26 research outputs found
Valid auto-models for spatially autocorrelated occupancy and abundance data
Auto-logistic and related auto-models, implemented approximately as
autocovariate regression, provide simple and direct modelling of spatial
dependence. The autologistic model has been widely applied in ecology since
Augustin, Mugglestone and Buckland (J. Appl. Ecol., 1996, 33, 339) analysed red
deer census data using a hybrid estimation approach, combining maximum
pseudo-likelihood estimation with Gibbs sampling of missing data. However
Dormann (Ecol. Model., 2007, 207, 234) questioned the validity of auto-logistic
regression, giving examples of apparent underestimation of covariate parameters
in analysis of simulated "snouter" data. Dormann et al. (Ecography, 2007, 30,
609) extended this analysis to auto-Poisson and auto-normal models, reporting
similar anomalies. All the above studies employ neighbourhood weighting schemes
inconsistent with conditions (Besag, J. R. Stat. Soc., Ser. B, 1974, 36, 192)
required for auto-model validity; furthermore the auto-Poisson analysis fails
to exclude cooperative interactions. We show that all "snouter" anomalies are
resolved by correct auto-model implementation. Re-analysis of the red deer data
shows that invalid neighbourhood weightings generate only small estimation
errors for the full dataset, but larger errors occur on geographic subsamples.
A substantial fraction of papers applying auto-logistic regression to
ecological data use these invalid weightings, which are default options in the
widely used "spdep" spatial dependence package for R. Auto-logistic analyses
using invalid neighbourhood weightings will be erroneous to an extent that can
vary widely. These analyses can easily be corrected by using valid
neighbourhood weightings available in "spdep". The hybrid estimation approach
for missing data is readily adapted for valid neighbourhood weighting schemes
and is implemented here in R for application to sparse presence-absence data.Comment: Typos corrected in Table 1. Note that defaults in R package 'spdep'
have changed in response to this paper; some results using defaults are
therefore now version-dependen
Modeling stream fish distributions using interval-censored detection times
Controlling for imperfect detection is important for developing species distribution
models (SDMs). Occupancy-detection models based on the time needed to
detect a species can be used to address this problem, but this is hindered when
times to detection are not known precisely. Here, we extend the time-to-detection
model to deal with detections recorded in time intervals and illustrate the
method using a case study on stream fish distribution modeling. We collected
electrofishing samples of six fish species across a Mediterranean watershed in
Northeast Portugal. Based on a Bayesian hierarchical framework, we modeled
the probability of water presence in stream channels, and the probability of species
occupancy conditional on water presence, in relation to environmental and
spatial variables. We also modeled time-to-first detection conditional on occupancy
in relation to local factors, using modified interval-censored exponential
survival models. Posterior distributions of occupancy probabilities derived from
the models were used to produce species distribution maps. Simulations indicated
that the modified time-to-detection model provided unbiased parameter
estimates despite interval-censoring. There was a tendency for spatial variation
in detection rates to be primarily influenced by depth and, to a lesser extent,
stream width. Species occupancies were consistently affected by stream order,
elevation, and annual precipitation. Bayesian P-values and AUCs indicated that
all models had adequate fit and high discrimination ability, respectively. Mapping
of predicted occupancy probabilities showed widespread distribution by
most species, but uncertainty was generally higher in tributaries and upper
reaches. The interval-censored time-to-detection model provides a practical
solution to model occupancy-detection when detections are recorded in time
intervals. This modeling framework is useful for developing SDMs while controlling
for variation in detection rates, as it uses simple data that can be readily
collected by field ecologistsinfo:eu-repo/semantics/publishedVersio
Controllability under positivity constraints of multi-d wave equations
We consider both the internal and boundary controllability problems for wave
equations under non-negativity constraints on the controls. First, we prove the
steady state controllability property with nonnegative controls for a general
class of wave equations with time-independent coefficients. According to it,
the system can be driven from a steady state generated by a strictly positive
control to another, by means of nonnegative controls, when the time of control
is long enough. Secondly, under the added assumption of conservation and
coercivity of the energy, controllability is proved between states lying on two
distinct trajectories. Our methods are described and developed in an abstract
setting, to be applicable to a wide variety of control systems