The initial data set comprised 228 entries from 190 species (Table S1). As per the data selection criteria (Table S1), the full data set had 179 entries, including 101 PP, 56 LP and 22 NP (69 Asteroidea, 60 Echinoidea, 36 Holothuroidea, 14 Ophiuroidea; Fig. 1). There was a significant interaction between class and larval mode on PPD (F_{5,168} = 3.38, P = 0.006). Separate oneway ANOVAs and post hoc tests (Fig. 2) revealed: (1) significant differences only between NP and LP in asteroids (F_{2,66} = 4.01, P = 0.023; SNK, P = 0.011); (2) significant differences between LP and the two other larval modes in echinoids (F_{2,57} = 16.20, P < 0.001; SNK, P < 0.003); (3) no significant differences in PPD among larval modes in holothuroids (F_{2,33} = 1.14, P = 0.331); and (4) significant differences between LP and PP (NP mode absent) in ophiuroids (F_{1,12} = 22.54, P < 0.001; SNK, P < 0.001).
Once narrowed down to the two pelagic larval modes (56 LP; 101 PP), the data set comprised 54 Asteroidea, 58 Echinoidea, 31 Holothuroidea and 14 Ophiuroidea. A graphical illustration of PPD ranges is shown in Fig. 3. This subset still showed a significant interaction between class and larval mode (F_{3,149} = 4.62, P = 0.004). For further analyses we retained only species where time to gastrula was available (n = 87; Table S3) in order to separate the embryonic from the larval phase. Tests on this subset showed consistency with earlier results, i.e. a significant effect of the interaction term (class × larval mode) on PPD (F_{3,79} = 4.94, P = 0.003), with PP and LP modes showing comparable PPDs in asteroids and holothuroids, and significantly different PPDs in echinoids and ophiuroids (Fig. 4). The same interaction occurred when using shortest PPD instead of mean PPD (F_{3,79} = 4.25, P = 0.008) or when testing the pelagic larval duration (PLD) consisting of the PPD minus time to gastrula (F_{3,79} = 4.72, P = 0.004).
ANCOVAs (Table S4) were used in an effort to further tease out mediators of PPD. As expected, egg size was significantly smaller in PP than LP (mean of 136 vs. 530 μm; t = 9.21, d.f. = 82, P < 0.001). Therefore, distributions of egg sizes within each larval mode differed and regression slopes were highly heterogeneous among larval modes and classes (Fig. S1), prompting the use of a separate slope analysis. This revealed a significant interaction among class, larval mode and egg size on PPD (F_{8,68} = 2.16, P = 0.042). Slopes of predictor versus PPD were not parallel among groups for temperature (Fig. S2) and for latitude; results of separate slope analyses showed significant trivariate interactions in both cases (class × larval mode × temperature, F_{8,64} = 11.89, P < 0.001; class × larval mode × latitude, F_{8,68} = 4.54, P < 0.001). Combining egg size and temperature as covariates confirmed the abovementioned trivariate interactions and the absence of any other significant effect on PPD (Table S4). Comparable results were obtained when the three continuous predictors (egg size, temperature, latitude) were included as covariates. Combined with the ANOVA results, these findings emphasized the need for taxonspecific and regionspecific approaches.
Analysis by class
Table 1 provides a summary of the classspecific results obtained using mean PPD. Asteroidea (16 PP; 13 LP) did not exhibit any significant difference in PPD between larval modes (t = −1.11, d.f. = 27, P = 0.276). Time to gastrula did not vary significantly between larval modes (U = 71.50, P = 0.160) but ratio of time to gastrula to PPD was greater in LP than in PP (mean of 11.4 vs. 2.5%; t = 4.01, P < 0.001). There was no significant difference in rearing temperature between the larval modes (t = −1.94, P = 0.062). A significant negative correlation between PPD and temperature (r_{s} = 0.74; P < 0.001) and a positive correlation between PPD and latitude (r_{s} = 0.68, P < 0.001) were found. There was no relationship between egg size and time to gastrula (P = 0.088) and no correlation between egg size and PPD (P = 0.431). A multiple linear regression showed that both temperature and egg size (F_{2,25} = 27.54, P < 0.001) accounted for the predicted PPD in this class (r^{2} = 0.69), although egg size was only influential across pooled larval modes, not within PP (P = 0.446) or LP (P = 0.292).
Table 1. Summary of per class analyses on echinoderm species for which pelagic propagule duration (PPD) and time to gastrula were available (n = 87). Comparison between planktotrophic pelagic (PP) and lecithotrophic pelagic (LP) larval modes on the basis of PPD, time to gastrula stage, time to gastrula relative to PPD, and temperature at which the PPD was measured. Correlations (positive, negative, absent) between PPD and temperature or latitude and between egg size and time to gastrula or PPD are also shown (see also Figs S1 and S2Class  Comparisons between larval modes  Correlations 

 PPD  Time to gastrula  Time to gastrula relative to PPD  Temperature  PPD versus temperature  PPD versus latitude  Egg size versus time to gastrula  PPD versus egg size 


Asteroidea  PP = LP  PP = LP  PP < LP  PP = LP  Negative  Positive  Absent  Absent 
Echinoidea  PP > LP  PP = LP  PP < LP  PP = LP  Negative  Positive  Absent  Absent 
Holothuroidea  PP = LP  PP < LP  PP < LP  PP > LP  Absent  Absent  Positive  Absent 
Ophiuroidea  PP > LP  PP = LP  PP < LP  PP = LP  Absent  Absent  Absent  Negative 
Pooled  PP > LP  PP < LP  PP < LP  PP > LP  Negative  Positive  Positive  Absent 
Echinoidea (16 PP; 4 LP) showed longer PPDs for PP than for LP (mean of 42 vs. 10 days; t = 4.60, d.f. = 18, P < 0.001). Time to gastrula was not significantly related to larval mode (t = −0.19, P = 0.849) but ratio of time to gastrula to PPD was greater in LP than PP (mean of 15.3 vs. 3.2%; t = −3.94, P < 0.001). Temperature did not differ significantly between larval modes (U = 16.00, P = 0.221). However, there was a significant negative correlation between PPD and temperature (r_{s} = 0.69, P = 0.001) and a positive one between PPD and latitude (r_{s} = 0.58, P = 0.013). There was no significant relationship between egg size and time to gastrula (P = 0.962) nor between egg size and PPD (P = 0.061). A multiple linear regression (F_{2,15} = 8.40, P = 0.004, r^{2} = 0.53) revealed that temperature (P = 0.005) but not egg size (P = 0.052) accounted for the predicted PPD. Sample size in LP was too low to examine withinmode results.
In Holothuroidea (11 PP; 14 LP) there was no significant difference in PPD between larval modes (U = 52.0, d.f. = 23, P = 0.180). Both time to gastrula (t = −4.66, d.f. = 23, P < 0.001) and the ratio of time to gastrula to PPD (t = −4.44, P < 0.001) were significantly greater in LP (mean of 64.6 h and 19.2%) than in PP (17.3 h; 4.5%). Furthermore, PP modes were associated with significantly warmer temperatures than PL modes (mean of 25.3 vs. 9.9 °C; t = 9.73, d.f. = 19, P < 0.001). There was no significant correlation between PPD and latitude (P = 0.154), temperature (P = 0.863) or egg size (P = 0.843), but there was a positive relationship between egg size and time to gastrula (r_{s} = 0.61, P = 0.002). A multiple linear regression could not predict PPD using egg size and temperature (F_{2,16} = 1.60, P = 0.232). Neither factor was a significant predictor of PPD within PP (P > 0.737), whereas both factors were significant predictors of PPD within LP (P < 0.027).
In Ophiuroidea (10 PP; 4 LP) PPDs were significantly longer in PP than in LP (mean of 34 vs. 5 days; t = 4.33, d.f. = 12, P < 0.001). Larval mode did not have any effect on time to gastrula (t = 0.32, P = 0.756), whereas the ratio of time to gastrula to PPD was significantly greater in LP than in PP (mean of 19.9 vs. 4.6%; t = −4.11, d.f. = 12, P = 0.001). Larval modes did not show a significant difference in rearing temperature (t = −1.01, P = 0.335). There was no correlation between PPD and temperature (P = 0.526) or latitude (P = 0.197), nor between egg size and time to gastrula (P = 0.276). However, there was a significant negative relationship between egg size and PPD (r_{s} = 0.70, P = 0.005). Egg size (P = 0.002) but not temperature (P = 0.204) was a predictor of PPD in a multiple linear regression analysis (F_{2,10} = 10.63, r^{2} = 0.68). Sample size in LP was too low to examine withinmode results.
In pooled classes (52 PP; 35 LP) PPDs were significantly longer in PP than in LP (mean of 37 vs. 25 days; t = −3.64, d.f. = 85, P < 0.001). Time to gastrula (obligate nonfeeding phase) was significantly longer in LP than PP (87.3 vs. 27.2 h; U = 551, P = 0.002), as was the ratio of time to gastrula to PPD (15.8 vs. 3.6%; t = 7.83, P < 0.001). Furthermore, rearing temperatures in LP were significantly lower than in PP (mean of 15.0 vs. 21.0 °C; U = 473.5, P = 0.005). There was a significant negative correlation between PPD and temperature (r_{s} = 0.42, P < 0.001) and a positive correlation with latitude (r_{s} = 0.30, P < 0.006). The overall relationship between egg size and time to gastrula was significant and positive (r_{s} = 0.32, P = 0.003), but the relationship between egg size and PPD was not (P = 0.064). Within larval modes, a significant positive relationship was found between egg size and PPD in LP (r_{s} = 0.531, P = 0.001), but not in PP (P = 0.818). Both egg size (F_{2,74} = 16.37, P = 0.016) and temperature (P < 0.001) were significant predictors of PPD in a multiple linear regression analysis (r^{2} = 0.31).
On the whole, patterns associated with larval mode in the Echinodermata do not clearly follow any phylogenetic trend (Table 1). Asteroidea and Holothuroidea showed no correlation between PPD and larval mode, while Echinoidea and Ophiuroidea did. The classes in which differences emerged each had data sets skewed towards planktotrophs (71% in Ophiuroidea and 80% in Echinoidea), whereas the classes in which no difference in PPD was found had nearly equal representatives of the two modes. Apart from the consistently greater egg size and ratio of time to gastrula to PPD in lecithotrophs than in planktotrophs, the various effects and correlations were often skewed by only one or two classes, and not always the same ones (Table 1).
Analysis by geographic region
The full subset for analysis of PPD among geographic regions (defined in Table S2) comprised 135 entries (84 PP; 51 LP) distributed as shown in Fig. 5(a) and (b). PPD was found to vary significantly amongst the 14 regions (F_{13,121} = 4.72, P < 0.001). Twoway ANOVAs were conducted on a condensed subset that included only the regions with at least five species and representatives of both larval modes (73 PP and 51 LP distributed in nine regions; Fig. 5c). There were significant differences in PPD between modes (F_{1,106} = 25.47, P < 0.001) and across regions (F_{8,106} = 9.24, P < 0.001), with Antarctica showing consistently longer PPDs in pairwise comparisons (P < 0.001). No significant interaction was found between region and larval mode (F_{8,106} = 1.43, P = 0.191). A significant difference in PPD between larval mode was observed in four regions (northeast Pacific, northwest Pacific, temperate southwest Pacific, Caribbean–Gulf of Mexico; Fig. 5c; SNK, P < 0.05) but not in the five others (Antarctica, P = 0.682; northwest Atlantic, P = 0.661; northeast Atlantic, P = 0.072; Red Sea, P = 0.419; tropical west Pacific, P = 0.181). Significant egg size differences between PP and LP occurred in all regions (F_{8,99} = 130.02, P < 0.001; SNK, P < 0.036), except the Red Sea (P = 0.113).
Analysis by climate zone
The subset for this analysis contained 120 entries (74 PP; 46 LP) for which the precise sampling latitude and experimental seawater temperature were known, allowing us to separate them into climate zones (tropical, temperatewarm, temperate, temperatecold, polar; defined in Fig. 6). A significant interaction occurred between larval mode and climate zone (F_{4,110} = 4.27, P = 0.003; Fig. 6). In separate ttests, species from tropical, temperatewarm and temperate climes exhibited distinct PPDs on the basis of larval mode (P < 0.001) but species from temperatecold (P = 0.921) and polar climes (P = 0.593) did not. There was a smoother more continuous decline in PPD across climes in PP than in LP (Fig. 6). When focusing on the echinoderm class with representatives of both larval modes in all climate zones (Asteroidea: 23 PP; 22 LP), we found a similar pattern except there was no significant interaction between the factors (F_{4,35} = 1.29, P = 0.292). Only temperate and temperatewarm species displayed a significant difference in PPD between PP and LP modes (SNK, P = 0.020 and 0.001, respectively) while tropical species joined polar and temperatecold species in not exhibiting any significant difference (P > 0.194).
Analysis of range size
In a subset of species from all classes (29 PP; 13 LP) that exhibited relatively long PPDs (≥ 30 days; Table S5), PPD was not significantly different between LP and PP (t = 0.52, d.f. = 40, P = 0.607). The range size based on surface area was on average larger in LP (1847 × 10^{4} km^{2}) than in PP (1501 × 10^{4} km^{2}), but not statistically so (t = 1.61, d.f. = 40, P = 0.114), whereas the greater species range based on maximal linear distance in LP (10,835 km) than in PP (6815 km) was statistically supported (t = 2.11, d.f. = 40, P = 0.041; Fig. 7). There was no correlation between PPD and either measure of distribution range (P = 0.854 and 0.932 for area and distance, respectively). Twoway ANOVAs could not be performed on this subset because there were no LP modes in Echinoidea and Ophiuroidea. There was no significant correlation between egg size and PPD (P = 0.235) or egg size and range size, whether measured as surface area (P = 0.420) or linear distance (P = 0.162). Temperature was inversely related to PPD (r_{s} = 0.362, P = 0.026) but not to either measure of range size (P > 0.05).
In species with short PPDs (< 30 days; Table S6) from all classes (24 LP; 47 PP), PPD was significantly influenced by larval mode (F_{1,63} = 31.56, P < 0.001), with post hoc tests showing significance in echinoids (P = 0.003) and ophiuroids (P = 0.001) but not in asteroids (P = 0.461) or holothuroids (P = 0.557). Species range was on average significantly greater in PP than in LP, both based on surface area (2726 × 10^{4} vs. 794 × 10^{4} km^{2}; t = −2.80, P = 0.007) and maximum distance (9467 vs. 4828 km; t = −3.53, P < 0.001; Fig. 7). Still, there was no correlation between PPD and range size (P = 0.985 and 0.432 for area and distance, respectively). Relationships with temperature and egg size contrasted those for PPD > 30 days. Significant negative relationships occurred between egg size and PPD (r_{s} = 0.495, P < 0.001), and between egg size and range based on area (r_{s} = 0.241, P = 0.0495) and distance (r_{s} = 0.311, P = 0.010); but temperature was not correlated to PPD or any measure of range size (P > 0.203). Twoway ANOVAs (class × larval mode) showed that geographic range based on area was not significantly different between larval modes (F_{1,63} = 3.40, P = 0.070), whereas range based on maximum distance was (F_{1,63} = 5.90, P = 0.018); post hoc tests did not reveal any significant differences in PPD between LP and PP within any of the classes (P > 0.05).
While lecithotrophs exhibited greater geographic ranges at PPDs ≥ 30 days and planktotrophs exhibited greater ranges at PPDs < 30 days, PPDs did not directly explain the greater geographic range within either group. Temperature differed significantly among short and long PPDs (mean of 23.6 vs. 12.0 °C; U = 351, P < 0.001) but was unrelated to range size within the groups and related to PPD only in species with long PPDs. Egg size was not significantly different between the two groups (t = 1.37, P = 0.173); it had an influence on both PPD and range within short PPDs and no effect on any variable within long PPDs. Species pooled regardless of PPD length showed no significant difference in range size between PP and LP, whether based on maximum area (U = 1265, P = 0.390, n = 113) or distance (U = 1205.5, P = 0.221). Twoway ANOVAs did not reveal any interactions, or any differences in range among classes or larval modes. Finally, a threeway ANOVA (class × larval mode × PPD category), restricted to Asteroidea and Holothuroidea to ensure nonempty cells, confirmed the interacting effects of PPD category (short versus long) and larval mode (PP versus LP) on the range area (F_{1,57} = 5.45, P = 0.023) and distance (F_{1,57} = 13.55, P < 0.001). Pairwise analyses mirrored the inverse trends shown in Fig. 7.