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Abstract Reordering of abundances among species is a common response in communities whether affected by anthropogenic drivers or natural disturbance. However, understanding how competitive relationships drive community dynamics under global environmental change remains limited, primarily due to uncertainties related to changes in species interactions and the scarcity of long‐term observations. By combining long‐term data and time series analysis tools, we quantified the compositional dynamics and causal interactions among functional groups of an arid grassland community under chronic nutrient enrichment for 15 years following wildfire. We hypothesized that chronic nutrient addition would promote species reordering among dominant grasses and subordinate annual forbs after wildfire, thereby increasing biomass and compositional variation over the long term. Contrary to expectations, while the abundance of the dominant grassBouteloua eriopoda(black grama) declined immediately after the wildfire, the increase in annual forbs under N addition did not occur until a decade later. Convergent cross‐mapping revealed that annuals were causally influenced by black grama abundance and maintained relatively lower abundance in control plots. However, with N addition, this causal interaction from black grama to annuals disappeared. Accordingly, temporal variability of biomass and community composition increased as the abundance of annuals rose. Combined with evidence of precipitation response, these results imply that the competitive advantage of perennial plants over annual forbs could serve as a stabilizing mechanism for community variability by limiting the response of annuals to precipitation fluctuations. However, this stabilizing process is disrupted by the cumulative effects of chronic nitrogen addition. This long‐term experiment provides new insights into the destabilizing effects of community reordering, without changes in species richness, in response to anthropogenic nutrient loading. 

Abstract Wilk’s theorem, which offers universal chi-squared approximations for likelihood ratio tests, is widely used in many scientific hypothesis testing problems. For modern datasets with increasing dimension, researchers have found that the conventional Wilk’s phenomenon of the likelihood ratio test statistic often fails. Although new approximations have been proposed in high dimensional settings, there still lacks a clear statistical guideline regarding how to choose between the conventional and newly proposed approximations, especially for moderate-dimensional data. To address this issue, we develop the necessary and sufficient phase transition conditions for Wilk’s phenomenon under popular tests on multivariate mean and covariance structures. Moreover, we provide an in-depth analysis of the accuracy of chi-squared approximations by deriving their asymptotic biases. These results may provide helpful insights into the use of chi-squared approximations in scientific practices.