The following supplement accompanies the article

Crustacean symbiosis with Caribbean sea anemones 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 [AA] or [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, 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. Parameter estimates, standard errors (SE), and lower and upper 95% confidence intervals from the negative binomial regression model used to assess differences in group size between Periclimenes yucatanicus (PY) and Ancylomenes pedersoni (AP) associated with sea anemones Bartholomea annulata at the Flat Cay reef site on St. Thomas, US Virgin Islands. AP served as the baseline (intercept) and random intercept corresponds to census. The overdispersion parameter theta is reported.

Parameter Estimate SE Lower Upper Fixed effects Intercept -0.036 0.074 -0.182 0.110 PY -0.874 0.115 -1.099 -0.648 Theta 0.620 0.114 Random effect (census) Intercept 0.045

Table S4. Parameter estimates, standard errors (SE), and lower and upper 95% confidence intervals from the best-approximating Poisson regression models that relate census period and the body size (tentacle crown surface area, TCSA in cm2) of sea anemones Bartholomea annulata to the number of associated anemoneshrimp Alpheus armatus at two coral reef sites on St. Thomas, US Virgin Islands. September 2006 served as the baseline (intercept).

Site Parameter Estimate SE Lower Upper Brewers Bay Fixed effects Intercept -0.929 0.158 -1.239 -0.619 TCSA 0.003 0.001 0.001 0.004 Dec 2006 -1.078 0.365 -1.794 -0.361 March 2007 -0.482 0.254 -0.979 0.015 June 2007 -0.956 0.274 -1.493 -0.418 Sept 2007 -0.680 0.239 -1.147 -0.212 Dec 2007 -0.487 0.230 -0.938 -0.037 March 2008 -0.061 0.206 -0.464 0.342 Sept 2008 -0.332 0.210 -0.743 0.079 March 2009 -0.089 0.216 -0.513 0.334 Flat Cay Fixed effects Intercept -1.295 0.205 -1.697 -0.984 TCSA 0.012 0.002 0.008 0.016 Dec 2006 -0.219 0.331 -0.867 0.429 March 2007 0.336 0.306 -0.264 0.937 June 2007 0.638 0.232 0.183 1.093 Sept 2007 0.242 0.279 -0.789 0.305 Dec 2007 0.399 0.252 -0.096 0.983 March 2008 0.299 0.255 -0.201 0.799 Sept 2008 0.751 0.248 0.265 1.238 March 2009 -0.019 0.326 -0.657 0.619

4 Table S5. Parameter estimates, standard errors (SE), and lower and upper 95% confidence intervals from the best-approximating negative binomial regression models that relate the body size (tentacle crown surface area, TCSA in cm2) of sea anemones Bartholomea annulata to the number of associated mysids Heteromysis actiniae at two coral reef sites on St. Thomas, US Virgin Islands. The overdispersion parameter theta is reported.

Site Parameter Estimate SE Lower Upper Brewers Bay Fixed effects Intercept 0.660 0.149 0.368 0.952 TCSA 0.009 0.002 0.005 0.013 Theta 0.117 0.009 Flat Cay Fixed effects Intercept -1.150 0.285 -1.708 -0.591 TCSA 0.034 0.009 0.017 0.052 Theta 0.077 0.011

Table S6. Parameter estimates, standard errors (SE), and lower and upper 95% confidence intervals from the best-approximating negative binomial regression models that relate census period and the body size (tentacle crown surface area, TCSA in cm2) of sea anemones Bartholomea annulata to the number of associated anemoneshrimp Periclimenes yucatanicus at two coral reef sites on St. Thomas, US Virgin Islands. Random intercept corresponds to anemone tag locations. September 2006 served as the baseline (intercept) for Flat Cay. The overdispersion parameter theta is reported.

Site Parameter Estimate SE Lower Upper Brewers Bay Fixed effects Intercept -3.818 0.396 -4.594 -3.043 TCSA 0.005 0.002 0.002 0.008 Theta 4.556 10.509 Random effect (tag location) Intercept 1.879 Flat Cay Fixed effects Intercept -1.475 0.256 -1.977 -0.974 TCSA 0.006 0.003 0.000 0.012 Dec 2006 -1.442 0.625 -2.667 -0.217 March 2007 -0.178 0.413 -0.987 0.632 June 2007 0.295 0.290 -0.274 0.863 Sept 2007 0.233 0.293 -0.341 0.806 Dec 2007 0.358 0.297 -0.225 0.941 March 2008 0.391 0.293 -0.183 0.964 Sept 2008 0.714 0.294 0.138 1.290 March 2009 -0.418 0.427 -1.255 0.419 Theta 403.430 1.464 Random effect (tag location) Intercept 0.386

5 Table S7. Parameter estimates, standard errors (SE), and lower and upper 95% confidence intervals from the best-approximating negative binomial regression models that relate census period and the body size (tentacle crown surface area, TCSA in cm2) of sea anemones Bartholomea annulata to the number of associated anemoneshrimp Ancylomenes pedersoni at two coral reef sites on St. Thomas, US Virgin Islands. September 2006 served as the baseline (intercept) for Brewers Bay. The overdispersion parameter theta is reported.

Site Parameter Estimate SE Lower Upper Brewers Bay Fixed effects Intercept -0.847 0.219 -1.277 -0.418 TCSA 0.005 0.001 0.003 0.007 Dec 2006 -1.198 0.391 -1.965 -0.431 March 2007 -0.752 0.308 -1.356 -0.148 June 2007 -0.966 0.298 -1.552 -0.381 Sept 2007 -0.622 0.274 -1.160 -0.085 Dec 2007 -1.062 0.299 -1.648 -0.477 March 2008 -0.775 0.288 -1.339 -0.212 Sept 2008 -0.841 0.277 -1.385 -0.298 March 2009 -0.257 0.280 -0.806 0.293 Theta 0.871 0.251 Random effect (tag location) Intercept 0.502 Flat Cay Fixed effects Intercept -1.257 0.133 -1.517 -0.997 TCSA 0.019 0.003 0.014 0.024 Theta 9.542 8.955 Random effect (tag location) Intercept 1.073

6 Table S8. Parameter estimates, standard deviations (SD), and lower and upper 95% credible intervals for the best-approximating 3-state dynamic occupancy models for anemoneshrimp Alpheus armatus (AA) associated with sea anemones Bartholomea annulata (BA) at two coral reef sites on St. Thomas, US Virgin Islands.

Site Parameter Mean SD Lower Upper Brewers Bay Extinction (ε)

Fixed effects Intercept (BA) -0.124 0.270 -0.653 0.406 TCSA (BA) -0.004 0.001 -0.007 -0.002 Intercept (AA) 0.111 0.293 -0.482 0.707 Random effects (census) Intercept (BA) 0.657 0.271 0.322 1.341 Intercept (AA) 0.515 0.385 0.032 1.462 Colonization (γ) Fixed effects Intercept (BA) -1.108 0.278 -1.639 -0.550 Intercept (AA) -1.153 0.222 -1.586 -0.708 Random effects (census) Intercept (BA) 0.670 0.276 0.317 1.367 Intercept (AA) 0.504 0.236 0.167 1.091 Flat Cay Extinction (ε) Fixed effects Intercept (BA) 0.896 0.403 0.078 1.703 TCSA (BA) -0.024 0.006 -0.036 -0.014 Intercept (AA) -0.828 0.609 -2.126 0.403 Random effects (census) Intercept (BA) 1.007 0.432 0.441 2.103 Intercept (AA) 1.487 1.012 0.180 4.096 Colonization (γ) Fixed effects Intercept (BA) -1.596 0.333 -2.251 -0.901 Intercept (AA) -0.488 0.206 -0.900 -0.069 Random effects (census) Intercept (BA) 0.930 0.376 0.456 1.870 Intercept (AA) 0.392 0.252 0.027 0.987

7 Table S9. Parameter estimates, standard deviations (SD), and lower and upper 95% credible intervals for the best-approximating 3-state dynamic occupancy models for anemone shrimp Ancylomenes pedersoni (AP) associated with sea anemones Bartholomea annulata (BA) at two coral reef sites on St. Thomas, US Virgin Islands. The second best-approximating model for Brewers Bay is also included.

Site and Model Parameter Mean SD Lower Upper Brewers Bay Extinction (ε)

Best-approximating Fixed effects model Intercept (BA) -0.127 0.261 -0.665 0.393 TCSA (BA) -0.004 0.001 -0.007 -0.002 Intercept (AP) -0.080 0.338 -0.791 0.547 Random effects (census) Intercept (BA) 0.653 0.265 0.318 1.309 Intercept (AP) 0.624 0.430 0.051 1.656 Colonization (γ) Fixed effects Intercept (BA) -1.117 0.248 -1.624 -0.605 Intercept (AP) -1.590 0.131 -1.851 -1.334 Random effects (census) Intercept (BA) 0.660 0.258 0.320 1.317 Intercept (AP) 0.171 0.142 0.006 0.530 Brewers Bay Extinction (ε)

Second best- Fixed effects approximating Intercept (BA alone) -0.177 0.302 -0.788 0.440 model TCSA (BA alone) -0.003 0.002 -0.007 0.000 Intercept (BA with AP) -0.015 0.370 -0.731 0.730 TCSA (BA with AP) -0.007 0.003 -0.014 -0.002 Intercept (AP) -0.078 0.336 -0.811 0.556 Random effects (census) Intercept (BA alone) 0.762 0.295 0.376 1.513 Intercept (BA with AP) 0.677 0.411 0.071 1.660 Intercept (AP) 0.601 0.430 0.040 1.623 Colonization (γ) Fixed effects Intercept (BA) -1.101 0.267 -1.609 -0.546 Intercept (AP) -1.593 0.133 -1.861 -1.334 Random effects (census) Intercept (BA) 0.670 0.276 0.321 1.342 Intercept (AP) 0.175 0.142 0.008 0.531 Flat Cay Extinction (ε)

Best-approximating Fixed effects model Intercept (BA) 0.899 0.411 0.031 1.694 TCSA (BA) -0.024 0.006 -0.035 -0.014 Intercept (AP) -0.740 0.325 -1.383 -0.091 Random effects (census)

8 Intercept (BA) 1.014 0.433 0.452 2.106 Intercept (AP) 0.471 0.404 0.021 1.437 Colonization (γ) Fixed effects Intercept (BA) -1.571 0.398 -2.305 -0.687 Intercept (AP) -0.631 0.484 -1.560 0.451 Random effects (census) Intercept (BA) 0.949 0.402 0.455 1.978 Intercept (AP) 1.268 0.556 0.560 2.673

Table S10. Parameter estimates, standard deviations (SD), and lower and upper 95% credible intervals for the three best-approximating 5-state dynamic occupancy models for anemoneshrimps Periclimenes yucatanicus (PY) and Ancylomenes pedersoni (AP) associated with sea anemones Bartholomea annulata (BA) at the Flat Cay coral reef site on St. Thomas, US Virgin Islands.

Model Parameter Mean SD Lower Upper Best- Extinction (ε) approximating Fixed effects model Intercept (BA) 0.916 0.407 0.092 1.735 TCSA (BA) -0.024 0.006 -0.035 -0.013 Intercept (AP) -0.737 0.325 -1.378 -0.088 Intercept (PY) 0.059 0.459 -0.825 1.029 Random effects (census) Intercept (BA) 1.017 0.434 0.454 2.128 Intercept (AP) 0.460 0.376 0.022 1.440 Intercept (PY) 0.881 0.759 0.033 2.886 Colonization (γ) Fixed effects Intercept (BA) -1.591 0.352 -2.258 -0.805 Intercept (AP) -0.639 0.501 -1.635 0.425 Intercept (PY) -0.986 0.274 -1.560 -0.436 Random effects (census) Intercept (BA) 0.933 0.372 0.457 1.884 Intercept (AP) 1.268 0.523 0.568 2.566 Intercept (PY) 0.539 0.360 0.035 1.434

9 Second best- Extinction (ε) approximating Fixed effects model Intercept (BA) 0.934 0.409 0.117 1.746 TCSA (BA) -0.024 0.006 -0.036 -0.013 Intercept (AP) -0.739 0.337 -1.404 -0.081 Intercept (PY) 0.439 0.679 -0.978 1.809 Intercept (Py) -0.659 0.720 -2.198 0.715 Random effects (census) Intercept (BA) 1.018 0.438 0.450 2.115 Intercept (AP) 0.490 0.387 0.032 1.482 Intercept (PY) 1.447 1.229 0.098 4.687 Intercept (Py) 1.443 1.298 0.093 4.924 Colonization (γ) Fixed effects Intercept (BA) -1.601 0.352 -2.282 -0.860 Intercept (AP) -0.608 0.457 -1.512 0.338 Intercept (PY) -1.358 0.334 -1.986 -0.766 Intercept (Py) -0.754 0.274 -1.343 -0.238 Random effects (census) Intercept (BA) 0.926 0.362 0.459 1.830 Intercept (AP) 1.249 0.532 0.561 2.556 Intercept (PY) 0.433 0.432 0.011 1.394 Intercept (Py) 0.498 0.386 0.032 1.470 Third best- Extinction (ε) approximating Fixed effects model Intercept (BA alone) 1.140 0.579 0.022 2.371 TCSA (BA alone) -0.016 0.010 -0.038 0.003 Intercept (BA with shrimp) 0.733 0.460 -0.139 1.691 TCSA (BA with shrimp) -0.024 0.007 -0.038 -0.011 Intercept (AP) -0.744 0.323 -1.398 -0.114 Intercept (PY) 0.073 0.478 -0.824 1.121 Random effects (census) Intercept (BA alone) 1.027 0.458 0.406 2.160 Intercept (BA with shrimp) 1.400 0.755 0.430 3.297 Intercept (AP) 0.466 0.358 0.025 1.370 Intercept (PY) 0.899 0.758 0.051 2.812 Colonization (γ) Fixed effects Intercept (BA) -1.599 0.345 -2.292 -0.889 Intercept (AP) -0.581 0.479 -1.473 0.470 Intercept (PY) -0.990 0.269 -1.547 -0.446 Random effects (census) Intercept (BA alone) 0.950 0.416 0.463 1.967 Intercept (AP) 1.277 0.589 0.560 2.665 Intercept (PY) 0.538 0.360 0.026 1.417

10