Species selection and model parameterisation

I was primarily interested in species with the potential to expand their distributions in response to climate change, and so I only modelled southerly-distributed species (Table A5.1.1). Thus

northern species, migrants and ubiquitous species were excluded (for a species to be considered ubiquitous it must have at least one 10 km resolution record in every 100 km grid square of mainland Britain in 1970-82, according to distributions in Asher et al., 2001). Further criteria for species selection are described below.

Climate suitability, habitat availability and the initial distribution of occupied areas (used to seed the model) are all species-specific parameters. Maximum carrying capacity was kept the same across species, and dispersal ability and maximum population growth rate (Rmax) were varied in

the same way among species to examine their impact on range expansion. Parameterisation of each variable is described below.

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5.3.1.1 Climate suitability

Species’ climate envelopes were determined using European climate and species’ distribution data (excluding Britain) and the annual climate suitability for each species was then projected for Britain at a 10 km grid resolution (see Chapter 4 for details), providing species-specific annual gridded data at 10 km grid resolution. Species were excluded from the analysis if it was not possible to determine the availability of suitable climate in Britain from European distribution data (five species excluded, see below). For each species, climate suitability was projected on a scale from zero (unsuitable) to one (suitable), and a ‘climate threshold’ was identified for each species, which was the minimum climatic suitability value at which a species was expected to achieve reproductive replacement (i.e. R = 1). I would expect that species’ populations would occur only where climate suitability was projected to be at or above the climate threshold (as below this threshold populations are expected to decline). I would also expect that some species may fail to occupy all areas in Britain which are predicted to be climatically suitable (e.g. due to limited habitat availability, inter-specific interactions and/or dispersal constraints). I therefore determined the climate envelope fit for each species in Britain using sensitivity measures, where sensitivity quantifies the proportion of the observed distribution of a given species projected to be at, or above, the climate threshold, but this measure does not consider the proportion of unoccupied but climatically suitable squares. Thus the sensitivity measure assumes that a species must have suitable climate where it is present, but suitable climate may also exist where the species is absent. For each species, I calculated the mean projected climate suitability of each 10 km grid cell in Britain for the period 1970-82 and used the observed species distribution in 1970- 82 to calculate the sensitivity of each species’ climate layer (i.e. the proportion of occupied 10 km grid squares which had a projected climate suitability that was at or above the climate threshold). I then excluded four species (Aricia agestis, Melanargia galathea, Polyommatus bellargus and

Polyommatus coridon) with a sensitivity of < 0.6, for which many of the observed distribution

records in 1970-82 fell outside the region predicted to be climatically suitable. This suggests that the climate models for these four species were unreliable. A fifth species, Melitaea cinxia, was excluded as the majority of its populations occur on islands/coasts (Isle of Wight, Guernsey and Alderney; Asher et al., 2001) which were not adequately covered by the climate data. The remaining 28 species (Table A5.1.1) had a sensitivity of > 0.8 (27/28 remaining species had a sensitivity of > 0.95), indicating that the climate models parameterised from their European (excluding Britain) distributions gave an accurate representation of the regions that were climatically suitable for them in Britain in the 1970s.

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5.3.1.2 Habitat availability

Habitat availability was determined from Land Cover Map 2007 (Morton et al., 2011) using species-specific habitat associations identified in Chapter 3 (see Appendix 3) and assuming that each species was able to reach its maximum density in each habitat type it used (following

population growth). Species’ habitat availability (quantified as the proportion of 25 m grid squares in the 100 km squares of the species’ distribution containing suitable habitat, to avoid computing habitat availability beyond the species’ current range) varied among the 28 study species. An overall mean of 0.0712 (7%; median = 0.0648) of the land surface was deemed suitable, averaged across species, ranging from a minimum of 0.0004 (0.04% of land surface deemed suitable for

Thymelicus acteon) to a maximum of 0.1828 (18% of land surface deemed suitable for Gonepteryx rhamni).

5.3.1.3 Initial distribution area for seeding models

Species’ seed distributions were the observed distribution in 1970-82 at a 10 km resolution. Each model run was seeded by randomly allocating individuals to 1 km grid cells containing suitable habitat until 70% of the maximum density was reached within the 1 km grid. This was an arbitrary threshold selected to allow the population in each seeded cell to either increase or decrease (rather than already be at maximum carrying capacity) at the start of the model run.

5.3.1.4 Carrying capacity

I set the maximum grid cell carrying capacity at 1000 individuals (this was a trade-off between high densities to promote population persistence and low densities to promote faster model runs). This was kept constant across all species for all analyses.

5.3.1.5 Population growth rate

I varied the maximum population growth rate (Rmax) in the same way for each species. From

published literature the intrinsic rate of population increase (r) has been calculated to be between 0.2 and 0.4 for three generalist butterfly species in Britain (Pararge aegeria, Aphantopus

hyperantus and Pyronia tithonus; Willis et al. (2009b). Since R = er, I varied the intrinsic rate of population increase (r) from 0 to 1.5 at intervals of 0.1, and calculated the corresponding Rmax

values (i.e. Rmax varied from 1.0 to 4.48). This provided a range of Rmax values that probably

encompassed the likely range of Rmax values among the butterfly study species, and allowed the

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5.3.1.6 Dispersal ability

I also varied dispersal in the same way for each species. I set short-distance dispersal to a mean distance of 100 m and long-distance dispersal to a mean of 5000 m, and examined the effect of dispersal by varying the proportion of individuals following long distance dispersal. The dispersal ability selected for my initial analysis was the proportion of individuals following long distance dispersal = 0.01 (i.e. 1% of individuals showing displacement movement), and I varied dispersal through 0.0001, 0.001, 0.01 and 0.1 allocated to long-distance dispersal for further analyses (Table 5.1). This captured a range of dispersal abilities from highly sedentary (0.0001; 0.01% of individuals showing long-distance movement) to highly mobile (0.1; 10% of individuals showing long-distance movement). The aim was to encompass a similar magnitude of variation in dispersal ability as existed in species-specific habitat availability (habitat availability varied from 0.04% through to 18% of land surface containing suitable habitat, see above), in order to allow as direct a comparison as possible between the two variables.

Table 5.1. The range of values used to parameterize the model for all 28 study species (listed in

Table A5.1).

Parameter Value Maximum density in 1 km grid cells that

contain all suitable habitat

1000 Short distance dispersal mean 100m Long distance dispersal mean 5000m Proportion following long-distance

dispersal

0.0001, 0.001, 0.01, 0.1 Density of seeded cells 0.7 x max density

Rmax 1.00, 1.11, 1.22, 1.35, 1.49, 1.65, 1.82, 2.01,

2.23, 2.46, 2.72, 3.00, 3.32, 3.67, 4.06, 4.48 (corresponding to values of r ranging from 0 to 1.5 at intervals of 0.1)

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