Summary Invasive species are one of the most severe threats to biodiversity, and an ability to predict the extent of potential invasions can help conservation strategies. Species distribution models (SDMs) have been widely used to project the potential range of invasive species. These models assume that species retain their niche properties during invasion (niche conservatism), although this assumption is seldom verified. We gathered occurrence records for the crayfish Procambarus clarkii from the U.S.A. and Mexico (native + invasive ranges) and from the Iberian Peninsula (invasive) to test for niche conservatism across continents using niche overlap metrics (Schoener's D). To test for differences in the climate space occupied by the species on the different continents, we performed two principal component analyses (PCAs) on the environmental data extracted from occurrence records: first, separately for each occurrence data set (i.e. each continent) and secondly, using the pooled data. Subsequently, we projected the model to South America, where this species has the potential to become invasive. Schoener's D showed high overlap (0.68) between the two regions (the Americas and Iberia), and there was no difference between the regions in both PCAs. The crayfish has conserved its niche across continents, and therefore, our model projection to South America may accurately demonstrate where invasion is most likely to occur. Large parts of South America are apparently suitable, mainly Argentina, Chile, Paraguay, Uruguay and southern Brazil. This result is of great concern since this invasive species can spread quickly in suitable areas. Stronger laws and regulations should be made to protect native biodiversity and agricultural land. Our approach could be replicated for the study of invasions by other species where extensive data on the potentially invaded areas are available.

Theoretical models have been developed to understand how animals decide to withdraw from a contest. They provide testable predictions regarding the relationship between resource holding potential (RHP) and contest duration that assume linear relationships among RHP traits. However, RHP traits might scale with body size according to power laws. Furthermore, investment across different RHP traits may vary. Herein, we provide a model that encompasses the allometric relationship between body size and other RHP traits. First, we partition RHP traits into "offensive" traits (i.e., the ability to inflict damage) and "defensive" traits (i.e., persistence in a contest). Defensive traits may in turn be subdivided into "damage endurance" (DE) or the ability to absorb damage and "stamina." We then model scenarios where: 1) there are power relationships among RHP traits; 2) individuals invest differently in defensive and offensive traits; 3) offensive traits and DE have a positive/negative relationship with body size. We modeled sized-matched injurious contests where 1) offensive capacity (OC) increases superlinearly with body size, 2) DE increases superlinearly, and 3) OC increases superlinearly but DE increases sublinearly. Our analyses indicate that if RHP traits scale linearly current predictions are upheld for injurious contests-contest duration increases with body size. However, with power relationships we can expect nonlinear relationships. Here, contest duration increased with body size until a maximum, decreasing afterwards. Thus, considering allometric relationships between body size and RHP traits may lead to new insights in animal contest theory and may help to solve discrepancies between current theory and empirical data.

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Since the 1970's, models based on evolutionary game theory, such as war of attrition (WOA), energetic war of attrition (E-WOA), cumulative assessment model (CAM) and sequential assessment model (SAM), have been widely applied to understand how animals settle contests. Despite the important theoretical advances provided by these models, empirical evidence indicates that rules adopted by animals to settle contests vary among species. This stimulated recent discussions about the generality and applicability of models of contest. A meta-analysis may be helpful to answer questions such as: (i) is there a common contest rule to settle contests; (ii) do contest characteristics, such as the occurrence of physical contact during the fight, influence the use of specific contest rules; and (iii) is there a phylogenetic signal behind contest rules? To answer these questions, we gathered information on the relationship between contest duration and traits linked to contestants' resource holding potential (RHP) for randomly paired rivals and RHP-matched rivals. We also gathered behavioural data about contest escalation and RHP asymmetry. In contests between randomly paired rivals, we found a positive relationship between contest duration and loser RHP but did not find any pattern for winners. We also found a low phylogenetic signal and a similar response for species that fight with and without physical contact. In RHP-matched rivals, we found a positive relationship between contest duration and the mean RHP of the pair. Finally, we found a negative relation between contest escalation and RHP asymmetry, even though it was more variable than the other results. Our results thus indicate that rivals settle contests following the rules predicted by WOA and E-WOA in most species. However, we also found inconsistencies between the behaviours exhibited during contests and the assumptions of WOA models in most species. We discuss additional (and relatively untested) theoretical possibilities that may be explored to resolve the existing inconsistencies.