An analysis of yields of grasses in mixed and pure stands

To describe competition species must be compared with a standard. By conventional standards, such as grammes dry matter, tiller number and sq. cm leaf area, two species and even one species cannot be compared in the course of the season. Therefore a standard without dimensions was needed. Dividing yield of a species (expressed in any unit) in mixed culture by that in monoculture gave a figure without dimensions, called relative yield.Conclusions were based on my own pot experiments under controlled conditions and on field experiments of others.1. The rate at which one species replaces another is independent of the proportion of a species in the mixture.2. Competitive vigour of a grass species is independent of the other species or varieties associated with it in the mixture. This implies that if there are two experiments in which species A is competing with each of two morphologically identical varieties of species B, the result of competition between the varieties of B can be calculated. Competition in mixtures of two species will predict the competitive trend in more complex mixtures. In all these experiments the monocultures may never be omitted.3. When a treatment limits growth, in general competition changes at the expense of the more productive species. This is because there will be less competition for light as yield decreases, so benefiting the lower yielding species. Under these conditions the shoot/root ratio of the lower yielding species seems to decrease, another reason why the lower yielding species benefits in competition by suboptimum soil conditions. The above- ground production of a species with a large proportion of roots will respond less sharply to a shortage of minerals or water than a species with a higher shoot/root ratio. Hence, the change in competition in adverse conditions does not depend on the nature of the factor limiting growth.4. Sowing experiments show that pH considerably affects the development of seedlings, even though pH values within the range 4.2 - 6.8 does not affect competition between fully grown plants. In general the period of establishment and the competition afterwards should be stricktly separated. If this is omitted, completely erroneous conclusions may be drawn about the competitive ability of the species.5. Monocultures are preferred to mixed cultures for the following reasons.a. Because the higher yielding species in a mixture is not always the dominant species (Montgomery effect); the apparent advantage is often even a drawback. The risk of the lower yielding species becoming dominant should not be underestimated.b. The possibility that light is better utilized through the sod structure in a mixed culture can only be important during the period that the leaf canopy of the sod is not yet closed. In absolute terms this advantage is only small, especially if yields per cut are high; under grazing this possibility may be of more importance.c. A mixture of species with different growth rhythms might yield more. If so the increased yield will only be worthwhile if the species alter their order of dominance within the growing season. But changes in botanical composition are more gradual, so that this advantage of a mixture is lost.d. When the more productive species fails for some reason, the less productive species in the mixture could temporarily take over the production. But this temporary advantage may change into a persistent drawback, when recovery of the main species is hampered by the other species. On sown permanent grassland, especially under suboptimum conditions, less productive or otherwise undesirable species may in time invade the sward. It remains to be seen whether this is more efficiently prevented by a mixture or by a monoculture.e. The problem in sowing grassland is the choice of the highest yielding species under the prevailing conditions, rather than the choice of the highest yielding mixture

Competition between herbage plants

Starting from work with annuals a model of competition between herbage plants is discussed. It is shown that their mutual interference can only be described adequately if they are grown in mixture and also in monocultur

Fractional smoothness and applications in finance

This overview article concerns the notion of fractional smoothness of random variables of the form $g(X_T)$, where $X=(X_t)_{t\in [0,T]}$ is a certain diffusion process. We review the connection to the real interpolation theory, give examples and applications of this concept. The applications in stochastic finance mainly concern the analysis of discrete time hedging errors. We close the review by indicating some further developments.Comment: Chapter of AMAMEF book. 20 pages

The PL calibration for Milky Way Cepheids and its implications for the distance scale

The rationale behind recent calibrations of the Cepheid PL relation using the Wesenheit formulation is reviewed and reanalyzed, and it is shown that recent conclusions regarding a possible change in slope of the PL relation for short-period and long-period Cepheids are tied to a pathological distribution of HST calibrators within the instability strip. A recalibration of the period-luminosity relation is obtained using Galactic Cepheids in open clusters and groups, the resulting relationship, described by log L/L_sun = 2.415(+-0.035) + 1.148(+-0.044)log P, exhibiting only the moderate scatter expected from color spread within the instability strip. The relationship is confirmed by Cepheids with HST parallaxes, although without the need for Lutz-Kelker corrections, and in general by Cepheids with revised Hipparcos parallaxes, albeit with concerns about the cited precisions of the latter. A Wesenheit formulation of Wv = -2.259(+-0.083) - 4.185(+-0.103)log P for Galactic Cepheids is tested successfully using Cepheids in the inner regions of the galaxy NGC 4258, confirming the independent geometrical distance established for the galaxy from OH masers. Differences between the extinction properties of interstellar and extragalactic dust may yet play an important role in the further calibration of the Cepheid PL relation and its application to the extragalactic distance scale.Comment: Accepted for Publication (Astrophysics & Space Science

Formality theorems for Hochschild complexes and their applications

We give a popular introduction to formality theorems for Hochschild complexes and their applications. We review some of the recent results and prove that the truncated Hochschild cochain complex of a polynomial algebra is non-formal.Comment: Submitted to proceedings of Poisson 200