An evaluation of the costs of making specific secondary metabolites: does the yield penalty incurred by host plant resistance to insects due to competition for resources?

The presumption that the synthesis of 'defence' compounds in plants must incur some 'trade-off' or penalty in terms of annual crop yields has been used to explain observed inverse correlations between resistance to herbivores and rates of growth or photosynthesis. An analysis of the cost of making secondary compounds suggests that this accounts for only a small part of the overall carbon budget of annual crop plants. Even the highest reported amounts of secondary metabolites found in different crop species (flavonoids, allylisothiocyanates, hydroxamic acids, 2-tridecanone) represent a carbon demand that can be satisfied by less than an hour's photosynthesis. Similar considerations apply to secondary compounds containing nitrogen or sulphur, which are unlikely to represent a major investment compared to the cost of making proteins, the major demand for these elements. Decreases in growth and photosynthesis in response to stress are more likely the result of programmed down-regulation. Observed correlations between yield and low contents of unpalatable or toxic compounds may be the result of parallel selection during the refinement of crop species by humans.

On the stability of populations of mammals, birds, fish and insects

A key concern for conservation biologists is whether populations of plants and animals are likely to fluctuate widely in number or remain relatively stable around some steady-state value. In our study of 634 populations of mammals, birds, fish and insects, we find that most can be expected to remain stable despite year to year fluctuations caused by environmental factors. Mean return rates were generally around one but were higher in insects (1.09 +/- 0.02 SE) and declined with body size in mammals. In general, this is good news for conservation, as stable populations are less likely to go extinct. However, the lower return rates of the large mammals may make them more vulnerable to extinction. Our estimates of return rates were generally well below the threshold for chaos, which makes it unlikely that chaotic dynamics occur in natural populations - one of ecology's key unanswered questions.

Response to comment on "On the regulation of populations of mammals, birds, fish, and insects"

Our conclusions are unaffected by removal of the time series identified by Peacock and Garshelis as harvest data. The relationship between a population's growth rate and its size is generally concave in mammals, irrespective of their body sizes. However, our data set includes quality data for only five mammals larger than 20 kilograms, so strong conclusions cannot be made about these animals.

Response to comments on "On the regulation of populations of mammals, birds, fish, and insects"

The technical comments by Getz and Lloyd-Smith, Ross, and Doncaster focus on specific aspects of our analysis and estimation and do not demonstrate any results opposing our key conclusion-that, contrary to what was previously believed, the relation between a population's growth rate (pgr) and its density is generally concave.

On the regulation of populations of mammals, birds, fish, and insects

A key unresolved question in population ecology concerns the relationship between a population's size and its growth rate. We estimated this relationship for 1780 time series of mammals, birds, fish, and insects. We found that rates of population growth are high at low population densities but, contrary to previous predictions, decline rapidly with increasing population size and then flatten out, for all four taxa. This produces a strongly concave relationship between a population's growth rate and its size. These findings have fundamental implications for our understanding of animals' lives, suggesting in particular that many animals in these taxa will be found living at densities above the carrying capacity of their environments.

Investigation of support vector machine for the detection of architectural distortion in mammographic images

This paper investigates detection of architectural distortion in mammographic images using support vector machine. Hausdorff dimension is used to characterise the texture feature of mammographic images. Support vector machine, a learning machine based on statistical learning theory, is trained through supervised learning to detect architectural distortion. Compared to the Radial Basis Function neural networks, SVM produced more accurate classification results in distinguishing architectural distortion abnormality from normal breast parenchyma.

Characterization and classification of tumor lesions using computerized fractal-based texture analysis and support vector machines in digital mammograms

Objective: This paper presents a detailed study of fractal-based methods for texture characterization of mammographic mass lesions and architectural distortion. The purpose of this study is to explore the use of fractal and lacunarity analysis for the characterization and classification of both tumor lesions and normal breast parenchyma in mammography. Materials and methods: We conducted comparative evaluations of five popular fractal dimension estimation methods for the characterization of the texture of mass lesions and architectural distortion. We applied the concept of lacunarity to the description of the spatial distribution of the pixel intensities in mammographic images. These methods were tested with a set of 57 breast masses and 60 normal breast parenchyma (dataset1), and with another set of 19 architectural distortions and 41 normal breast parenchyma (dataset2). Support vector machines (SVM) were used as a pattern classification method for tumor classification. Results: Experimental results showed that the fractal dimension of region of interest (ROIs) depicting mass lesions and architectural distortion was statistically significantly lower than that of normal breast parenchyma for all five methods. Receiver operating characteristic (ROC) analysis showed that fractional Brownian motion (FBM) method generated the highest area under ROC curve (A z = 0.839 for dataset1, 0.828 for dataset2, respectively) among five methods for both datasets. Lacunarity analysis showed that the ROIs depicting mass lesions and architectural distortion had higher lacunarities than those of ROIs depicting normal breast parenchyma. The combination of FBM fractal dimension and lacunarity yielded the highest A z value (0.903 and 0.875, respectively) than those based on single feature alone for both given datasets. The application of the SVM improved the performance of the fractal-based features in differentiating tumor lesions from normal breast parenchyma by generating higher A z value. Conclusion: FBM texture model is the most appropriate model for characterizing mammographic images due to self-affinity assumption of the method being a better approximation. Lacunarity is an effective counterpart measure of the fractal dimension in texture feature extraction in mammographic images. The classification results obtained in this work suggest that the SVM is an effective method with great potential for classification in mammographic image analysis.

Finding the point on Bezier Curves with the normal vector passing an external point

Two algorithms for finding the point on non-rational/rational Bezier curves of which the normal vector passes through a given external point are presented. The algorithms are based on Bezier curves generation algorithms of de Casteljau's algorithm for non-rational Bezier curve or Farin's recursion for rational Bezier curve, respectively. Orthogonal projections from the external point are used to guide the directional search used in the proposed iterative algorithms. Using Lyapunov's method, it is shown that each algorithm is able to converge to a local minimum for each case of non-rational/rational Bezier curves. It is also shown that on convergence the distance between the point on curves to the external point reaches a local minimum for both approaches. Illustrative examples are included to demonstrate the effectiveness of the proposed approaches.