Reference |
DOI,
PDF,
HTML |
Response
data
type |
Notes |

Antoine & McCune
(2004) |
DOI |
quantitative (growth rates and abundance classes) |
Local mean NPMR, Gaussian weights, 1-predictor models, small sample
size |

Berryman & McCune
(2006) |
DOI |
quantitative (lichen biomass) |
Local mean NPMR, Gaussian weights used to relate lichen biomass to
stand structure and topography. Based on the response surfaces observed with NPMR, they
chose final models of three types: NPMR, nonlinear regression, and multiple linear
regression. |

Binder & Ellis
(2008) |
DOI |
binary (species presence and randomly generated
pseudoabsences) |
Local mean NPMR, Gaussian weights. Modeled responses to pollutant
loads and climate variables under various climate change scenarios; randomization tests;
evaluated spatial autocorrelation |

Casazza et al (2007) |
DOI |
quantitative (number of endemic taxa) |
Local mean NPMR, uniform weights (“SpOcc” model). Modeled
diversity of endemic plants in relation to glacial limit, substrate type, and
thermoclimatic belts. |

Cristofolini et
al. (2008) |
DOI |
quantitative (lichen diversity) |
Local mean NPMR, uniform weights (“SpOcc” model). Modeled
overall lichen diversity and nitrophytic lichen diversity in response to pollutant
concentrations, stand characteristics, and other environmental variables. |

DeBano et al. (2010) |
PDF |
quantitative (insects trapped per month) |
Local mean NPMR, Gaussian weights, modeling insect pests trapped
per month against weather and other environmental variables. Numerous 3D wireframe
response surfaces, sensitivity analysis, and randomization tests. Clear 1-page explanation
of NPMR. |

Derr et al. (2007) |
DOI |
quantitative (species richness in relation to
geography and community ordination scores) |
Local linear NPMR, Gaussian weights. Compared fit of species
richness to four different sets of predictors: topographic+geographic, vascular plants,
the combination of the two preceding sets, and community ordination scores. |

Ellis &
Coppins (2007) |
DOI |
quantitative (species richness) |
Local mean NPMR, Gaussian weights. Stepwise selection of predictors
representing climate and forest structure; randomization test. Predictors were selected
from a pool of 15 variables and evaluated with a randomization test. Models were used to
generate predictions based on future climate scenarios. |

Ellis et al.
(2007a) |
DOI |
binary (species presence) |
Local mean NPMR, Gaussian weights. Modeled species presence against
climatic predictors. Applied models to climate change scenarios. |

Ellis et al.
(2007b) |
DOI |
binary (species presence) for 26 species |
Local mean NPMR, Gaussian weights. Modeled species presence against
climatic predictors; included randomization tests and AUCs. They present NPMR models for
many species, depicted them geographically rather than response surfaces in the predictor
space. |

Engelbrecht et al.
2007 |
DOI |
NPMR for an ecological purpose |
Example of NPMR with respect to a single predictor. The probability
of species occurrence was modelled versus dry season duration. |

Fenton & Bergeron
(2008) |
DOI |
Species richness and evenness |
Assessed the relative roles of age and habitat in creating and
maintaining species diversity. "The use of multiple overlapping data sets
[predictors] with NPMR and subsequent comparison permits complex interactions between
different variables to be teased out." |

Flitcroft (2008) |
DOI |
quantitative (log density of a species) |
Log density of juvenile salmon regressed against habitat
characteristics , using local mean and Gaussian weights. Used NPMR because of failure of
parametric modeling. |

Giordani
(2007) |
DOI |
quantitative (diversity) |
Local mean NPMR, uniform weights (“SpOcc” model).
Diversity regressed against pollutants and other environmental variables. |

Giordani &
Incerti (2008) |
DOI |
quantitative (species abundance) |
Local mean NPMR, uniform weights ("SpOcc" model).
Regressed many species against macroclimatic variables. Combined results with multivariate
community analysis of the same data set. |

Grundel & Pavlovic
(2008) |
DOI |
quantitative (bird species density) |
Local mean NPMR, Gaussian weights, modeling the density of many
bird species in relationship to numerous habitat factors. This paper gives a lucid
explanation of NPMR, three dimensional response surfaces, and some nice examples of
interacting nonlinear responses. |

Hosten et al. (2007) |
PDF |
Grazing utilization |
Local mean NPMR, Gaussian weights. Modeled the relationship of
maximum utilization and average utilization to environmental factors, vegetative
descriptors, and management activities |

Jovan (2003) |
DOI |
quantitative (species abundance classes) |
Local mean NPMR, Gaussian weights, 1- to 3-predictor models |

Jovan & McCune
(2005) |
PDF |
Species abundance in relation to scores on NMS
ordinations |
Local mean NPMR, Gaussian weights. Used optimum value for a species
on one axis while fitting the response curve to another axis. In effect this slices a
response surface along a particular plane. |

Jovan & McCune
(2006) |
DOI |
Nitrophile abundance in relation to elevation. |
Local mean NPR, Gaussian weights, 1 predictor. Compared to
nonlinear regression and simple linear regression. |

Kohler (2007) |
DOI |
quantitative, log(abundance of species) |
Local mean NPR, Gaussian weights. Regressed population size
(density of an insect species) against "hemlock woolly adelgid population score" |

Lintz et al. (2011) |
DOI |
binary and quantitative (simulated and real data) |
Local mean NPMR with Gaussian weights. Compared the performance of
Random Forests, Classification and Regression Trees, and NPMR using a large variety of 3D
response surfaces. They found: "The accuracy of each method depends on the threshold
strength and diagonality of the original data structure with each method differing in
degree of dependence (Fig. 4). The accuracy of most methods decreases as diagonality
increases and threshold strength decreases with the exception of NPMR with continuous
data... NPMR demonstrates the least variability (seen as quantile bars in Fig. 4) and the
greatest accuracy (seen as medians in Fig. 4) compared to the other methods for a given
response shape. The sensitivities of modeling methods to shape attributes of data
structure arises from features specific to each modeling method, which manifest in visual
differences of predicted surfaces for different shapes (Fig. 5). For our subsequent
analyses using real ecological data, we choose the most accurate and robust method we
test, NPMR." |

McCune (2006) |
DOI |
binary (species presence) and quantitative (species
abundance) |
Local mean NPMR, Gaussian weights, medium and large sample sizes,
simulated and real data, comparison of linear, logistic and NPMR models. |

McCune (2007) |
PDF |
quantitative (potential direct incident radiation) |
Local linear NPMR, Gaussian weights, with slope, aspect, and
latitude as predictors |

McCune et al.
(2003) |
PDF |
binary (species presence) |
Local mean NPMR, uniform weighting function (predates inclusion of
Gaussian weights in HyperNiche), 1- and 2-predictor models |

Miller et al. (2007) |
DOI |
quantitative (community ordination scores, species
richness and density of particular functional groups) |
Local mean NPMR, Gaussian weights, used to model stream insect
communities in relation to longitudinal gradients. Detailed, clear explanation of NPMR,
including model specification and sensitivity analysis. Nice exposition of detecting
interactions. |

Minuto et al. (2006) |
DOI |
quantitative (genetic diversity) |
Local mean NPMR, uniform weights; regressed genetic diversity
against geography (latitude, longitude, elevation) and population features (number of
individuals, occupancy area, occupancy rate). |

Ponzetti et al.
(2007) |
DOI |
quantitative (species abundance classes and
community ordination scores) |
Local linear NPMR, Gaussian weights; regressed many species against
ordination scores; also quantitative community ordination scores regressed against
disturbance and cheatgrass. |

Ponadera &
Potapova (2007) |
DOI |
quantitative (abundance of diatom species) |
Local linear NPMR, Gaussian weights. Regional-scale analysis of
diatom species abundance in relation to water chemistry. |

Rood et al. (2010) |
DOI |
quantitative (willow cover) |
Local mean NPMR with Gaussian weights, regressing willow cover
against environmental variables. Illustrations include 2D response curves superimposed on
scatterplots. |

Potapova & Wintel
(2006) |
PDF |
quantitative (% relative abundance and
log-transformed cell densities |
Local linear and local mean NPMR, Gaussian weights. Modeled
abundance of three diatom species in relation to water quality variables. Includes a table
comparing fits for local linear and local mean models. In general, the fits were slightly
higher for local linear models. |

Reusser & Lee
(2008) |
DOI |
binary (species presence) in benthic estuarine and
coastal communities |
Local mean NPMR, Gaussian weights, used to model species presence
in relation to habitat and geographic variables at two scales. "NPMR generally
performs well at both spatial scales and that distributions of non-indigenous species are
predicted as well as those of native species." |

Wedderburn et al.
(2007) |
DOI |
quantitative (fish species abundance) |
Used NPR to relate individual fish species abundance to salinity. |

Yost (2006) |
HTML |
binary (species presence) |
Local mean NPMR with Gaussian weights, regressing presence of
selected species against site factors, past management, and stand characteristics. |

Yost (2008) |
DOI |
binary (species presence) |
Local mean NPMR with Gaussian weights. "NPMR was compared with
logistic regression (LR) by building reduced models from variables selected as best by
NPMR and full models from variables identified as significant with a forward stepwise
process and further manual testing. LogB was used to select models with the highest
predictive capability. NPMR models were less complex and had higher predictive capability
than LR for all modeling approaches. Spatial coordinates were among the most powerful
predictors and the modeling approach with physiographic and stand structural variables
together was the most improved relative to the average frequency of occurrence. GIS
probability maps produced with the application of the physiographic models showed good
spatial congruence between high probability values and plots that contained CLUN. NPMR
proved to be a reliable probability modeling and mapping tool that could be used as the
analytical link between monitoring and quantifying the status and trends of vegetation
resources." |