THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Understanding and predicting ecosystem functioning (e.g., carbon and water fluxes) and the role of soils in carbon storage requires an accurate assessment of plant rooting distributions. Here, in a comprehensive literature synthesis, we analyze rooting patterns for terrestrial biomes and compare distributions for various plant functional groups. We compiled a database of 250 root studies, subdividing suitable results into 11 biomes, and fitted the depth coefficient β to the data for each biome (Gale and Grigal 1987). β is a simple numerical index of rooting distribution based on the asymptotic equation Y=1-βd, where d = depth and Y = the proportion of roots from the surface to depth d. High values of β correspond to a greater proportion of roots with depth. Tundra, boreal forest, and temperate grasslands showed the shallowest rooting profiles (β=0.913, 0.943, and 0.943, respectively), with 80-90% of roots in the top 30 cm of soil; deserts and temperate coniferous forests showed the deepest profiles (β=0.975 and 0.976, respectively) and had only 50% of their roots in the upper 30 cm. Standing root biomass varied by over an order of magnitude across biomes, from approximately 0.2 to 5 kg m-2. Tropical evergreen forests had the highest root biomass (5 kg m-2), but other forest biomes and sclerophyllous shrublands were of similar magnitude. Root biomass for croplands, deserts, tundra and grasslands was below 1.5 kg m-2. Root/shoot (R/S) ratios were highest for tundra, grasslands, and cold deserts (ranging from 4 to 7); forest ecosystems and croplands had the lowest R/S ratios (approximately 0.1 to 0.5). Comparing data across biomes for plant functional groups, grasses had 44% of their roots in the top 10 cm of soil. (β=0.952), while shrubs had only 21% in the same depth increment (β=0.978). The rooting distribution of all temperate and tropical trees was β=0.970 with 26% of roots in the top 10 cm and 60% in the top 30 cm. Overall, the globally averaged root distribution for all ecosystems was β=0.966 (r 2=0.89) with approximately 30%, 50%, and 75% of roots in the top 10 cm, 20 cm, and 40 cm, respectively. We discuss the merits and possible shortcomings of our analysis in the context of root biomass and root functioning.

A global analysis of root distributions for terrestrial biomes

The depth at which plants are able to grow roots has important implications for the whole ecosystem hydrological balance, as well as for carbon and nutrient cycling. Here we summarize what we know about the maximum rooting depth of species belonging to the major terrestrial biomes. We found 290 observations of maximum rooting depth in the literature which covered 253 woody and herbaceous species. Maximum rooting depth ranged from 0.3 m for some tundra species to 68 m for Boscia albitrunca in the central Kalahari; 194 species had roots at least 2 m deep, 50 species had roots at a depth of 5 m or more, and 22 species had roots as deep as 10 m or more. The average for the globe was 4.6±0.5 m. Maximum rooting depth by biome was 2.0±0.3 m for boreal forest. 2.1±0.2 m for cropland, 9.5±2.4 m for desert, 5.2±0.8 m for sclerophyllous shrubland and forest, 3.9±0.4 m for temperate coniferous forest, 2.9±0.2 m for temperate deciduous forest, 2.6±0.2 m for temperate grassland, 3.7±0.5 m for tropical deciduous forest, 7.3±2.8 m for tropical evergreen forest, 15.0±5.4 m for tropical grassland/savanna, and 0.5±0.1 m for tundra. Grouping all the species across biomes (except croplands) by three basic functional groups: trees, shrubs, and herbaceous plants, the maximum rooting depth was 7.0±1.2 m for trees, 5.1±0.8 m for shrubs, and 2.6±0.1 m for herbaceous plants. These data show that deep root habits are quite common in woody and herbaceous species across most of the terrestrial biomes, far deeper than the traditional view has held up to now. This finding has important implications for a better understanding of ecosystem function and its application in developing ecosystem models.

Maximum rooting depth of vegetation types at the global scale.

Global biogeochemical models have improved dramatically in the last decade in their representation of the biosphere. Although leaf area data are an important input to such models and are readily available globally, global root distributions for modeling water and nutrient uptake and carbon cycling have not been available. This analysis provides global distributions for fine root biomass, length, and surface area with depth in the soil, and global estimates of nutrient pools in fine roots. Calculated root surface area is almost always greater than leaf area, more than an order of magnitude so in grasslands. The average C:N:P ratio in living fine roots is 450:11:1, and global fine root carbon is more than 5% of all carbon contained in the atmosphere. Assuming conservatively that fine roots turn over once per year, they represent 33% of global annual net primary productivity.

https://www.pnas.org/content/pnas/94/14/7362.full.pdf

A global budget for fine root biomass, surface area, and nutrient contents

Studies in global plant biogeography have almost exclusively analyzed re- lationships of abiotic and biotic factors with the distribution and structure of vegetation aboveground. The goal of this study was to extend such analyses to the belowground structure of vegetation by determining the biotic and abiotic factors that influence vertical root distributions in the soil, including soil, climate, and plant properties. The analysis used a database of vertical root profiles from the literature with 475 profiles from 209 geographic locations. Since most profiles were not sampled to the maximum rooting depth, several techniques were used to estimate the amount of roots at greater depths, to a maximum of 3 m in some systems. The accuracy of extrapolations was tested using a subset of deeply ( .2 m) sampled or completely sampled profiles. Vertical root distributions for each profile were characterized by the interpolated 50% and 95% rooting depths (the depths above which 50% or 95% of all roots were located). General linear models incorporating plant life-form dominance, climate, and soil var- iables explained as much as 50% of the variance in rooting depths for various biomes and life-forms. Annual potential evapotranspiration (PET) and precipitation together accounted for the largest proportion of the variance (12-16% globally and 38% in some systems). Mean 95% rooting depths increased with decreasing latitude from 808 to 308 but showed no clear trend in the tropics. Annual PET, annual precipitation, and length of the warm season were all positively correlated with rooting depths. Rooting depths in tropical veg- etation were only weakly correlated with climatic variables but were strongly correlated with sampling depths, suggesting that even after extrapolation, sampling depths there were often insufficient to characterize root profiles. Globally,.90% of all profiles had at least 50% of all roots in the upper 0.3 m of the soil profile (including organic horizons) and 95% of all roots in the upper 2 m. Deeper rooting depths were mainly found in water- limited ecosystems. Deeper 95% rooting depths were also found for shrublands compared to grasslands, in sandy soils vs. clay or loam soils, and in systems with relatively shallow

https://www.jstor.org/stable/info/3100092

The global biogeography of roots

Above- and belowground biomass distribu- tion, isotopic composition of soil and xylem water, and carbon isotope ratios were studied along an aridity gradi- ent in Patagonia (44-45~ Sites, ranging from those with Nothofagus forest with high annual rainfall (770 ram) to Nothofagus scrub (520 mm), Festuca (290 mm) and Stipa (160 mm) grasslands and into desert vegetation (125 ram), were chosen to test whether root- ing depth compensates for low rainfall. Along this gradi- ent, both mean above- and belowground biomass and leaf area index decreased, but average carbon isotope ra- tios of sun leaves remained constant (at -27%o), indicat- ing no major differences in the ratio of assimilation to stomatal conductance at the time of leaf growth. The depth of the soil horizon that contained 90% of the root biomass was similar for forests and grasslands (about 0.80-0.50 m), but was shallower in the desert (0.30 m). In all habitats, roots reached water-saturated soils or ground water at 2-3 m depth. The depth profile of oxy- gen and hydrogen isotope ratios of soil water corre- sponded inversely to volumetric soil water contents and showed distinct patterns throughout the soil profile due to evaporation, water uptake and rainfall events of the past year. The isotope ratios of soil water indicated that high soil moisture at 2-3 m soil depth had originated from rainy periods earlier in the season or even from past rainy seasons. Hydrogen and oxygen isotope ratios of xylem water revealed that all plants used water from re- cent rain events in the topsoil and not from water-saturat- ed soils at greater depth. However, this study cannot ex- plain the vegetation zonation along the transect on the basis of water supply to the existing plant cover. Al- though water was accessible to roots in deeper soil layers in all habitats, as demonstrated by high soil moisture, earlier rain events were not fully utilized by the current plant cover during summer drought. The role of seedling establishment in determining species composition and vegetation type, and the indirect effect of seedling estab- lishment on the use of water by fully developed plant cover, are discussed in relation to climate change and vegetation modelling.

/pdf/rooting-depth-water-availability-and-vegetation-cover-along-1gh29kla28.pdf

Rooting depth, water availability, and vegetation cover along an aridity gradient in Patagonia

Mean annual precipitation accounts for a large proportion of the variation in mean above-ground net primary production (ANPP) of grasslands worldwide. However, the inter-annual variation in production in any grassland site is only loosely correlated with precipitation. The longest record of variation in production and precipitation for a site corre- sponds to a shortgrass steppe in Colorado, USA. A previous study of this record showed that current-year precipitation accounted for 39% of the inter-annual variation in ANPP. In this note, we show that ca. one third of the unexplained variation is related to previous-year ANPP: ANPP per mm of precipitation was higher in years preceded by wet, more productive years than in years preceded by average years; similarly, ANPP per mm of precipitation was lower in years preceded by dry, less productive years than in years preceded by average years. Since previous-year ANPP was, in turn, associated with precipitation of a year before, current-year ANPP was also explained by precipitation of two previous years. Our finding not only in- creases our predictive ability, but it also changes our under- standing of how ANPP responds to fluctuations in precipitation. If ANPP is thought to vary according to current-year precipita- tion only, it will simply track annual precipitation in time. According to this new result, however, ANPP fluctuations are buffered if wet, more productive years alternate with dry, less productive years, and they are amplified if wet or dry se- quences of several years take place.

/pdf/inter-annual-variation-in-primary-production-of-a-semi-arid-3u7fads2rl.pdf

Inter-annual variation in primary production of a semi-arid grassland related to previous-year production

Effects of Flooding and Drought on the Anatomy of Paspalum dilatatum

Many studies have analysed plant responses to flooding or drought separately, without addressing the relations between plant resistance to each of these factors. In this paper, we compare the responses to drought and flooding under glasshouse conditions of three populations of Paspalum dilatatum, a perennial C4 grass dominant at different positions along a topographic gradient in the flooding pampa of Argentina. Our results showed that flooding effects on yield were negative on an upland, null on an intermediate, and positive on a lowland population, whereas drought reduced yield equally across populations, showing that resistance to flooding was not related to resistance to drought at a population level. Drought decreased height and aerenchyma, and increased the proportion of roots, while flooding had opposite effects on these traits. The responses of the single clones that made up each population showed a positive relation between the resistances to both factors: along the ecocline formed by 58 clones, those more resistant to drought were also more resistant to flooding. In addition, the combined resistance of each clone to both factors was negatively related to yield at field capacity, (i.e. the most resistant clones were less productive) and unrelated to the proportion of roots and aerenchyma. This result agrees with predictions of Grime's plant strategy theory and differs from a few previous studies, which showed negative relations between the resistances to flooding and drought among genera and species.

Intraspecific variation in the resistance to flooding and drought in populations of Paspalum dilatatum from different topographic positions

Net primary production (NPP) and nutrient dynamics of grasslands are regulated by different biotic and abiotic factors, which may differentially affect functional plant groups. Most studies have dealt with grasslands that have extremely low or zero production over a significant period of the year. Here we explore the relative importance of a few environmental factors as controls of aerial and below-ground plant biomass production and nutrient dynamics in a grassland that is active throughout the year. We investigate their effect on the response of three main plant functional groups (warm- and cool-season graminoids and forbs). We conducted a factorial experiment in a continuously grazed site in the Flooding Pampa grassland (Argentina). Factors were seasons (summer, autumn, winter and spring), and environmental agents (mowing, shade, addition of phosphorus (P) and nitrogen (N)). N addition had the largest and most extended impact: it tripled aerial NPP in spring and summer but had no effect on below-ground biomass. This positive effect was accompanied by higher N acquisition and higher soil N availability. Mowing increased aerial NPP in winter, increased root biomass in the first 10 cm during autumn and winter and promoted N and P uptake by plants. Shading did not affect aerial NPP, but stimulated N and P uptake by plants. P addition had no effect on aerial NPP, but increased shallow root biomass and its N content in spring, and tripled P accumulation in plant biomass. The three plant functional groups differentially accounted for these ecosystem-level responses. Graminoids explained the greater biomass production of N-fertilized plots and mowing tended to promote forbs. These results suggest that the environmental controls of aerial NPP in this grassland vary among seasons, differentially impact the major floristic groups, and affect the energy and nutrient transfer to herbivores.

/pdf/controls-of-primary-productivity-and-nutrient-cycling-in-a-2wvxkpw3wb.pdf

Juan Loreti

Papers

Rooting depth, water availability, and vegetation cover along an aridity gradient in Patagonia

Inter-annual variation in primary production of a semi-arid grassland related to previous-year production

Effects of Flooding and Drought on the Anatomy of Paspalum dilatatum

Intraspecific variation in the resistance to flooding and drought in populations of Paspalum dilatatum from different topographic positions

Controls of primary productivity and nutrient cycling in a temperate grassland with year‐round production