Statistics for Spatial Data.

Presence-only records may provide data on the distributions of rare species, but commonly suffer from large, unknown biases due to their typically haphazard collection schemes. Presence-absence or count data collected in systematic, planned surveys are more reliable but typically less abundant.We proposed a probabilistic model to allow for joint analysis of presence-only and survey data to exploit their complementary strengths. Our method pools presence-only and presence-absence data for many species and maximizes a joint likelihood, simultaneously estimating and adjusting for the sampling bias affecting the presence-only data. By assuming that the sampling bias is the same for all species, we can borrow strength across species to efficiently estimate the bias and improve our inference from presence-only data.We evaluate our model's performance on data for 36 eucalypt species in south-eastern Australia. We find that presence-only records exhibit a strong sampling bias towards the coast and towards Sydney, the largest city. Our data-pooling technique substantially improves the out-of-sample predictive performance of our model when the amount of available presence-absence data for a given species is scarceIf we have only presence-only data and no presence-absence data for a given species, but both types of data for several other species that suffer from the same spatial sampling bias, then our method can obtain an unbiased estimate of the first species' geographic range.

/pdf/bias-correction-in-species-distribution-models-pooling-d0cjwrog5l.pdf

Bias correction in species distribution models: pooling survey and collection data for multiple species.

Summary
Presence-only data are widely used for species distribution modelling, and point process regression models are a flexible tool that has considerable potential for this problem, when data arise as point events.
In this paper, we review point process models, some of their advantages and some common methods of fitting them to presence-only data.
Advantages include (and are not limited to) clarification of what the response variable is that is modelled; a framework for choosing the number and location of quadrature points (commonly referred to as pseudo-absences or ‘background points’) objectively; clarity of model assumptions and tools for checking them; models to handle spatial dependence between points when it is present; and ways forward regarding difficult issues such as accounting for sampling bias.
Point process models are related to some common approaches to presence-only species distribution modelling, which means that a variety of different software tools can be used to fit these models, including maxent or generalised linear modelling software.

https://besjournals.onlinelibrary.wiley.com/doi/pdf/10.1111/2041-210X.12352

Point process models for presence-only analysis

1. The need to understand the processes shaping population distributions has resulted in a vast increase in the diversity of spatial wildlife data, leading to the development of many novel analytical techniques that are fit-for-purpose. One may aggregate location data into spatial units (e.g. grid cells) and model the resulting counts or presence–absences as a function of environmental covariates. Alternatively, the point data may be modelled directly, by combining the individual observations with a set of random or regular points reflecting habitat availability, a method known as a use-availability design (or, alternatively a presence – pseudo-absence or case–control design). 2. Although these spatial point, count and presence–absence methods are widely used, the ecological literature is not explicit about their connections and how their parameter estimates and predictions should be interpreted. The objective of this study is to recapitulate some recent statistical results and illustrate that under certain assumptions, each method can be motivated by the same underlying spatial inhomogeneous Poisson point process (IPP) model in which the intensity function is modelled as a log-linear function of covariates. 3. The Poisson likelihood used for count data is a discrete approximation of the IPP likelihood. Similarly, the presence–absence design will approximate the IPP likelihood, but only when spatial units (i.e. pixels) are extremely small (Electric Journal of Statistics, 2010, 4, 1151–1201). For larger pixel sizes, presence–absence designs do not differentiate between one or multiple observations within each pixel, hence leading to information loss. 4. Logistic regression is often used to estimate the parameters of the IPP model using point data. Although the response variable is defined as 0 for the availability points, these zeros do not serve as true absences as is often assumed; rather, their role is to approximate the integral of the denominator in the IPP likelihood (The Annals of Applied Statistics, 2010, 4, 1383–1402). Because of this common misconception, the estimated exponential function of the linear predictor (i.e. the resource selection function) is often assumed to be proportional to occupancy. Like IPP and count models, this function is proportional to the expected density of observations. 5. Understanding these (dis-)similarities between different species distribution modelling techniques should improve biological interpretation of spatial models and therefore advance ecological and methodological cross-fertilization.

https://besjournals.onlinelibrary.wiley.com/doi/pdf/10.1111/j.2041-210X.2011.00141.x

Comparative interpretation of count, presence-absence and point methods for species distribution models

Summary 1. Presence-only records may provide data on the distributions of rare species, but commonly suffer from large, unknown biases due to their typically haphazard collection schemes. Presence–absence or count data collected in systematic, planned surveys are more reliable but typically less abundant. 2. We proposed a probabilistic model to allow for joint analysis of presence-only and survey data to exploit their complementary strengths. Our method pools presence-only and presence–absence data for many species and maximizes a joint likelihood, simultaneously estimating and adjusting for the sampling bias affecting the presence-only data. By assuming that the sampling bias is the same for all species, we can borrow strength across species to efficiently estimate the bias and improve our inference from presence-only data. 3. We evaluate our model’s performance on data for 36 eucalypt species in south-eastern Australia. We find that presence-only records exhibit a strong sampling bias towards the coast and towards Sydney, the largest city. Our data-pooling technique substantially improves the out-of-sample predictive performance of our model when the amount of available presence–absence data for a given species is scarce 4. If we have only presence-only data and no presence–absence data for a given species, but both types of data for several other species that suf fer from the same spatial sampling bias, then our method can obtain an unbiased estimate of the first species’ geographic range.

SPECIAL FEATURE PAPER: NEW OPPORTUNITIES AT THE INTERFACE BETWEEN ECOLOGY AND STATISTICS Bias correction in species distribution models: pooling survey and collection data for multiple species

In the analysis of spatial point patterns, an important role is played by statistical tests based on simulation envelopes, such as the envelope of simulations of Ripley's K function. Recent ecological literature has correctly pointed out a common error in the interpretation of simulation envelopes. However, this has led to a widespread belief that the tests themselves are invalid. On the contrary, envelope-based statistical tests are correct statistical procedures, under appropriate conditions. In this paper, we explain the principles of Monte Carlo tests and their correct interpretation, canvas the benefits of graphical procedures, measure the statistical performance of several popular tests, and make practical recommendations. There are several caveats including the under-recognized problem that Monte Carlo tests of goodness of fit are probably conservative if the model parameters have to be estimated from data. Finally, we discuss whether graphs of simulation envelopes can be used to infer the scale of...

/pdf/on-tests-of-spatial-pattern-based-on-simulation-envelopes-uuiwdmx7qw.pdf

On tests of spatial pattern based on simulation envelopes

In Geographical Information Systems, spatial point pattern data are often analysed by dividing space into pixels, recording the presence or absence of points in each pixel, and fitting a logistic regression. We study weaknesses of this approach, propose improvements, and demonstrate an application to prospective geology in Western Australia. Models based on different pixel grids are incompatible (a ‘change-of-support’ problem) unless the pixels are very small. On a fine pixel grid, a spatial logistic regression is approximately a Poisson point process with loglinear intensity; we give explicit distributional bounds. For a loglinear Poisson process, the optimal parameter estimator from pixel data is not spatial logistic regression, but complementary log-log regression with an offset depending on pixel area. If the pixel raster is randomly subsampled, logistic regression is conditionally optimal. Bias and efficiency depend strongly on the spatial regularity of the covariates. For discontinuous covariates, we propose a new algorithmic strategy in which pixels are subdivided, and demonstrate its efficiency.

/pdf/spatial-logistic-regression-and-change-of-support-in-poisson-4gx5icdk4g.pdf

Andrew Hardegen

Papers

On tests of spatial pattern based on simulation envelopes

Spatial logistic regression and change-of-support in Poisson point processes

On two-stage Monte Carlo tests of composite hypotheses