Weather data were obtained from the Meteorological Office station at St Catherine’s Point Lighthouse (SZ497753). The June mean maximum temperature was used in the analysis (i.e. the mean of the daily maxima; a measure of the warmth of June days), as June coincides with the peak adult emergence and egg laying period. This data was used to assess the relationship between temporal variation in ambient air temperature and larval web abundance, and to test interactions with other parameters. Air temperature ranged from 16.2 degrees (1998 and 2002) to 18.4 degrees (2006), with a median of 17.3 degrees.
Statistical Analysis
The data comprise 803 estimates (patch-year combinations) of larval web abundance on 70 patches at 8 sites over 15 years. Habitat quality, area and isolation all vary among patch - year combinations, although the inter-annual variation in all three variables is small. Ambient temperature varies among years only.
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The aim of this study was to determine Glanville fritillary abundance (number of larval webs) as a function of annual variations in temperature (mean maximum June temperature from the
previous year - i.e. the temperature at the time the eggs were laid), area, isolation and habitat
quality and assess which factor was most important. Additionally, variation in annual temperature was tested as an interaction with the other parameters, by using both multiple regression and mixed effect models. Prior to the analysis, both the parameters of area and isolation were transformed by natural logarithm.
Initially, abundance was modelled as a linear function of temperature, area, isolation and habitat quality using General Linear Model (GLM) with quasipoisson errors as the data were overdispersed. Significance for each parameter was assessed using an F-test (α=0.05) to compare pairs of nested models (with and without the parameter of interest). Secondly, as the data comprises repeated measures across 803 patch – year combinations (with temperature a constant between patches and sites), all parameters were included in a Generalised Linear Mixed Effects (GLME) model with patch, site and year as random effects to allow for a lack of independence among individual abundance estimates (Cowlishaw et al. 2009; Isaac et al. 2011b), and to control for variation among patches not accounted for by the landscape parameters. Patch identity is nested within site, and year is crossed with the other random effects. The models also included a random effect at the observation level (repeat measures on the same patch), to control for the fact that abundance data were overdispersed (Roy et al. 2012). Poisson errors were used in the mixed effect model as the data comprised of actual counts of larval webs, rather than using normal errors on log-transformed counts (O’Hara & Kotze 2010). Significance for each parameter was also assessed using p values (α=0.05) from Wald Z tests, as recommended by Bolker et al (2009). These models assessed the importance of each parameter in determining butterfly abundance [H1]. All models were fit in R, with GLMEs employing the lme4 package (Bates & Maechler 2010; R Development Core Team 2010).
Secondly, to the models above I added an interaction between temperature and each of the other three fixed effects (area, isolation, quality) as single, separate predictors, to ascertain whether the strength of the relationship of the three landscape factors varied depending on air temperature [H2]. As in the previous chapter, I estimated the effect sizes as the range of fitted abundances over the range of observed variation in the parameter of interest.
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Therefore, I ran a total of eight models: a GLM and a GLME model, both including temperature, area, isolation and habitat quality as explanatory variables [H1]. A further three GLMs (one for each landscape parameter – area, isolation and habitat quality) and three GLMEs models were fitted to explore interaction effects between landscape parameters and temperature [H2].
Results
The results show that there are statistically significant, strong positive relationships between number of Glanville fritillary larval webs and habitat quality, ambient temperature and area. There is also a statistically strong negative relationship between web numbers and isolation (Figure 2.2 and Tables 2.2 & 2.3).
Figure 2.2. A scatterplot showing the relationship between Glanville fritillary numbers (logex) and
habitat quality, temperature (mean maximum June temperature at the time the eggs were laid), area (logex) and isolation (logex).
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Table 2.2. The results of a multiple regression (GLM) of Glanville fritillary web numbers against habitat quality, temperature, isolation and area (with quasipoisson errors). Dispersion parameter = 57.1.
Estimate Std. Error t value P value Intercept -5.917 1.686 -3.508 <0.001 Habitat Quality 0.046 0.006 7.267 <0.001 Temperature 0.288 0.095 3.033 <0.001 log(Isolation) -0.152 0.032 -4.773 <0.001 log(Area) 0.453 0.055 8.202 <0.001
Table 2.3. The results of a linear mixed model of Glanville fritillary web numbers against habitat quality, temperature, isolation and area (with poisson errors and observation-level random effect).
Estimate Std. Error z value P value Intercept -13.453 4.918 -2.735 0.006 Habitat Quality 0.060 0.012 5.156 <0.001 Temperature 0.574 0.274 2.099 0.036 log(Isolation) -0.174 0.041 -4.220 <0.001
log(Area) 0.513 0.180 2.842 0.004
Web abundance was higher in areas of better quality habitats in both the GLM (Table 2.2) and GLME (Table 2.3). This suggests that for the Glanville fritillary on the ‘average’ site, an increase of 1 on the habitat quality scale is associated with an increase of 4.7% (e0.046 = 1.047) in the GLM or 6.2% (e0.06 = 1.062) in the GLME, corresponding to a 9 - 18 fold difference in fitted in abundance between the highest and lowest quality habitat (observed range 0-48).
An increase in ambient air temperature also increases web abundance within both the GLM and GLME. Thus, across the range of temperatures (2.2 degrees) web counts increase by a factor of e0.288*2.2 = 1.88 (in the GLM) or e0.574*2.2 = 3.5 (in GLME) fold fitted difference in abundance from the coldest to the warmest years.
Area also shows a strong, positive relationship within the GLM and the GLME. Thus, an increase of 1 on the ln(area) scale corresponds to an increase in abundance, on the ‘average’ site, of between e0.45 = 57% (GLM) and e0.51 = 67% (GLME), or 45% - 51% for a doubling of area. From the smallest patch (45 m2) to the largest (25000 m2), this corresponds to an increase of over 17-26 fold increase in web abundance.
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Isolation has a strong negative influence on abundance within the GLM and GLME. An increase of 1 on the ln(isolation) scale corresponds to an change in abundance on the ‘average’ site of between e-0.15 = -14% (GLM) and e-0.17 = -16% (GLME), or 15% - 17% decrease for a doubling of isolation. From the most isolated patch (10000 m) to the least isolated (1 m), this corresponds to a 4-5 fold difference in web abundance.
The results from the GLME also suggest that the largest component of variation is patch within site (50% of the total), site contributes 16% and year just 9%, with the remainder attributable to observation-level variance. Therefore, the inter-annual variation (modelled in Chapter 1) is the smallest proportion of the variance total, and by substantially increasing the number of sites, and particularly patches within sites, this multisite study can explain a considerably higher proportion of the variation in abundance of the Glanville fritillary.