Driving factors in the colonization of Oceania: developing island-level statistical models to test competing hypotheses (Electronic Supporting Material)

To test the model specification and fitting algorithms, we simulated data using randomly generated parameters, settlement chronology, and accessibility matrix for N islands. Using the function optim in R, we found the maximum likelihood estimates and compared them with the "true" parameter values used to simulate the data. We repeated this process 100 times to assess the estimation process.

Electronic Supporting Material to DRIVING FACTORS IN THE COLONIZATION OF OCEANIA: DEVELOPING ISLAND-LEVEL STATISTICAL MODELS TO TEST COMPETING HYPOTHESES Adrian V. Bell1, Tom Currie2, Geoffrey Irwin3, and Christopher Bradbury4 1 Department of Anthropology, University of Utah, USA 2Department of Anthropology, University of Exeter, UK 3Department of Anthropology, University of Auckland, New Zealand 4 Department of Geology, January Simulations for parameter esti­mation To test the model specification and fitting algo­rithms, we simulated data using randomly gen­erated parameters, settlement chronology, and accessibility matrix for N islands. Using the function optim in R, we found the maximum likelihood estimates and compared them with the "true" parameter values used to simulate the data. We repeated this process 100 times to assess the estimation process. Supplemen­tary Fig. 1 shows that an increase in the value of the accessibility parameter increases the bias in the maximum likelihood estimates. This likely occurs as larger parameter values will cause col­onization to happen quickly, such that several University of Utah, USA 23, 2015 nodes may colonize any one time period. Con­sider the extreme example, where an effect size of 1000 or 10000 will have all nodes colonized within one or two time periods. Thus, the decreased time variation of short chronologies makes it more difficult to estimate the driving force of colonization with good precision. We can see this more clearly if we compare the like­lihood profile for a small and large parameter value used to simulate data. Figure 1 shows that larger parameter values result in a shal­lower likelihood curve to the right, making it possible to overestimate the "true" value used to simulate data. Overall, however, we are satisfied with the performance of the estimation procedure and we will evaluate our results of real data with UU IR Author Manuscript UU IR Author Manuscript University of Utah Institutional Repository Author Manuscript AO generated data Supporting Figure 1: Test of the model-fitting and model selection procedure. Left-top panel: red curve marks true value, while the blue curve is the average value for the maximum-likelihood estimated parameters. Green line is the curve generated from points weighted by the inverse of parameter precision. Data points axe individual estimates. Left-bottom panels show the systematic bias in estimation. Red dot indicates the "true value" of z used to simulate data. Right panels shows the ability of model selection using AIC to support models that generated the simulated data. AO - accessibility model (e.g. inter-island distance); IP - model using island properties (e.g. island area). this bias in mind, noting that the colonization dates used in the analysis are not close to simul­taneous, making the bias less likely to be impor­tant. R code for these simulations axe available on request. Simulations for model selection We expect to test our hypotheses for coloniza­tion using information criteria (i.e. Akaike In­formation criteria, AIC) as a model perfor­mance metric. We simulate data from two dis­tinct models of colonization - one that consid­ers accessibility as a driving force, and the other that solely considers island properties. On aver­age, the simulations show that Information Cri­teria scores can favor "generating" models, but the level of support suggests that in our analy­sis of the real data, we should declare a model to be the best supported when the model score is greater than 5 or 10 points. The Bayesian UU IR Author Manuscript UU IR Author Manuscript University of Utah Institutional Repository Author Manuscript formulation for Information Criteria, DIC, fol­lowed closely the relative AIC score differences between models. UU IR Author Manuscript UU IR Author Manuscript University of Utah Institutional Repository Author Manuscript Island group Austronesian language EA Hierarchy Class New Caledonia/Loyalty Dehu LIFU 1 1 Fiji FijianBau MBAUFIJIA 1 0 Bismarck/Solomons GhariGuadalcanal KAOKA 0 0 Hawaii Hawaiian HAWAIIANS 1 1 Fanning Kiribati ONOTOA 1 0 Santa Cruz/Reef Islands MaloSantaCruz SANTACRUZ 0 0 Mangareva Mangareva MANGAREVA 1 1 New Zealand (North) Maori MAORI 1 1 Marquesas Marquesan MARQUESAN 1 1 Marshalls Marshallese MARSHALLE 1 1 Vanuatu Mota MOTA 0 0 Niue Niue NIUEANS 1 1 Pukapuka Penrhyn TONGAREVA 1 - Easter Island RapanuiEasterlsland EASTER 1 1 Southern Cooks Rarotongan MANGAIANS 1 1 Samoa Samoan SAMOANS 1 1 Society Islands TahitianModern TAHITIANS 1 1 Tikopia Tikopia TIKOPIA 1 1 Tonga Tongan TONGANS 1 1 Tuvalu Tuvalu ELLICE 1 1 Australs Rurutuan Not in EA - Pitcairn No native language/population at time of European discovery Not in EA - Kermadec No native language/population at time of European discovery Not in EA - Chatham Not included in sample Not in EA - Supporting Table 1: Island groups matched to ethnographic data (from the Ethnographic Atlas [EA])used to reconstruct ancestral states of hierarchy in Oceanic societies, for those languages in the sample of Aus-tronesian phylogenetic trees. Two ethnographic variables were considered: Levels o f Jurisdictional Hierarchy beyond the Local Level (Hierarchy)(more than one level is coded as present (1), otherwise absent (0)), and the presence (1) or absence (0) of Hereditary Class Stratification (Class). Sensitivity analysis was conducted varying values for islands without sufficient data to estimate ancestral states. UU IR Author Manuscript UU IR Author Manuscript University of Utah Institutional Repository Author Manuscript Island(s) Land Area (km?) Elevation (m) 14C Date ESC (Error) Material A R (error) Lab number Reference Bismarck and Solomon Islands 100407 2679 3470 (90) marine 365 (50) ANU-5088 [18] Santa Cruz and Reef Islands 1159 883 3192 (51) marine -81 (64) WK-12304 [25] Vanuatu 15878 3405 2961 (36) terrestrial - WK-16830 [3] New Caledonia and Loyalty Islands 23586 1563 2930 (90) terrestrial - Beta-92753 [24] Fiji 21266 1278 2852 (57) terrestrial - WK-10294 [15] Tonga 488 269 2790 (50) terrestrial - CAMS-59624 [6] Samoa 3907 1811 3062 (66) marine 57 (23) NZA-5800 [22] Niue 355 58 1920 (90) terrestrial - ANU-9684 [31] Pukapuka 10 12 2310 (65) terrestrial - * [8] cited in [16] Southern Cook Islands 170 602 982 (32) terrestrial - Wk-23344 [2] Austral Islands 159 386 805 (30) terrestrial - NOSAMS-48157 [4] Society Islands 2161 1680 982 (32) terrestrial - Wk-23344 [2] Mangareva 57 390 970 (40) terrestrial - Beta-271082 [17] Marquesas 658 1181 855 (45) terrestrial - OZI977 [1] Hawaii 20972 4148 1350 (230) terrestrial - Beta-20852b [30] Fanning 731 19 1560 (85) terrestrial - * [27] Pitcairn 80 296 1120 (50) terrestrial - B-45596 [32] Easter 253 466 870 (40) terrestrial - Beta-209904 [14] Kermadec 62 466 1100 (45) marine -157 (68) Wk-2282 [13] New Zealand 172265 2545 891 (106) terrestrial - NZ-7889 [23] Chatham 1442 287 780 (38) marine 104 (14) NZ-7492 [20] Marshall 353 3 1900 (100) terrestrial - * [26] Tuvalu 11 6 870 (70) marine -37 (19) * [29] Tikopia 17 314 2680 (90) terrestrial - UCR-964 [19] Supporting Table 2: Islands, their characteristics, and proxies for island colonization times used in the analysis. Archaeological dating of early sites yield approximate colonization times, providing sets S and C in the model. *Not available. UU IR Author Manuscript UU IR Author Manuscript University of Utah Institutional Repository Author Manuscript DIC weight 1 2 4 6 8 10 Level of Uncertainty in Settlement Times from Calibrated Dates Supporting Figure 2: Model ranking with increasing uncertainty around settlement times using calibrated dates (the mean date and standard error from the calendar date density distribution). See the caption to Supplementary Fig. 2 for method details. As exactly with the case of uncalibrated dates, we see that the Angle of Target model remains the top model for up to 5 times the original standard error in settlement time, afterwards gradually replaced by the RISK models SBE 100 and Est. SBE. This suggests that support for the Angle of Target and SBE models are robust. 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