Appendix Chapter
A3.4 SUPPLEMENTARY REFERENCES
5.3 SUPPLEMENTARY INFORMATION FOR FIGURE A5.2
In order to ascertain the importance and direction of any interactive effects between explanatory variables (e.g. do species with greater habitat availability benefit more from increased dispersal than species with low habitat availability), I applied a multi-model inference approach to each value of Rmax separately. The global model included change in distribution area as the response
variable, species was included as a random variable, and dispersal ability, habitat availability, climate suitability and starting distribution area were potential explanatory variables, with all two- way interactions included. The best-fit and averaged models for each value of Rmax are presented
in full in Table A5.1.3.
Starting distribution area did not appear in the top models for all values of Rmax, however when it
was an important variable, it consistently showed a negative interaction with dispersal ability and habitat availability, and a positive interaction with climate suitability (Table A5.1.3). Thus, species with small starting distribution areas showed a greater increase in rate of distribution expansion given higher dispersal ability and habitat availability than did species with large starting
distribution areas. In contrast, the species with large starting distribution areas benefited
relatively more from increased climatic suitability than did species with small starting distribution areas.
Other interactions were less consistent as Rmax was varied, therefore I have selected three
examples (Rmax = 1, 1.1 and 1.6) to present the interactions between dispersal, habitat and climate
as Rmax is varied (Fig A5.2.1). To illustrate interactions, I used the best-fitting model to predict
distribution change for (i) variation in climate suitability at minimum, median and maximum habitat availability (from across species, min = 0.0004, median = 0.0648, max = 0.1824; starting distribution area and dispersal ability were kept constant by using the median starting distribution area and proportion following long distance dispersal = 0.01 respectively) (Fig A5.2.1a,d,g); (ii) variation in climatic suitability at each of the four dispersal abilities (keeping starting distribution area and habitat availability constant by using the median values of each) (Fig A5.2.1b,e,h); and (iii) variation in habitat availability at each of the four dispersal abilities (keeping starting distribution area and climate suitability constant by using the median values of each) (Fig
A5.2.1c,f,i). I then fitted regression lines to the predicted values to highlight the direction of each interaction.
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At Rmax=1 (reproductive replacement), all of the interactions were relatively weak, given that all
species were either contracting slightly or expanding slightly (Fig A5.2.1a-c). At low habitat availability, increased dispersal ability actually resulted in greater distribution retraction (through high dispersal-related mortality), whereas at high habitat availability, increased dispersal ability resulted in greater distribution expansion (Fig A5.2.1c).
At Rmax=1.1, the effects were much larger, as some species continued to decline, whereas species
with favourable combinations of habitat, dispersal and climate could expand (Fig A5.2.1d-f). Species with high climate suitability showed relatively greater increases in distribution expansion given greater habitat availability (Fig A5.2.1d) or greater dispersal ability (Fig A5.2.1e), compared to species with low climate suitability. Similarly, species with high habitat availability benefited more from increased dispersal ability than did species with low habitat availability (Fig A5.2.1f). At Rmax=1.6, effects were larger still (Fig A5.2.1g-i). As before, species with high climate suitability
or high habitat availability benefited relatively more from increased dispersal ability compared to species with low climate suitability (Fig A5.2.1h) or habitat availability (Fig A5.2.1i).
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