Approximate Profile Maximum Likelihood

We propose an efficient algorithm for approximate computation of the profile maximum likelihood (PML), a variant of maximum likelihood maximizing the probability of observing a sufficient statistic rather than the empirical sample. The PML has appealing theoretical properties, but is difficult to compute exactly. Inspired by observations gleaned from exactly solvable cases, we look for an approximate PML solution, which, intuitively, clumps comparably frequent symbols into one symbol. This amounts to lower-bounding a certain matrix permanent by summing over a subgroup of the symmetric group rather than the whole group during the computation. We extensively experiment with the approximate solution, and find the empirical performance of our approach is competitive and sometimes significantly better than state-of-the-art performance for various estimation problems

Climate and Human Pressure Constraints Co-Explain Regional Plant Invasion at Different Spatial Scales

<div><p>Alien species invasion represents a global threat to biodiversity and ecosystems. Explaining invasion patterns in terms of environmental constraints will help us to assess invasion risks and plan control strategies. We aim to identify plant invasion patterns in the Basque Country (Spain), and to determine the effects of climate and human pressure on that pattern. We modeled the regional distribution of 89 invasive plant species using two approaches. First, distance-based Moran’s eigenvector maps were used to partition variation in the invasive species richness, S, into spatial components at broad and fine scales; redundancy analysis was then used to explain those components on the basis of climate and human pressure descriptors. Second, we used generalized additive mixed modeling to fit species-specific responses to the same descriptors. Climate and human pressure descriptors have different effects on S at different spatial scales. Broad-scale spatially structured temperature and precipitation, and fine-scale spatially structured human population density and percentage of natural and semi-natural areas, explained altogether 38.7% of the total variance. The distribution of 84% of the individually tested species was related to either temperature, precipitation or both, and 68% was related to either population density or natural and semi-natural areas, displaying similar responses. The spatial pattern of the invasive species richness is strongly environmentally forced, mainly by climate factors. Since individual species responses were proved to be both similarly constrained in shape and explained variance by the same environmental factors, we conclude that the pattern of invasive species richness results from individual species’ environmental preferences.</p></div

Numerical summaries of the response and descriptor variables.

<p>Numerical summaries of the response and descriptor variables.</p

Generalized Additive Mixed Modeling results for the 37 most frequent invasive alien plant species in the Basque Country (northern Spain).

<p>Generalized Additive Mixed Modeling results for the 37 most frequent invasive alien plant species in the Basque Country (northern Spain).</p

Location of the Basque Country (study area) in the Iberian Peninsula.

<p>Main cities: Bi (Bilbao), SS (San Sebastián) and Vi (Vitoria).</p

RDA canonical axis modeling fine-scale spatial structures.

<p>RDA canonical axis modeling fine-scale spatial structures.</p

Spatial pattern of S, the number of invasive alien plant species per 10 km x 10 km UTM cell in <i>n</i> = 104 cells (a) and spatial correlogram based on Moran’s I statistic for S (b).

<p>The plot displays the spatial correlation values against distance (1: 0–10 km, 2: 10–20 km, etc.). Distance (d) is in units of 10 km.</p

Relationships between serum levels (A, TI value; B, TM value) and net increments (C, TI value; D, TM value) of lutein after intervention and DNA damage after 20′ of repair.

<p>Lines represent mean fit lines and 95% regression prediction lines.</p

Patterns of invasive alien plant species per cell (S) in the Basque Country at broad (a) and fine (b) spatial scales.

<p>The maps represent fitted scores (<i>n</i> = 104) of RDA canonical axes modeling broad-scale (adjusted-<i>R</i>² = 50.8% of the total variance in S) and fine-scale spatial structures (adjusted-<i>R</i>² = 20.1% of the total variance in S). Distance (d) is in units of 10 km. See the environmental analysis of these spatial patterns in Tables <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0164629#pone.0164629.t002" target="_blank">2</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0164629#pone.0164629.t003" target="_blank">3</a>.</p

Fitted Generalized Additive Mixed Models for six example species, with 95% confidence bands.

<p>The smoothers show the probability of occurrence with increasing mean annual temperature (Temperature, a–b), annual precipitation (Precipitation, c), natural log-transformed human population density (ln-HPD, d) and percentage of natural and semi-natural areas (Natural area) in a given UTM cell (e–f). See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0164629#pone.0164629.t004" target="_blank">Table 4</a> for statistical details.</p