The bird distribution data used in these analyses can be accessed via the National Biodiversity 543
Network Gateway (1968–1972 records: https://data.nbn.org.uk/Datasets/GA000600; 1988–1991 544
records: https://data.nbn.org.uk/Datasets/GA000147), whilst the climate data can be accessed via 545
the Climate Research Unit (http://www.cru.uea.ac.uk/cru/data/hrg/).
546 547
ACKNOWLEDGEMENTS 548
GR received funding from the Biotechnology and Biological Sciences Research Council 549
(BBSRC) and Old Mutual plc. DR received support under the Biological Records Centre 550
partnership between NERC (through the Centre for Ecology & Hydrology) and the Joint Nature 551
Conservation Committee. This paper is a contribution from the Imperial College grand 552
Challenges in Ecosystems and the Environment initiative. We thank Morgan Tingley and four 553
anonymous reviewers for some insightful comments on previous versions of this paper.
554 555
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Tables 677
Table 1: Prediction accuracy measures derived from temporal validation plots of the four 678
environmental functional responses of our virtual species 679
Prediction accuracy measures
AccTV CorTV BiasTV
Truth 0.930 0.996 -0.004
Incomplete 0.789 0.976 0.213
Collinear 0.603 0.993 -0.424
Incomplete and Collinear 0.424 -0.187 -0.271
680 681 682 683 684 685 686
687 688 689 690 691 692 693 694
Figures 695
696
Fig. 1 697
698
699
Figure 1: Four alternative environmental functional responses of a virtual species to three 700
simulated variables over a simplified landscape of 30 x 30 grid cells. Right panels show 701
simulated values for (a) temperature, (b) precipitation, (c) covar across the simplified landscape;
702
hotter colours indicate higher values (see figure legend). Right panels show how probability of 703
presence varies with (d) temperature, (e) precipitation, (f) covar (whilst keeping all other 704
variables constant at 0) according to each functional response – the Truth (thick black), the 705
Incomplete model (orange), the Collinear model (blue), and the Incomplete and Collinear model 706
726
Fig. 2 727
Figure 2: Quantifying the agreement between observed distribution changes and weighted 728
changes in modelled probabilities of presence (Δmweighted) between time periods t and t + 1 for 729
the four functional responses of our virtual species using TV plots. (a) Observed distributional 730
changes in simulated space of our virtual species (gains, losses, stable presences and stable 731
absences) between time periods. (b) Δmweighted values across the landscape according to the true 732
functional response of our virtual species. Bluer and redder colours indicate increases and 733
decreases in probability of presence, respectively. (c) TV plot for the true functional response of 734
our virtual species. Shown are the model temporal validation curve (thick black) – the sum of the 735
plotted gain function (blue curve) and loss function (red curve) – and confidence intervals of ± 2 736
standard errors of the mean (orange). The dashed black line represents the expectation for an 737
ideal temporal validation curve. The rug plots show model values at observed gain sites (blue, 738
top of the plot), loss sites (red, bottom of the plot) and stable absences/losses (grey, top of the 739
plot) and stable presences/gains (grey, bottom of the plot). (d-f) TV plots (top panels) and 740
Δmweighted (bottom panels) for (d) the Incomplete model, (e) the Collinear model, and (f) the 741
Incomplete and Collinear model.
742
743 744 745 746 747 748 749 750
751
Fig. 3 752
753 754
Figure 3: Visualisations of the three measures of prediction accuracy from TV plots (AccTV, 755
CorTV and BiasTV), exemplified using the TV plot for the Collinear model. (a) AccTV equals 1 756
minus the mean absolute distance between the model’s and the ideal y values (black lines), 757
weighted by the corresponding x values, at each observed site (tick marks). (b) CorTV is the 758
Pearson’s r coefficient between the model’s and the ideal y values, weighted by the 759
corresponding x values, at each observed site (tick marks). (c) BiasTV is the difference between 760
the area under the model curve (thick black) and the area under the ideal curve (dashed black); it 761
is equivalent to the dark grey minus the light grey area. Note that observed sites shown in scatter 762
and rug plots have been subsampled to aid visualisation.
763
764 765 766 767 768 769 770 771 772 773 774 775 776
777
Fig.4 778
779 780 781 782 783 784
Figure 4: Sensitivity analysis of the effect of species’ initial prevalence, magnitude and spatial 785
extent of environmental change on (a) AccTV, (b) CorTV, and (c) BiasTV measured from TV plots 786
of the four functional responses of our virtual species. Initial prevalence is the number of 787
species’ presences in t divided by the total number of grid cells (n = 25). Magnitude of 788
environmental change corresponds to the standard deviation of the normal distribution from 789
which we sampled environmental change values (n = 25). Spatial extent of change is the number 790
of grid cells over which we sampled environmental change divided by the total number of grid 791
cells (n =30). For each measure, values shown represent the mean values of 100 randomisations 792
of each alternative environmental scenario.
793
794 795 796 797 798 799 800 801 802 803 804 805 806 807 808
809
Fig. 5 810
811
Figure 5: Temporal validation of a climate-based species distribution model of the Pied Wagtail 812
across Great Britain between t and t +1. (a) Observed changes in the distribution of the Pied 813
Wagtail between time periods. (b) Weighted changes in modelled probability of presence 814
(Δmweighted) from a climate-based SDM. Bluer and redder colours indicate increases and 815
decreases in probability of presence, respectively. (c) TV plot of the climate-based SDM. Shown 816
are the model temporal validation curve (thick black) – the sum of the plotted gain function (blue 817
curve) and loss function (red curve) – and confidence intervals of ± 2 standard errors of the mean 818
(orange). The dashed black line represents the expectation for an ideal temporal validation curve.
819
The rug plots show model values at observed gain sites (blue, top of the plot), loss sites (red, 820
bottom of the plot) and no-gain and no-loss sites (grey, top and bottom of the plot).
821
822
Fig. 6 823
Figure 6: Temporal validation of a climate-based species distribution model of the Turtle Dove 824
across Great Britain between t and t +1. (a) Observed changes in the distribution of the Turtle 825
Dove between time periods. (b) Δmweighted from a climate-based SDM. Bluer and redder colours 826
indicate increases and decreases in probability of presence, respectively. (c) TV plot of the 827
climate-based SDM. Shown are the model temporal validation curve (thick black) – the sum of 828
the plotted gain function (blue curve) and loss function (red curve) – and confidence intervals of 829
± 2 standard errors of the mean (orange). The dashed black line represents the expectation for an 830
ideal temporal validation curve. The rug plots show model values at observed gain sites (blue, 831
top of the plot), loss sites (red, bottom of the plot) and no-gain and no-loss sites (grey, top and 832
bottom of the plot).
833