Crustacean Symbiosis with Caribbean Sea Anemones Bartholomea Annulata: Occupancy Modeling, Habitat Partitioning, and Persistence
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The following supplement accompanies the article Crustacean symbiosis with Caribbean sea anemones Bartholomea annulata: occupancy modeling, habitat partitioning, and persistence Lindsay K. Huebner*, Colin P. Shea, Paul M. Schueller, Ashley D. Terrell, Stephen G. Ratchford, Nanette E. Chadwick *Corresponding author: [email protected] Marine Ecology Progress Series 631: 99–116 (2019) Text S1. Probabilistic equations for the modeling framework The model framework for Hypothesis 3 (hosts persist longer in the presence of anemoneshrimps that are known to provide mutualistic benefits) included nine possible state transitions of anemones (Bartholomea annulata [BA]) and associated shrimps (either Alpheus armatus [AA] or Ancylomenes pedersoni [AP]) at tag locations between census periods: 1) P[zt+1 = 1|zt = 1] = (1-γAA/AP)*(1-εBA) 2) P[zt+1 = 2|zt = 1] = γAA/AP*(1-εBA) 3) P[zt+1 = 3|zt = 1] = εBA 4) P[zt+1 = 1|zt = 2] = εAA/AP*(1-εBA) 5) P[zt+1 = 2|zt = 2] = (1-εAA/AP)*(1-εBA) 6) P[zt+1 = 3|zt = 2] = εBA 7) P[zt+1 = 1|zt = 3] = (1-γAA/AP)*γBA 8) P[zt+1 = 2|zt = 3] = γAA/AP*γBA 9) P[zt+1 = 3|zt = 3] = (1-γBA) An additional set of nine possible state transitions of anemones BA and associated shrimps AA or AP at tag locations between census periods included a new parameter which represents anemone extinction probability in the presence of AA or AP: 10) P[zt+1 = 1|zt = 1] = (1-γAA/AP)*(1-εBA) 11) P[zt+1 = 2|zt = 1] = γAA/AP*(1-εBA) 12) P[zt+1 = 3|zt = 1] = εBA 13) P[zt+1 = 1|zt = 2] = εAA/AP*(1-εBA_AA/AP) 14) P[zt+1 = 2|zt = 2] = (1-εAA/AP)*(1-εBA_AA/AP) 15) P[zt+1 = 3|zt = 2] = εBA_AA/AP 16) P[zt+1 = 1|zt = 3] = (1-γAA/AP)*γBA 17) P[zt+1 = 2|zt = 3] = γAA/AP*γBA 18) P[zt+1 = 3|zt = 3] = (1-γBA) The model framework for Hypothesis 4 (cleaner shrimps reduce each other’s persistence but enhance the persistence of hosts) included twenty-five possible state transitions of anemones BA and associated cleaner shrimps AP and Periclimenes yucatanicus (PY) at tag locations between census periods: 1 19) P[zt+1 = 1|zt = 1] = (1-εAP)*(1-γPY)*(1-εBA) 20) P[zt+1 = 2|zt = 1] = εAP*γPY*(1-εBA) 21) P[zt+1 = 3|zt = 1] = (1-εAP)*γPY*(1-εBA) 22) P[zt+1 = 4|zt = 1] = εAP*(1-γPY)*(1-εBA) 23) P[zt+1 = 5|zt = 1] = εBA 24) P[zt+1 = 1|zt = 2] = γAP*εPY*(1-εBA) 25) P[zt+1 = 2|zt = 2] = (1-γAP)*(1-εPY)*(1-εBA) 26) P[zt+1 = 3|zt = 2] = γAP*(1-εPY)*(1-εBA) 27) P[zt+1 = 4|zt = 2] = (1-γAP)*εPY*(1-εBA) 28) P[zt+1 = 5|zt = 2] = εBA 29) P[zt+1 = 1|zt = 3] = (1-εAP)*εPY*(1-εBA) 30) P[zt+1 = 2|zt = 3] = εAP*(1-εPY)*(1-εBA) 31) P[zt+1 = 3|zt = 3] = (1-εAP)*(1-εPY)*(1-εBA) 32) P[zt+1 = 4|zt = 3] = εAP*εPY*(1-εBA) 33) P[zt+1 = 5|zt = 3] = εBA 34) P[zt+1 = 1|zt = 4] = γAP*(1-γPY)*(1-εBA) 35) P[zt+1 = 3|zt = 4] = (1-γAP)*γPY*(1-εBA) 36) P[zt+1 = 3|zt = 4] = γAP*γPY*(1-εBA) 37) P[zt+1 = 4|zt = 4] = (1-γAP)*(1-γPY)*(1-εBA) 38) P[zt+1 = 5|zt = 4] = εBA 39) P[zt+1 = 1|zt = 5] = γAP*(1-γPY)*γBA 40) P[zt+1 = 2|zt = 5] = (1-γAP)*γPY*γBA 41) P[zt+1 = 3|zt = 5] = γAP*γPY*γBA 42) P[zt+1 = 4|zt = 5] = (1-γAP)*(1-γPY)*γBA 43) P[zt+1 = 5|zt = 5] = 1-γBA Table S1. Parameter estimates, standard errors (SE), and lower and upper 95% confidence intervals from the set of models relating the aggregation pattern of sea anemones Bartholomea annulata (aggregated versus isolated anemones) to two metrics of their associated crustaceans, species richness (Poisson regression model) and abundance (negative binomial model), at the Brewers Bay reef site on St. Thomas, US Virgin Islands. Aggregations served as the baseline (intercept) and random intercepts corresponded to census. The overdispersion parameter theta is reported. Crustacean Metric Parameter Estimate SE Lower Upper Species richness Fixed effects Intercept 0.600 0.101 0.403 0.798 Isolated anemones -0.552 0.083 -0.715 -0.390 Random effect (census) Intercept 0.199 Abundance Fixed effects Intercept 2.294 0.188 1.925 2.662 Isolated anemones -0.935 0.181 -1.290 -0.580 Theta 0.382 0.058 Random effect (census) Intercept 0.234 2 Table S2. Variation in patterns of association with sea anemones Bartholomea annulata by six species of crustaceans (Alpheus armatus, Heteromysis actiniae, Periclimenes yucatanicus, Ancylomenes pedersoni, Thor amboinensis, and Stenorhynchus seticornis) across 9 census periods and between an inshore (Brewers Bay [BB]) and offshore (Flat Cay [FC]) coral reef site on St. Thomas, US Virgin Islands. Shown are the number (No.) and percent (% Occ.) of anemone tag locations (individual anemones or aggregations of 2-4 individuals) that were occupied by crustaceans, and the mean (Size) and standard error (SE) of the group size (number of individual crustaceans per occupied anemone tag location) for each crustacean species. A. armatus H. actiniae P. yucatanicus Census Site No. % Occ. Size SE No. % Occ. Size SE No. % Occ. Size SE Sept BB 40 42.6 1.1 0.1 29 30.9 17.6 2.8 2 2.1 1.0 0.0 2006 FC 24 34.3 1.2 0.1 16 22.9 6.9 1.3 18 25.7 1.3 0.1 Dec BB 9 15.5 1.0 0.0 20 34.5 8.1 1.3 3 5.2 1.7 0.7 2006 FC 13 36.1 1.1 0.1 7 19.4 3.7 0.7 3 8.3 1.0 0.0 March BB 20 23.0 1.2 0.1 26 29.9 22.0 3.3 9 10.3 1.0 0.0 2007 FC 13 40.6 1.3 0.1 3 9.4 3.7 1.3 8 25.0 1.1 0.1 June BB 19 17.3 1.0 0.0 28 25.5 10.0 1.8 7 6.4 1.1 0.1 2007 FC 44 54.3 1.3 0.1 14 17.3 6.9 1.4 28 34.6 1.2 0.1 Sept BB 29 25.0 1.0 0.0 31 26.7 10.8 2.2 7 6.0 1.3 0.3 2007 FC 22 31.9 1.0 0.0 11 15.9 8.7 1.9 22 31.9 1.4 0.2 Dec BB 31 26.1 1.1 0.0 31 26.1 7.7 1.1 8 6.7 1.1 0.1 2007 FC 27 39.1 1.3 0.1 9 13.0 3.1 0.5 27 39.1 1.1 0.1 March BB 44 38.9 1.1 0.1 34 30.1 7.8 1.0 8 7.1 1.0 0.0 2008 FC 31 44.3 1.1 0.1 15 21.4 4.5 1.0 26 37.1 1.3 0.2 Sept BB 43 32.3 1.1 0.0 40 30.1 9.7 1.2 4 3.0 1.5 0.5 2008 FC 30 61.2 1.3 0.1 2 4.1 7.5 2.5 23 46.9 1.4 0.2 March BB 37 39.8 1.1 0.1 41 44.1 11.4 2.2 8 8.6 1.3 0.2 2009 FC 12 21.1 1.2 0.1 5 8.8 10.6 5.0 6 10.5 1.3 0.3 A. pedersoni T. amboinensis S. seticornis Census Site No. % Occ. Size SE No. % Occ. Size SE No. % Occ. Size SE Sept BB 36 38.3 2.0 0.2 1 1.1 1.0 NA 27 28.7 1.2 0.1 2006 FC 36 51.4 2.6 0.4 2 2.9 1.0 0.0 10 14.3 1.3 0.2 Dec BB 11 19.0 1.2 0.1 0 0.0 10 17.2 1.0 0.0 2006 FC 20 55.6 2.2 0.4 0 0.0 3 8.3 1.0 0.0 March BB 18 20.7 1.7 0.3 1 1.1 1.0 NA 13 14.9 1.2 0.2 2007 FC 17 53.1 1.5 0.2 0 0.0 2 6.3 1.0 0.0 June BB 21 19.1 1.6 0.2 0 0.0 15 13.6 1.7 0.6 2007 FC 29 35.8 1.8 0.2 2 2.5 1.0 0.0 1 1.2 1.0 Sept BB 30 25.9 1.9 0.2 1 0.9 1.0 NA 19 16.4 1.4 0.2 2007 FC 33 47.8 2.7 0.4 2 2.9 1.5 0.5 3 4.3 1.0 0.0 Dec BB 21 17.6 1.5 0.1 0 0.0 33 27.7 1.2 0.1 2007 FC 27 39.1 2.3 0.3 0 0.0 5 7.2 1.0 0.0 March BB 27 23.9 1.5 0.1 0 0.0 30 26.5 1.3 0.1 2008 FC 18 25.7 2.4 0.4 0 0.0 2 2.9 1.0 0.0 Sept BB 28 21.1 1.7 0.2 0 0.0 41 30.8 1.2 0.1 2008 FC 13 26.5 2.8 0.5 0 0.0 7 14.3 1.0 0.0 March BB 30 32.3 1.9 0.2 1 1.1 2.0 NA 40 43.0 1.3 0.1 2009 FC 14 24.6 3.2 0.6 0 0.0 4 7.0 1.0 0.0 3 Table S3.