Here, we present a modified version of the equation for the zs-MART proxy based on appropriate regression analysis and estimation of the error associated with the predicted values. We use this improved version to recalculate data used in studies that used the zs-MART proxy and evaluate their conclusions against revised estimates for seasonal regimes. The zs-MART approximation (mean annual temperature range derived from zooid size) is used to estimate paleoseasonality based on morphometric analyzes of cheilostomes (Bryozoa: Gymnolaemata: Cheilostomata).
When constructing the original data, O'Dea and Okamura assumed that the error in obs-MART is negligible and that all colonies from a single locality experienced the same obs-MART. The best approximation of the relationship between these variables is thus obtained through an ordinary least squares (OLS) linear regression, which minimizes the distance of the points from the regression line only on the CVZA axis. There are three components that contribute to the uncertainty in the zs-MART values generated by equation 1: (i) the confidence limits of the position of individual points (error bars in Fig. 1); (ii) 95% confidence interval of the regression (CI, Fig. 2A, 2C); and (iii) the 95% prediction interval (PI, Fig. 2A, 2C).
The CVZA value for each colony is a function of the standard deviation of the zooid areas sampled. Confidence in the CVZA value is itself a function of the standard deviation and increases at higher CVZA values. Using an appropriate ordinary least squares regression (see Section 2.1) and adopting the corresponding significant figures for coefficients and errors (see Section 2.2), the revised equation relating obs-MART and CVZA is:. 3) Uncertainty in zs-MART values is mainly determined by PI i.
Although the relationship between obs-MART and CVZA is well constrained, the spread of the data on this line is large, and therefore the predictive power is low.
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Improving the zs-MART proxy
Zooids were only measured if they met the criteria of O'Dea and Okamura (2000) and Knowles et al. Each zooid originates from its proximal neighbor, so the zooid size profile along the transect represents a pseudo-time series. Because zooid size has a temperature-controlled component to TSR, any colony that has grown for more than 1 year should show some degree.
If this is not observed, it is unlikely that variation in zooid size is dominated by a seasonal variable. The smoothing parameter () was varied to change the sensitivity of the trend component to the variability in the data, with the aim of separating the inter-annual and intra-annual variations into trends and cycles, respectively. Of the 19 specimens studied, five exhibited oscillatory signals in their zooid length profiles that exceeded the above criteria.
However, values thus generated will relate to the ambient water temperature and will require knowledge of the depth habitat of the relevant bryozoan species in order to make a reasonable estimate of sea surface temperature. The relative magnitude of the effect of position is greatest on the zooid area, second most on the zooid. The effect of increasing zooid size with position was also observed in at least three other species (Watersipora sp., Cryptosula pallasiana and Thalamoporella californica; McClelland unpublished data), and may be widespread.
In any future derivation of the zs-MART proxy, zooid ranges should be corrected for positional bias using this equation (for Acanthodesia) or an equivalent generated specifically for the taxa studied. Oscillations in zooid size observed in Flustra foliacea (O'Dea and Okamura, 2000b) were correlated with seasonal growth control lines, and oscillations in zooid size in Pentapora foliacea shaded isotopic patterns caused by seasonal variation in. Forms with lower bifurcation frequency and thus longer range length will have an inherently greater variation in zooid size and therefore zs-MART.
The inflated variance in zooid size due to the positional effect is removed when the data are transformed using equation 6, although line arrays whose within-line zooid size gradients differ from the mean described by equation 5 will still show artificial fluctuation. Such future derivations of the zs-MART proxy should include taxon-specific corrections for zooid position. Therefore, zooid size profiling should be performed as a preliminary analysis, and species lacking evidence of true externally controlled oscillatory variation in zooid size should be discarded.
Certain properties of cheilostome bryozoans make them very attractive as proxies for paleoclimate inference (Okamura et al., 2011). Third, many cheilostomes show polymorphism that produces zooids specialized for feeding, reproduction, and defense, which may be related to the life history of that colony (e.g., see O'Dea et al., 2011).
Conclusions
Acknowledgements
Environmental changes before the K-T boundary inferred from temporal variation in the morphology of cheilostome bryozoans. Influence of seasonal variation in temperature, salinity and food availability on module size and estuarine colony growth. Cheilostome bryozoans as indicators of seasonality in the Neogene epicontinental sea of Western Europe. eds) Proceedings of the 11th International Bryozoology Association Conference.
PIMART is the relevant error in the MART axis and is directly proportional to PICV, where the proportionality constant = the gradient of the regression line. As shown, the growth is from right to left, with “1” being the first button autozooid of the new row and “5” being the last. Live specimens collected locally in October 2007 at Veracruz Beach in the Gulf of Panama by A.
Existing zs-MART estimates from the literature using the original equation (Equation 1) have been modified using the revised equation from this study (Equation 2). 5.3 ± 4oC Yes Miocene zs-MART estimate is within the error of the modern analogue, the Bay of Biscay. oC Yes Pliocene zs-MART estimate is within error of the modern value for southern England.
No Upside and non-upside of Panama face high and low seasonality, respectively, as reflected in the zs-MART scores. No Upside and non-upside of Panama face high and low seasonality, respectively, as reflected in the zs-MART scores. This is interpreted as a transition from an upwelling to a no-upwelling regime coinciding with and resulting from the closure of the Strait of Panama.
N/A Revised zs-MART estimates are closer to the measured annual temperature range, but the error is much larger than for oxygen isotopes. The magnitude of the increase in zs-MART prior to the K/T boundary is significant in both species, and is mirrored by other proxies. Frequency distribution shapes of zs-MART values are used to form arguments about the upwelling regime.
N/A The shapes of frequency distributions of zs-MART values are independent of the absolute values. However, when the large error associated with each zs-MART value is included in the analysis, confidence in the shape of the distribution decreases.
