A simple model is developed to describe crop yield loss as a function of weed density. The model, a rectangular hyperbola, has two agronomically meaningful parameters which together can be used as indices of competitiveness. Examples are given where the model is fitted to experiments from the literature. Seventeen other models are compared through application to 22 data sets. It was found that for the data available two-parameter yield loss models were generally sufficient. The hyperbolic model gave the best description of data, but this was only marginally better than three other models. This conclusion is discussed with reference to the popular sigmoidal model.

Publication of The Genetics of Colonizing Species in 1965 launched the field of invasion genetics and highlighted the value of biological invasions as natural ecological and evolutionary experiments. Here, we review the past 50 years of invasion genetics to assess what we have learned and what we still don't know, focusing on the genetic changes associated with invasive lineages and the evolutionary processes driving these changes. We also suggest potential studies to address still-unanswered questions. We now know, for example, that rapid adaptation of invaders is common and generally not limited by genetic variation. On the other hand, and contrary to prevailing opinion 50 years ago, the balance of evidence indicates that population bottlenecks and genetic drift typically have negative effects on invasion success, despite their potential to increase additive genetic variation and the frequency of peak shifts. Numerous unknowns remain, such as the sources of genetic variation, the role of so-called expansion load and the relative importance of propagule pressure vs. genetic diversity for successful establishment. While many such unknowns can be resolved by genomic studies, other questions may require manipulative experiments in model organisms. Such studies complement classical reciprocal transplant and field-based selection experiments, which are needed to link trait variation with components of fitness and population growth rates. We conclude by discussing the potential for studies of invasion genetics to reveal the limits to evolution and to stimulate the development of practical strategies to either minimize or maximize evolutionary responses to environmental change.

The cotiipet(ti.ve abilities of a wide range of genotypes of wheat {Trilicwnaestivum L.) and durum wheat {Triticum durum Desf.) against Lolium rigidunt Gatud. (annual ryegrassj were examined lo determine the potential for breeders to select strongly competiti-ve varieties. Considerable potential within the wheat genonie to hreed varieties with greater competitive ability was demonstrated. In 1993. 250 genotypes from aroimd the world were screened and in 1994 st subset of 45 (mainly Australian) genotypes were further examined. A uniform deasity of L. rigidum reduced grain peld of wheat by up to about 80% in 1993 and to 50% in 1994, depending on wheat genotype. Reduction in grain yield was correlated with i. rigidum dry matter. Wheats varied in competitive ability with source, and durum wheats were less competiifive than T. aestivum. The old' standard wheat varieties (released between 1880 and 1950) suppressed the weed more than all the current varieties, with the exception of eight Fi hybrids. A doubling of the crop seeding rate of 10 of the genotypes in 1994 reduced the biomass of L. rigidum by an average of 25% compared with the standard seeding rate. Ranking of competitive ability of varieties at high deosity was consistent at both seeding rates. The strongly competitive genotypes had high early biomass accumulation, large numbers of tillers, and were taU with extensive leaf display. The potential for breeding enhanced competitive ability in wheat is discussed.

The design and analysis of competition experiments should be based on an unambiguous objective. Recent criticisms of particular designs have been made without reference to objectives and may be misleading. Three common designs are discussed: additive, replacement series, and response surface. Additive designs are well suited to agronomic objectives; replacement series are useful for comparing pairs of species; response surface designs can be used for most objectives but may be unnecessarily complex. The published criticisms of additive and replacement series designs are argued to be acceptable limitations within the bounds of the objectives for which they are used. Concerns about these designs confounding density and proportion are irrelevant to the objectives for which they are most suited. The continued use of multiple comparison tests is argued to be illogical. Regression approaches to analysis are more relevant, many non-linear equations are now easy to fit to data and these can be used without the need for linearization. However, there are various pitfalls not adequately reported to date. In particular, error structures need to be checked carefully and over-elaborate equations should be avoided.

What are the ecological attributes of weeds that confer the ability to interfere with human activities? Roger Cousens and Martin Mortimer place weed management within an ecological context, with the focus on the manipulation of population size. The dynamics of abundance and spatial distribution are considered at both geographic and local scales. The basic processes of dispersal, reproduction and mortality are described, together with the factors that influence them. Management is shown to modify patterns of behaviour that are intrinsic to populations. Attention is given to the evolution and management of resistance to herbicides. This book provides weed science with the conceptual basis that has previously been lacking. It also gives ecologists access to the extensive database on the population ecology of weeds.

SUMMARYA hyperbolic model relating crop yield to weed density is extended to include crop density as a further variable. Other models were obtained from published sources, eight being originally applied to yield of above-ground biomass and six to marketable yield. Data were obtained from a field experiment in which spring wheat and spring barley were planted either in monoculture or together and at a range of densities. Further data were obtained from a published experiment on Sinapis alba and barley grown in containers. The models were fitted to data using maximum likelihood estimation. Comparisons of residual sums of squares showed that for the wheat and barley field experiment biomass yield and marketable yield were sufficiently described by a three-parameter model. The Baeumer & de Wit (1968) equation proposed for replacement series experimental designs is considered reasonable for the analysis of field additive designs provided the parameters are interpreted in agronomic terms. For the Sinapis alba and barley experiment more complex models could be justified.

Summary An equation is presented lo describe the relationship of a plant response to herbicide dose where there is stimulation of response al low doses. Us properties are discussed and examples of its use are given. The equation includes the most commonly used sigmoidal curve as a special case.

Aim Correlative species distribution models (SDMs) often involve some degree of projection into novel covariate space (i.e. extrapolation), because calibration data may not encompass the entire space of interest. Most methods for identifying extrapolation focus on the range of each model covariate individually. However, extrapolation can occur that is well within the range of univariate variation, but which exhibits novel combinations between covariates. Our objective was to develop a tool that can detect, distinguish and quantify these two types of novelties: novel univariate range and novel combinations of covariates.Location Global, Australia, South Africa. Methods We developed a new multivariate statistical tool, based on the Mahalanobis distance, which measures the similarity between the reference and projection domains by accounting for both the deviation from the mean and the correlation between variables. The method also provides an assessment tool for the detection of the most influential covariates leading to dissimilarity. As an example application, we modelled an Australian shrub (Acacia cyclops) widely introduced to other countries and compared reference data, global distribution data and both types of model extrapolation against the projection globally and in South Africa. ResultsThe new tool successfully detected and quantified the degree of dissimilarity for points that were either outside the univariate range or formed novel covariate combinations (correlations) but were still within the univariate range of covariates. For A. cyclops, more than half of the points (6617 of 10,785) from the global projection space that were found to lie within the univariate range of reference data exhibited distorted correlations. Not all the climate covariates used for modelling contributed to novelty equally over the geographical space of the model projection.Main conclusions Identifying non-analogous environments is a critical component of model interrogation. Our extrapolation detection (ExDet) tool can be used as a quantitative method for exploring novelty and interpreting the projections from correlative SDMs and is available for free download as standalone software from http://www.climond.org/exdet.