Spatial correlation modeling comprises both spatial autocorrelation and spatial cross-correlation processes. The spatial autocorrelation theory has been well-developed. It is necessary to advance the method of spatial cross-correlation analysis to supplement the autocorrelation analysis. This paper presents a set of models and analytical procedures for spatial cross-correlation analysis. By analogy with Moran’s index newly expressed in a spatial quadratic form, a theoretical framework is derived for geographical cross-correlation modeling. First, two sets of spatial cross-correlation coefficients are defined, including a global spatial cross-correlation coefficient and local spatial cross-correlation coefficients. Second, a pair of scatterplots of spatial cross-correlation is proposed, and the plots can be used to visually reveal the causality behind spatial systems. Based on the global cross-correlation coefficient, Pearson’s correlation coefficient can be decomposed into two parts: direct correlation (partial correlation) and indirect correlation (spatial cross-correlation). As an example, the methodology is applied to the relationships between China’s urbanization and economic development to illustrate how to model spatial cross-correlation phenomena. This study is an introduction to developing the theory of spatial cross-correlation, and future geographical spatial analysis might benefit from these models and indexes.

Reference Information

Provenance for this README

• File name: README_Dataset-AugStreamTempBanff_v0.1.0.txt
• Authors: Daniel P. Struthers
• Other contributors: Lee F.G. Gutowsky, Tim C.D. Lucas, Neil J. Mochnacz; Christopher M. Carli, Mark K. Taylor
• Date created: 2024-01-23
• Date modified: 2024-01-23

Dataset Version and Release History

• Current Version:
  • Number: 1.0.0
  • Date: 2024-01-23
  • Persistent identifier: DOI: 10.5061/dryad.5bk4c
  • Summary of changes: n/a
• Embargo Provenance: n/a
  • Scope of embargo: n/a
  • Embargo period: n/a

Dataset Attribution and Usage

• Dataset Title: Data for the article "Statistical stream temperature modelling with SSN and INLA: an introduction for conservation practitioners"
• Persistent Identifier: https://doi.org/10.5061/dryad.5bk4c
• Dataset Contributors:
  • Creators: Daniel P. Struthers, Mark K. Taylor
• Date of Issue: 2024-01-23
• Publisher: Parks Canada, Banff National Park
• L...

Imputation of missing features in spatial transcriptomics is urgently demanded due to technology limitations, while most existing computational methods suffer from moderate accuracy and cannot estimate the reliability of the imputation.
To fill the research gaps, we introduce a computational model, TransImp, that imputes the missing feature modality in spatial transcriptomics by mapping it from single-cell reference. Uniquely, we derived a set of attributes that can accurately predict imputation uncertainty, hence enabling us to select reliably imputed genes. Also, we introduced a spatial auto-correlation metric as a regularization to avoid overestimating spatial patterns. Multiple datasets from various platforms have demonstrated that our approach significantly improves the reliability of downstream analyses in detecting spatial variable genes and interacting ligand-receptor pairs. Therefore, TransImp offers a way towards a reliable spatial analysis of missing features for both matched and unseen modalities, e.g., nascent RNAs.

***significant at 1% confidence level;**significant at 5% confidence level.Diagnostics Multiple linear regression: F-statistics: 16.6 (p = 0); Koenker’s studentized Breusch-Pagan Statistic: 3.38 (p = 0.49); Jarque-Bera statistics: 4.17 (p = 0.12); Multicollinearity condition number: 21.8; Spatial autocorrelation of residuals: Moran’s I: 0.01 (p = 0.74); Langrange multiplier (lag): 0.82 (p = 0.36); Langrange multiplier (error): 0.08 (p = 0.78).

Secondary compounds in nectar can function as toxic chemical defences against floral antagonists, but may also mediate plant-pollinator interactions. Despite their ecological importance, few studies have investigated patterns of spatial variation in toxic nectar compounds in plant species, and none outside their native range. Grayanotoxin I (GTX I) occurs in nectar of invasive Rhododendron ponticum where it is toxic to honeybees and some solitary bee species. We examined (i) geographic variation in the composition of nectar GTX I, as well as GTX III (which is not toxic to these species), in the native and introduced range of R. ponticum, (ii) how their expression is structured at patch and landscape scales within ranges, and (iii) if climatic and environmental factors underpin spatial patterns. While both GTXs varied within ranges, variation in GTX I, but not GTX III, was detected between ranges. GTX I expression was thus markedly lower or (in 18% of cases) absent from nectar in introduced plants. Spatial autocorrelation was apparent at both patch and landscape scales, and in part related to heat load interception by plants (a function of latitude, aspect and slope). As expression of nectar GTXs was generally robust to environmental variation, and aggregated in space, this trait has the potential to be spatially discriminated by consumers. Given the specificity of change to GTX I, and its differential toxicity to some bee species, we conclude that its expression was likely to have been influenced during invasion by interaction with herbivores/consumers, either via pollinator-mediated selection or enemy-release from floral antagonists. Synthesis. As the first demonstration of large-scale geographic variation and spatial structure in toxic nectar compounds, this work deepens our understanding of the chemical ecology of floral interactions in native and introduced species. Spatially explicit studies of nectar secondary compounds are thus required to show how the extent and structure of spatial variation may affect floral ecology. Future development of invasion theory should incorporate a holistic view of plant defence, beyond antagonistic interactions, which integrates the consequences of chemically defended mutualist rewards.

Global spatial autocorrelation test results of urban innovation and integrated transport efficiency under the economic space distance weight matrix in the Yangtze River Delta.

***significant at 1% confidence interval;**significant at 5% confidence interval;*significant at 10% confidence interval.

Incremental spatial autocorrelation Global Moran’s I’s analysis of childhood morbidity (1993–2014).

Spatial autocorrelation estimation of different years using Moran's I index and General G statistics in Qom City, Central Iran, 2009–2013.

Spatial autocorrelation (Moran’s I) of CMRFs.

Global spatial autocorrelation of TB distribution in Gurage Zone, Southern Ethiopia, 2007–2016.

Spatial variation in talent attraction in China from 2010 to 2018.