Ecological Archives A021-105-A4

John A. Nagy, Deborah L. Johnson, Nicholas C. Larter, Mitch W. Campbell, Andrew E. Derocher, Allicia Kelly, Mathieu Dumond, Danny Allaire, and Bruno Croft. 2011. Subpopulation structure of caribou (Rangifer tarandus L.) in arctic and sub-Arctic Canada. Ecological Applications 21:2334–2348.

Appendix D. Values of the validity functions (i.e., fuzziness performance index and normalized classification entropy) for and appropriate number of subpopulations indicated by fuzzy clustering of movement data for migratory and tundra-wintering barren-ground, Dolphin and Union island, and boreal caribou in the Northwest Territories, Nunavut, and northern Alberta, Canada.

TABLE D1. Fuzzy performance indicators of the appropriate number of subpopulations from fuzzy clustering of movement data for female migratory barren-ground caribou that used calving ground A, B, C, D, E-1 and F (west-central) in the Northwest Territories and Nunavut. Results are based on fuzzy clustering of median monthly interval x, y coordinates for each caribou (i.e., 12 months or 24 variables). Numbers in bold indicate optimal number of subpopulations.

Fuzzy
Exponent
(m)
Fuzziness Performance Index, F   Normalized Classification Entropy, H
Number of Subpopulations   Number of Subpopulations
2 3 4 5 6 7 8 9 10   2 3 4 5 6 7 8 9 10
1.5 0.144 0.112 0.118 0.138 0.144 0.181 0.197 0.252 0.286   0.170 0.131 0.130 0.143 0.137 0.160 0.168 0.207 0.223
1.6 0.177 0.163 0.170 0.197 0.229 0.246 0.263 0.285 0.326   0.210 0.189 0.188 0.206 0.215 0.221 0.229 0.244 0.264
1.7 0.209 0.217 0.228 0.231 0.263 0.313 0.367 0.384 0.406   0.252 0.250 0.251 0.235 0.255 0.285 0.322 0.324 0.335
1.8 0.243 0.272 0.289 0.290 0.327 0.381 0.465 0.434 0.463   0.296 0.311 0.315 0.295 0.318 0.349 0.401 0.383 0.398
1.9 0.278 0.326 0.351 0.349 0.425 0.445 0.469 0.524 0.551   0.340 0.370 0.378 0.353 0.404 0.411 0.424 0.451 0.473
2.0 0.314 0.379 0.411 0.406 0.450 0.505 0.555 0.596 0.621   0.384 0.425 0.438 0.410 0.437 0.469 0.501 0.520 0.533
2.1 0.351 0.430 0.467 0.460 0.539 0.573 0.616 0.624 0.641   0.427 0.477 0.493 0.462 0.515 0.528 0.551 0.564 0.580
2.2 0.388 0.477 0.519 0.509 0.589 0.608 0.649 0.697 0.708   0.467 0.525 0.543 0.510 0.564 0.570 0.596 0.618 0.627
2.3 0.424 0.521 0.566 0.555 0.603 0.651 0.704 0.697 0.751   0.506 0.568 0.588 0.554 0.583 0.613 0.640 0.641 0.669
2.4 0.459 0.562 0.608 0.596 0.643 0.689 0.709 0.791 0.769   0.542 0.607 0.628 0.594 0.623 0.652 0.665 0.703 0.693
2.5 0.492 0.599 0.646 0.633 0.679 0.722 0.743 0.769 0.782   0.575 0.642 0.664 0.630 0.658 0.686 0.700 0.719 0.725
2.6 0.523 0.632 0.679 0.745 0.711 0.751 0.792 0.799 0.821   0.606 0.674 0.695 0.738 0.690 0.716 0.736 0.750 0.753
2.7 0.553 0.663 0.709 0.696 0.738 0.776 0.812 0.812 0.846   0.634 0.702 0.723 0.692 0.717 0.741 0.760 0.767 0.784
2.8 0.581 0.690 0.735 0.723 0.761 0.796 0.817 0.838 0.855   0.660 0.727 0.747 0.718 0.741 0.764 0.778 0.795 0.797
2.9 0.607 0.715 0.758 0.747 0.783 0.815 0.835 0.860 0.870   0.683 0.750 0.768 0.741 0.763 0.784 0.798 0.808 0.815
3.0 0.631 0.738 0.778 0.826 0.802 0.832 0.859 0.873 0.887   0.705 0.770 0.787 0.819 0.782 0.803 0.815 0.825 0.837

TABLE D2. Fuzzy performance indicators of the appropriate number of subpopulations from fuzzy clustering of movement data for female migratory barren-ground caribou that used calving ground A (Cape Bathurst subpopulation) in the Northwest Territories. Results are based on fuzzy clustering of median monthly interval x, y coordinates for each caribou (i.e., 12 months or 24 variables used in analyses). Numbers in bold indicate values = 0.90 for robust subpopulations.

Fuzzy
Exponent
(m)
Fuzziness Performance Index   Normalized Classification Entropy
Number of Subpopulations   Number of Subpopulations
2 3 4 5 6 7 8 9 10   2 3 4 5 6 7 8 9 10
1.5 0.111 0.038 0.024 0.008 0.007 0.016 0.005 0.007 0.003   0.136 0.044 0.026 0.010 0.007 0.017 0.006 0.008 0.004
1.6 0.256 0.118 0.081 0.056 0.118 0.058 0.062 0.053 0.053   0.289 0.128 0.083 0.056 0.110 0.057 0.062 0.051 0.049
1.7 0.353 0.214 0.385 0.281 0.221 0.232 0.237 0.192 0.195   0.405 0.237 0.375 0.265 0.202 0.215 0.220 0.166 0.179
1.8 0.456 0.325 0.528 0.442 0.455 0.421 0.417 0.385 0.371   0.521 0.361 0.509 0.405 0.423 0.374 0.374 0.333 0.326
1.9 0.558 0.441 0.638 0.545 0.582 0.514 0.554 0.564 0.550   0.627 0.482 0.615 0.503 0.541 0.471 0.496 0.505 0.496
2.0 0.651 0.552 0.727 0.635 0.726 0.719 0.719 0.682 0.656   0.716 0.593 0.703 0.591 0.666 0.655 0.658 0.616 0.594
2.1 0.730 0.658 0.777 0.836 0.856 0.870 0.824 0.835 0.802   0.786 0.697 0.759 0.793 0.811 0.828 0.760 0.776 0.736
2.2 0.794 0.894 0.822 0.868 0.887 0.894 0.851 0.856 0.861   0.840 0.900 0.810 0.843 0.848 0.857 0.799 0.808 0.817
2.3 0.846 0.918 0.869 0.892 0.966 0.914 0.915 0.922 0.919   0.883 0.924 0.862 0.871 0.952 0.882 0.886 0.889 0.889
2.4 0.887 0.938 0.959 0.968 0.975 0.979 0.981 0.985 0.927   0.915 0.943 0.957 0.961 0.965 0.969 0.969 0.971 0.905
2.5 0.919 0.954 0.969 0.977 0.982 0.985 0.987 0.989 0.990   0.940 0.958 0.968 0.972 0.974 0.977 0.979 0.979 0.980
2.6 0.945 0.967 0.978 0.984 0.988 0.989 0.990 0.992 0.993   0.959 0.970 0.977 0.981 0.985 0.983 0.984 0.985 0.986
2.7 0.965 0.977 0.984 0.989 0.991 0.992 0.993 0.994 0.995   0.974 0.979 0.984 0.987 0.989 0.988 0.989 0.990 0.990
2.8 0.981 0.986 0.990 0.992 0.994 0.995 0.996 0.996 0.997   0.986 0.987 0.989 0.991 0.992 0.993 0.993 0.993 0.994
2.9 0.993 0.993 0.994 0.995 0.996 0.997 0.998 0.998 0.998   0.995 0.994 0.994 0.994 0.995 0.996 0.996 0.996 0.997
3.0 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

TABLE D3. Fuzzy performance indicators of the appropriate number of subpopulations from fuzzy clustering of movement data for female migratory barren-ground caribou that used calving ground B (Bluenose-West subpopulation) in the Northwest Territories. Results are based on fuzzy clustering of median monthly interval x, y coordinates for each caribou (i.e., 12 months or 24 variables used in analyses). Numbers in bold indicate values = 0.90 for robust subpopulations.

Fuzzy
Exponent
(m)
Fuzziness Performance Index   Normalized Classification Entropy
Number of Subpopulations   Number of Subpopulations
2 3 4 5 6 7 8 9 10   2 3 4 5 6 7 8 9 10
1.5 0.598 0.574 0.555 0.594 0.590 0.564 0.554 0.560 0.543   0.668 0.611 0.566 0.591 0.572 0.545 0.527 0.523 0.505
1.6 0.695 0.672 0.654 0.715 0.694 0.683 0.671 0.665 0.649   0.757 0.706 0.665 0.703 0.674 0.659 0.641 0.624 0.607
1.7 0.775 0.753 0.738 0.785 0.816 0.801 0.821 0.761 0.741   0.826 0.781 0.746 0.773 0.792 0.770 0.785 0.726 0.697
1.8 0.839 0.820 0.808 0.840 0.865 0.884 0.868 0.879 0.868   0.878 0.841 0.813 0.829 0.845 0.859 0.836 0.845 0.833
1.9 0.888 0.875 0.869 0.885 0.902 0.914 0.923 0.929 0.932   0.917 0.890 0.870 0.875 0.885 0.894 0.901 0.906 0.907
2.0 0.927 0.923 0.923 0.956 0.962 0.939 0.943 0.946 0.948   0.946 0.931 0.921 0.946 0.950 0.922 0.925 0.927 0.930
2.1 0.956 0.966 0.969 0.967 0.969 0.973 0.974 0.974 0.974   0.968 0.968 0.966 0.959 0.959 0.963 0.963 0.964 0.965
2.2 0.978 0.980 0.980 0.978 0.976 0.978 0.976 0.975 0.975   0.984 0.982 0.979 0.973 0.968 0.969 0.966 0.966 0.967
2.3 0.995 0.992 0.990 0.988 0.982 0.983 0.985 0.976 0.980   0.996 0.992 0.989 0.986 0.976 0.975 0.977 0.968 0.973
2.4 1.000 1.000 1.000 1.000 1.000 1.000 0.988 0.982 0.980   1.000 1.000 1.000 1.000 1.000 1.000 0.981 0.976 0.974
2.5 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.6 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.7 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.8 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.9 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
3.0 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

TABLE D4. Fuzzy performance indicators of the appropriate number of subpopulations from fuzzy clustering of movement data for female migratory barren-ground caribou that used calving ground C (Bluenose-East subpopulation) in Nunavut. Results are based on fuzzy clustering of median monthly interval x, y coordinates for each caribou (i.e., 12 months or 24 variables used in analyses). Numbers in bold indicate values = 0.90 for robust subpopulations.

Fuzzy
Exponent
(m)
Fuzziness Performance Index   Normalized Classification Entropy
Number of Subpopulations   Number of Subpopulations
2 3 4 5 6 7 8 9 10   2 3 4 5 6 7 8 9 10
1.5 0.502 0.477 0.604 0.623 0.552 0.601 0.526 0.512 0.526   0.584 0.533 0.603 0.612 0.524 0.579 0.495 0.476 0.495
1.6 0.606 0.602 0.707 0.730 0.715 0.700 0.692 0.656 0.667   0.682 0.651 0.703 0.718 0.696 0.674 0.660 0.620 0.623
1.7 0.694 0.706 0.785 0.832 0.849 0.807 0.861 0.841 0.809   0.759 0.746 0.778 0.813 0.821 0.777 0.827 0.800 0.769
1.8 0.765 0.792 0.832 0.873 0.888 0.898 0.898 0.902 0.899   0.819 0.820 0.827 0.857 0.865 0.869 0.866 0.865 0.861
1.9 0.822 0.922 0.871 0.901 0.922 0.929 0.936 0.942 0.937   0.865 0.924 0.868 0.888 0.905 0.907 0.911 0.917 0.911
2.0 0.867 0.944 0.904 0.924 0.940 0.948 0.955 0.960 0.955   0.901 0.946 0.901 0.913 0.926 0.931 0.935 0.940 0.928
2.1 0.902 0.958 0.932 0.943 0.954 0.963 0.968 0.971 0.975   0.927 0.960 0.929 0.934 0.943 0.950 0.953 0.955 0.958
2.2 0.929 0.969 0.958 0.959 0.966 0.972 0.977 0.980 0.982   0.948 0.970 0.955 0.951 0.956 0.962 0.966 0.968 0.970
2.3 0.950 0.978 0.983 0.973 0.976 0.980 0.993 0.986 0.987   0.964 0.979 0.982 0.968 0.968 0.971 0.988 0.977 0.978
2.4 0.967 0.984 0.989 0.992 0.993 0.994 0.995 0.996 0.996   0.976 0.985 0.988 0.989 0.991 0.991 0.992 0.992 0.993
2.5 0.980 0.990 0.994 0.995 0.996 0.996 0.997 0.997 0.998   0.985 0.991 0.993 0.993 0.994 0.994 0.995 0.995 0.995
2.6 0.990 0.994 0.997 0.997 0.998 0.998 0.998 0.999 0.999   0.993 0.995 0.996 0.996 0.997 0.997 0.997 0.997 0.997
2.7 1.000 0.998 0.999 0.999 0.999 0.999 0.999 1.000 1.000   1.000 0.998 0.999 0.999 0.999 0.999 0.999 0.999 0.999
2.8 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.9 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
3.0 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

TABLE D5. Fuzzy performance indicators of the appropriate number of subpopulations from fuzzy clustering of movement data for female migratory barren-ground caribou that used calving ground D (Bathurst subpopulation) in Nunavut. Results are based on fuzzy clustering of median monthly interval x, y coordinates for each caribou (i.e., 12 months or 24 variables used in analyses). Numbers in bold indicate values = 0.90 for robust subpopulations.

Fuzzy
Exponent
(m)
Fuzziness Performance Index   Normalized Classification Entropy
Number of Subpopulations   Number of Subpopulations
2 3 4 5 6 7 8 9 10   2 3 4 5 6 7 8 9 10
1.5 0.618 0.630 0.699 0.686 0.628 0.657 0.634 0.647 0.637   0.685 0.640 0.684 0.665 0.601 0.612 0.593 0.601 0.592
1.6 0.716 0.741 0.822 0.827 0.797 0.798 0.814 0.822 0.829   0.774 0.745 0.792 0.791 0.752 0.752 0.768 0.777 0.784
1.7 0.796 0.830 0.864 0.890 0.908 0.886 0.896 0.904 0.911   0.842 0.830 0.839 0.858 0.877 0.847 0.858 0.869 0.877
1.8 0.859 0.896 0.899 0.915 0.929 0.939 0.918 0.924 0.930   0.893 0.895 0.878 0.889 0.903 0.914 0.888 0.896 0.902
1.9 0.907 0.934 0.926 0.934 0.945 0.952 0.958 0.961 0.964   0.931 0.935 0.911 0.913 0.924 0.933 0.939 0.944 0.947
2.0 0.944 0.963 0.951 0.944 0.954 0.960 0.965 0.968 0.978   0.959 0.965 0.943 0.925 0.936 0.944 0.950 0.954 0.970
2.1 0.972 0.983 0.969 0.952 0.960 0.965 0.969 0.980 0.979   0.979 0.984 0.964 0.936 0.944 0.950 0.955 0.972 0.972
2.2 0.992 0.995 0.996 0.985 0.994 0.969 0.983 0.981 0.980   0.994 0.996 0.995 0.980 0.992 0.956 0.976 0.975 0.974
2.3 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.4 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.5 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.6 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.7 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.8 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.9 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
3.0 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

TABLE D6. Fuzzy performance indicators of the appropriate number of subpopulations from fuzzy clustering of movement data for female migratory barren-ground caribou that used calving ground E-1 and F (Beverly subpopulation) in Nunavut. Results are based on fuzzy clustering of median monthly interval x, y coordinates for each caribou (i.e., 12 months or 24 variables used in analyses). Numbers in bold indicate values = 0.90 for robust subpopulations.

Fuzzy
Exponent
(m)
Fuzziness Performance Index   Normalized Classification Entropy
Number of Subpopulations   Number of Subpopulations
2 3 4 5 6 7 8 9 10   2 3 4 5 6 7 8 9 10
1.5 0.621 0.481 0.508 0.447 0.511 0.537 0.540 0.527 0.526   0.687 0.521 0.516 0.436 0.481 0.500 0.485 0.475 0.469
1.6 0.708 0.590 0.604 0.546 0.619 0.645 0.652 0.659 0.684   0.766 0.629 0.612 0.534 0.583 0.602 0.599 0.600 0.618
1.7 0.779 0.687 0.686 0.755 0.778 0.811 0.834 0.822 0.775   0.828 0.722 0.692 0.735 0.750 0.776 0.795 0.777 0.707
1.8 0.837 0.773 0.755 0.814 0.847 0.871 0.884 0.881 0.893   0.876 0.800 0.758 0.794 0.819 0.840 0.851 0.840 0.850
1.9 0.884 0.843 0.813 0.855 0.883 0.903 0.917 0.927 0.925   0.913 0.862 0.814 0.837 0.858 0.875 0.889 0.900 0.889
2 0.920 0.895 0.862 0.888 0.910 0.925 0.936 0.945 0.951   0.940 0.907 0.861 0.872 0.888 0.901 0.912 0.921 0.927
2.1 0.948 0.935 0.909 0.917 0.931 0.975 0.952 0.959 0.960   0.962 0.942 0.906 0.902 0.912 0.967 0.932 0.939 0.935
2.2 0.970 0.962 0.962 0.969 0.975 0.980 0.960 0.986 0.988   0.978 0.966 0.960 0.964 0.969 0.973 0.942 0.979 0.981
2.3 0.986 0.978 0.971 0.975 0.980 0.984 0.987 0.989 0.991   0.990 0.980 0.970 0.971 0.975 0.978 0.981 0.983 0.985
2.4 1.000 0.992 0.980 0.981 0.984 0.987 0.990 0.991 0.993   1.000 0.993 0.979 0.977 0.980 0.982 0.984 0.986 0.988
2.5 1.000 1.000 1.000 1.000 0.988 0.990 1.000 0.993 1.000   1.000 1.000 1.000 1.000 0.984 0.986 1.000 0.989 1.000
2.6 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.7 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.8 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.9 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
3 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

TABLE D7. Fuzzy performance indicators of the appropriate number of subpopulations from fuzzy clustering of movement data for female migratory barren-ground that used calving grounds C, D, E-1, and F and Dolphin and Union island caribou (central) in Nunavut. Results are based on fuzzy clustering of median monthly interval x, y coordinates for each caribou (i.e., 12 months or 24 variables used in analyses). Numbers in bold indicate optimal number of subpopulations.

Fuzzy
Exponent
(m)
Fuzziness Performance Index, F   Normalized Classification Entropy, H
Number of Subpopulations   Number of Subpopulations
2 3 4 5 6 7 8 9 10   2 3 4 5 6 7 8 9 10
1.5 0.255 0.200 0.153 0.171 0.186 0.187 0.302 0.314 0.331   0.319 0.227 0.173 0.182 0.185 0.181 0.259 0.262 0.273
1.6 0.333 0.334 0.220 0.246 0.272 0.389 0.395 0.374 0.408   0.404 0.376 0.248 0.261 0.275 0.351 0.345 0.327 0.337
1.7 0.404 0.335 0.292 0.327 0.358 0.442 0.429 0.479 0.521   0.477 0.379 0.325 0.343 0.361 0.414 0.387 0.431 0.446
1.8 0.465 0.468 0.365 0.407 0.444 0.505 0.538 0.580 0.604   0.540 0.515 0.400 0.423 0.445 0.474 0.490 0.514 0.526
1.9 0.520 0.529 0.435 0.483 0.582 0.627 0.637 0.651 0.666   0.594 0.575 0.469 0.496 0.563 0.580 0.578 0.584 0.584
2.0 0.568 0.584 0.500 0.552 0.645 0.612 0.670 0.711 0.748   0.641 0.628 0.533 0.563 0.624 0.590 0.622 0.645 0.672
2.1 0.611 0.633 0.558 0.614 0.679 0.736 0.752 0.761 0.765   0.681 0.674 0.589 0.621 0.655 0.690 0.695 0.698 0.692
2.2 0.649 0.676 0.611 0.668 0.716 0.778 0.792 0.823 0.830   0.716 0.714 0.638 0.671 0.704 0.733 0.738 0.756 0.757
2.3 0.683 0.714 0.657 0.715 0.784 0.765 0.825 0.839 0.865   0.747 0.748 0.681 0.715 0.760 0.739 0.774 0.782 0.798
2.4 0.714 0.747 0.697 0.754 0.815 0.842 0.853 0.868 0.885   0.774 0.778 0.718 0.752 0.792 0.801 0.805 0.817 0.830
2.5 0.741 0.775 0.732 0.787 0.831 0.854 0.874 0.888 0.885   0.797 0.803 0.750 0.783 0.815 0.819 0.835 0.841 0.832
2.6 0.765 0.800 0.762 0.815 0.857 0.878 0.893 0.904 0.916   0.817 0.825 0.778 0.809 0.841 0.845 0.853 0.861 0.867
2.7 0.787 0.822 0.789 0.839 0.876 0.899 0.910 0.925 0.935   0.835 0.844 0.802 0.832 0.851 0.866 0.873 0.887 0.891
2.8 0.806 0.841 0.812 0.858 0.894 0.910 0.922 0.917 0.929   0.851 0.861 0.823 0.851 0.875 0.881 0.888 0.878 0.888
2.9 0.823 0.857 0.832 0.874 0.906 0.921 0.935 0.941 0.950   0.865 0.875 0.841 0.866 0.888 0.893 0.907 0.909 0.917
3.0 0.823 0.857 0.832 0.874 0.906 0.924 0.932 0.941 0.949   0.865 0.875 0.841 0.866 0.891 0.902 0.900 0.909 0.916

TABLE D8. Fuzzy performance indicators of the appropriate number of subpopulations from fuzzy clustering of movement data for female migratory and tundra-wintering barren-ground caribou that showed fidelity to calving ground E including E-1, F, G, H, and I (east-central) in Nunavut. Results are based on fuzzy clustering of median x, y coordinates for 26 14-day periods for each caribou (i.e., 52 variables used in analyses). Numbers in bold indicate optimal number of subpopulations.

Fuzzy
Exponent
(m)
Fuzzy Performance Index   Normalized Classification Entropy
Number of subpopulations   Number of subpopulations
2 3 4 5 6 7 8 9 10   2 3 4 5 6 7 8 9 10
1.5 0.252 0.091 0.263 0.182 0.311 0.314 0.323 0.358 0.364   0.314 0.117 0.254 0.179 0.266 0.255 0.254 0.283 0.290
1.6 0.320 0.136 0.213 0.369 0.394 0.394 0.455 0.477 0.479   0.390 0.176 0.236 0.337 0.345 0.329 0.397 0.382 0.378
1.7 0.383 0.190 0.293 0.405 0.490 0.470 0.518 0.536 0.563   0.458 0.241 0.319 0.378 0.420 0.402 0.439 0.456 0.453
1.8 0.441 0.249 0.457 0.416 0.548 0.484 0.592 0.621 0.634   0.520 0.308 0.456 0.410 0.496 0.457 0.510 0.523 0.535
1.9 0.495 0.310 0.463 0.482 0.608 0.672 0.654 0.679 0.704   0.575 0.374 0.481 0.477 0.542 0.605 0.573 0.584 0.607
2.0 0.544 0.370 0.570 0.660 0.669 0.709 0.705 0.725 0.740   0.623 0.436 0.571 0.617 0.618 0.634 0.628 0.637 0.639
2.1 0.590 0.427 0.584 0.703 0.697 0.747 0.747 0.777 0.785   0.666 0.494 0.598 0.663 0.639 0.677 0.675 0.701 0.700
2.2 0.631 0.481 0.660 0.738 0.732 0.745 0.806 0.811 0.818   0.703 0.546 0.662 0.702 0.679 0.689 0.740 0.739 0.737
2.3 0.667 0.530 0.695 0.769 0.763 0.790 0.816 0.847 0.842   0.736 0.592 0.699 0.735 0.714 0.734 0.752 0.766 0.769
2.4 0.700 0.575 0.715 0.795 0.790 0.826 0.850 0.868 0.863   0.765 0.633 0.723 0.764 0.745 0.772 0.795 0.804 0.790
2.5 0.730 0.616 0.748 0.817 0.813 0.837 0.866 0.886 0.887   0.790 0.670 0.754 0.789 0.772 0.791 0.810 0.817 0.826
2.6 0.756 0.652 0.780 0.835 0.871 0.860 0.880 0.888 0.910   0.811 0.702 0.784 0.810 0.838 0.816 0.829 0.834 0.845
2.7 0.779 0.684 0.802 0.850 0.884 0.875 0.893 0.901 0.912   0.831 0.731 0.805 0.828 0.853 0.835 0.846 0.852 0.861
2.8 0.799 0.713 0.821 0.864 0.863 0.888 0.906 0.912 0.925   0.847 0.756 0.824 0.843 0.833 0.851 0.860 0.867 0.874
2.9 0.818 0.739 0.836 0.876 0.877 0.899 0.916 0.922 0.934   0.862 0.778 0.838 0.857 0.848 0.865 0.881 0.881 0.891
3.0 0.834 0.761 0.851 0.887 0.913 0.909 0.922 0.933 0.941   0.875 0.798 0.853 0.870 0.890 0.878 0.885 0.895 0.901

TABLE D9. Fuzzy performance indicators of the appropriate number of subpopulations from fuzzy clustering of movement data for female migratory and tundra-wintering barren-ground caribou that showed fidelity to calving ground E including E-1 and F (Beverly A and B and Queen Maude Gulf A subpopulations) in Nunavut. Results are based on fuzzy clustering of median x, y coordinates for 26 14-day periods for each caribou (i.e., 52 variables used in analyses). Numbers in bold indicate optimal number of subpopulations.

Fuzzy
Exponent
(m)
Fuzzy Performance Index   Normalized Classification Entropy
Number of subpopulations   Number of subpopulations
2 3 4 5 6 7 8 9 10   2 3 4 5 6 7 8 9 10
1.5 0.321 0.407 0.513 0.536 0.484 0.530 0.568 0.560 0.585   0.403 0.443 0.511 0.524 0.460 0.490 0.517 0.506 0.524
1.6 0.452 0.513 0.607 0.699 0.635 0.643 0.681 0.714 0.714   0.538 0.547 0.602 0.672 0.600 0.596 0.622 0.651 0.644
1.7 0.590 0.604 0.685 0.769 0.813 0.820 0.757 0.785 0.835   0.669 0.633 0.678 0.740 0.779 0.778 0.701 0.725 0.780
1.8 0.728 0.680 0.750 0.817 0.854 0.876 0.870 0.872 0.882   0.788 0.704 0.740 0.790 0.822 0.844 0.828 0.824 0.829
1.9 0.842 0.744 0.803 0.856 0.887 0.906 0.918 0.927 0.937   0.880 0.763 0.792 0.832 0.859 0.877 0.890 0.900 0.906
2 0.914 0.797 0.846 0.888 0.913 0.929 0.940 0.933 0.937   0.936 0.811 0.834 0.866 0.888 0.904 0.916 0.900 0.897
2.1 0.956 0.842 0.876 0.907 0.928 0.942 0.951 0.958 0.964   0.968 0.851 0.865 0.888 0.906 0.919 0.930 0.937 0.944
2.2 0.983 0.879 0.899 0.923 0.940 0.952 0.960 0.966 0.971   0.988 0.885 0.889 0.906 0.921 0.932 0.941 0.948 0.953
2.3 1.000 0.999 0.919 0.937 0.951 0.960 0.967 0.972 0.976   1.000 0.999 0.909 0.922 0.933 0.943 0.950 0.956 0.960
2.4 1.000 1.000 1.000 1.000 1.000 1.000 0.980 0.983 0.986   1.000 1.000 1.000 1.000 1.000 1.000 0.968 0.972 0.975
2.5 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.988   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.978
2.6 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.7 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.8 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.9 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
3 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

TABLE D10. Fuzzy performance indicators of the appropriate number of subpopulations from fuzzy clustering of movement data for female migratory barren-ground caribou that showed fidelity to calving ground G (Qamanirjuaq subpopulation) in Nunavut. Results are based on fuzzy clustering of median 14-day period x and y coordinates for each caribou Results are based on fuzzy clustering of median x, y coordinates for 26 14-day periods for each caribou (i.e., 52 variables used in analyses). Numbers in bold indicate values = 0.90 for robust subpopulations.

Fuzzy
Exponent
(m)
Fuzzy Performance Index   Normalized Classification Entropy
Number of subpopulations   Number of subpopulations
2 3 4 5 6 7 8 9 10   2 3 4 5 6 7 8 9 10
1.5 0.748 0.779 0.761 0.75 0.741 0.732 0.739 0.749 0.763   0.802 0.803 0.77 0.747 0.725 0.706 0.706 0.708 0.716
1.6 0.844 0.886 0.884 0.884 0.89 0.891 0.889 0.888 0.893   0.881 0.897 0.884 0.877 0.876 0.87 0.864 0.861 0.864
1.7 0.916 0.95 0.963 0.971 0.976 0.98 0.982 0.984 0.985   0.937 0.954 0.961 0.966 0.969 0.971 0.972 0.973 0.974
1.8 0.968 0.983 0.988 0.991 0.993 0.994 0.995 0.996 0.996   0.977 0.985 0.988 0.989 0.99 0.991 0.992 0.992 0.992
1.9 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.1 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.2 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.3 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.4 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.5 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.6 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.7 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.8 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2.9 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
3 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000   1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

TABLE D11. Fuzzy performance indicators of the appropriate number of subpopulations from fuzzy clustering of movement data for female tundra-wintering barren-ground caribou that showed fidelity to calving ground E including E-1, H, and I (Queen Maude Gulf B, Lorillard, and Wager Bay subpopulations) in Nunavut. Results are based on fuzzy clustering of median x, y coordinates for 26 14-day periods for each caribou (i.e., 52 variables used in analyses). Numbers in bold indicate optimal number of subpopulations.

Fuzzy
Exponent
(m)
Fuzzy Performance Index   Normalized Classification Entropy
Number of subpopulations   Number of subpopulations
2 3 4 5 6 7 8 9 10   2 3 4 5 6 7 8 9 10
1.5 0.342 0.227 0.205 0.374 0.379 0.350 0.366 0.373 0.398   0.398 0.263 0.223 0.350 0.344 0.309 0.325 0.318 0.333
1.6 0.404 0.294 0.278 0.460 0.472 0.453 0.477 0.508 0.501   0.468 0.338 0.302 0.430 0.430 0.399 0.422 0.443 0.432
1.7 0.464 0.362 0.355 0.536 0.554 0.534 0.585 0.588 0.591   0.533 0.412 0.383 0.503 0.505 0.474 0.514 0.519 0.513
1.8 0.521 0.429 0.435 0.604 0.621 0.682 0.652 0.630 0.646   0.593 0.482 0.464 0.569 0.569 0.617 0.578 0.555 0.583
1.9 0.575 0.494 0.517 0.662 0.676 0.718 0.750 0.721 0.735   0.646 0.548 0.543 0.627 0.625 0.657 0.679 0.654 0.669
2 0.623 0.555 0.592 0.713 0.722 0.778 0.792 0.810 0.774   0.692 0.607 0.615 0.678 0.671 0.714 0.724 0.740 0.714
2.1 0.667 0.611 0.660 0.753 0.773 0.819 0.831 0.832 0.816   0.732 0.660 0.679 0.720 0.731 0.766 0.775 0.776 0.764
2.2 0.706 0.663 0.720 0.786 0.804 0.844 0.855 0.843 0.855   0.767 0.708 0.734 0.756 0.766 0.796 0.804 0.788 0.803
2.3 0.740 0.712 0.769 0.814 0.829 0.863 0.872 0.885 0.842   0.796 0.753 0.778 0.785 0.795 0.820 0.827 0.838 0.790
2.4 0.770 0.769 0.846 0.834 0.850 0.878 0.885 0.899 0.907   0.822 0.803 0.835 0.809 0.819 0.839 0.845 0.857 0.866
2.5 0.796 0.836 0.869 0.851 0.866 0.888 0.895 0.906 0.914   0.843 0.859 0.856 0.829 0.838 0.854 0.859 0.869 0.879
2.6 0.819 0.864 0.883 0.888 0.893 0.897 0.902 0.911 0.914   0.862 0.883 0.871 0.869 0.867 0.866 0.871 0.879 0.881
2.7 0.839 0.885 0.933 0.900 0.925 0.903 0.908 0.913 0.922   0.878 0.901 0.925 0.883 0.902 0.876 0.881 0.886 0.894
2.8 0.857 0.903 0.942 0.909 0.931 0.909 0.914 0.920 0.922   0.892 0.916 0.936 0.894 0.911 0.885 0.889 0.894 0.896
2.9 0.872 0.917 0.949 0.958 0.936 0.939 0.944 0.923 0.951   0.904 0.928 0.944 0.949 0.918 0.919 0.923 0.900 0.929
3 0.885 0.929 0.955 0.963 0.973 0.976 0.980 0.982 0.984   0.914 0.938 0.950 0.955 0.962 0.964 0.967 0.968 0.969

TABLE D12. Fuzzy performance indicators of the appropriate number of subpopulations from fuzzy clustering of movement data for female boreal caribou in the Northwest Territories and northern Alberta, Canada. Results are based on fuzzy clustering of median monthly interval x, y coordinates for each caribou (i.e., 12 months or 24 variables used in analyses). Numbers in bold indicate optimal number of subpopulations.

Fuzzy
Exponent
Fuzziness Performance Index, F’   Normalized Classification Entropy, H’
Number of Subpopulations   Number of Subpopulations
2 3 4 5 6 7 8 9 10   2 3 4 5 6 7 8 9 10
1.5 0.060 0.138 0.083 0.090 0.099 0.147 0.176 0.129 0.124   0.079 0.143 0.089 0.091 0.092 0.122 0.137 0.104 0.099
1.6 0.081 0.167 0.117 0.129 0.139 0.190 0.223 0.186 0.175   0.107 0.176 0.126 0.132 0.134 0.164 0.179 0.154 0.143
1.7 0.104 0.197 0.156 0.174 0.187 0.238 0.272 0.236 0.234   0.140 0.212 0.168 0.178 0.182 0.210 0.224 0.202 0.196
1.8 0.131 0.230 0.198 0.223 0.286 0.289 0.344 0.317 0.307   0.176 0.251 0.213 0.229 0.265 0.260 0.291 0.265 0.256
1.9 0.160 0.264 0.241 0.274 0.337 0.384 0.394 0.372 0.364   0.214 0.291 0.259 0.280 0.315 0.337 0.339 0.317 0.309
2.0 0.191 0.300 0.286 0.325 0.389 0.432 0.442 0.426 0.421   0.254 0.331 0.306 0.332 0.365 0.384 0.385 0.368 0.362
2.1 0.223 0.336 0.330 0.376 0.433 0.477 0.487 0.477 0.476   0.293 0.371 0.352 0.382 0.413 0.429 0.429 0.417 0.413
2.2 0.256 0.371 0.374 0.425 0.479 0.520 0.529 0.523 0.526   0.332 0.410 0.397 0.431 0.458 0.471 0.471 0.462 0.461
2.3 0.289 0.406 0.416 0.472 0.554 0.560 0.574 0.565 0.573   0.370 0.447 0.440 0.476 0.516 0.511 0.518 0.504 0.507
2.4 0.322 0.440 0.457 0.516 0.595 0.596 0.608 0.602 0.605   0.407 0.482 0.481 0.519 0.552 0.548 0.553 0.542 0.539
2.5 0.354 0.473 0.496 0.556 0.625 0.630 0.639 0.634 0.639   0.442 0.515 0.519 0.558 0.584 0.582 0.585 0.575 0.573
2.6 0.386 0.504 0.532 0.593 0.653 0.660 0.668 0.664 0.671   0.475 0.547 0.555 0.593 0.613 0.614 0.616 0.607 0.606
2.7 0.416 0.533 0.566 0.626 0.680 0.688 0.694 0.692 0.700   0.505 0.576 0.588 0.625 0.641 0.643 0.643 0.636 0.636
2.8 0.445 0.561 0.598 0.656 0.703 0.714 0.718 0.718 0.734   0.534 0.603 0.618 0.653 0.666 0.669 0.669 0.663 0.671
2.9 0.472 0.587 0.627 0.682 0.725 0.737 0.740 0.741 0.750   0.562 0.628 0.646 0.678 0.689 0.694 0.692 0.688 0.690
3.0 0.499 0.611 0.654 0.706 0.745 0.758 0.761 0.762 0.772   0.587 0.651 0.672 0.702 0.711 0.716 0.714 0.711 0.713

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