@article {VerHoef2007QuasiPoisson,
	title = {Quasi-Poisson vs. negative binomial regression: how should we model overdispersed count data?},
	journal = {Ecology},
	volume = {88},
	number = {11},
	year = {2007},
	month = {November},
	pages = {2766{\textendash}2772},
	abstract = {Quasi-Poisson and negative binomial regression models have equal numbers of parameters, and either could be used for overdispersed count data. While they often give similar results, there can be striking differences in estimating the effects of covariates. We explain when and why such differences occur. The variance of a quasi-Poisson model is a linear function of the mean while the variance of a negative binomial model is a quadratic function of the mean. These variance relationships affect the weights in the iteratively weighted least-squares algorithm of fitting models to data. Because the variance is a function of the mean, large and small counts get weighted differently in quasi-Poisson and negative binomial regression. We provide an example using harbor seal counts from aerial surveys. These counts are affected by date, time of day, and time relative to low tide. We present results on a data set that showed a dramatic difference on estimating abundance of harbor seals when using quasi-Poisson vs. negative binomial regression. This difference is described and explained in light of the different weighting used in each regression method. A general understanding of weighting can help ecologists choose between these two methods.},
	keywords = {distribution, ecology, overdispersion, poisson, statistics},
	issn = {0012-9658},
	url = {http://www.biomedexperts.com/Abstract.bme/18051645},
	author = {Ver Hoef, Jay M. and Boveng, Peter L.}
}
@article {Potts2006Comparing,
	title = {Comparing species abundance models},
	journal = {Predicting Species Distributions - Results from a Second Workshop on Advances in Predictive Species Distribution Models, held in Riederalp, Switzerland, 2004},
	volume = {199},
	number = {2},
	year = {2006},
	month = {November},
	pages = {153{\textendash}163},
	abstract = {Five regression models (Poisson, negative binomial, quasi-Poisson, the hurdle model and the zero-inflated Poisson) were used to assess the relationship between the abundance of a vulnerable plant species, Leionema ralstonii, and the environment. The methods differed in their capacity to deal with common properties of ecological data. They were assessed theoretically, and their predictive performance was evaluated with correlation, calibration and error statistics calculated within a bootstrap evaluation procedure that simulated performance for independent data.The hurdle model performed best, with the highest correlations between the observed and predicted abundances. This model was also well calibrated, giving the closest agreement between observed and predicted abundances. The negative binomial was the worst performing model. It had weaker correlations than the other models and resulted in a strong, inconsistent bias in predictions. The standard Poisson model which accommodates neither zero-inflation nor over-dispersion gave accurate estimates of regional population abundance, but at the individual population level they were inconsistent and biased.The strong performance of the hurdle model, coupled with theoretical properties that suit it for these data and for the ecology of this species, suggest that it is a useful alternative to other modelling methods. The gains in performance have practical advantages where predictions are used by conservation planners to understand population dynamics or to assess the relative risks of alternative management scenarios.},
	keywords = {distribution, ecology, modelling, poisson},
	doi = {10.1016/j.ecolmodel.2006.05.025},
	url = {http://dx.doi.org/10.1016/j.ecolmodel.2006.05.025},
	author = {Potts, Joanne M. and Elith, Jane}
}
@article {TiteuxInclusion,
	title = {Inclusion of soil data improves the performance of bioclimatic envelope models for insect species distributions in temperate Europe},
	journal = {Journal of Biogeography},
	volume = {9999},
	number = {9999},
	year = {Submitted},
	abstract = {Aim To analyse the effect of the inclusion of soil and land-cover data on the performance of bioclimatic envelope models for the regional-scale prediction of butterfly (Rhopalocera) and grasshopper (Orthoptera) distributions. Location Temperate Europe (Belgium). Methods Distributional data were extracted from butterfly and grasshopper atlases at a resolution of 5 km for the period 1991{\textendash}2006 in Belgium. For each group separately, the well-surveyed squares (n = 366 for butterflies and n = 322 for grasshoppers) were identified using an environmental stratification design and were randomly divided into calibration (70\%) and evaluation (30\%) datasets. Generalized additive models were applied to the calibration dataset to estimate occurrence probabilities for 63 butterfly and 33 grasshopper species, as a function of: (1) climate, (2) climate and land-cover, (3) climate and soil, and (4) climate, land-cover and soil variables. Models were evaluated as: (1) the amount of explained deviance in the calibration dataset, (2) Akaike{\textquoteright}s information criterion, and (3) the number of omission and commission errors in the evaluation dataset. Results Information on broad land-cover classes or predominant soil types led to similar improvements in the performance relative to the climate-only models for both taxonomic groups. In addition, the joint inclusion of land-cover and soil variables in the models provided predictions that fitted more closely to the species distributions than the predictions obtained from bioclimatic models incorporating only land-cover or only soil variables. The combined models exhibited higher discrimination ability between the presence and absence of species in the evaluation dataset. Main conclusions These results draw attention to the importance of soil data for species distribution models at regional scales of analysis. The combined inclusion of land-cover and soil data in the models makes it possible to identify areas with suitable climatic conditions but unsuitable combinations of vegetation and soil types. While contingent on the species, the results indicate the need to consider soil information in regional-scale species{\textendash}climate impact models, particularly when predicting future range shifts of species under climate change.},
	keywords = {distribution, insects, model, prediction},
	author = {Titeux, Nicolas and Maes, Dirk and Marmion, Mathieu and Luoto, Miska and Heikkinen, Risto K.}
}
