Modeling species distributions over space and time is one of the major research topics in both ecology and conservation biology. Joint Species Distribution models (JSDMs) have recently been introduced as a tool to better model community data, by inferring a residual covariance matrix between species, after accounting for species' response to the environment. However, these models are computationally demanding, even when latent factors, a common tool for dimension reduction, are used. To address this issue, Taylor-Rodriguez et al. (2017) proposed to use a Dirichlet process, a Bayesian nonparametric prior, to further reduce model dimension by clustering species in the residual covariance matrix. Here, we built on this approach to include a prior knowledge on the potential number of clusters, and instead used a Pitman–Yor process to address some critical limitations of the Dirichlet process. We therefore propose a framework that includes prior knowledge in the residual covariance matrix, providing a tool to analyze clusters of species that share the same residual associations with respect to other species. We applied our methodology to a case study of plant communities in a protected area of the French Alps (the Bauges Regional Park), and demonstrated that our extensions improve dimension reduction and reveal additional information from the residual covariance matrix, notably showing how the estimated clusters are compatible with plant traits, endorsing their importance in shaping communities.

1. In the current biodiversity crisis, one of the crucial questions is how quickly plant communities can acclimate to climate warming and longer growing seasons to buffer the impairment of community functioning. Answering this question is pivotal especially for mountain grasslands that experience harsh conditions but provide essential ecosystem services to people. We conducted a reciprocal transplant experiment along an elevation gradient(1,920 m vs. 2,450 m) in the French Alps to test the ability of plant species and communities to acclimate to warming and cooling. For 3 years, we measured weekly the timing of phenological events (e.g. start of flowering or greening) and the length of phenological stages linked to demographic performance (e.g. lengths of flowering or greening periods).3. We found that warming (and cooling) changed the timing of phenological events strongly enough to result in complete acclimation for graminoids, for communities in early and mid-season, but not at all for forbs. For example, warming resulted in later greening of communities and delayed all phenophases of graminoids. Lengths of phenological stages did not respond strongly enough to climate change to acclimate completely, except for graminoids. For example, warming led to an acclimation lag in the community's yearly productivity and had a strong negative impact on flowering of forbs. Overall, when there was an acclimation failure, responses to cooling were mostly symmetric and confirmed slow acclimation in mountain grasslands. Synthesis.Our study highlights that phenological plasticity cannot prevent disruption of community functioning under climate warming in the short term. The failures to acclimate after 3 years of warming signals that species and communities underperform and are probably at high risk of being replaced by locally betteradapted plants.