How much is enough? Influence of number of presence observations on the performance of species distribution models

Species distribution modeling (SDM) can be useful for many applied purposes, e.g., mapping and monitoring of rare and endangered species. Sparse presence data are a recurrent, major obstacle to precise modeling of species distributions. Thus, knowing the minimum number of presences required to obtain reliable distribution models is of fundamental importance for applied use of SDM. This study uses a novel approach to assess the critical sample size (CSS) sufficient for an accurate prediction of species distributions with Maximum Entropy Modeling (MaxEnt). Large presence datasets for thirty insect species, ranging from generalists to specialists regarding their responses to main bioclimatic gradients, were used to produce reference distribution models. Models based on replicated subsamples of different size drawn randomly from the full dataset were compared to the reference model using the index of vector similarity distribution models. Models based on replicated subsamples of different size drawn randomly from the full dataset were compared to the reference model using the index of vector similarity (IVS). Two thresholds for IVS were determined based on comparison of nine reference models to random null models. The threshold values correspond to 0.95 and 0.99 probability that a model outperforms a random null model in terms of similarity to the reference dataset. For 90% of the species, clearly nonrandom models were obtained with less than 10 presence observations, and for 97% of the species with less than 15 presence observations. We conclude that the number of presence observations required to produce nonrandom models is generally low and, accordingly, that even sparse datasets may be useful for distribution modelling.

Sampling bias in presence-only data used for species distribution modelling: theory and methods for detecting sample bias and its effects on models

This paper provides a theoretical understanding of sampling bias in presence-only data in the context of species distribution modelling. This understanding forms the basis for two integrated frameworks, one for detecting sampling bias of different kinds in presence-only data (the bias assessment framework) and one for assessing potential effects of sampling bias on species distribution models (the bias effects framework). We exemplify the use of these frameworks to museum data for nine insect species in Norway, for which the distribution along the two main bioclimatic gradients (related to oceanicity and temperatures) are modelled using the MaxEnt method. Models of different complexity (achieved by use of two different model selection procedures that represent spatial prediction or ecological response modelling purposes, respectively) were generated with different types of background data (uninformed and background-target-group [BTG]). The bias assessment framework made use of comparisons between observed and theoretical frequency-of-presence (FoP) curves, obtained separately for each combination of species and bioclimatic predictor, to identify potential sampling bias. The bias effects framework made use of comparisons between modelled response curves (predicted relative FoP curves) and the corresponding observed FoP curves for each combination of species and predictor. The extent to which the observed FoP curves deviated from the expected, smooth and unimodal theoretical FoP curve, varied considerably among the nine insect species. Among-curve differences were, in most cases, interpreted as indications of sampling bias. Using BTG-type background data in many cases introduced strong sampling bias. The predicted relative FoP curves from MaxEnt were, in general, similar to the corresponding observed FoP curves. This indicates that the main structure of the data-sets were adequately summarised by the MaxEnt models (with the options and settings used), in turn suggesting that shortcomings of input data such as sampling bias or omission of important predictors may overshadow the effect of modelling method on the predictive performance of distribution models. The examples indicate that the two proposed frameworks are useful for identification of sampling bias in presence-only data and for choosing settings for distribution modelling options such as the method for extraction of background data points and determining the appropriate level of model complexity.

A strict maximum likelihood explanation of MaxEnt, and some implications for distribution modelling

Distribution modelling - research with the purpose of modelling the distribution of observable objects of a specific type - has become established as an independent branch of ecological science, with strong proliferation of approaches and methods in recent years. Since it was first made available to distribution modellers in 2004, the maximum entropy modelling method (MaxEnt) has established itself as a state-of-the-art method for distribution modelling. Default options and settings in the user-friendly Maxent software has become established as a standard practice for distribution modelling by MaxEnt.A mini-review of 87 recent publications in which MaxEnt was used with empirical data to model distributions showed that the ‘standard MaxEnt practice’ is followed by a large majority of users and questioned by few. However, the review also provides indications that MaxEnt models obtained by the standard practice are sometimes overfitted to the data used to parameterise the model; examples of cases in which simpler MaxEnt models with predictive performance do exist. Results of the review motivate strongly for a better understanding of the ecological implications of the maximum entropy principle, as a basis for choosing MaxEnt options and settings.This paper provides a thorough explanation of MaxEnt for ecologists, ending with a set of suggestions for improvements to the current practice of distribution modelling by MaxEnt. The explanation for MaxEnt given in the paper differs from previous explanations by being based on the maximum likelihood principle and by being based upon a gradient analytic perspective on distribution modelling. Four new findings are particularly emphasised: (1) that a strict maximum likelihood explanation of MaxEnt is possible, which places MaxEnt among regression methods in the widest sense; (2) that the true degrees of freedom for the residuals of a Max- Ent null model is N - n, the difference between the number of background and the number of presence observations used in the modelling; (3) that likelihood-ratio and F-ratio tests can be used to compare nested MaxEnt models; and (4) that subset selection methods are likely to be preferential to shrinkage methods for model selection in MaxEnt. Methods for internal model performance assessment, model comparison, and interpretation of MaxEnt model predictions (MaxEnt output), are described and discussed. Two simulated data sets are used to explore and illustrate important issues relating to MaxEnt methodology.Arguments for development of a generally applicable ‘consensus MaxEnt practice’ for spatial prediction modelling are given, and elements of such a practice discussed. Five main additions or amendments to the ʻstandard MaxEnt practiceʼ are suggested: (1) flexible, interactive tools to assist deriving of variables from raw explanatory variables; (2) interactive tools to allow the user freely to combine model selection methods, methods and approaches for internal model performance assessment, and model improvement criteria, into a data-driven modelling procedure, (3) integration of independent presence/absence data into the modelling process, for external model performance assessment, for model calibration, and for model evaluation; (4) new output formats, notably a probability-ratio output format which directly expresses the ʻrelative suitability of one place vs. anotherʼ for the modelled target; and (5) development of options for discriminative use of MaxEnt, i.e., use of with presence/absence data. The most important research needs are considered to be: (1) comparative studies of strategies for construction of parsimonious sets of derived variables for use in MaxEnt modelling; and (2) comparative tests on independent presence/absence data of the predictive performance of MaxEnt models obtained with different model selection strategies, different approaches for internal model performance assessment, and different model improvement criteria.

A gradient analytic perspective on distribution modelling

After massive proliferation over the last decade, distribution modelling (DM) – research with the purpose of modelling the distribution of observable objects of a specific type – has grown into an independent branch of ecological science. There is consensus that this new discipline needs a stronger theoretical foundation. I describe DM as an inductive scientific process with 12 steps, organised into three composite steps: ecological model, data model, and statistical model. Step 8, modelling of the overall ecological response, places DM unambiguously among gradient analysis techniques and motivates for a gradient analytic (GA) perspective on DM. DM terminology is reviewed and revised accordingly. Three fundamental insights of the GA perspective are described: (1) that external ‘factors’ do not influence the species one by one, but act on the species in concert; (2) that a few major complex-gradients normally account for most of the variation in species composition that can be explained environmentally; and (3) that species occur within a restricted interval along each major complex-gradient. These insights are developed into a theoretical platform for DM. General patterns of species performance variation along environmental complex-gradients and the structuring processes responsible for these patterns are reviewed. Three categories of ecoclines, i.e., gradients of variation in species composition and the environment, are recognised: regional ecoclines, local ecoclines, and condition or impact ecoclines. Causes and implications of the unimodal shape of species’ responses to environmental complex-gradients are reviewed. Structuring processes are divided into three categories: limited physiological tolerance, interspecific interactions, and demographic processes. Relationships between categories of ecoclines, the processes responsible for variation in species performance along them, and the spatial and temporal scale intervals in which variation is large, are reviewed. The GA perspective forms the basis for discussions of important steps in the DM process. Initially, the controversial concepts of the habitat and the niche are reviewed and their role in the ecological model (Step 1) discussed. I conclude that neither of these concepts are necessary, nor useful, for DM. As an alternative to conceptual models based upon the niche concept, I propose a new conceptual modelling framework for DM, the HED framework, which is rooted in the gradient analytic perspective. I show how this new framework can be used, in initial phases of a DM study to formulate a meta-model for factors that influence distributions, and in the analytic phase to guide important choices of methods and options and to assist interpretation of modelling results. Important data model issues are: collection of data for the modelled target and preparation of raw response variables (Steps 2 and 6); collection of explanatory data (Step 3); conceptualisation of the study area (Step 4); collection of data for calibration and evaluation (Step 9); and transformation of explanatory variables to derived variables subjected to DM (Step 5,ii). Important statistical model issues are: statistical model formulation, i.e. choice of method (Step 7,i) and model specification (Step 7,ii); model selection and internal assessment of model performance (Steps 8,i and 8,ii); and model evaluation (Step 10). Two points are emphasised: (1) that modelling purpose should inform choice of methods and options; and (2) the importance of an independently collected presence/absence data set, which can be used to calibrate, evaluate and iteratively improve models. Finally I list seven challenges of particular importance for progress in DM: (1) that more knowledge of patterns of natural variation is needed; (2) that a better mechanistic understanding of causes of patterns of natural variation is needed; (3) that the availability of relevant rasterised explanatory variables needs to be improved; (4) that more studies of patterns at local and micro spatial scales, in addition to multiple-scale studies using DM methods, are needed; (5) that evaluation by independent data should be established as a standard in DM; (6) that further insights into statistical modelling methods and their options, with particular reference to appropriateness for different types of data and DM purposes, are needed; and (7) that DM methods should be incorporated in studies with a broader scope. I conclude that there are considerable potentials for improvement of DM methods and practice. Increased return from DM in terms of contributions that improve our understanding of patterns of natural variation and their causes, should be expected.

Vegetation composition, gradients and environment relationships of birch forest in six reference areas in Norway

Vegetation composition, gradients and environment relationships of birch forest in six reference areas in NorwayTerrestrial Monitoring of boreal birch forest ecosystems (TOV) was initiated in 1989 by the Directorate for Nature Management. The programme has a multidisciplinary approach and integrates studies of precipitation, soil water, soil, understorey vegetation composition, lichens on birch trunks, population studies of birds and mammals and environmental pollutants in plants and animals. Here we present studies of forest floor vegetation at establishment, which supplements and complements two studies established in boreal coniferous forests in 1988: ‘The effect of acid precipitation on forest and forest understorey vegetation in Gjerstad, South Norway’ and ‘Vegetational and environmental monitoring of boreal spruce forest in ten reference areas’, the latter initiated by the Norwegian Institute of Land Inventory (NIJOS) as part of a forest health monitoring programme.The reference areas were selected to span regional gradients in climatic conditions and deposition of airborne pollutants, in old-growth bilberry-dominated birch forest in Norway. Ten macro plots in each reference area were located to span differences in nutrient and soil moisture conditions, terrain features, etc. by a sampling design similar to the one used in coniferous forests. Fifty 1×1 m meso sample plots, randomly chosen within the ten macro plots, were subjected to vegetation analysis, using frequency in subplots as well as percent cover as species abundance measures.The main vegetational gradients were found by parallel use of DCA and GNMDS ordination methods; the results of which were subjected to environmental interpretation by means of non-parametric correlation and split-plot GLM analyses. Both ordination methods gave to large degree similar, interpretable, vegetation gradients. The most important ecoclines were related to variation in nutrient conditions, best expressed by pH, Ca, K and S. Tree influence, topographic (un)favourability, soil moisture and soil depth were other factors which were correlated with one of the two main vegetation gradients (ecoclines).The main vegetational gradients and environmental/climatic/geographical complex gradients in the total data set were found by DCA and subsequent interpretation of the axes. The main complex gradient corresponded to the variation in the vegetation from sites with low pH and low content of nutrients (low concentrations of macro nutrients like C, Ca, Mn, S and Total N) and high loss on ignition to vice versa. The second gradient corresponded to variation in the vegetation from sites with high effective temperature sums at low latitudes and high soil concentrations of Mn and S, to sites with opposite characteristics. Most of the variation (> 80%) in the vegetation compositions could be ascribed to the between macro plots scale level, leaving a small residual variation on the between area and in the plots within macro plot scale level.

The lichen flora of Svalbard

The lichen flora of Svalbard742 species, including 151 reported for the first time, are treated from Svalbard (exclusive of Bjørnøya). New to science are: Bryocaulon hyperborea Øvstedal (also known from Greenland), Buellia insularis Øvstedal, Lepraria svalbardensis Tønsberg, Placynthium pulvinatum Øvstedal (also recorded from mainland Norway), Rhizocarpon dahlii Øvstedal, R. tephromelae Øvstedal, and Tephromela lucifuga Øvstedal & Tønsberg. New combinations are: Aspicilia major (Lynge) Øvstedal, Aspicilia punctiformis (Lynge) Øvstedal, Cetraria racemosa (Lynge) Øvstedal, Miriquidica picea (Lynge) Øvstedal, and Stereocaulon compactum (I. M. Lamb) Øvstedal. Information on morphology, anatomy, chemistry, substrate preferences and distribution is included for all taxa. Keys to genera and species are provided. Separate keys are provided for sorediate species on rock and on soil/bryophytes. 6 % of the species are defined as cosmopolitan. More than one third has a bipolar distribution, whereas about 60 % are restricted to the Northern Hemisphere, 52 species are high-arctic and lacking from Fennoscandia, and 12 species are at present known as Svalbard endemics.

Gradients analyses of forests ground vegetation and its relationships to environmental variables in five subtropical forest areas, S and SW China

Gradients analyses of forests ground vegetation and its relationships to environmental variables in five subtropical forest areas, S and SW ChinaMonitoring of ground vegetation and environmental variables in subtropical forests in China was initiated in 1999 as part of the "Integrated Monitoring Programme of Acidification of Chinese Terrestrial Systems". The study areas were selected to span regional gradients, in deposition of airborne pollutants and climatic conditions. All five study areas are located in the southern and south-western parts of China and consist of subtropical forests. In each study area 50 1-m2 plots were randomly chosen within each of ten 10×10 m macro plots, each in turn positioned in the centre of 30×30 m extended macro plot. All 250 1-m2 plots were subjected to vegetation analysis, using frequency in subplots as measure of species abundance. A total of 33 environmental variables were recorded for 1-m2 plots as well as 10×10 m macro plots. A major objective of this study is to identify the environmental variables that are most strongly related to the species composition of ground vegetation in S and SW Chinese subtropical forests, as a basis for future monitoring.Comparison among DCA, LNMDS and GNMDS ordination methods, an additional objective of the study, was achieved by using a set of different techniques: calculation of pair-wise correlation coefficients between corresponding ordination axes, Procrustes comparison, assessment of outlier influence, and split-plot GLM analysis between environmental variables and ordination axes. LNMDS and GNMDS consistently produce very similar ordinations. GNMDS ordinations are generally more similar to DCA than LNMDS to DCA. In most cases DCA, LNMDS and GNMDS extract the same main ground vegetation compositional gradients and the choice of LNMDS or GNMDS is therefore hardly decisive for the results. GNMDS was chosen for interpretation and presentation of vegetation-environment relationships. The dimensionality of GNMDS (number of reliable axes) was decided by demanding high correspondence of all axes with DCA and LNMDS axes. Three dimensions were needed to describe the variation in vegetation in two of the areas (TSP and LXH), two dimensions in the other three areas (LCG, LGS and CJT).Environmental interpretation of ordinations (identification of ecoclines; gradients in species composition and the environment) was made by split-plot GLM analysis and non-parametric correlation analysis. Plexus diagrams and PCA ordination were used to visualize correlations between environmental variables. Several graphical means were used to aid interpretation.Complex gradients in litter-layer depth, topography, soil pH/soil nutrient, and tree density/crown cover were found to be most strongly related to vegetation gradients. However, the five study areas differed somewhat with respect to which of the environmental variables that were most strongly related to the vegetation gradients (ordination axes). Litter-layer depth was related to vegetation gradients in four areas (TSP, LCG, CJT and LXH); topography in four study areas (TSP, LGS, CJT and LXH); soil pH in three areas (LCG, LGS and CJT); soil nutrients in one area (LGS); and tree density/crown cover in one area (LCG).The ecological processes involved in relationships between vegetation and main complex-gradi-ents in litter-layer depth, topography, soil pH/soil nutrient, and tree density/crown cover, in subtropical forests, are discussed. We find that gradient relationships of subtropical forests are complex, and that heavy pollution may increase this complexity. Furthermore, our results suggest that better knowledge of vegetation-environment relationships has potential for enhancing our understanding of subtropical forests that occupy vast areas of the S and SW China.

Cortinarius alpinus as an example for morphological and phylogenetic species concepts in ectomycorrhizal fungi

Cortinarius alpinus as an example for morphological and phylogenetic species concepts in ectomycorrhizal fungiExtensive morphological and molecular analyses of closely related species from alpine, subalpine and montane habitats should enable a comparison of ecological, morphological and phylogenetic species concepts in ectomycorrhizal mushrooms. One fundamental question of this study was whether alpine species really exist, and which criteria, besides the specific habitat, could reliably be used for the de-limitation of such taxa. For this reason, 56 rDNA ITS sequences were generated or downloaded from GenBank for 10 closely related species of Cortinarius subgenus Myxacium, section Myxacium. Several collections were sequenced for each of the following taxa: Cortinarius absarokensis, C. alpinus, C. favrei, C. fennoscandicus, C. grallipes, C. mucosus, C. muscigenus, C. septentrionalis, C. trivialis and C. vernicosus. Moreover, spore statistics were carried out for 38 collections of alpine and subalpine taxa. These data provide clear evidence for C. favrei being a synonym of C. alpinus. C. absarokensis and C. alpinus can clearly be delimited based on pileus diameter and average dry weight per basidiome, even in overlapping habitats, but spore size and shape is not a good distinguishing character. Phylograms have very short branches, and base differences between ITS sequences are generally very low in this group, and give no resolution for the included taxa of this section. Based on these results, species concepts of ectomycorrhizal mushrooms are discussed in detail.

New records of Hygrocybe hygrocyboides (Kühner) Arnolds (Fungi, Basidiomycota, Hygrocybeae)

New records of Hygrocybe hygrocyboides (Kühner) Arnolds (Fungi, Basidiomycota, Hygrocybeae)Recent collections from South Greenland and northern Sweden are referred to Hygrocybe hygrocyboides (Kühner) Arnolds, a species closely related to Hygrocybe pratensis (Pers.: Fr.) Murrill. These collections deviate slightly from the holotype both in macroscopic and microscopic characters. However, these differences are ascribed to intraspecific variation within this little known taxon. The new records of Hygrocybe hygrocyboides are the first outside The Alps.