Many species are projected to become vulnerable to twenty-first-century climate changes, with consequent effects on the tree of life. If losses were not randomly distributed across the tree of life, climate change could lead to a disproportionate loss of evolutionary history. Here we estimate the consequences of climate change on the phylogenetic diversities of plant, bird and mammal assemblages across Europe. Using a consensus across ensembles of forecasts for 2020, 2050 and 2080 and high-resolution phylogenetic trees, we show that species vulnerability to climate change clusters weakly across phylogenies. Such phylogenetic signal in species vulnerabilities does not lead to higher loss of evolutionary history than expected with a model of random extinctions. This is because vulnerable species have neither fewer nor closer relatives than the remaining clades. Reductions in phylogenetic diversity will be greater in southern Europe, and gains are expected in regions of high latitude or altitude. However, losses will not be offset by gains and the tree of life faces a trend towards homogenization across the continent.

Aim  The study of biological invasions has long considered species invasiveness and community invasibility as separate questions. Only recently, there is an increasing recognition that integrating these two questions offers new insights into the mechanisms of biological invasions. This recognition has renewed the interest in two long‐standing and seemingly contradictory hypotheses proposed by Darwin: phylogenetic relatedness of invaders to native communities is predicted to promote naturalization because of appropriate niche‐adaptation but is at the same time predicted to hamper naturalization because of niche overlap with native species. The latter is known as Darwin’s naturalization hypothesis. Location  Global. Methods and Results  We review the studies that have tested these hypotheses and summarize their largely inconsistent outcomes. We argue that most of the inconsistency arises from discrepancies in the applied conceptual frameworks and analytical approaches and not from different model organisms and different ecological contexts. First, observed patterns and results can be seriously flawed by different spatial and phylogenetic scales, which do not equally reveal community assembly mechanisms. Second, different studies have used different metrics, which may test for different specific hypotheses. Thus, we propose a set of metrics derived from the alpha niche concept to measure invaders relatedness to native communities. Finally, approximating species niche differentiation from phylogenetic relatedness is not exempt of assumptions, and invasive species naturalization may result from various ecological mechanisms of biotic resistance that are not necessarily revealed by species phylogeny alone. Main conclusions  The quest for resolving the conundrum of Darwin’s naturalization hypothesis will only be successful if appropriate scales, metrics and analytical tests are thoroughly considered. We give several recommendations and suggest, whenever possible, to use trait‐based measurements of species dissimilarity as the most promising avenue to unravel the mechanisms driving alien species invasions.