Comparisons of Treatments After an Analysis of Variance in Ecology
TL;DR: The statistical literature on tests to compare treatments after the analysis of variance is reviewed, and the use of these tests in ecology is examined, and particular strategies are recommended.
Abstract: The statistical literature on tests to compare treatments after the analysis of variance is reviewed, and the use of these tests in ecology is examined. Monte Carlo simulations on normal and lognormal data indicate that many of the tests commonly used are inappropriate or inefficient. Particular tests are recommended for unplanned multiple comparisons on the basis of controlling experimentwise type I error rate and providing maximum power. These include tests for parametric and nonparametric cases, equal and unequal sample sizes, homogeneous and heterogeneous variances, non-independent means (repeated measures or adjusted means), and comparing treatments to a control. Formulae and a worked example are provided. The problem of violations of assumptions, especially variance heterogeneity, was investigated using simulations, and particular strategies are recommended. The advantages and use of planned comparisons in ecology are discussed, and the philosophy of hypothesis testing with unplanned multiple comparisons is consid- ered in relation to confidence intervals and statistical estimation.
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TL;DR: In this article, a non-parametric method for multivariate analysis of variance, based on sums of squared distances, is proposed. But it is not suitable for most ecological multivariate data sets.
Abstract: Hypothesis-testing methods for multivariate data are needed to make rigorous probability statements about the effects of factors and their interactions in experiments. Analysis of variance is particularly powerful for the analysis of univariate data. The traditional multivariate analogues, however, are too stringent in their assumptions for most ecological multivariate data sets. Non-parametric methods, based on permutation tests, are preferable. This paper describes a new non-parametric method for multivariate analysis of variance, after McArdle and Anderson (in press). It is given here, with several applications in ecology, to provide an alternative and perhaps more intuitive formulation for ANOVA (based on sums of squared distances) to complement the description pro- vided by McArdle and Anderson (in press) for the analysis of any linear model. It is an improvement on previous non-parametric methods because it allows a direct additive partitioning of variation for complex models. It does this while maintaining the flexibility and lack of formal assumptions of other non-parametric methods. The test- statistic is a multivariate analogue to Fisher's F-ratio and is calculated directly from any symmetric distance or dissimilarity matrix. P-values are then obtained using permutations. Some examples of the method are given for tests involving several factors, including factorial and hierarchical (nested) designs and tests of interactions.
12,328 citations
TL;DR: It is concluded that no single factor or mechanism fully accounts for primary succession at Glacier Bay and that changes in competitive balance accompanying successional changes in environment provide the mechanism for changes in species dominance.
Abstract: In primary succession following deglaciation at Glacier Bay, Alaska, we tested the hypothesis that the major effect of initial nitrogen-fixing colonizers is to facilitate establishment of late-successional dom- inants and that other possible causes of successional change (e.g., life history factors governing seed rain and competitive interactions among species) need not be invoked. Environment changed dramatically through the first 200 yr of succession. Soil organic matter increased 10-fold in the upper mineral soil with corresponding increases in soil moisture, total nitrogen (N), and capacity to support plant growth and declines in bulk density, pH, and total phosphorus (P). Plant growth in pioneer soils tended to be simultaneously limited by both N and P, as well as by unknown factors (perhaps lack of mycorrhizae), whereas only P limited growth in older soils. Light availability to seedlings declined through succession. Early-successional species (Epilobium latifolium, Dryas drummondii) had smaller seeds, younger age at first reproduction, shorter life-span, and shorter height at maturity than did mid-successional (alder, Alnus sinuata) and late-successional species (sitka spruce, Picea sitchensis). Seed rain of alder and spruce was negligible in the pioneer stage, increased prior to the stage in which a species was dominant, and was greatest in the stage in which a species dominated. Vegetation in each successional stage inhibited germination and initial establishment of sown alder and spruce seeds (except a tendency of the "black-crust" algal/microbial community in the pioneer stage to enhance survivorship). Removal of the surface litter layer generally enhanced germination and survi- vorship, particularly of alder. Comparisons of germination in the greenhouse and the field indicated that climatic or indirect vegetation effects (e.g., differential seed predation) and allelopathy also reduced germination and establishment in vegetated communities. Naturally occurring spruce seedlings grew most rapidly in the Dryas and alder stages and most slowly in the spruce stage. Similarly, growth of spruce seedlings transplanted into each successional stage was facilitated by the Dryas (nonsignificantly) and alder stages but inhibited by the spruce stage, relative to earlier successional stages. Facilitation of growth of natural and transplanted spruce seedlings by Dryas and alder stages was associated with higher N and P uptake and tissue nutrient concentrations, whereas nutrient uptake and concentration in spruce seedlings declined in the spruce stage. By contrast, transplanted alder seedlings grew rapidly and accu- mulated most nutrients in the pioneer stage and were strongly inhibited by subsequent stages. The facilitative effect of Dryas and alder comes primarily from inputs of organic matter and associated N. Addition of alder litter stimulated nutrient uptake and growth of transplanted spruce seedlings in the pioneer and Dryas stages, whereas shading had no effect on growth of spruce seedlings. Root trenching and planting of spruce near isolated alders indicated that, although the net effect of alder is facilitative, alder also inhibits growth of spruce seedlings through competition for soil resources. Strong root competition also occurs in the spruce stage. Alder competitively inhibits Dryas, primarily by shading but also through the physical and allelopathic effects of its litter. In general, both at Glacier Bay and elsewhere, life history traits determine the pattern of succession. Changes in competitive balance accompanying successional changes in environment provide the mechanism for changes in species dominance. Initial site conditions (and facilitation, where present) influence the rate of change and final state of community composition and productivity. We conclude that no single factor or mechanism fully accounts for primary succession at Glacier Bay.
955 citations
TL;DR: In 2011, the waters along the west coast of Australia experienced an unprecedented (in recorded times) warming event with warming anomalies of 2-4°C that persisted for more than ten weeks.
Abstract: In 2011 the waters along the west coast of Australia—a global hotspot of biodiversity—experienced an unprecedented (in recorded times) warming event with warming anomalies of 2–4 °C that persisted for more than ten weeks. Now research shows that biodiversity patterns of temperate seaweeds, invertebrates and fishes were significantly different following the warming event.
916 citations
TL;DR: Evaluated non—pioneer tree species in primary tropical wet forest at the La Selva Biological Station, Costa Rica showed a capacity for growth responses to small increases in light, substantial height and diameter increments at higher light levels, equal ability to survive 4—yr periods of no growth, and very low mortality rates at intermediate—to—large juvenile sizes.
Abstract: To assess the diversity of tropical tree life histories, a conceptual framework is needed to guide quantitative comparative study of many species. We propose one such framework, which focuses on long—term performance through ontogeny and over the natural range of microsites. For 6 yr we annually evaluated survival, growth, and microsite conditions of six non—pioneer tree species in primary tropical wet forest at the La Selva Biological Station, Costa Rica. The species were: Lecythis ampla, Hymenolobium mesoamericanum, Dipteryx panamensis, Pithecellobium elegans, Hyeronima alchorneoides (all emergents), and Minquartia guianensis (a canopy species). The study was based on long—term measurement of individuals from all post—seedling size classes. Trees were sampled from 150 ha of primary forest spanning several watersheds and soil types. To evaluate individuals' microsites we recorded the number of overtopping crowns, forest phase (gap, building, mature), and crown illumination index (an estimate of the tree's light environment). For comparison, we also evaluated the microsites of three species that have been categorized as pioneers (Cecropia insignis, C. obtusifolia) or high—light demanders (Simarouba amara). For the six species of non—pioneers, mortality rates declined with increasing juvenile size class. As a group, these emergent and canopy trees showed a much lower exponential annual mortality rate (0.44%/yr at >10 cm diameter) than has been found for the La Selva forest as a whole. Growth rates increased with juvenile size class for all six species. As adults (trees >30 cm in diameter), all five emergent species showed substantial annual diameter increments (medians of 5—14 mm/yr). Small saplings and adults of all species had significant year—to—year variation in diameter growth, with much greater growth occurring in the year of lowest rainfall. Passage time analysis suggests that all six species require >150 yr for growth from small saplings to the canopy. Evaluation of all nine species revealed four patterns of microsite occupancy by juveniles. Among the non—pioneers, one species pair (Lecythis and Minquartia: Group A) was associated with low crown illumination and mature—phase forest in all juvenile stages. For two species (Dipteryx and Hymenolobium: Group B) the smallest saplings were in predominantly low—light, mature—forest sites, but crown illumination and association with gap— or building—phase sites increased with juvenile size (Simarouba also showed this pattern). Two species (Pithecellobium and Hyeronima: Group C) were strongly associated with gap or building phase as small juveniles (≤4 cm diameter) and again as subcanopy trees (>10—20 cm diameter), but were predominantly in mature—phase sites at intermediate sizes. Juveniles of the two pioneer species (Cecropia: Group D) showed the highest crown illumination and association with gap or building sites. Among the six non—pioneer species, only one aspect of juvenile performance clearly varied according to microsite group. The smallest saplings (≤1 cm diameter) of Groups B and C showed significant mortality differences across a small gradient in crown illumination; neither of the Group A species showed this pattern. Otherwise, juvenile performance was strikingly similar among the six species. All showed a capacity for growth responses to small increases in light, substantial height and diameter increments at higher light levels, equal ability to survive 4—yr periods of no growth, and very low mortality rates at intermediate—to—large juvenile sizes. Species differed significantly in growth rates, but relative differences shifted with tree size and were unrelated to microsite group. These findings do not support prevailing paradigms concerning trade—offs and correlated suites of traits. For non—pioneer tropical trees, life history classification based on generalized concepts such as gap dependence and shade tolerance is inadequate to describe the complex size—dependent patterns of life history differences and similarities that exist among species.
744 citations
Macquarie University1, University of Minnesota2, VU University Amsterdam3, University of Oslo4, Curtin University5, Tohoku University6, Landcare Research7, University of Concepción8, University of Tartu9, Polish Academy of Sciences10, University of Tokyo11, Utrecht University12, University of New South Wales13
TL;DR: To quantify climatic influences on key leaf traits and relationships at the global scale provides insight into how plants have adapted to different environmental pressures, and will lead to better calibration of future vegetation‐climate models.
Abstract: Aim Our aim was to quantify climatic influences on key leaf traits and relationships at the global scale. This knowledge provides insight into how plants have adapted to different environmental pressures, and will lead to better calibration of future vegetation‐climate models. Location The data set represents vegetation from 175 sites around the world. Methods For more than 2500 vascular plant species, we compiled data on leaf mass per area (LMA), leaf life span (LL), nitrogen concentration (N mass ) and photosynthetic capacity (A mass ). Site climate was described with several standard indices. Correlation and regression analyses were used for quantifying relationships between single leaf traits and climate. Standardized major axis (SMA) analyses were used for assessing the effect of climate on bivariate relationships between leaf traits. Principal components analysis (PCA) was used to summarize multidimensional trait variation. Results At hotter, drier and higher irradiance sites, (1) mean LMA and leaf N per area were higher; (2) average LL was shorter at a given LMA, or the increase in LL was less for a given increase in LMA (LL‐LMA relationships became less positive); and (3) A mass was lower at a given N mass , or the increase in A mass was less for a given increase in N mass . Considering all traits simultaneously, 18% of variation along the principal multivariate trait axis was explained by climate.
711 citations
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01 Dec 1969TL;DR: The concepts of power analysis are discussed in this paper, where Chi-square Tests for Goodness of Fit and Contingency Tables, t-Test for Means, and Sign Test are used.
Abstract: Contents: Prefaces. The Concepts of Power Analysis. The t-Test for Means. The Significance of a Product Moment rs (subscript s). Differences Between Correlation Coefficients. The Test That a Proportion is .50 and the Sign Test. Differences Between Proportions. Chi-Square Tests for Goodness of Fit and Contingency Tables. The Analysis of Variance and Covariance. Multiple Regression and Correlation Analysis. Set Correlation and Multivariate Methods. Some Issues in Power Analysis. Computational Procedures.
115,069 citations
21,056 citations
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01 Jan 1968
TL;DR: The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid.
Abstract: A fuel pin hold-down and spacing apparatus for use in nuclear reactors is disclosed. Fuel pins forming a hexagonal array are spaced apart from each other and held-down at their lower end, securely attached at two places along their length to one of a plurality of vertically disposed parallel plates arranged in horizontally spaced rows. These plates are in turn spaced apart from each other and held together by a combination of spacing and fastening means. The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid. This apparatus is particularly useful in connection with liquid cooled reactors such as liquid metal cooled fast breeder reactors.
17,939 citations