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Abstract Elucidating biodiversity patterns and their background processes is critical in biodiversity science. Dissimilarity, which is calculated based on multivariate biological quantities, is a major component of biodiversity. As spatial and temporal biodiversity information availability increases, the scope of dissimilarity studies has been expanded to cover various levels and types of spatiotemporal biodiversity facets (e.g. gene, community and ecosystem function), and diverse pairwise dissimilarity indices have been developed. However, further development of the dissimilarity concept is required in comparative studies on spatiotemporal structures of biodiversity compositional patterns, such as those exploring commonalities of biogeographical boundaries among taxa, compared to the conventional ones to consider higher dimensions of dissimilarity: dissimilarity of dissimilarity structures. This study proposes a novel and general concept, higher‐order dissimilarity (HOD), for quantitatively evaluating the dissimilarities of spatial or temporal dissimilarity structures among different datasets, proposes specific implementations of HOD as operational indices, and illustrates the potential resolution of scientific and practical questions through HOD. We further demonstrate the advantages of the HOD concept by applying it to actual patterns, such as long‐term and/or large‐spatial hypothetical monitoring datasets. Our conceptual framework on HOD extends the existing framework of biodiversity science and is versatile, with many potential applications in acquiring more valuable information from ever‐increasing biodiversity data.

Abstract Conservation biologists have a daunting task of understanding the causes of species decline associated with anthropogenic factors and predicting the extinction risk of a growing number of endangered species. By reducing variances of estimates with information on closely related species, phylogenetic information among species can bridge gaps in information on species with small range sizes when modelling large numbers of endangered species. However, modelling many species with the Gaussian process (GP), which underlies the evolutionary process of phylogenetic random effects, remains a challenge owing to the computational burden in estimating the large variance–covariance matrix. Here, we applied a phylogenetic generalised mixed model with random slopes and random intercepts to 1010 endangered vascular plant taxa in Japan following phylogenetic GPs implemented by nearest neighbour GP (NNGP) approximation. NNGP enables flexibility in changing the proximity on the phylogenetic tree of species from which information is borrowed to reduce the variances of estimates with a realistic computational burden. We evaluated the effectiveness of phylogenetic models by comparing the predictive performance and descriptive power of phylogenetic and non‐phylogenetic models and identified the anthropogenic factors contributing to the decline of each of the studied endangered species. We found that the model with phylogenetic information had better prediction performance than the model without phylogenetic information. The results showed that across all explanatory variables, the phylogenetic model could detect interspecific differences in response to environmental factors in a number of species more clearly. Combined with the phylogenetic signal results, we could also detect a phylogenetic bias in the species that could benefit from the positive effects of protected areas but reduce the local extinctions of 95% of all studied taxa. In conclusion, our model, considering phylogenetic information with NNGP, allows the elucidation of factors causing the decline of many endangered species. In future analyses, the estimation of extinction probability linked to environmental change might be applied to future climate–land use scenarios, advancing the comprehensive assessment of biodiversity degradation and threats to species at multiple scales.

Whereas undetected species contribute to estimation of species diversity, undetected alleles have not been used to estimated genetic diversity. Although random sampling guarantees unbiased estimation of allele frequency and genetic diversity measures, using undetected alleles may provide biased but more precise estimators useful for conservation. We newly devised kernel density estimation (KDE) for allele frequency including undetected alleles and tested it in estimation of allele frequency and nucleotide diversity using population generated by coalescent simulation as well as well as real population data. Contrary to expectations, nucleotide diversity estimated by KDE had worse bias and accuracy. Allele frequency estimated by KDE was also worse except when the sample size was small. These might be due to finity of population and/or the curse of dimensionality. In conclusion, KDE of allele frequency does not contribute to genetic diversity estimation.