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Estimation Methods

For the estimation of climatic parameters from inventories of plant species from fossil assemblages, we provide two portfolios of data—one designed for use with the MCR_{un} approach, the other for the MCR_{wt} approach. A companion publication (Thompson and others, 2012) provides explorations of the strengths and weaknesses of each approach based on continental-scale estimations of climatic parameters from modern vegetation data. The two approaches differ in that MCR_{un} seeks only to identify the range of overlap of climatic tolerances of taxa in an assemblage, whereas MCR_{wt} employs knowledge of modern relations between a climatic parameter and the distribution of each taxon to reduce the influence of extreme values on a climatic estimate.

The weighting scheme for the MCR_{wt} approach is based on the cumulative percentage scale described in Thompson and others (1999a) and used in all previous volumes of this atlas. The cumulative percentages are obtained as follows: the procedure begins at the low end of a given parameter’s range and moves up the scale until the first occurrence of the taxon is encountered (and the associated climatic value at this point is designated as "0 percent"). From here, the cumulative number of occurrences of the taxon is tallied up the scale of the parameter until, for example, we have accumulated 10 percent of the total number of grid points occupied by the taxon, and the corresponding value of the parameter is designated as "10 percent" (Thompson and others, 1999c). For this report, this procedure was used to designate the values of a given parameter that correspond with the 0, 1, 5, 10, 90, 95, 99, and 100 percent of the cumulative occurrences of a given taxon.

For the MCR_{wt} approach, the values of each parameter associated with the cumulative percentage scale are used to determine weights of 1× to 4× within the climatic range where the taxon occurs. Equal weight of 4× is applied to climatic increments representing the 10th to 90th percentiles of the taxon’s distributions, and progressively smaller weights are applied toward the tails of the population (3× for 6th to 9th and 91st to 94th percentiles, 2× for 2nd to 5th and 95th to 99th percentiles, and 1× for the uppermost and lowermost percentiles).

For estimation of climatic parameters by the MCR_{un} approach, we identify the upper and lower bounds of the values of a given climatic parameter where there is complete overlap of the climatic distributions of constituent taxa in an assemblage. In this approach, the climatic limits of a species are set as the lowest and highest values associated with its distribution in relation to the climatic parameter under consideration (these are the 0- and 100-percent values in the cumulative scale discussed above). These limits are then compared among the species present in a fossil assemblage to determine the highest and lowest values of a parameter that would permit these species to coexist. In the data matrices accompanying this report, the incremental divisions for a parameter between the high and low limits of a species are encoded as "1" and the divisions outside of this range are encoded as "0." The MCR of an assemblage is then calculated by adding the data from all species together and determining the climatic range where the sum is equal to the number of species in the assemblage. In situations where a single reconstructed value is sought, we take the midpoint of this range of complete overlap. The technique is similar for the MCR_{wt} approach except that instead of summing ones and zeros (for presences or absences), we obtain a sum of the weights across all taxa in an assemblage and identify the upper and lower bounds of the climatic range associated with the highest sum of weights, and for single-value reconstruction, we use the midpoint of this range.