, et al, 2019;Datry et al, 2014;Leigh & Datry, 2017) but also for algae (Robson & Matthews, 2004;Robson, Matthews, Lind, & Thomas, 2008), our result confirms that drying can have, in some cases, a legacy effect long after rewetting. Here, drying reaches were still exhibiting a lower taxonomic richness than perennial reaches even after up to 6-9 months of flowing conditions.…”

“…In general, ecologists are using either proxies for dispersal (e.g. using biological traits, Aspin et al, 2018;Crabot, Clappe, et al, 2019) or statistical tools (e.g. distance-decay relationships, variance partitioning) to unravel its roles F I G U R E 3 Alpha-diversity distribution (mean ± standard deviation) for perennial (black circle) and intermittent (grey triangle) reaches for each fragmented headwater and for both sampling period (before and after the drying season) Table 2 for exact values of r) for each combination of community type (Chao dissimilarity index) and distance matrices for each fragmented headwater (FHW) before and after the drying season, for the whole community (a), the community of taxa with aerial stages (b), and strictly aquatic taxa (c).…”

“…β-diversity, distance decays, drying, invertebrates, man-made structure variations in network topology (e.g. Crabot, Clappe, et al, 2019;Heino, Grönroos, Soininen, Virtanen, & Muotka, 2012;Tonkin et al, 2016). This clearly calls for considering multiple river networks when aiming to disentangle the factors shaping headwater metacommunities rather than focusing on a single one, as is usually done (e.g.…”

Metacommunity Structures of Macroinvertebrates and Diatoms in High Mountain Streams, Yunnan, China

“…For example, the presence of spatial autocorrelation between distance matrices may cause Mantel test results to have an inflated Type I error, that is, rejecting the null hypothesis even though it is true (Guillot and Rousset, 2013). Partial Mantel tests are often used to control for an underlying spatial matrix, but research has suggested that partial Mantel tests may not be adequate for controlling for spatial autocorrelation (Guillot and Rousset, 2013;Crabot et al, 2019). Future research focused on how abiotic (physical distance, local environment) and biotic (competition, predation, symbiosis) factors interact will provide more insight to the different roles that each factor plays in shaping metacommunities (Chiu et al, 2020).…”

Riparian and in-channel habitat properties linked to dragonfly emergence

“…Separate models were created for each of the four dragonfly responses (abundance, biomass, diversity and assemblage). Because increasing the number of variables in partial Mantel models is known to inflate type I error rates 46 , we chose to only assess high-level models using this approach and applied false discovery rate corrections to path p -values within each model to account for multiple comparisons 47 . In order to assess the associations between specific environmental variables and dragonfly responses, we developed distance-based linear models (DistLM) in PRIMER 7 48 using a step-wise procedure and Akaike Information Criterion with corrections (AICc) to find the best fitted model even with a large number of predictor variables.…”