Linear Models With R Faraway Pdf 63
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We explored the most influential stand-scaled drivers of ectomycorrhizal, terricolous saprotrophic, and wood-inhabiting (main functional groups) macrofungal species richness in mixed forests by applying regression models. We tested 67 potential explanatory variables representing tree species composition, stand structure, soil and litter conditions, microclimate, landscape structure, and management history. Within the main functional groups, we formed and modeled guilds and used their drivers to more objectively interpret the drivers of the main functional groups. Terricolous saprotrophic fungi were supported by air humidity and litter mass. Ectomycorrhizal fungi were suppressed by high soil nitrogen content and high air temperature. Wood saprotrophs were enhanced by litter pH (deciduous habitats), deadwood cover, and beech proportion. Wood saprotrophic guilds were determined often by drivers with hidden effects on all wood saprotrophs: non-parasites: total deadwood cover; parasites: beech proportion; white rotters: litter pH; brown rotters: air temperature (negatively); endophytes: beech proportion; early ruderals: deciduous stands that were formerly meadows; combative invaders: deciduous tree taxa; heart rotters: coarse woody debris; late stage specialists: deciduous deadwood. Terricolous saprotrophic cord formers positively responded to litter mass. Studying the drivers of guilds simultaneously, beech was a keystone species to maintain fungal diversity in the region, and coniferous stands would be more diverse by introducing deciduous tree species. Guilds were determined by drivers different from each other underlining their different functional roles and segregated substrate preferences. Modeling guilds of fungal species with concordant response to the environment would be powerful to explore and understand the functioning of fungal communities.
Within species richness models, the biological interpretation of drivers is sometimes problematic: both the studied environment and the species composition of the modeled species group must be considered. Reviewing the environmental aspects, the relative influence of drivers depends on the scale of the investigation (Lilleskov and Parrent 2007); and regularly, different drivers emerge with significant effects along ecological (e.g., moisture or elevation; Sundqvist et al. 2013) and geographical (Bahram et al. 2018) gradients. Moreover, the importance of drivers always varies among habitats due to environmental heterogeneity (Stein et al. 2014), and those drivers that actually limit fungal growth can have disproportionately high influence (Jumpponen and Egerton-Warburton 2005). Focusing on the modeled species group, there is a potential source of misleading results when a group of functionally highly different species is tested instead of a functionally homogeneous species group. When modeling a functionally highly heterogeneous species group, there is a strong possibility to fail to detect concordant (statistically strong and clear) species response to the environment because each fungal species has different environmental requirements (Mori et al. 2016).
Working with functionally homogeneous species groups, models could reveal highly significant but scarcely interpretable drivers. Such drivers often have indirect effects on the studied species group. In this case, one can only hypothesize a suitable biological interpretation, which is a general problem in the evaluation of results in ecological modeling. To overcome this problem, we completed a strategic hierarchical subset of the three main macrofungal functional groups, created a nested data structure, modeled each subset separately with the same methods, and evaluated the drivers of subsets simultaneously to obtain additional evidence for an objective interpretation of the drivers of the main functional groups.
For the exploration of the relationships between species richness data and environmental variables, we built multiple regression models, applied general linear modeling (GLM) based on Faraway (2005, 2006), and used the statistical software R for Windows 3.0.1 (R Core Team 2013).
We classified the drivers revealed by the GLMs in Fig. 3 to separate the most important (determinative) ones from those of with marginal or probable indirect effects (Table 2). Checking the drivers for common occurrences in the same models, we marked (asterisk) three drivers in category A to have probable indirect effects on macrofungi in the region.
The group of all wood-inhabiting fungi was primarily determined by litter pH. To our knowledge, litter pH has never been detected as a driver of this functional group. Here, in 8 models of 11, litter pH was significant and selected together with drivers characterizing deciduous habitats. This provides some evidence that litter pH rather represents a general preference of deciduous habitats not the special impacts of litter pH per se. Another variable of probable indirect effects on wood-inhabiting fungi was moss cover, always with suppressing effects and acting as a follower of beech proportion (in 5 models out of 7). Working in shaded, beech-dominated habitats with a generally poor moss layer, Heilmann-Clausen and Christensen (2005) also confirmed this observation. Similarly, Scots pine proportion was always co-acted with beech proportion and rather had marginal effects on wood-inhabiting fungi. We found no drivers with probable indirect effects for terricolous saprotrophic and ECM fungi.
Our generally weaker models on ECM fungi can be explained by the following reasons: (i) we probably did not measure those environmental variables that really influence these species in the region, (ii) it is not yet clear which of these species form a guild and have similar environmental requirements, and (iii) it is highly probable that our model on all ECM fungi contains several guilds (species) that are driven principally by different environmental drivers. Deveautour et al. (2020) also suggested numerous guilds within ECM communities. It would be especially worthwhile for ECM fungi to find the environmental requirements of single species using linear regression models. With such models, we could define ECM guilds that consist of species with similar responses to the environment and thus better understand the functioning of the whole ECM community.
Due to limited literature data, it was not yet possible to form complete guilds within ECM and litter saprotrophic fungi according to species life history strategies; however, the presence of embedded guilds within these main groups was highly likely after comparing the explanatory power of models.
It would be worthwhile for all macrofungi to find the environmental requirements of each species using linear regression models or composing and modeling fungal guilds with species of similar substrate preferences or exploitation strategies. With such models, we could define fungal community components that consist of species with similar responses to the environment to better understand the fundamental roles of macrofungi in ecosystem functioning.
Coefficients from the regression models for both identity scales are given in Table 1, with their 95% confidence intervals. Where coefficients are not given for a factor, it means the effect was not retained following the model selection procedure described in the method. Coefficients indicate the change in the outcome variable associated with the change in level of each factor (effectively the mean difference between levels within the model, not the sample means). For both measures, there is a significant difference between scores relating to student and doctor identities, with those for doctor identity being higher. Additionally, men score lower on the importance scale than women, while strength scores are lower at the end of the year than at the beginning (sample means are in Table 2).
To determine the optimum development temperature (Topt) and the maximum development rate associated with this temperature (μmax) (see ), a non-linear curve-fitting approach was adopted using TableCurve 2D (v. 5.01, SYSTAT Software Inc., 2002, San Jose, California, USA) (Additional files 5, 6, 7) (see ). Topt and μmax were determined from the equations for the best fit curve, which differed among stages and between species (Table 1, Additional files 8 and 9). To compare Topt and μmax of An. arabiensis to that of An. funestus, one replicate for each temperature treatment was selected at random (without replacement) to provide 25 separate curves for overall development rate for each species and for each life stage. The equations used to obtain Topt and μmax for overall development and development of each stage across all 25 replicates are presented in Additional file 10. Except in a few cases (pupal development rates) these equations all had r2 values above 0.90. The same equations for all 25 replicates were chosen to minimize discrepancies when comparing Topt and μmax between species. Topt and μmax were then compared, for overall development and for each life stage, between the species using t-tests (R v. 2.15.1, R Foundation for Statistical Computing, Vienna, Austria).
Although development rate generally increases with increasing temperature up to the optimum [50, 51], high development rates are often accompanied by mortality and reduced population output [7, 50, 52]. In consequence, overall survival from egg to adult was recorded as the proportion of eggs that emerged as adults (expressed as a percentage). This % survival was recorded for all 25 replicates per temperature treatment. To assess differences in survival between the fluctuating temperature treatments and their constant mean (25°C), a generalized linear model with a binomial distribution of errors and logit link function was used (R v. 2.15.1). To illustrate the effect of temperature on survival of each species, mean percentage survival (± standard error) was plotted at each constant temperature and in a comparison between the two fluctuating temperatures and constant mean of 25°C. 2b1af7f3a8