2 Local versus Regional Factors Infl uencing Habitat Occupancy and Population Processes
2.1 Partitioning methods for assessing fragmentation effects
Variation partitioning and hierarchical partitioning are statistical methods that allow unequivocal decomposition of variation in a response variable among explanatory variables or groups of variables (Chevan and Sutherland, 1991; Borcard et al., 1992). These methods thus provide better understanding of the relative importance of different explanatory variables than traditional stepwise regression models (MacNally, 2000). A shortcoming of the latter methods is that in the case of multicollinear data-sets, variables with higher statistical significance tend to receive more attention than other variables that may be ecologically more meaningful (Graham, 2003; Heikkinen et al., 2005).
We illustrate here with an example on the clouded apollo butterfly (Parnassius mnemosyne) how variation in habitat occupancy and abundance can be decomposed into independent and joint effects of three groups of variables (Heikkinen et al., 2005). The data on butterfly occupancy and abun- Table 8.2. Binomial general linear models (GLMs) for factors potentially explaining the
incidence of signifi cant isolation effect, stronger impact of regional over local factors (REGIONAL), and equal importance of local and regional factors (UNDETERMINED) in 38 published studies on insects (Table 8.1). Model coeffi cients with standard errors (SE) and statistical signifi cance (χ2 test) are given.
Explanatory ISOLATION (n = 35 ) REGIONAL (n = 36) UNDETERMINED (n = 36) variablea Coeff. p value Coeff. p value Coeff. p value
SCOPE −2.15 ± 0.92 0.019 −2.24 ± 1.22 0.066
LANDECO 1.61 ± 0.85 0.058
HYPOTHESIS 2.14 ± 1.22 0.079
aExplanatory variables: (i) measure of connectivity (nearest neighbour, buffer or Eq. 8.1); (ii) type of study (observational or experimental); (iii) binary variable indicating whether the study used a landscape ecological description of landscape structure (LANDECO; typically some description of habitat complexity within a buffer zone); (iv) taxonomic scope of the study (SCOPE; single species or multispecies); (v)
metapopulation approach versus a more general comparison between local and regional factors (HYPOTHESIS; metapopulation studies focused on testing habitat patch area and connectivity effects against local quality);
(vi) spatial scale of the study (in km);and (vii) year of publication (1993–2005).
dance and on the explanatory variables were collected in 1999 from 2408 grid squares 50 × 50 m in size and located along a river valley in south-west Finland. The three groups of explanatory variables were: (i) larval and adult resources in each grid cell, including the abundance of the sole larval host plantCorydalis solida and nectar sources; (ii) habitat quantity and connectiv- ity, consisting of the coverage of the four main habitat types (semi- natural grassland, agricultural field, deciduous forest and coniferous forest) in each grid cell, and connectivity calculated for the breeding habitat (semi-natural grass- land) using Eq. 8.1 but ignoring habitat occupancy (thus the pj values were set to 1); and (iii) microclimate, including radiation and average wind speed in each grid cell (details in Luoto et al., 2001). We also included in the analysis an autocovariate for the response variable, describing the number of but- terflies in the surrounding grid cells and calculated with Eq. 8.1 including habitat occupancy (pj).
The variation partitioning method (Borcard et al., 1992) was used to decompose variation in grid occupancy among the three groups of explana- tory variables. Variation in the occupancy data was partitioned using a series of partial binomial generalized linear models. Quadratic terms of the predictors were included to take into account curvilinear relationships between butter- fly occupancy and the predictor variables. Partitioning among three environ- mental matrices results in eight fractions of variance (Liu, 1997; Anderson and Gribble, 1998). Variation in the abundance data was decomposed in a similar manner, but using only the 349 grid cells in which P. mnemosyne was present as well as a series of partial regressions with redundancy analysis.
The largest variance fractions in the occupancy data were the independent effects of the habitat quantity variables (26.4%; Fig. 8.1a), the joint effect of habitat quantity and resources (17.3%) and the joint effect of all three groups of predictors (9.8%). The independent effects of resources and microclimate were small though still statistically significant. Fitting the autocovariate as an additional variable to the final model resulted in a statistically significant (p < 0.001) deviance change, accounting for 3.0% of the deviance in butterfly occupancy. In the results for abundance data, the independent effect of habitat quantity variables (9.2%) and the joint effect between them and the resource variables (4.3%) were the largest fractions (Fig. 8.1b). The independent effects of resources and microclimate were higher than in the corresponding results for habitat occupancy.
The hierarchical partitioning method (Chevan and Sutherland, 1991) considers all possible models in a hierarchical multivariate regression set- ting. This method involves calculation of the increase in the fit of all models, including a particular predictor, compared with the respective models with- out that variable, and averaging the improvement in the fit across all possible models with the focal predictor. Thus, hierarchical partitioning provides an estimate for each explanatory variable of the variance fractions that are inde- pendent and joint with all other variables (Chevan and Sutherland, 1991;
MacNally, 2000). Hierarchical partitioning was conducted using the hier.part package (MacNally and Walsh, 2004). A drawback of the current implemen- tation of this package is that it assumes monotonic relationships between
the response and predictor variables. Some predictor variables were trans- formed to improve the linearity of their relationships with butterfly variables (Heikkinen et al., 2005).
In the occupancy data, the independent effects of all variables were statis- tically significant, although some made only a small contribution (Fig. 8.2a).
Consistent with variation partitioning, cover of semi-natural grassland and habitat connectivity made the highest independent contributions, and the independent contributions of the autocovariate and larval host plant abun- dance were also high. The negative joint contribution of radiation indicates that the majority of the relationships with other predictors are suppressive rather than additive (Chevan and Sutherland, 1991). In the abundance data, cover of semi-natural grassland made the largest independent contribu- tion, followed by the autocovariate and nectar plant abundance (Fig. 8.2b).
Independent effects of all predictors were statistically significant but a con- siderable part of the total variation was accounted for by their joint effects (Fig. 8.2b).
In summary, the independent effect of habitat quantity variables (habitat area and connectivity) accounted for the largest fraction of the variation in the clouded apollo habitat occupancy and abundance, though habitat con- nectivity made a major contribution for habitat occupancy only. Perhaps not surprisingly, the independent effects of resources and microclimate were greater for abundance than occupancy. A considerable amount of variation in the butterfly data was accounted for by the joint effects of the predictors and may thus be causally related to two or all three groups of variables.
Abundance of the butterfly in the surroundings of the focal grid cell (the
Habitat (H) 9.2%
Resources (R) 3.5%
1.2% 0.5%
Undetermined variation (U) 74.8%
3.5%
Microclimate (M) 4.3%
3.0%
(b)
Habitat (H)
26.4% Resources (R)
1.4%
2.2% 0.3%
Undetermined variation (U) 40.4%
2.2%
Microclimate (M) 17.3%
9.8%
(a)
Fig. 8.1. Variation partitioning for (a) habitat occupancy and (b) local abundance of the butterfl y Parnassius mnemosyne. Percentage of the explained variation is indicated for each fraction.
Statistical models for habitat occupancy were built as generalized linear models with binomial errors and the signifi cance of the variables (linear and non-linear effects) in each group was tested with an F ratio test. Abundance data were analysed using a series of partial regressions with redundancy analysis. (From Heikkinen et al., 2005.)
Fig. 8.2. The independent and joint contributions (as percentages of the total variance explained) of the predictor variables for (a) habitat occupancy and (b) local abundance of Parnassius mnemosyne, estimated with hierarchical partitioning. Habitat occupancy was analysed using binomial logistic regression and local abundance using linear regression. (From Heikkinen et al., 2005.)
Agricultural field Semi-natural grassland Coniferous forest Deciduous forest
Radiation Windiness Host plant Nectar plant Connectivity Autocovariate
0 5 10 15 20 25
(a)
(b)
Independent Joint 0
5 10 15 20 25
Explained variance (%)
autocovariate) had a significant effect in all analyses, independently of the effects of other predictors. This result points to the role of migration in influ- encing habitat occupancy and local abundance.