Competition between three lichen species using a factorial experimental design

Competition between three foliose lichens common on slate rock in south Gwynedd, Wales was studied in the field using a factorial experimental design. The lichens were grown as fragments glued to pieces of slate in two- and three-species mixtures. In the two-species mixtures, Parmelia conspersa (Ehrh. Ex Ach.) Ach. outcompeted Parmelia glabratula ssp. fuliginosa (Fr. ex Duby) Laund. strongly and Physcia orbicularis (Neck.) Poetsch less strongly, while P. orbicularis outcompeted P. glabratula weakly. Significant two-factor interactions indicated that the results from the three-species mixture could not be predicted from the two-species mixtures. Parmelia glabratula and P. orbicularis grew better in the presence of two competitors than one. This result suggests that the three species may co-occur on well-lit rock surfaces at the site.

Data methods in optometry Part 9: experimental design and analysis of variance

The key to the correct application of ANOVA is careful experimental design and matching the correct analysis to that design. The following points should therefore, be considered before designing any experiment: 1. In a single factor design, ensure that the factor is identified as a 'fixed' or 'random effect' factor. 2. In more complex designs, with more than one factor, there may be a mixture of fixed and random effect factors present, so ensure that each factor is clearly identified. 3. Where replicates can be grouped or blocked, the advantages of a randomised blocks design should be considered. There should be evidence, however, that blocking can sufficiently reduce the error variation to counter the loss of DF compared with a randomised design. 4. Where different treatments are applied sequentially to a patient, the advantages of a three-way design in which the different orders of the treatments are included as an 'effect' should be considered. 5. Combining different factors to make a more efficient experiment and to measure possible factor interactions should always be considered. 6. The effect of 'internal replication' should be taken into account in a factorial design in deciding the number of replications to be used. Where possible, each error term of the ANOVA should have at least 15 DF. 7. Consider carefully whether a particular factorial design can be considered to be a split-plot or a repeated measures design. If such a design is appropriate, consider how to continue the analysis bearing in mind the problem of using post hoc tests in this situation.

Field experiments on competition between three foliose lichens using the de Wit experimental design

Competition between three foliose, saxicolous lichens common on slate rock in South Gwynedd, Wales, U.K. was studied experimentally using the de Wit design. Fragments of the three species were cut from the edges of large thalli, glued to 5 x 5 cm plots marked out on pieces of slate which were then placed on boards in the field. For each combination of pairs of species, the two species were grown either in monoculture at a density of 24 fragments per plot or together in three mixtures in differing proportions, i.e. species A:B with 16:8, 12:12 and 8:16 fragments per plot; the density remaining constant throughout. Area of the species in the plots after 3 years was used as an estimate of growth. Physcia orbicularis and Parmelia glabratula ssp. fuliginosa grew similarly in monoculture. In mixtures of the two, growth of each species was linearly related to its proportion in a mixture, suggesting little competition had occurred during three years. By contrast, the growth of Parmelia conspersa in monoculture was significantly greater than that of P. orbicularis or P. glabratula. In addition, the growth of both species was substantially reduced in mixtures with P. conspersa; P. glabratula being eliminated in the mixture in which it was the minority species. These results suggest that P. conspersa should predominate in communities with either of the other two species and, in the absence of P. conspersa, communities dominated by P.orbicularis and P. glabratula should be more stable.

Approximately optimal experimental design for heteroscedastic Gaussian process models

This paper presents a greedy Bayesian experimental design criterion for heteroscedastic Gaussian process models. The criterion is based on the Fisher information and is optimal in the sense of minimizing parameter uncertainty for likelihood based estimators. We demonstrate the validity of the criterion under different noise regimes and present experimental results from a rabies simulator to demonstrate the effectiveness of the resulting approximately optimal designs.

Teaching our children when to eat:how parental feeding practices inform the development of emotional eating-a longitudinal experimental design

Background: Emotional eating in children has been related to the consumption of energy-dense foods and obesity, but the development of emotional eating in young children is poorly understood. Objectives: We evaluated whether emotional eating can be induced in 5-7-y-old children in the laboratory and assessed whether parental use of overly controlling feeding practices at 3-5 y of age predicts a greater subsequent tendency for children to eat under conditions of mild stress at ages 5-7 y. Design: Forty-one parent-child dyads were recruited to participate in this longitudinal study, which involved parents and children being observed consuming a standard lunch, completing questionnaire measures of parental feeding practices, participating in a research procedure to induce child emotion (or a control procedure), and observing children's consumption of snack foods. Results: Children at ages 5-7 y who were exposed to a mild emotional stressor consumed significantly more calories from snack foods in the absence of hunger than did children in a control group. Parents who reported the use of more food as a reward and restriction of food for health reasons with their children at ages 3-5 y were more likely to have children who ate more under conditions of negative emotion at ages 5-7 y. Conclusions: Parents who overly control children's food intake may unintentionally teach children to rely on palatable foods to cope with negative emotions. Additional research is needed to evaluate the implications of these findings for children's food intake and weight outside of the laboratory setting. This trial was registered at clinicaltrials.gov as NCT01122290.

Competitive interactions between four foliose lichen species with and without nutrient enrichment

Competition between four foliose lichen species, common on slate rock surfaces in South Gwynedd, Wales, UK, was studied in experimental plots with and without nutrient enrichment by bird droppings. Fragments of the four lichens were glued to pieces of slate on horizontal boards in monoculture and in two-, three- and four-species mixtures in a factorial experimental design. In monoculture, nutrient enrichment increased thallus area of Parmelia conspersa (Ehrh. ex. Ach.) Ach., decreased thallus areas of Parmelia saxatilis (L.) Ach. and Parmelia glabratula ssp. fuliginosa (Fr. ex. Duby) Laundon, and did not affect thallus area of Phaeophyscia orbicularis (Necker) Moberg compared with untreated thalli. In the mixtures, P. conspersa and Ph. orbicularis were equally effective competitors in plots with and without nutrient enrichment. Addition of bird droppings, however, altered the ability of P. saxatilis and P. glabratula ssp. fuliginosa, to compete with the other species, the competitive ability of both species being reduced in some mixtures but increased in others. The results suggest that nutrient enrichment may alter the competitive balance between the four lichen species and this may be a factor determining their relative abundance on rock surfaces in South Gwynedd.

Competitive interactions between four foliose lichens on north and south facing rock surfaces

Competition between four foliose lichen species which have distinct aspect distributions on slate rock in South Gwynedd, Wales, U.K. was studied in the field using a factorial experimental design. The lichens were grown as fragments glued to pieces of slate in monoculture and in two-, three- and four-species mixtures. The pieces of slate were placed to face a northerly or southerly direction. Growth in area (mm2) was used as a measure of performance in the experiment. The growth in area of Parmelia conspersa in south facing plots was not reduced in the presence of any of its competitors but its growth was reduced in the presence of Parmelia saxatilis in north facing plots. The growth of Parmelia glabratula ssp. fuliginosa was reduced in the presence of P. conspersa and P. saxatilis in south and north facing plots. Physcia orbicularis was reduced by P. conspersa in south facing plots and by both P. glabratula ssp. fuliginosa and P. saxatilis in north facing plots. The growth of P. saxatilis was increased by P. glabratula ssp. fuliginosa in south facing plots but was not reduced by any of its competitors in north facing plots. Significant two and three factor interactions suggested that the results from the three- and four-species mixtures were not always predictable from the results of the two-species mixtures. The results of the experiment may help to explain the existing aspect distribution of the four species on slate rock in South Gwynedd.

The application of analysis of variance (ANOVA) to different experimental designs in optometry

Analysis of variance (ANOVA) is the most efficient method available for the analysis of experimental data. Analysis of variance is a method of considerable complexity and subtlety, with many different variations, each of which applies in a particular experimental context. Hence, it is possible to apply the wrong type of ANOVA to data and, therefore, to draw an erroneous conclusion from an experiment. This article reviews the types of ANOVA most likely to arise in clinical experiments in optometry including the one-way ANOVA ('fixed' and 'random effect' models), two-way ANOVA in randomised blocks, three-way ANOVA, and factorial experimental designs (including the varieties known as 'split-plot' and 'repeated measures'). For each ANOVA, the appropriate experimental design is described, a statistical model is formulated, and the advantages and limitations of each type of design discussed. In addition, the problems of non-conformity to the statistical model and determination of the number of replications are considered. © 2002 The College of Optometrists.