Richard Armas

1Once neglected, the role of facilitative interactions in plant communities has received considerable attention in the last two decades, and is now widely recognized. It is timely to consider the progress made by research in this field.2We review the development of plant facilitation research, focusing on the history of the field, the relationship between plant–plant interactions and environmental severity gradients, and attempts to integrate facilitation into mainstream ecological theory. We then consider future directions for facilitation research.3With respect to our fundamental understanding of plant facilitation, clarification of the relationship between interactions and environmental gradients is central for further progress, and necessitates the design and implementation of experiments that move beyond the clear limitations of previous studies.4There is substantial scope for exploring indirect facilitative effects in plant communities, including their impacts on diversity and evolution, and future studies should connect the degree of non-transitivity in plant competitive networks to community diversity and facilitative promotion of species coexistence, and explore how the role of indirect facilitation varies with environmental severity.5Certain ecological modelling approaches (e.g. individual-based modelling), although thus far largely neglected, provide highly useful tools for exploring these fundamental processes.6Evolutionary responses might result from facilitative interactions, and consideration of facilitation might lead to re-assessment of the evolution of plant growth forms.7Improved understanding of facilitation processes has direct relevance for the development of tools for ecosystem restoration, and for improving our understanding of the response of plant species and communities to environmental change drivers.8Attempts to apply our developing ecological knowledge would benefit from explicit recognition of the potential role of facilitative plant–plant interactions in the design and interpretation of studies from the fields of restoration and global change ecology.9Synthesis: Plant facilitation research provides new insights into classic ecological theory and pressing environmental issues. Awareness and understanding of facilitation should be part of the basic ecological knowledge of all plant ecologists.Once neglected, the role of facilitative interactions in plant communities has received considerable attention in the last two decades, and is now widely recognized. It is timely to consider the progress made by research in this field.We review the development of plant facilitation research, focusing on the history of the field, the relationship between plant–plant interactions and environmental severity gradients, and attempts to integrate facilitation into mainstream ecological theory. We then consider future directions for facilitation research.With respect to our fundamental understanding of plant facilitation, clarification of the relationship between interactions and environmental gradients is central for further progress, and necessitates the design and implementation of experiments that move beyond the clear limitations of previous studies.There is substantial scope for exploring indirect facilitative effects in plant communities, including their impacts on diversity and evolution, and future studies should connect the degree of non-transitivity in plant competitive networks to community diversity and facilitative promotion of species coexistence, and explore how the role of indirect facilitation varies with environmental severity.Certain ecological modelling approaches (e.g. individual-based modelling), although thus far largely neglected, provide highly useful tools for exploring these fundamental processes.Evolutionary responses might result from facilitative interactions, and consideration of facilitation might lead to re-assessment of the evolution of plant growth forms.Improved understanding of facilitation processes has direct relevance for the development of tools for ecosystem restoration, and for improving our understanding of the response of plant species and communities to environmental change drivers.Attempts to apply our developing ecological knowledge would benefit from explicit recognition of the potential role of facilitative plant–plant interactions in the design and interpretation of studies from the fields of restoration and global change ecology.Synthesis: Plant facilitation research provides new insights into classic ecological theory and pressing environmental issues. Awareness and understanding of facilitation should be part of the basic ecological knowledge of all plant ecologists.

The presence of a vertebral deformity increases the risk of subsequent spinal deformities. The aim of this analysis was to determine whether the presence of vertebral deformity predicts incident hip and other limb fractures. Six thousand three hundred and forty-four men and 6788 women aged 50 years and over were recruited from population registers in 31 European centers and followed prospectively for a median of 3 years. All subjects had radiographs performed at baseline and the presence of vertebral deformity was assessed using established morphometric methods. Incident limb fractures which occurred during the follow- up period were ascertained by annual postal questionnaire and confirmed by radiographs, review of medical records and personal interview. During a total of 40 348 person-years of follow-up, 138 men and 391 women sustained a limb fracture. Amongst the women, after adjustment for age, prevalent vertebral deformity was a strong predictor of incident hip fracture, (rate ratio (RR) = 4.5; 95% CI 2.1–9.4) and a weak predictor of ‘other’ limb fractures (RR = 1.6; 95% CI 1.1–2.4), though not distal forearm fracture (RR = 1.0; 95% CI 0.6–1.6). The predictive risk increased with increasing number of prevalent deformities, particularly for subsequent hip fracture: for two or more deformities, RR = 7.2 (95% CI 3.0–17.3). Amongst men, vertebral deformity was not associated with an increased risk of incident limb fracture though there was a nonsignificant trend toward an increased risk of hip fracture with increasing number of deformities. In summary, prevalent radiographic vertebral deformities in women are a strong predictor of hip fracture, and to a lesser extent humerus and ‘other’ limb fractures; however, they do not predict distal forearm fractures.

A method for autoregressive (AR) modeling of stationary stochastic signals is extended to AR moving-average (ARMA) models, including the special case of AR signals in white noise. Both AR and ARMA examples are presented. The method differs from the well-known method of overdetermined normal equations in that fitting error, not equation error, is minimized, and significantly improved performance is obtained.

We study the problems of bias correction in the estimation of low order ARMA(p, q) time series models. We introduce a new method to estimate the bias of the parameters of ARMA(p, q) process based on the analytical form of the GLS transformation matrix of Galbraith and Zinde-Walsh (1992). We show that the resulting bias corrected estimator is consistent and

Augmented Dickey-Fuller unit root tests may severely overreject when the DGP is a general linear process. The use of the AR sieve bootstrap, proposed by Park (2002) and Chang and Park (2003), may alleviate this problem. We propose sieve bootstraps based on MA and ARMA approximations. Invariance principles for the partial sum processes built from these sieve bootstrap DGPs are established and a proof of the asymptotic validity of the resulting ADF bootstrap tests is provided. Through Monte Carlo experiments, we find that the rejection probabilities of the MA and ARMA sieve bootstraps are often lower and more robust to the underlying DGP than that of the AR sieve bootstrap. In particular, the new sieve bootstraps perform much better than the AR sieve when a large MA root is present. We also find that the ARMA sieve bootstrap requires only a very parsimonious specification to achieve excellent results.

... suggest that no long-term stable relationship exists between the levels of general price and real output. 4. Estimation results. The univariate ARMA model. The UARMA model for inflation is based on procedures previously described in Holmes and Shamsuddin (1988). ...

A method for autoregressive (AR) modeling of stationary stochastic signals has been proposed based upon fitting the model auto-correlation function to the estimated (biased) autocorrelation in the least-squares sense over more than the minimum number of autocorrelation values (Ref. 7). In this paper, the method is extended to the case of autoregressive-moving-average (ARMA) models, including the special case of AR signals in white noise, and both AR and ARMA examples are presented. This method differs from the well known method of overdetermined normal equations in that fitting error, not equation error, is minimized. The bias in the estimated correlation values is also readily compensated without amplifying the higher (noisy) correlation lags. Iterative algorithms are derived to solve the resulting nonlinear equations.

Speciation involves the origin of trait differences that limit or prevent gene exchange and ultimately results in daughter populations that form monophyletic or exclusive genetic groups. However, for recently diverged populations or species between which reproductive isolation is often incomplete, gene genealogies will be discordant, and most regions of the genome will display nonexclusive genealogical patterns. In these situations, genome regions for which one or both species are exclusive groups may mark the footprint of recent selective sweeps. Alternatively, such regions may include or be closely linked to "speciation genes," genes involved in reproductive isolation. Therefore, comparisons of gene genealogies allow inferences about the genetic architectures of both reproductive isolation and adaptation. Contrasting genealogical relationships in sexually isolated pheromone strains of the European corn borer moth (Ostrinia nubilalis) demonstrate the relevance of this approach. Genealogies for five gene regions are discordant, and only one molecular marker, the sex-linked gene Tpi, has evidence for pheromone strain exclusivity. Tpi maps to a position on the sex chromosome that is indistinguishable from a major factor (Pdd) affecting differences in postdiapause development time. The major factor (Resp) determining male behavioral response to pheromone is also sex-linked, but maps 20-30 cM away. Exclusivity at Tpi may be a consequence of these linkage relationships because evidence from phenotypic variation in natural populations implicates both Pdd and Resp as candidates for genes involved in recent sweeps and/or reproductive isolation between strains. genealogy | genetic linkage map | introgression | selective sweep | speciation <HR ALIGN=LEFT WIDTH=50% NOSHADE SIZE=1>

This paper considers estimation of the parameters for the fractionally integrated class of processes known as ARFIMA. We consider the small sample properties of a conditional sum-of-squares estimator that is asymptotically equivalent to MLE. This estimator has the advantage of being relatively simple and can estimate all the parameters, including the mean, simultaneously. The simulation evidence we present indicates that estimation of the mean can make a considerable difference to the small sample bias and MSE of the other parameter estimates.