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850 JULIAN D. OLDEN ET AL. Ecology, Vol. 89, No. 3 altered physical habitat conditions, predation by non- native fishes, competition with nonnative fishes, or other biological interactions, e.g., hybridization or disease). From the questionnaire results we used a majority rule to place each species into one of five categories that combined perceived level of extinction risk and primary source of threat over their lifetime (Appendix B): (1) none/low risk; (2) moderate risk-environmental degra- dation (first three sources listed above); (3) moderate risk-species invasions (last three sources listed above), (4) high risk-environmental degradation, and (5) high risk-species invasions. We assessed inter-respondent reliability by comparing the actual assignment to random assignments of the species to the five extinction level-source categories according to Fleiss' kappa (1971). Fleiss' kappa is interpreted as the extent to which the observed amount of agreement among raters exceeds what would be expected if all raters made their ratings completely randomly (complete agreement then x = 1, no agreement then x < 0). For the 22 fish species, we found that x = 0.41 (representing a mean concordance among participants of 66.8%); a value significantly greater than chance (P = 0.038). This indicates good inter-respondent consistency for assigning species to one of the five extinction level-source categories. Statistical analyses We used classification and regression trees (CART; Breiman et al. 1984) to model species' rarity (expressed as total kilometers of stream reaches occupied), fre- quency of local extirpation (probability between 0 and 1), and perceived level and source of extinction risk (five nominal categories) as functions of the 10 biological traits and two indices of phylogenetic relatedness. CART is particularly powerful for ecological analyses because it allows the modeling of nonlinear, nonadditive relationships among mixed variable types, it is invariant to monotonic transformations of the data that are often required prior to using traditional methods, and it facilitates the examination of intercorrelated variables in the final model (De'ath and Fabricius 2000). Thus, the CART methodology is well suited for analyzing trait synergisms among inherently correlated biological traits that are both continuous and categorical. The CART methodology uses a recursive partitioning algorithm to repeatedly partition the data set according to the explanatory variables (i.e., biological traits) into a nested series of mutually exclusive groups, each as homogeneous as possible with respect to the response variable (i.e., rarity, extirpation, extinction). The branching topology of the resulting decision tree reveal nonadditive (or synergistic) trait effects, and the primary splits represent the most important predictor traits as well as indicating the best competitive traits (called surrogate splits) that show similar classification power. Therefore, the CART methodology has the favorable characteristic of allowing the simultaneous examination of biological traits (e.g., age and length at maturity) that may have similar predictive roles in the final model. We used the Gini impurity criterion to determine the optimal variable splits (minimum parent node size: n = 5; minimal terminal node size: n = 2), and we determined the optimal size of the decision tree by constructing a series of cross-validated trees and selecting the smallest tree based on the one-standard-error rule (De'ath and Fabricius 2000). Cohen's x coefficient of agreement (classification tree) and Pearson's moment correlation coefficient (regression tree) were used to assess the predictive performance of the decision trees compared to random expectations (Fielding and Bell 1997). Analyses were conducted using CART 5.0 (Salford Systems, San Diego, California, USA). RESULTS Rarity Species rarity varied as a function of ecological and life-history traits (R = 0.72, P = 0.0002, Fig. 1). The branching sequence of the regression tree indicates that trophic specialization and reproductive strategy were the most important trait predictors of species' present-day range size (inversely related to rarity). Species with an herbivore/detritivore feeding behavior--considered a generalist trophic guild that consumes living and dead plant matter in benthic habitats-were three times more widespread compared to the other species (Fig. 1, node A). Of the species in the remaining trophic guilds (n = 18), two groups had high rarity: those providing a low degree of parental care (surrogate split: non-guarders spawning on open substrates, i.e., low energetic contri- butions to reproduction with respect to guarding and nest building; node B), and those having high parental care coupled with low diet breadth (node Q. In contrast, species characterized by relatively high parental care and high diet breadth occupied considerably larger ranges (node D). Because the regression tree was optimized to separate species into relatively homogenous groups with respect to their level of rarity, it is useful to examine species that contribute the greatest to terminal node impurity (i.e., model error). By comparing predicted to actual species range sizes (Appendix C), we found that the range sizes of Catostomus clarkii (desert sucker, node A) and Gila robusta (roundtail chub, node B) were underestimated by the model (i.e., according to the model these species should exhibit greater rarity), whereas the range sizes of C. latipinnis (flannelmouth sucker, node A), Oncorhyn- chus gilae apache (Gila trout, node C) and Poeciliopsis occidentalis (Gila topminnow, node D) were overesti- mated by the model (i.e., according to the model these species should exhibit lower rarity). Frequency of extirpation Species frequency of local extirpation was highly predictable as a function of multiple, interacting biological traits (R = 0.87, P < 0.0001, Fig. 2). Fish species with the highest frequency of local extirpation