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Effect of plant population density and shading on the productivity of beans (Phaseolus vulgaris L.) and… Muli, Musyimi Benjamin 1995

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EFFECT OF PLANT POPULATION DENSITY AND SHADING ON THE PRODUCTIVITY OF BEANS (Phaseolus vulgaris L.) AND BEETS (Beta vulgaris L.) UNDER INTERCROPPING by MUSYTMI BENJAMIN MULI B. Sc. (Agric), University of Nairobi (1985) A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department of Plant Science) We accept this thesis as conforming ^9/the required standard THE UNIVERSITY OF BRITISH COLUMBIA March 1995 ©MUSYTMI BENJAMIN MULI, 1995 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of ptKrJT S^(^rJC<£ The University of British Columbia Vancouver, Canada Date f V p ^ 3. DE-6 (2/88) i i ABSTRACT Intercropping is a common practice throughout the world, but sole cropping systems predominate where advanced production technologies are widely available. The associated species in an intercropping system tend to interfere, mainly through either competition for mutually required resources or release of allelopathic chemicals to the microenvironment. This interference intensifies as the density of each component species increases. An experiment was performed to determine the effect of species population densities and shade on yield and yield components of beans (Phaseolus vulgaris L.) and beets (Beta vulgaris L.). Plants of each species were sown at four densities, in a split-plot randomized complete block design under two light intensity levels (full sun and partial shade). Analysis of variance, yield-density regressions, land equivalent ratios and light absorption-density regressions were used to quantify and interpret the treatment effects. The analysis of variance indicated that yield per plant was significantly reduced by increasing density of each species, and by decreasing light intensity for most of the growth measures. Inverse regression parameter values for most of the yield variables revealed that beet was a stronger competitor than bean. Beet was also found to be more competitive than bean under full sun, but not under shade. Bean dry-matter allocation to leaves, stems and pods was also observed to decrease with increasing bean and beet population densities. An exception to this was the allocation to leaves, which was not significantly affected by bean density. Beet density had no significant effect on its dry-matter allocation, but bean density caused significant reduction in beet dry-matter allocation to petioles and storage root. Land equivalent ratios (LER) were approximately equal to 1 indicating neither overyielding nor underyielding. The contribution of bean to LER was always lower than that of beet for all the variables. i i i Light interception was found to increase with species population densities and time. Bean was superior to beet in terms of light interception, which may account for the competitive improvement of bean observed under shade. i v TABLE OF CONTENTS Page ABSTRACT ii TABLE OF CONTENTS iv LIST OF TABLES vii LIST OF FIGURES viii LIST OF APPENDICES ix LIST OF SYMBOLS xi ACKNOWLEDGEMENTS xiv 1. INTRODUCTION 1 2. LITERATURE REVIEW 3 2.1 The test crops 3 2.1.1 Common beans 3 2.1.2 Beets 5 2.2 Crop mixtures 7 2.2.1 Importance of crop mixtures 7 2.2.2 Interference in crop mixtures 9 2.2.3 Effect of plant population density and spatial arrangement 10 2.2.4 Yield density relationships 12 2.2.4.1 Monoculture models 13 2.2.4.2 Mixture models 14 2.2.5 Yield advantages in crop mixtures . 15 2.3 Light 16 2.3.1 Importance of light as a growth factor 16 2.3.2 Light interception by leaf canopies 17 2.3.3 Monoculture and mixture crop response to light 19 V 3. MATERIALS AND METHODS 21 3.1 Site description, experimental design and crop production procedures 21 3.2 Harvesting and data collection 23 3.3 Data analysis 24 3.3.1 Analysis of variance 25 3.3.2 Yield-density regression analysis 26 3.3.3 Yield advantages in crop mixtures 26 3.3.4 Light absorption-density regression 26 4. RESULTS 28 4.1 Visual observations during growth 28 4.2 Data analysis 28 4.2.1 Analysis of variance 28 4.2.1.1 Bean results 29 4.2.1.1.1 Primary measures 29 4.2.1.1.2 Bean growth indices and dry-matter partitioning 32 4.2.1.2 Beet results 36 4.2.1.2.1 Primary measures 36 4.2.1.2.2 Beet growth indices and dry-matter partitioning 36 4.3 Yield-density regressions 39 4.4 Yield advantages in crop mixtures 52 4.5 Light absorption-density regression 53 5. DISCUSSION 55 5.1 Physiology (growth and productivity) 55 5.2 Crop ecology 57 5.3 Agricultural productivity 59 6. CONCLUSIONS 61 REFERENCES APPENDICES V l l LIST OF TABLES 3.1 Treatment combinations for bean and beet 22 3.2 Primary measures and growth indices for bean 24 3.3 Primary measures and growth indices for beet 25 4.1 Analysis of variance results for the loge transformed bean data: Variance ratios for the effect of shade (S), bean population density (Xi) and beet population density (X 2) on primary measures of growth 30 4.2 Analysis of variance results for the loge transformed bean data: Variance ratios for the effect of shade (S), bean population density (X{) and beet population density (X2) on growth indices 31 4.3 Analysis of variance results for the loge transformed beet data: Variance ratios for the effect of shade (S), beet population density (X x) and bean density (X 2) on primary measures of growth 3 7 4.4 Analysis of variance results for loge transformed beet data: Variance ratios for the effect of shade (S) beet population density (Xj) and bean population density (X 2) on growth indices 38 4.5 Estimate of model (Equations 3.1 & 3.2) parameter values for the response of primary measures of growth to species' population densities 52 4.6 Predicted and observed different yield variables at mixture population densities (D) of 10 and 20 plants m"2 and component species population densities of 5 and 10 plants m"2 53 * 4.7 Model (Equation 3.5) coefficient values for the effect of species population densities on light absorption 54 V l l l LIST OF FIGURES 4.1 (a) Effect of beet population density on bean dry-matter partitioning, at bean density of 5 plants m'2 33 4.1 (b) Effect of beet population density on bean dry-matter partitioning, at bean density of 10 plants m"2 34 4.1 (c) Effect of beet population density on bean dry-matter partitioning, at bean density of 20 plants m"2 3 5 4.2. (a) Effect of bean population density on beet dry-matter partitioning, at beet density of 5 plants m"2 40 4.2. (b) Effect of bean population density on beet dry-matter partitioning, at beet density of 10 plants m"2 41 4.2. (c) Effect of bean population density on beet dry-matter partitioning, at beet density of 20 plants m"2 42 4.3 Response of bean leaf area to bean and beet plant population densities 43 4.4 Response of bean leaf dry weight to bean and beet plant population densities 44 4.5 Response of bean shoot dry weight to bean and beet plant population densities 45 4.6 Response of beet leaf area to beet and bean plant population densities 46 4.7 Response of beet leaf dry weight to beet and bean plant population densities 47 4.8 (a) Response of beet shoot dry weight to beet and bean plant population densities, under shade 48 4.8 (b) Response of beet shoot dry weight to beet and bean plant population densities, in full sun 49 ix LIST OF APPENDICES 8.1 Homogeneity of variance test for bean leaf area data 69 8.2 Homogeneity of variance test for bean leaf dry weight data 70 8.3 Homogeneity of variance test for pod dry weight data 71 8.4 Homogeneity of variance test for bean shoot dry weight data 72 8.5 Homogeneity of variance test for beet leaf area data 73 8.6 Homogeneity of variance test for beet leaf dry weight data 74 8.7 Homogeneity of variance test for storage root dry weight data 75 8.8 Homogeneity of variance test for beet shoot dry weight data 76 8.9 Analysis of variance for loge transformed bean leaf area data 77 8.10 Analysis of variance for loge transformed bean leaf dry weight data 77 8.11 Analysis of variance for loge transformed stem dry weight data 78 8.12 Analysis of variance for loge transformed bean pod fresh weight data 78 8.13 Analysis of variance for loge transformed bean pod dry weight data 79 8.14 Analysis of variance for loge transformed number of pods data 79 8.15 Analysis of variance for loge transformed marketable number of pods data 80 8.16 Analysis of variance for loge transformed bean shoot dry weight data 80 8.17 Analysis of variance for loge transformed beet leaf area data 81 8.18 Analysis of variance for loge transformed beet leaf dry weight data 81 8.19 Analysis of variance for loge transformed petiole dry weight data 82 8.20 Analysis of variance for loge transformed storage root fresh weight data 82 8.21 Analysis of variance for loge transformed storage root dry weight data 83 8.22 Analysis of variance for loge transformed storage root diameter data 83 8.23 Analysis of variance for loge transformed beet shoot dry weight data 84 8.24 Response of stem dry weight to bean and beet population densities 85 8.25 Response of pod fresh weight to bean and beet population densities 86 8.26 Response of pod dry weight to bean and beet population densities 87 8.27 Response of petiole dry weight to beet and bean population densities 88 xi LIST OF SYMBOLS Symbols Page Definition (First appearance) A 24 Land area in m a 13 Intercept in yield-density models ANOVA 24 Analysis of variance b 13 Regression coefficient in yield-density models BLK 30 Block c 27 Regression coefficient in light absorption-density model D 53 Total population density df 30 Degrees of freedom DR 25 Storage root diameter per plant e 24 Base of natural logarithm F 24 Leaf area ratio H 24 Harvest index I 18 Light flux density below the canopy I 0 18 Light flux density above the canopy k 18 Extinction coefficient LAI 17 Leaf area index LA 24 Leaf area per plant LAD 17 Leaf area duration LER 15 Land equivalent ratio for a mixture LWR 24 Leaf weight ratio MPN 24 NPK(20:20:10) 22 PAR 22 PC 25 PN 24 PP 17 PWR 25 S 30 Sam. Error 30 SAS 25 SLA 24 SWR 24 W 24 WL 24 WP 25 WPD 24 WPF 24 WRD 25 WRF 25 WST 24 X 13 Y 13 Marketable pods number per plant Compound fertilizer comprising of 20% nitrogen, 20% phosphorus and 10% potassium Photosynthetically active radiation Personal computer Pod number per plant Photosynthetic potential Petiole weight ratio Shade Sampling error Statistical analysis system Specific leaf area Stem weight ratio Shoot dry weight per plant Leaf dry weight per plant Petiole dry weight Pod dry weight Pod fresh weight Storage root dry weight per plant Storage root fresh weight per plant Stem dry weight per plant Population density of a species (plants per land area) Yield per land area x i i i y 13 Yield per plant x 2 13 and 14 Subscripts indicating species. respectively Subscript 1 denotes the test species. Subscript 2 denotes the companion species xiv ACKNOWLEDGMENTS I am sincerely grateful to my supervisor Dr. Peter A. JollifFe for his patience, guidance and encouragement throughout my study program. His assistance in preparing this thesis is highly appreciated. I would also like to extend my sincere thanks to the members for my supervisory committee Drs. Art Bomke, Brian Holl and Mahesh K. Upadhyaya for their assistance and advice during the preparation of this thesis. Sincere acknowledgments are extended to Dr. Brian Ellis, Robyne Allan, Bev Busch and Ashley Herath for their assistance in all departmental administrative matters. The assistance offered by all my Kenyan friends during sowing, weeding and harvesting is highly appreciated. Special thanks are extended to Andy Benowicz for his full time assistance in field work. Thanks to you, Al Neighbour for your technical input during land preparation, irrigation and removal of crop residuals from the field. I am grateful to Dr. Eaton, Soenarto and Yassaman Bayani for their assistance in statistical data analysis. Many thanks to my friends; Francis Njenga, Upenyu Mazarura, Mesfin Tesfaye and Elisa Stabell for their unlimited assistance to me in various ways. I acknowledge the Canadian International Development Agency and Kenya Agricultural Research Institute for their financial support. I would also like to thank my wife Mwikali, daughters; Makaa and Wamutwa, for their patience and encouragement during the period I have been away from them. This thesis is also dedicated to them. Last but not least, I wish to acknowledge my mom Makaa, and the other members of my family for their encouragement throughout my stay.in Canada. 1. INTRODUCTION l Intercropping is a cropping system that involves the growing of two or more crops simultaneously on the same piece of land (Nnko & Doto, 1980). It is the most common production system used in subsistence tropical agriculture. In intercropping, the component species are not necessarily sown at the same time and their harvest times may be different, but they are simultaneous for a significant part of their growing period. Intercropping patterns also vary according to arrangement of component species in time and space. Intercropping system has potential for increasing yields, and in the drive to produce more food, this potential has to be exploited through research. Since changing the system has been found to be not acceptable to most farmers, efforts are being directed to the ways and means of improving the system to make it more productive. When two or more crops are planted together, the neighbouring plants tend to interfere through either competition for mutually required resources (Steiner, 1984) or non-competitive processes such as allelopathy (Rice, 1974). The intensity of this interference tends to increase with the increasing proximity among neighbouring plants. As plants grow, their leaves tend to overlap resulting in mutual shading. Shading is intensified by high population density, and the productivity of the component species in intercrops therefore depends on their ability to tolerate shading. The experimental work described in this thesis involves interference between intercropped beans (Phaseolus vulgaris L.) and beets (Beta vulgaris L.). This work was intended to establish the effects of various density treatments and shading on the productivity of beans and beets in monocultures and mixtures. The specific objectives for this research were: 1. to investigate and determine the overall relationship between species population densities and direct measures and derived indices of plant growth, 2. to establish the effects of species population densities on dry matter allocation to leaves, stems and pods for beans, and leaves petioles and storage roots for beets. 3. to determine the relative strengths of intra-and interspecific interference on yield measures of beans and beets. 4. to determine if shading modifies the competitive performance of the two plant species. 5. to establish whether intercrops overyield corresponding monocultures which alternatively might be grown on the same land. 6. to determine the effects of plant population densities and shading on light interception by shoot canopies. 3 2. LITERATURE REVIEW 2.1 The test crops 2.1.1 Common bean The common or field bean (Phaseolus vulgaris L.) is the most widely grown of the four cultivated species of Phaseolus (Laing et al, 1984), all of which have their origin in the Americas. The crop is a member of the Fabaceae, tribe Phaseoleae and subfamily Papilionoideae. The cultivated forms are herbaceous annuals, determinate or indeterminate in growth, and show considerable variations in vegetative characters, flower colour, and size, shape and colour of the pods and seeds. The papilionaceous flowers are borne in axillary and terminal racemes. All forms have a well developed tap root which grows rapidly, sometimes reaching a depth of 90 cm or more. The lateral roots are confined mainly to the top 15 cm of the soil and bear spherical or irregular nodules, approximately 6 mm in diameter. The stems are slender, twisted, angled and ribbed. The leaves are alternate, trifolioliate and often hairy with a long petiole. P. vulgaris is usually self fertilized, pollination taking place at the time the flower opens. The pods are slender, often glabrous, 7.5 to 20 cm long, straight or slightly curved with varying colour and number of seeds depending on the cultivar. Germination is epigeal, and requires 5 to 7 days at a soil temperature of 16°C (Adams et al., 1985). Time to flowering varies with cultivar, temperature and photoperiod and is usually between 28 and 42 days. As many as two-thirds of all flowers produced may abscise and under conditions of temperature or moisture stress young fruits and/or developing seeds may abort (Adams et al., 1985). Physiological maturity, the stage where no further increase in dry matter in seeds occurs, may be reached in the earliest dry seed varieties in only 60 to 65 days from seeding, but some genotypes in cooler regions may require up to 150 days. 4 As a monoculture P. vulgaris is usually planted in rows with inter-row spacing of 55 to 90 cm and intra-row spacing of 5 to 22.5 cm (Kay, 1979; Lorenz & Maynard, 1988). The depth of planting ranges from 2 to 5 cm depending on soil type and moisture conditions. A well drained and aerated soil is recommended (Peirce, 1987). The seeding rate varies from 22 to 55 Kg/ha depending on intra- and inter-row spacing. Beans are commonly intercropped with maize (Laing et al. 1984), but also with a number of other companion crops such as cassava (Manihot esculenta Cranz.), potatoes (Solatium tuberosum L.), coffee (Cqffea arabica L.) and sorghum (Sorghum vulgare IS). Competition between the crop species varies depending on the type of intercropping system employed. Determinate varieties are less competitive because of their morphology and give poor yields when intercropped with maize. P. vulgaris is mainly grown for dry seeds, mature green seeds (shell beans) and for fresh immature pods (Kay, 1979; Splittstoesser, 1984; Peirce, 1987). The tender pods are also used as potherbs in some parts of the world. As a green vegetable, the pods are harvested before they are fully grown and while the seeds are still small. All cultivars should be harvested before the seeds are large enough to cause the pod to bulge around the seeds (Thomson & Kelly, 1957), (i.e. about 12 to 14 days after the first blossoms are open depending on weather conditions) The time of harvesting is a compromise between total yield and high quality (Salunkhe & Desai, 1984). Harvesting is therefore be done at such a time that the grower will obtain the highest yield of high quality pods. Picking is usually done by hand. P. vulgaris is susceptible to a large number of diseases some of which are limited by climatic conditions and certain insect carriers and are not present in the common beans producing areas. The diseases are fungal: e.g. anthracnose (Colletotrichum lindemuthianum), bean rust (Uromyces phaseoli var. typica), angular leaf spot (Isariopsis griseold), ascochyta leaf spot (Ascochyta phaseolorum), ashy stem blight (Macrophomina phaseoli) downey mildew (Erysiphe polygoni) Sclerotinia wilt (Scleroiinia sclerotiorum); bacterial: e.g. haloblight 5 (Pseudomonas phaseolicold), bean wilt (Corynebacteriian flaccumfaciens), common blight (Xanthomonasphaseoli) and viral diseases e.g. common bean mosaic, bean yellow mosaic virus, curly top, golden mosaic and mottle dwarf virus. Insect pests such as aphids, Mexican bean beetle, corn earworm and leafhopper also limit common bean production. 2.1.2 Beet The beet (Beta vulgaris) is a member of the Chenopodiaceae or goose foot family. The species B. vulgaris encompasses the common garden beet, stock beet or mangel, sugar beet, and Swiss chard (Salunkhe & Desai, 1984). In this thesis, beets or B. vulgaris will refer only to the garden beet which is believed to be a native of Europe. Although beets have been grown as a potherb throughout recorded history, they were first grown for their roots in the 1500's (Splittstoesser, 1984). However, it was not until the late 1800's that much interest was shown in beet cultivars. B. vulgaris behaves as a biennial, producing a thickened root and a rosette of leaves in the first year and flowers and seeds in the second year. The crop is grown for either its storage root or for the tops as greens (Salunkhe & Desai, 1984). Beet cultivars have been developed that are classified according to the shape of the storage root and time of maturity. Beet roots are most often round, but may be flat or elongated. The fleshy roots are usually red, but golden cultivars are available. The stem is short and plate4ike; the leaves are simple and arranged in a closed spirals on a short stem called the crown (Ware & McCollum, 1975). Leaf colour varies from dark red to light green. The 'seed' of beets is actually a dried fruit containing 2 to 6 true seeds (Ware & McCollum, 1975; Salunkhe & Desai, 1984). A monogerm cultivar, in which each fruit has only one seed has also been released (Peirce, 1987). The storage root is as a result of the swelling of the hypocotyl plus a small portion of the tap root. The swelling is caused by growth of several concentric vascular cambia which are visible as 'rings' when the root is sectioned. The edible portion of the root consists of alternating circular bands of conducting and storage tissues. The bands of storage tissues are 6 relatively broad and dark; and those of conducting tissues are relatively narrow and light. The red colour in B. vulgaris is due to betacyanin pigment, but roots also contain a yellow pigment, the betaxanthin (Peirce, 1987). The actual root system is characterised by a prominent tap root that develops rapidly and can reach a depth of 3 m (Peirce, 1987). Lateral roots tend to develop at the base of the swollen edible structure and some of them extend to a substantial distance, laterally and vertically (Peirce, 1987). B. vulgaris grows best in cool climates, at temperature means of 16° to 18°C (Yamaguchi, 1983). Although B. vulgaris is said to be able to tolerate both hot and cold temperatures (Splittstoesser, 1984) it will not withstand severe freezing. The crop requires a cold temperature of 4° to 10°C for two weeks or longer for flower initiation (Yamaguchi, 1983). B. vulgaris thrives best in well-drained, slightly acidic soils including sandy loams, loams, silt loams, and mucks (Ware & McCollum, 1975). The crop will do well over a fairly wide pH range, but is quite sensitive to soils of high acidity. The optimum pH range is 6.0 to 7.0 (Ware & McCollum, 1975). B. vulgaris is usually planted at a depth of 1.5 to 2.5 cm in rows spaced at 45 to 61 cm apart (Peirce, 1987). The seeds are normally drilled and later thinned to a spacing of 5 to 10 cm within the rows (Lorenz & Maynard, 1988). Seeds germinate at a wide range of soil temperature, 7° to 29°C. Fertiliser requirement varies with soil type and fertility. Beets are commonly grown in monocultures, and have not been exploited as intercrops. B. vulgaris is harvested either mechanically or manually. Time of harvesting depends on its intended use. Early harvesting is usually for greens. Beets for fresh market (bunching) are harvested when they attain a diameter of about 4 cm (Salunkhe & Desai, 1984). The 'baby beet' is harvested when the roots are between 4 and 5 cm in diameter. Roots for pickling and canning are harvested when they attain diameters of about 7 cm. The mature harvesting stage is when the roots are between 7 and 10 cm in diameter. The tops for mature roots are removed, and the roots may be stored for several months after harvest (Shoemaker, 1953). While small 7 sized beet roots are marketed intact, larger sizes are used for sliced or diced products. Mechanically harvested beets are topped, washed and pre-packaged in transparent film bags for sale in retail stores. This practice extends the shelf life over that of beets with tops (Ware & McCollum, 1975; Salunkhe & Desai, 1984). Nearly all the beets destined for processing are mechanically harvested with a machine that lifts, tops and conveys the roots into trucks. Diseases are relatively minor problems in beet production (Peirce, 1987). The most common diseases are leaf spot (Cercospora beticola), downey mildew (Peronospora schachtis), black rot (Pythium spp) and curly top virus. Their most common insect pests are leaf miners (Pegomyia hyoscyami), aphids (Aphis spp.), leafhoppers (Empoasca faabae), flea beetles (Epitrix cucumeris) and webworms (Hymenia recurvalis). Lack of boron in the soil may also cause black pitting, surface cankers, heart rot or dry rot (Shoemaker, 1953). 2.2 Crop mixtures 2.2.1 Importance of crop mixtures A crop mixture is said to exist where more than one crop are grown in association on the same piece of land in the same season so that there is a spatial and temporal overlap during their growth (Osiru & Willey, 1972). Although crop mixtures are extensively grown throughout the world, sole crops predominate where advanced crop production technologies are widely available (Potdar, 1986); mainly north America and Europe. In these regions the most common form of crop mixtures are those of grass pastures and forage crops. Two systems for growing crop mixtures are practiced: mixed cropping and intercropping. The two involve the growing of two or more crop species simultaneously in the same piece of land, but in intercropping the plants are grown in rows whereas mixed cropping lacks the distinct row arrangement (Andrews & Kassam, 1976). 8 Crowing of mixtures is a notable characteristic of tropical and subtropical agriculture (Francis et al, 1978). Several reasons have been suggested for the popularity of these systems: insurance against vagaries of weather (Beets, 1982; Federer, 1993); enhanced control of diseases, weeds and insect pests (Andrews & Kassam, 1976; Kyamanywa (unpublished); Federer, 1993) and better utilization of environmental resources (Baker & Norman, 1975; Beets, 1982; Federer, 1993). By planting more than one crop simultaneously in the same field, the farmer is also maximizing soil fertility maintenance and soil erosion control (Federer, 1993). Intercropping or mixed cropping also entail some social economic benefits such as greater stability of the systems (Beets, 1982), broader economic base, improved human nutrition and better labour utilization (Baker & Norman, 1975). Intercropping or mixed cropping can also be disadvantageous if large yield reduction occurs due to inter-specific competition (Harper, 1961; Donald, 1963), allellopathic effects (Rice, 1974) or possibly greater incidence of pests or diseases (Pinchinat et al, 1976). The system is also said to be impractical where a high level of mechanization is required (Willey, 1979). In intercropping and mixed cropping, the component species are not necessarily sown or harvested at the same time but they overlap for a significant part of their growing season (Willey, 1979). Also, intercropping patterns vary according to spatial arrangement of the component species. Accordingly, several classes of intercropping have been identified: row intercropping (growing two or more crops simultaneously where one or more crops is/are planted in rows), strip intercropping (growing two or crops simultaneously in different strips narrow enough to permit agronomic interaction), relay intercropping (growing two or more crops simultaneously during only part of their life cycles), multi-storey (interculture) intercropping (the association of tall perennials with short, mostly biannual and annual crops) and patch intercropping (growing crop mixtures in patches). Crop mixtures are believed to have the potential to yield more than monocultures on an equivalent land area basis (Trenbath, 1974; Andrews & Kassam, 1976). This holds true where 9 competitive processes dominate crop performance and inter-specific competition is lower than intra-specific competition. This could be due to fuller exploitation of the environmental resources due to niche differentiation among the component species (Trenbath, 1974). Many different species combinations have been grown in association. In Kenya, for example, plant combinations differ depending on ecological zones, farmers' tastes, culture and relative market values. Common mixture combinations include: maize (Zea mays L.) with pulse crops such as common bean (Phaseolus vulgaris L.), pigeon peas (Cajanus cajan L.), cowpeas (Vigna unguiculata L.), green grams (Phaseolus aureus Roxb.), hyacinth bean (Dolichos lablab L.) and groundnuts (Arachis hypogaea L.); coffee (Coffea arabica L.) with common beans, and sorghum (Sorghum vulgare L.) with any of the pulse crops. Multi-species crop mixtures such as maize with pigeon peas and common beans, maize with cotton (Gossypium hirsutum L.) and cowpeas, maize with cassava (Manihot esculenta Cranz.) and cowpeas, coconut (Cocos nucifera L.) with cashewnut (Anacardium occidentale L.) and maize, and coconut with citrus and maize are also common. Crop mixtures involving vegetable crops have not been popular, and research attention is only now being directed to this area. Information on bean and beet intercrops is scarce (Mchaina, 1991). There is also no evidence of the performance of the two crops having been evaluated under different light regimes. The two crops were chosen for this study on the basis of climatic suitability, similar recommended monoculture densities, similar duration required for the crops to mature, and the contrasting ability of beans to fix nitrogen, unlike beets. 2.2.2 Interference in crop mixtures Botanists define 'plant interference' as the response of an individual plant or species to the environment as modified by the presence of another plant or species (Harper, 1961; Hall, 1974; Trenbath, 1974). Such interference can be non-competitive, competitive or complementary. Non-competitive interference occurs when one plant/species modifies its 10 neighbour's environment either through production of allelochemicals or through the influence on diseases, weeds and insect pests. Competitive interference or competition among plant species for limited resources may occur if either one species depletes resources more quickly than another (Grime, 1977) or a more successful competitor depletes resources to a level below which another species cannot extract sufficient quantities for growth, survival and reproduction (Tilman, 1982). Complementary interference occurs when one plant/species helps another as in the case of legumes fixing their own nitrogen and therefore leaving the soil nitrogen for cereals to extract. Other interactions between plant root systems however, may, also be involved. For example, the colonization of plant roots by bacteria and/or fungi can be influenced by the presence of roots of other species (Christie et al., 1978). Interference occurs among plants of the same species in single stands and among plants of the same and different species in intercropped systems. Competition or complementarity between plants species is the normal situation in farmers fields (Steiner, 1984). In intercropping systems, the component plant species are not necessarily competing for the same overall growth factors, and thus inter-specific competition may be less than intra-specific competition. Maximizing intercropping advantages is therefore a matter of maximizing the degree of complementarity between the component species and niinimizing the inter-specific competition. This implies that intercropping advantages are more likely to occur where the component crops are very different (Willey, 1979). 2.2.3 Effect of plant population density and spatial arrangement Crop plants are usually not grown as isolated individuals but are grown in closely spaced populations. During the establishment and early seedling phases of growth, individual plants are usually sufficiently widely spaced that they do not interfere with each other (Harper, 1983). At some point as plants grow, they start to interfere with their neighbours and competition for resources begins. In populations of plants of similar genotypes, in the absence of weeds, the 11 competition is intra-specific, i.e. within species. Where different species of crops are grown in mixtures and where weeds are present, the competition is inter-specific, i.e. between species (Harper, 1983). In essence, the examination of intra-specific competition in crop plants is the study of plant population density. The effect of plant population density on yields, and the cost of seeds and other propagating materials are the key reasons for needing to quantify the optimum plant population for each crop in a range of production systems (Harper, 1983) Plant competition, coupled to population density, also affects the size variation that occurs within a population. The frequency distribution of individual plant weight is usually normal at early seedling stage, but thereafter the distribution of plant weights becomes progressively skewed, with few large individuals and many small ones (Koyama & Kira, 1956). The rate of change from normal to skewed distributions varies greatly between populations, but is usually higher at high population densities. The arrangement of the plants within a given population is also an important factor determining crop yields (Holliday, 1960; Beets, 1982; Harper, 1983; Steiner, 1984). The way a given number of plants is laid out in the field influences the growth, development and yield of the individual plants as well as the crop as a whole (Beets, 1982). Equidistant spacing or square planting gives the minimum competitive effect on neighbours since the distance to the neighbours is maximized and this, theoretically leads to maximum plant yield (Donald, 1963). Since individual plants respond to the number of neighbouring plants, it might be expected that that the relative growth rates of plants will be functions of the space available to individuals, since this will affect the availability of resources (Benjamin & Hardwick, 1986). Plant arrangement or rectangularity can be varied by changing the row width and the spacing between plants in a row. Comparisons of effects of plant populations should be made at a standard row widths to remove any effects of plant arrangement (Harper, 1983). Three aspects of competition due to plant density are important in determining the effects on yields: the amount, intensity, and the time of its onset. At very low densities, with 12 most crop plants, competition may not occur at all and resources are not efficiently used (Beets, 1982). The selection of an appropriate plant population density for a crop must avoid the inefficient use of resources at low levels and the excessive competition at high ones. The time of onset of competition is affected by planting date, speed of emergence and the arrangement of the leaves. The leaf area of rosette plants like beets is less effectively distributed in terms of light interception than that of cereals or potato crop (Harper, 1983). The relationship between the final yield of a crop and the plant population is either asymptotic or parabolic (Holliday, 1960; Willey & Heath, 1969; Harper, 1983). 2.2.4 Yield-density relationships The relationship between plant yield and population density has long been appreciated as important from both a theoretical and practical point of view (Kira et al., 1956; Mead, 1966: Gillis and Ratkowski, 1978). The yield per unit area increases linearly with increasing population density over the lower range but thereafter the rate of increase declines until a maximum value is reached. Further increase in plant population density above this maximum does not produce further increase in yield. The yield of individual plants declines rapidly over the lower range of populations, but the decline is slower at higher densities (Holliday, 1960; Willey & Heath, 1969). The partitioning of dry matter is also affected by plant population. For example, in forage maize, the proportion of ear declines with increasing plant density (Harper, 1983). The control of size of individual plants by manipulating plant population is important in root vegetable crops. For example, close spacing of carrots results in a higher proportion of the roots in the canning size range (Harper, 1983). Higher plant populations have been observed to increase the risk of lodging in cereal crops, increase disease infestation and enhance weed control. 13 Various models have been used to describe the relationship between plant yield and population density. Two categories of yield density models exist: those that describe the plants growing in monoculture and those that describe plants growing in mixtures. Early attempts to construct yield density models, which form the basis of current models, have been reviewed by Willey and Heath (1969). For the yield-density models to be of greatest value, their parameters should possess meaningful biological interpretation. 2.2.4.1 Monoculture models The application of mathematical equations to yield-density relationships has drawn the attention of many plant scientists (Kira etal, 1953; Shinozaki & Kira, 1956; Holliday, 1960; Bleasdale & Nelder, 1960; Mead, 1966; Gillis & Ratkowski, 1978; Wright, 1981; Watkinson, 1980; Spitters, 1983; Vandermeer, 1984; Jolliffe, 1988; Rejmanek etal, 1989;Roush, 1985). Most of these equations show an asymptotic response in that an increase in population density results in an increase in yield per unit land area until an upper limit is reached at high population densities. This is a characteristic of data of total shoot biomass or other measures of vegetative part. However, reproduction yield, such as grain or seed, often shows a parabolic yield density relationship. It is preferable to model the relationship between plant density (X) and yield per plant (y), rather than yield per land area (Y), because the latter combines the dependent and independent variables (Mchaina, 1991). The application of mathematical models to yield-density relationships seems to have culminated in the general acceptance of reciprocal relationships (Bleasedale & Nelder, 1960; Holliday, 1960) between yield per plant and population density. Reciprocal models, which rely on multiple regression techniques, offer a more powerful approach. Kira et al (1953), Ikusima & Kira (1955) and Shinozaki & Kira (1956) derived theoretically and deterrnined empirically a linear relationship between the reciprocal of mean yield per plant and population density. This relationship is expressed as: 14 yf^+bnX! (2.1) where is the mean yield per plant and X is the plant population density. The intercept 'a' can be interpreted as the reciprocal mean yield of an isolated plant and the coefficient 'b' represents the 'crowding effect' i.e. the strength of intraspecific competition. This equation can only describe an asymptotic yield-density relationship. In an attempt to include the parabolic yield-density responses in reciprocal models, Holliday (1960) added a quadratic term: y i - ^ + buXi + bn*!2 (2-2) As in equation (1) parameter 'a' represents the inverse of mean yield of an isolated plant and b j j and b u' represents intraspecific competition. For an asymptotic relationship to prevail, b j j = 0 and bj j/ > 0 for parabolic relationship. This equation is observed to yield a good fit to experimental data (Willey, 1982) despite being purely empirical. 2.2.4.2 Mixture models Not only plants of the same species but also plants of different species compete with each other when they are growing in the field. If increasing the density of the same species affects 1/y additively, then it can be assumed that, increase in the density of another species affects 1/y also additively (Spitters, 1983). Wright (1981) and Spitters (1983) used this argument to expand the yield-density model to include species in mixtures. The resulting pair of equations were expressed as: y 1 2 - i = a 1 + b 1 1 X 1 + b 1 2 X 2 (2.3) y 2 1 - i = a 2 + b 2 2 X 2 + b 2 1 X 1 (2.4) In these equations, the first subscript corresponds to the species whose biomass is represented as dependent variable and the second subscript represents the companion species. Intra- and interspecific competition effects are quantified by the coefficients bj j or b 2 2 and b 1 2 or b 2 j respectively. The model therefore accounted for yield variation in binary mixtures by 15 separating intra- and interspecific competition. Once the models were fitted the values of the model parameters were used to interpret competitive relationships and to measure the degree of niche differentiation (Spitters, 1983). As emphasized by Spitters (1983), the ratio of the model coefficients (bi^/b22) o r f e r e a ' a direct assessment of the relative strengths of intra- and interspecific interference. 2.2.5 Yield advantages in crop mixtures The advantages which are achieved from growing crops in mixtures are partly dependent on the requirements of the grower (Willey & Osiru, 1972). If the requirement is simply to maximize yield irrespective of how much comes from either species, then for a mixture to give yield advantage, it must exceed the maximum yield of the higher yielding species in monoculture system. If this does not happen it would be more advantageous to grow only the higher yielding species. This argument holds true only when the two species are substitutes such as two cereals which are equally acceptable. When two species such as a cereal and a legume are being grown the situation is very different since the two species produce different types of yield, and the grower requires some yield of each species. Here, an advantage occurs if the mixture produces more yield from a given area of land than can be obtained by dividing that area of land into monocultures of each species. Therefore, in this case the yield advantage can occur without the mixture exceeding the yield of the higher yielding species (Willey & Osiru, 1972). Several indices to determine the performance of crop mixtures have been suggested as reviewed by Potdar (1986). The use of yield-density models for the interpretation of differential yield responses has been demonstrated by Jolliffe (1988). Land equivalent ratio (LER) is a useful index of the combined performance of species in binary mixtures (Willey & Osiru, 1972). The index is calculated as: L.E.R = (Y^/Yj!) + (Y 2 1/Y 2 2) (2.5) 16 where Y denotes yield per unit land area, the first subscript represents the species providing the data for Y and the second subscript designates the associated species, i.e. Y 1 2 indicates the yield per unit land area of species 1 in mixture with species 2. Similarly Y 2 2 is the yield per unit land area of species 2 in monoculture. In this situation the monocultures and mixtures are assessed at the same total population density. Three possible outcomes exist as indicated by Willey (1979): mutual inhibition (LER<1), mutual cooperation (LER>1) and mutual compensation (LER=1). 2.3 Light 2.3.1 Importance of light as a growth resource The supply of light to an area of land is the most reliable of the environmental resources for plant growth (Harper, 1977). In contrast with water and nutrients, light can not accumulate in the environment for future use. Neighbouring plants may interfere with and reduce the supply of light to one another by direct interception (Harper, 1977). The first leaf that intercepts an incoming ray of light may reflect it (in which case it may hit another leaf), or absorb it and convert it directly into photosynthetic product or into heat (in which case it may provide latent heat of evaporation), or transmit it, filtered so that it reaches the lower leaves dimmer and spectrally altered (Harper, 1977). Measurement of amount of light penetrating through leaf canopies provides evidence that light may become a resource in short supply (Harper, 1977). The individual leaf, isolated from the plant and from the neighbouring leaves and exposed to controlled light intensities, characteristically increases its rate of photosynthesis with increasing light intensity until a maximum rate is reached beyond which further increase in light intensity produces no change (Harper, 1977). The incident radiation is absorbed by all above ground plant organs. A major role is played by leaf blades, but absorption by sheaths and other green structures can also be effective in photosynthesis (Petr et al., 1988). 17 Light as a growth factor in crops differs from other growth factors (water and nutrients) in that it can not be influenced directly by man, especially at farm level. Solar radiation may be the main factor limiting crop growth and dry matter accumulation in irrigated and intensively fertilized crop stands (Beets, 1982; Steiner, 1984; Petr et al., 1988). Competition for solar radiation dictates the morphological structure attained by crop stand in the course of growth. 2.3.2 Light interception by leaf canopies Leaves, especially leaf blades, play a major role in absorbing the incident solar radiation. Whether crops are able to use effectively high radiation and light levels depends on the inherent ability of the species (Beets, 1982) and on leaf area index (LAI) which is the area of the assirnilatory organs per unit area of the soil surface. The LAI is used to measure the ability of the plant stand to absorb the solar radiation (Petr et al., 1988). Also, of importance in the evaluation of the plants' ability to absorb solar radiation are leaf area duration (LAD), the integral of leaf area over time and photosynthetic potential (PP) representing the cumulative photosynthetic area (m ) per plant for a defined part of the growing period (Watson, 1952; Petr et al., 1988) ( lm 2 per 24 hours is the basic unit). As the number of leaves and their sizes increase light absorption and the rate of dry matter accumulation increases (Beets, 1982). The optimum LAI depends on the crop species, season, and light intensity (Beets, 1982). A higher LAI will generally lead to more photosynthesis and therefore foliar development of the stand should attain the optimum LAI fastest upon crop emergence. This is approached in relay cropping systems since the canopies of such systems are formed of plants of different species which are in different stages of development (Beets, 1982). At a given stage the LAI of one of the species may be optimum or just below optimum, while the LAI of the other species which has just emerged is low. The LAI of the two species together may, however, be optimum (Allen et al., 1976; Beets, 1982), and the two species will be able to capture most of the light effectively. At a later stage, one of the 18 species will be harvested and its LAI reduced from optimum to nil, but the foliage of the second species will rapidly replace it (Allen et al., 1976). In an intercropping system, the situation is similar since the combined leaf area of the associated species is normally larger than in monocultures, and the build up of LAI is more rapid (Willey & Roberts, 1976). This is also supported by work carried out at the International Rice Research Institute (IRRI) in 1975, (cited by Beets, 1982) where LAI, photosynthetic efficiency, and dry matter production of maize (Zea mays L.) and rice (Oryza sativa L.) in monocultures and mixtures were measured. The maximum LAI for maize was reached six weeks after seeding, and the maximum LAI for rice was reached twelve weeks after seeding. The maximum LAI for the crops association was between these two times. Maize alone had relatively low LAI, while rice alone had a considerably higher LAI. As a result, the total dry matter production and the grain yield of the association was higher than those of either crop grown in monocultures. With mixed cropping, not only is the combined LAI important, but also the extent to which each species in the association contributes to the LAI (Beets, 1976). It is further important to know how mutual overshading takes place between species, since a high LAI for a tall species may lead to excessive overshading of the lower species. Light penetrating a crop stand is diminished through interception and absorption by the leaves and other parts of the shoot system (Trenbath, 1979; Petr et al., 1988). The potential share of the light that will be gained by the components of an intercrop is determined by the relative height of their canopies and by the efficiency with which they intercept and absorb light (Trenbath, 1979). When the distribution of foliage is fairly uniform in the horizontal plane, the penetration of light into the stand can be described approximately by the Bouguer-Lambert Law (Monsi and Saeki, 1953, cited by Loomis & Connor, 1992) I ^ o e - ^ A 1 and ln(I/Io) = -kLAI (2.6) where, I is the light flux density to horizontal surface below units of LAI; I 0 is the light flux incident to surface above the canopy; e is the base of natural logarithms; and k is an extinction 19 coefficient. This law is said to apply to a range of natural plant stands and it has been used widely to summarise the light interception characteristics of crops and pasture canopies (Sheehy & Cooper, 1973; Alvirn, 1977). When most of the light from the direct solar beam is coming from near the zenith, the prostrate-leaved (planophile) canopies have the greatest k and therefore intercept most light per unit LAI (Trenbath, 1979). Under these conditions, steeply-inclined leaf (erectophile) canopies have the lowest k and intercept the least light (Anderson, 1966). Under overcast conditions, planophile stands show k values of about 1 if the leaves are randomly distributed horizontally; and if the leaves are regularly distributed in light-catching mosaics, k values may be between 1 and 1.5 (Anderson, 1966). When most of the light is coming from an elevation of between 30° and 40°, leaf inclination has little effect on k. When light comes from elevations lower than 30°, the effect of leaf inclination is reversed and the prostrate leaves show the lower k (Anderson, 1966). On a cloudless day, as the sun moves towards zenith, direct sunlight penetrates deeper into all canopies with non-horizontal leaves. At the same time, the proportion of the incident light that is intercepted becomes less. 2.3.3 Monoculture and mixture crop responses to light One aim of cropping systems (sole or mixed) is to make optimum use of light (Steiner, 1984). This includes not only high light interception but also an efficient use of light. Peak values of light interception can in fact be achieved by sole crops with optimum plant population (Steiner, 1984). Willey and Natarajan (1980) were able to demonstrate that 90% of peak light interception by sorghum (Sorghum bicolor L.) and pigeonpea (Cqjanus cajan L.) intercrop was nearly identical to that sole sorghum, even though the intercrop gave a greater total dry matter yield and had slightly a greater LAI. In intercrops however, the available light may be more efficiently used, if the optimal LAI is more quickly obtained (Beets, 1978), especially in low 20 fertility soils. In intercropping systems, dominant (sun) plants are usually associated with dominated (shade) plants (Vandermeer, 1992). The taller plants are normally the dominant plants intercepting the greater share of the light. The reduction of the light intensity caused by interception within a leaf canopy is usually exponential (Trenbath, 1976). Consequently, the smaller dominated plants grow less than the dominant plants and slight differences in height even in early stages of growth can occasion strong competition effects and lead to increasing differences between dominant and dominated species. Successful intercropping systems aim at reducing the competition for light, i.e. lessening the shading effect of the dominant plants without reducing the light interception (Steiner, 1984). Various possibilities for this exist such as relay cropping (Beets, 1982), planting the dominant crops in double rows (Steiner, 1984), orientation of rows in east-west direction (Pendleton et al., 1963), increasing leaf inclination of the dominant crops (Trenbath, 1976), and growing of shade tolerant crops and, multi-storey cropping systems (Nair et al., 1979). A crop with a low LAI has a photosynthetic response to increasing incident light flux similar to that of a single leaf (Trenbath, 1976). In a crop with a high LAI, shaded leaves at the bottom of the canopy can continue to respond to an increase in incident light flux even if the leaves high in the stand are light saturated. As the canopy becomes thicker it also intercepts a greater proportion of incident light. The ratio of the fraction of incident light intercepted by the canopy i.e. ((Io-I)/I0)) rises asymptotically to near unity. 3. MATERIALS AND METHODS 21 3.1 Site description, experimental design and crop production procedures The experiment was conducted at Totem Park Field Station of the University of British Columbia in the summer of 1993. The field had a sandy loam soil with a pH of 6.1 and an organic matter content of 4.5%. The soil was deficient in nitrogen, but other major plant nutrients were present in acceptable quantities as indicated by previous year's soil analysis results. The study involved two plant species, Phaseolus vulgaris L. cv 'Contender' and Beta vulgaris L. cv 'Ruby Queen'. The experimental design was a split-plot randomized complete block with two light levels (partial shade and full sun) as the main plots and 15 plant density combinations of the two species as the sub-plots; resulting in a total of 30 treatments in each of the two blocks. The 15 plant population density combinations were made up of 9 different combinations of the 3 plant densities per species and the three monocultures of each species (Table 3.1). The two species were sown in standard inter-row spacing of 50cm. Different plant population densities were achieved by altering the within-row spacing to 10cm, 20cm, and 40cm corresponding to plant population densities of 5, 10 and 20 plants m". The main plots were 11.5m long and 11m wide and the sub-plots were 2.5 m long and 2.5m wide. Before sowing, shade support structures were constructed in two of the main plots (one in each block). Four wooden posts measuring 9.5cm by 9.5cm by 2.4m were erected on each corner of the main plots in previously dug holes which were 40cm deep. The height of each of these posts was adjusted to 2 meters and two more posts were erected at equal distances between any two of these four. Between any pair of these outer posts, two more similar posts were erected inside the plots at equal distances. This resulted in a total of 16 posts around each plot. The posts were joined at the top by nailing a board (4cm by 9cm by 4.25m) on the outer side of the outer posts. The outer posts were also joined to the inner ones using the same kind of lumber. 22 The whole experimental area was cultivated and treated with Bentazon (Basagran 480g/lSN) at a rate of 2.25 litres per hectare, two weeks before sowing for weed control. The experimental area was also fertilized before seeding with NPK (20:10:10) at a rate of 200 kg (of the compound) per hectare. Sowing was done by hand on June 8 and 10 for beets and June 21 for beans. Table 3.1 Treatment combinations for bean and beet Bean population density Beet population density (plants m ) (plants m" ) 0 5 10 20 Bean:Beet population density 0 0:5 0:10 0:20 5 5:0 5:5 5:10 5:20 10 10:0 10:5 10:10 10:20 20 20:0 20:5 20:10 20:20 Each species was overseeded at 3 to 5 or 2-3 seeds per hill for beets and beans respectively. The seedlings were thinned to one seedling per hill 5 days after emergence. The experimental area was maintained weed free throughout the growing period, and occasional irrigation was done as required to supplement the natural rainfall. Black plastic shade cloth, (Sharp and Son Ltd., Burnaby, B.C., Canada), which could provide 47% shade was applied to the support structure on July 22, 1993 when leaves of the plants in high density treatments had started to overlap and hence compete for light. This was followed by light measurements using LI-190S A Quantum Sensor (LI-COR, Lincoln, Nebraska) which measures photosynthetically active radiation (PAR) in the 400 to 700 nm waveband. Measurements were taken weekly for each block from August 6, 1993 until a harvesting began on August 26, 1993. Three measurements, above and below the canopy were 23 taken in each plot. Two of the measurements were taken near the edges of the plot and the third one at the centre, all within the three middle rows. 3.2 Harvesting and data collection Harvesting was done between August 26 and 29, as bean plant foliage was beginning to yellow. Ten plant samples per species were collected from each plot. Samples were taken from three central rows, at least 0.25m from the edges of each plot. The shoots of the bean plants were cut at the ground level, but the beets shoots were pulled from the ground together with the storage roots. Each plant was divided into components: leaves, stems and pods for beans and leaves, petioles and storage roots for beets. The area of the leaves on each plant was measured using an LI-COR LI 3000 (LI-COR, Lincoln Nebraska) leaf area meter. The total number of pods per plant was recorded and pods were visually classified into marketable and non-marketable categories. Fresh weights of the number of pods per plant and the storage root were recorded for beans and beets respectively. Storage root diameters of the beets were also measured. The plant components were then dried in forced air ovens at about 65°C for 7 days except for beet storage roots which were dried for 28 days until there was no further change in their weights. The dry weights of these components were then measured. From this data collection procedure, therefore, the primary measures obtained per sampled plant were: leaf area, leaf dry weight, and shoot dry weight for both species. Stem dry weight, number of pods and marketable number of pods for beans, and petiole dry weight, storage root fresh weight, storage root dry weight, storage root diameter for beets were also obtained. Growth indices were then derived from the primary measures. The growth indices recorded were specific leaf area, leaf area ratio, leaf area index, leaf weight ratio and harvest index for both beans and beets. Stem weight ratio for beans and petiole weight ratio for beets were also derived and recorded (Tables 3.2 and 3.3). 24 Table 3.2 Primary measures and growth indices for bean (a): Primary measures Measure Symbol Unit of measurement Land area A 2 m Leaf area LA 2 m Leaf dry weight WL g Stem dry weight WST g Pod fresh weight WPF g Pod dry weight WPD g Pod number PN (number) Marketable pod number MPN (number) Shoot dry weight W g (b) Growth indices Index Symbol Unit of measurement Specific leaf area (LA/WL) SLA mV Leaf area ratio (LAAV) F mV Leaf area index (LA/A) LAI 2 -2 m m Leaf weight ratio (WL/W) LWR gg-; Stem weight ratio WST/W) SWR gg-Harvest index (WPD/W) H gg-1 3.3 Data analysis Homogeneity of variance or homoscedasticity is a prerequisite for several statistical tests including ANOVA. This was tested for all primary variables by plotting the studentized residuals against predicted values as outlined by Weisberg (1985). Most variables showed heteroscedasticity, and this was partly remedied by transforming the data to log e and inverse scales for ANOVA and yield-density regressions respectively. The homogeneity of variance test was repeated on the transformed data and most variables showed improvement on their heteroscedasticity (Appendices 8.1 to 8.8). The inverse transformation was done in preparation for subsequent regression analysis because yield per plant is inversely related to plant population density (Jolliffe, 1988). 25 Table 3.3 Primary measures and growth indices for beet (a) Primary measures Measure Symbol Unit of measurement Land area A m2 Leaf area LA 2 m Leaf dry weight WL g Petiole dry weight WP g Storage root fresh weight WRF g Storage root dry weight WRD g Storage root diameter DR cm Shoot dry weight W g (b): Growth indices Index Symbol Unit of measurement Specific leaf area (LA/WL) SLA Leaf area ration (LAAV) F Leaf area index (LA/A) LAI Leaf weight ratio (WL/W) LWR Petiole weight ratio (WP/W) PWR Harvest index (WRDAV) H mV mV m2m2 gg 3.3.1 Analysis of variance Analysis of variance was applied to all primary measures and growth indices for each species. ANOVA was used to partition the sources of variation using Statistical Analysis System (SAS) version 6.08 (SAS/STAT Users' guide, 1989) in a PC. Due to the quantitative nature of the density treatment levels, trend contrasts were used to partition the ANOVA degrees of freedom and sum of squares into linear and deviations for the test species (i.e. the species whose yield was being analysed) and linear, quadratic and deviations for the companion species. 26 3.3.2 Yield-density regression analysis Yield-density regressions were formed using inverse models (Wright, 1981 and Spitters, 1983), which describe the decline in size per plant with increasing species population density (X): yi2A = a: + + b 1 2X 2 (3.1) In these equations, the first subscript corresponds to the species whose measure (y) is represented as dependent variable and the second subscript represents the competing species. Intra- and interspecific competition effects are quantified by the coefficients b u o r b 2 2 and b 1 2 or b 2 1 respectively. This was done through normal multiple regression procedures using S AS version 6.09 available in computing services of the University of British Columbia. 3.3.3 Yield advantages in crop mixtures Using the inverse yield-density models, the predicted combined yield per unit land area for mixtures of beans and beets was determined: LER = (an + 2bnX1)/2(au + b aXi + bi 2X 2) + (a 2 2 + 2b22X2)/2(a22+ b 2 2X 2 + b2iXi) (3.3) where LER stands for land equivalent ratio. Land equivalent ratios for leaf area, leaf dry weight, pod fresh weight pod dry weight and shoot dry weight were predicted at total monoculture and mixture densities of 10 and 20 plants m" . Predicted values of LER were then compared with observed values calculated using equation: LER=(Y 1 2/Y U) + (Y 2/Y 2 2) (3.4) where Y stands for observed yield per unit land area (yX). 3.3.4 Light absorption-density regression This followed ANOVA which had showed no significant differences due to block and shade. This observation made it possible for data to be pooled for blocks and shade during < 27 regression analysis. The fraction of incident light absorbed by the time it reaches the bottom of the shoot canopy i.e. light resource intercepted by the canopy can be expressed as: (Io-I)/Io. By analogy to the yield-density models, light interception was regressed against population densities for the two species using the equation: 0o-iyio = c 1 1X 1 + c 2 2X 2 (3.5) where I is the light flux below the canopy and Io is the light flux above the canopy, Cn and C22 are parameters which express the effects on light absorption of population densities of bean and beet, respectively. No intercept is included in this model since I = I0 at zero population density. 4. RESULTS 28 4.1 Visual observations during growth Beet seedlings started to emerge about 7 days after planting and emergence continued for about 4 days. Differences in emergence time may have been due the different planting dates and due to differences in depth of planting and soil compaction in some parts of the plots. Beans, which had been planted about 12 days later than beets, also started to emerge 7 days after planting. Emergence for beans was satisfactory, but some hills for beets failed to germinate necessitating gap filling. Seedlings were obtained for gap filling mainly from the overseeded hills, at the time of thinning. The transplanted plants appeared weak during the early stages of growth but they were not distinguishable from other plants later in the growing season. Within 3 weeks following the emergence of beans, leaves of adjacent plants at higher densities started to overlap. It was at this stage when the shade cloths were applied on one half of each block. Generally, the plants looked healthy but plants crowded in higher population density treatments were smaller than those in lower population density treatments. Bean plants were smallest when the lowest bean density was combined with the highest beet density. Some variation was also observed within the individual plots. After the shade cloths were applied the shaded plots were observed to remain more moist than the unshaded plots. This necessitated a reduction in the frequency of irrigation for the shade treatment. 4.2 Data analysis 4.2.1 Analysis of variance Analysis of variance was performed on loge transformed data for all primary measures and growth indices for both species. Pod fresh weight, pod number, marketable pod number and beet leaf area still indicated some heterogeneity after loge transformation. Nearly all the 29 primary measures and growth indices responded strongly to density treatments (Tables 1 to 4) The effect of light treatments on yields was different between the two species, with beets responding more than beans, for primary measures of plant growth. In addition to the main effects, there were occasional significant interactions between either the density treatments and/or density and light treatments. The density effects for both species revealed significant linear components of the trend contrasts. In addition to linear, a significant quadratic component due to beet density was shown by bean leaf area, pod fresh weight, total number of pods and marketable number of pods. The quadratic component due to beans as competing species was never significant for any variable. 4.2.1.1 Bean results 4.2.1.1.1 Primary measures ANOVA results for bean data showed significant yield responses to both test (beans) and companion (beets) species population densities. Only total number of pods showed a significant shade treatment effect. None of the primary variables had any significant block effect. The density of the companion species was observed to have a highly significant influence on all primary measures. Leaf area, leaf dry weight, pod fresh weight, pod dry weight, number of pods, and marketable number of pods were all significantly affected by the bean density. Bean density did not have a significant effect on stem dry weight. When density treatment effects were significant, increasing population density resulted in reduction of the mean yield per plant of that particular growth measure. Unlike the main effects, shade by either species population density or test by companion species population density interactions were never significant. 30 Table 4.1 Analysis of variance results for the loge transformed bean data: Variance ratios for the effect of shade (S), bean population density (X{) and beet population density (X 2) on primary measures of growth Variables Source of Variation df LA WL WST WPF WPD PN MPN W BLK 1 6.57ns 0.01ns 0.49ns 0.54ns 3.72ns 7.65ns 1.03ns 0.03ns S 1 2.70ns 4.78ns 4.68ns 7.78ns 19.11ns 315.96* 15.66ns 7.20ns Error 1 1 - - - - - - - -Xi 4.89* 4.22* 3.23ns 12.14** 15.80** 15.47** 14.22** 6.40** Linear 1 9.43**. 10.24** 6.38* 23.85** 30.48** 30.83** 28.05** 0.98ns Deviation 1 0.35ns 0.50ns 0.08ns 0.42ns 1.14ns 0.10ns 0.38ns 4.42* x 2 3 28.62** 22.96** 18.90** 15.13** 23.53** 16.43** 15.05** 21.30** Linear 1 71.74** 63.19** 52.25** 37.12** 67.75** 38.57** 34.62** 1.67ns Quadratic 1 10.59** 4.23ns 2.25ns 5.66* 3.83ns 6.80* 6.12* 0.15ns Deviation 1 3.53ns 1.49ns 2.19ns 2.59ns 2.99ns 3.91ns 4.40* 0.34ns S*Xi 2 0.04ns 0.15ns 0.15ns 0.22ns 0.14ns 0.35ns 1.24ns 0.05ns s*x2 3 0.78ns 0.90ns 0.90ns 1.22ns 0.39ns 0.58ns 1.16ns 0.36ns Xi*X 2 6 1.34ns 0.84ns 0.84ns 1.60ns 1.97ns 1.31ns 1.31ns 0.94ns S*Xi*X2 6 1.91ns 1.27ns 1.27ns 1.26ns 1.32ns 1.08ns 0.96ns 1.07ns Error 2 22 - - - - - - - -Sam. Error 432 - - - - - - - -Total 479 - - - - - - - -* Significant at P < 0.05>0.01 ** Significant at P< 0.01 ns Not significant 31 Table 4.2 Analysis of variance results for the loge transformed bean data: Variance ratios for the effect of shade (S), bean population density (Xx) density and beet population density (X 2) on growth indices Growth indices Source of Variation df SLA F LAI LWR SWR H BLK 1 66.67ns 2548.06* 1.35ns 7.38ns 42.44ns 38.97ns S 1 359.69* 13731.55** 0.41ns 40.17ns 2.83ns 10.88ns Error 1 1 - - - - - -Xi 2 5.91** 1.51ns 25.03** 0.46ns 49.49** 5.06* Linear 1 12.46** 9.78** 2.50ns 48.94** 0.67ns 91.15** Deviation 1 0.34ns 2.05ns 0.51ns 1.13ns 0.26ns 7.82** X 2 3 2.51ns 23.62** 23.54** 13.70** 57.64** 4.77** Linear 1 59.06** 7.53* 39.55** 63.30** 37.80** 10.89** Quadratic 1 2.95ns 0.01ns 1.26ns 5.46* 3.27ns 5.84* Deviation 1 1.89ns 0.00ns 0.01ns 1.85ns 0.02ns 0.56ns S*Xi 2 0.18ns 0.50ns * 0.04ns 1.26ns 2.87ns 0.21ns s * x 2 3 0.96ns 0.05ns 0.41ns 0.37ns 17.76ns 2.01ns Xi*X 2 6 1.62ns 0.56ns 0.06ns 0.55ns 5.15ns 0.39ns S*Xi*X2 6 3.77** 2.44ns 1.55ns 0.29ns 4.21ns T.42ns Error 2 22 - - - - -Sam. Error 432 - - - - - -Total 479 _ _ * Significant at P < 0.05>0.01 ** Significant at P< 0.01 ns Not significant 32 4.2.1.1.2 Bean growth indices and dry-matter partitioning Unlike the primary measures, there were significant shade effects on both specific leaf area and leaf area ratio. The other indices: leaf area index, leaf weight ratio, stem weight ratio and harvest index, did not significantly respond to shade treatment. The densities of both test and competing species had significant effects on yield indices. The density of the competing species resulted in a significant effect on all indices except specific leaf area. Bean density treatments also showed significant effects on all yield indices except leaf area ratio and leaf weight ratio. Unlike primary variables, the indices recorded some significant treatment interaction effects. This was observed with specific leaf area and stem weight ratio which showed significant three way interactions. Stem weight ratio also indicated significant two way interaction between the two density treatments and light by competing species density treatments. The effect of species densities on the dry matter partitioning is shown in Figure 4.1 (a-c). The ANOVA results indicated that bean density did not significantly influence the dry matter allocation to its leaves as indicated by LWR but it had a significant effect on the allocation to stems and pods as indicated by SWR and H respectively. As the bean density increased, more dry matter was allocated to stems and less to pods (Figure 4.1). Leaf weight ratio decreased with increasing beet density, but the rate of decrease was lower above the density of 10 plants m". Dry matter allocation to stems remained higher than the allocation to leaves and pods as the bean and beet densities increased. Generally, dry matter allocation to stems and pods increased with increasing beet density, except for bean density of 20 plants m"2 where initial allocation to stems decreased with beet density. 33 0.500 0.475 0.450 H 0.425 a 0.400 .2 | 0.375 is | 0.350 H i p 0.325 0.300 0.275 0.250 0.225 0.200 5 10 15 Beet Population Density (Plants m _ 2) 20 Figure 4.1 (a) Effect of beet population density on bean dry-matter partitioning, at bean density of 5 plants m " 34 a o o PL, I—< 0.500 0.475 0.450 0.425 H 0.400 0.375 0.350 0.325 0.300 0.275 -0.250 -0.225 0.200 0.175 0.150 -0.125 -0.100 Leaf Stem Pod 0 5 10 15 Beet Population Density (Plants m "2) 20 Figure 4.1 (b) Effect of beet population density on bean dry-matter partitioning, at bean density of 10 plants m 0.550 -0.525 -0.500 -0.475 -0.450 -0.425 -0.400 -0.375 -0.350 -0.325 -0.300 -0.275 0.250 -0.225 -0.200 -0.175 -0.150 — Leaf Stem Pod 5 10 15 Beet Population Density (Plants m *2) 20 ure 4.1 (c) Effect of beet population density on bean dry-matter partitioning, at bean density of 20 plants m " 2 36 4.2.1.2 Beet results 4.2.1.2.1 Primary measures Beet results were similar to those of beans but with a few exceptions. Unlike beans where shade treatments significantly influenced only one primary variable, beet storage root fresh weight, storage root dry weight, storage root diameter and shoot dry weight were all significantly affected by shade treatment. Other primary measures of beet growth: leaf area, leaf dry weight and petiole dry weight did not exhibit significant response to shade treatment. The density treatments of both test (beets) and companion (beans) species were observed to have a similar influence on all the primary variables. Highly significant differences due to density treatments of the two species were detected in all the primary variables tested. In addition to main effects, the light by test species density interaction effect was significant for petiole dry weight. Leaf area and leaf dry weight revealed significant bean by beet density interaction effects. The significant effects on all these measures were an increase in yield with unshaded compared to shaded treatment, and a reduction in yield with increase of plant population density of the two species. 4.2.1.2.2 Beet growth indices and dry-matter partitioning There were significant differences due to shade treatments on leaf weight ratio, petiole weight ratio and harvest index. These ratios were observed to be lower in shaded than in the unshaded treatment. The density of the test species recorded a significant influence on leaf area index only. Leaf area index increased with increasing beets density. The density of the companion species had a significant effect on all beet growth indices except leaf weight ratio. Bean by beet density treatment interactions did not produce any significant effect on any of the indices. 37 Table 4.3 Analysis of variance results for the loge transformed beet data: Variance ratios for the effect of shade (S), beet population density (X{) and bean density (X 2) on primary measures of growth Variables Source of Variation df LA WL WP WRF WRD DR W BLK 1 0.28ns 04.60s 5.42ns 2.14ns 1.69ns 4.58ns 3.94ns S 1 3.94ns 76.17s 24.80ns 225.96* 578.75* 552.13* 1006.45* Error 1 1 - - - - - - -Xi 2 61.77** 94.28* 51.09** 53.05** 30.85** 38.45** 65.95** Linear 1 119.4** 183.9** 100.6** 105.9** 61.67** 76.84** 113.5** Deviations 1 4.11ns 4.67* 1.57ns 0.17ns 0.03ns 0.07ns 0.39ns X 2 3 15.56** 43.42** 19.74** 32.63** 27.58** 26.04** 38.75** Linear 1 46.54** 128.7** 24.96 95.97** 81.55** 76.06** 114.2** Quadratic 1 0.14ns 1.27ns 4.15ns 1.69ns 0.82ns 1.92ns 1.65ns Deviations 1 0.01ns 0.23 0.10ns 0.22ns 0.37ns 0.15ns 0.33ns S*Xi 2 2.12ns 2.40ns 4.13* 0.68ns 0.58ns 0.32ns 1.52ns S*X2 3 0.41ns 0.29ns 0.77ns 1.45ns 0.59ns 1.09ns 0.56ns Xi*X 2 6 3.34* 3.65* 1.83ns 2.26ns 1.54ns 1.80ns 2.64ns S*Xi*X2 6 0.78ns 1.49ns 0.45ns 0.79ns 0.76ns 0.71ns 0.79ns Error 2 22 -Sam. Error 432 Total 479 * Significant at P < 0.05 > 0.01 ** Significant atP < 0.01 ns Not significant 38 Table 4.4 Analysis of variance results for loge transformed beet data: Variance ratios for the effect of shade (S) beet population density (Xi) and bean population density (X 2) on growth indices Growth indices Source of Variation df SLA F LAI LWR PWR H BLK 1 0.60ns 0.35ns 0.05ns 22.07ns 1.37ns 0.31ns S 1 17.09ns 40.90ns 9.42ns 6865.09** 444.11* 250.43* Error 1 1 - - - - - -Xi 2 2.65ns 0.71ns 96.72** 0.27ns 1.46ns 0.60ns Linear 1 4.35* 1.38ns 182.8** 0.00ns 2.53ns 0.74ns Deviation 1 0.96ns 0.05ns 10.63** 0.54ns 0.40ns 0.48ns x 2 3 15.29** 8.54** 17.91** 1.56ns 10.90** 5.36** Linear 1 43.53** 24.41** 52.53** 4.48* 32.36** 15.84** Quadratic 1 1.24ns 0.40ns 0.83ns 0.12ns 0.06ns 0.01ns Deviations 1 1.11ns 0.81ns 0.36ns 0.10ns 0.28ns 0.22ns S*Xi 2 0.70ns 0.35ns 4.44* 0.01ns 0.77ns 0.27ns S*X2 3 0.94ns 0.86ns 0.33ns 0.26ns 0.75ns 0.47ns Xi*X 2 6 2.05ns 0.15ns 2.16ns 0.18ns 0.34ns 0.08ns S*Xi*X2 6 2.14ns 0.88ns 0.67ns 1.10ns 0.58ns 0.72ns Error 2 22 Sam. Error 432 Total 479 * Significant at P < 0.05 > 0.01 ** Significant at P < 0.01 ns Not significant 39 ANOVA results showed that the beet density effect on its own dry matter allocation was never significant. However, bean density effects on beet dry matter allocation to petioles and storage root were significant. Bean density influence on dry matter allocation to beet leaves was never significant. Where bean density effect on beet dry matter allocation was significant, the outcome was a decrease in dry matter allocation to storage root and an increase in allocation to petioles with density increase (Figure 4.2). At lower bean densities of 5 and 10 plants m", less photosynthates were allocated to petioles than to leaves but this situation was reversed at the highest bean population density of 20 plants m" (Figure 4.2). The trend was different for beet population density of 10 plants m" in which the allocation to petioles remained lower than to leaves across the bean densities. 4.3 Yield-density Regressions Reciprocal models were used to define yield-density relationships in both moncultures and mixtures using equations 3.1 and 3.2 respectively. Each primary yield variable for each species was taken as a dependent variables in these models. Figures 4.3 to 4.8 and Appendices 8.24 to 8.27 show the response of reciprocal yield per plant to increase in the species densities. Generally, the reciprocal per plant yield increased with increasing densities, indicating per plant yield reduction as the density of each species increased. This general trend was observed to vary with both species densities and among the individual variables. As indicated by Figures 4.3 to 4.5, bean yield was observed to respond more to increase in beet density than to its own density. This suggests that beet was a stronger competitor than beans. For beans, LA, WL, WST, WPD and W were more responsive to beet density than was MPN which showed relatively the same response to both species densities. Pod number was more responsive to beet population density than to that of beans, under full sun, but the opposite occurred under shade. A notable deviation from these response trends was observed with WPF, which showed some interaction and had approximately the same 40 0.85 0.80 4 0.75 0.70 0.65 H 0.60 0.55 0.50 H 0.45 0.40 0.35 0.30 0.25 0.20 0.15 -0.10 0.05 — Leaf Petiole Storage root I 5 10 15 20 Bean Population Density (Plants m ~ ) Figure 4.2 (a) Effect of bean population density on beet dry-matter partitioning, at beet density of 5 plants m " 41 0.85 0.80 0.75 0.70 1 0.65 -0.60 -0.55 -0.50 -0.45 -0.40 -0.35 -0.30 -0.25 -0.20 0.15 Leaf Petiole Storage root 0.10 0.05 H 0.00 0 5 10 15 Bean Population Density (Plants m ~2) 20 Figure 4.2 (b) Effect of bean population density on beet dry-matter partitioning, at beet density of 10 plants m ~2 42 0.80 0.75 0.70 0.65 H 0.60 0.55 H 0.50 0.45 0.40 -0.35 -0.30 0.25 0.20 0.15 Leaf Petiole Storage root 0.10 -0.05 -0.00 0 5 10 15 Bean Population Density (Plants m ~2) 20 Figure 4.2 (c) Effect of bean population density on beet dry-matter partitioning, at beet density of 20 plants m " 43 Figure 4.3: Response of bean leaf area to bean and beet population densities Symbols are data for individual plants Figure 4.4 Response of bean leaf dry weight to bean and beet population densities Symbols are data for individual plants 45 Figure 4. 5: Response of bean shoot dry weight to bean and beet population densities Symbols are data for individual plants 46 Figure 4.6: Response of beet leaf area to beet and bean population densities Symbols are data for individual plants 47 Figure 4.7: Response of beet leaf dry weight to beet and bean population densities Symbols are data for individual plants 48 Figure 4.8 (a) Response of beet shoot dry weight to beet and bean population densities under shade Symbols are data for individual plants 49 Figure 4.8 (b) Response of beet shoot dry weight to beet and bean population densities in full sun Symbols are data for individual plants 50 response to both species densities. Beet growth measures: LA, WL (Figures 4.6 to 4.7) and WP (Appendix 8.27) revealed a similar trend as bean variables but with less magnitude of response. This also suggests that beet exhibited stronger intra- than interspecific competition. Beet LA and WL revealed interaction between the species' population density treatments. Beet WRF, WRD, DR and W (Figures not shown except for W) responded to bean population density more strongly than to its own under shade condition. The reverse occurred under full sun condition but the with less strength of response. The above observations were also supported by the values of parameters for the reciprocal yield-density models, equations (3.1 and 3.2) as shown in Table 4.5. As mentioned earlier, parameters a and b express different aspects of species performance and interrelationships. The parameter a (the intercept) represents reciprocal mean yield of an isolated plant i.e. in the absence of either intra- and interspecific competition. The regression coefficient bn measures how per plant yield declines with increasing population density of the same species and regression coefficient bi2 is a measure of plant responsiveness to interspecific competition. The ratio (bn/b12) or (b22/b2i)of these regression coefficients corresponds to the relative strengths of intra- and interspecific competition. For measures of plant mass, the parameter bn values for bean WPF, W and WST were relatively low, indicating relatively weak responses to intraspecific competition. Bean WPF and WPD respectively presented the lowest and the highest responses to intraspecific competition. The b i 2 values for most bean primary measures of growth were greater than the bn values indicating than interspecific competition was stronger than intraspecific competition Deviation from this was observed with MPN, which responded more to intra- than interspecific competition. Bean WPF indicated the lowest response to competition. Except for PN, the bean response to intra and interspecific competition did not change 51 with shade treatment. The bn value for PN was greater than b12 under shade than under full sun. The indicates that PN response to intraspecific competition was greater under shade but weaker under full sun {Table 4.5 (b) and (c)}. The R for all bean primary measures were low indicating that there were other major sources of variation apart from the experimental treatments. Beet WL and WP showed higher b22 compared to other primary measures of growth with the same scale of measurement. Beet WP indicated the highest response to intraspecific competition. The bn for these variables were lower than their corresponding b22 implying that their response to interspecific competition was lower than that of intraspecific competition. The responses of beet WRF, WRD, DR and W to intra- and interspecific competition were modified by the shade treatment. These variables responded slightly more strongly to interspecific competition under shade. This observation was reversed under full sun, with relative magnitude of response being even higher except for WRD whose response to both intra- and interspecific competition did not change much with shade treatment (Table 4.5: b and c). The parameter a 2 2 for both storage root fresh and dry weight under shade was observed to be negative, indicating the failure of the model to estimate the yield for an isolated plant. The same occurred for storage root fresh weight under sun. The ratio (bn/b12) or (b 2 2/b 2i) of the regression coefficients for most variables indicated that beet was a stronger competitor than bean both within and between species. For those variables whose response was modified by the shade treatment, beet registered a similar or weaker competitive ability than bean under shade. The R2 for bean regression analysis were lower than those for beet indicating that bean was affected more by non-treatment sources of variation than was beet. 52 Table 4.5 Estimate of model (Equations 3.1 & 3.2) parameter values for the response of primary measures of growth to species' population densities (a) Under shade and full sun Variable"1 an ° r a22 bnorb22 bn ort>2i bn/bi2 orb22/b2i df R 2 P LA 0.7731±0.006 0.002810.0004 0.006910.0003 0.408 2 0.49 0.001 WL 0.0702±0.008 0.002910.0006 0.008610.0005 0.346 2 0.43 0.001 WST 0.062910.005 0.001410.0004 0.004710.0003 0.308 2 0.36 0.001 WPF 0.0057±0.001 0.000410.0001 0.00041 0.0001 1.00 2 0.18 0.001 WPD 0.064110.007 0.003510.0004 0.004910.0004 0.715 2 0.34 0.001 MPN 0.0548±0.005 0.002610.0004 0.002210.0003 1.175 2 0.19 0.001 W 0.0214±0.003 0.001010.0002 0.002310.0001 0.425 2 0.40 0.001 LA* 0.820710.003 0.004110.0002 0.002110.0002 1.911 2 0.53 0.001 WL* 0.059710.005 0.006710.0004 0.005010.0003 1.346 2 0.58 0.001 WP* 0.105410.006 0.006610.0004 0.002710.0004 2.411 2 0.40 0.001 (b) Under shade PN 0.042510.005 0.001810.0003 0.001210.0003 1.406 2 0.21 0.001 WRF* -O.0021i0.001 0.0006310.0001 0.0006910.0001 0.919 2 0.50 0.001 WRD* -0.002110.006 0.003610.0004 0.004410.0003 0.823 2 0.50 0.001 DR* 0.095110.003 0.002410.0002 0:002510.0002 0.976 2 0.62 0.001 W* 0.005310.003 0.001910.0002 0.002110.0002 0.918 2 0.56 0.001 (c) Full sun PN 0.02710.003 0.001410.0002 0.001710.0002 0.854 2 0.35 0.001 WRF* -0.000310.0004 0.000410.0000 0.000210.0000 1.590 2 0.66 0.001 WRD* 0.003410.002 0.002010.0001 0.001910.0001 1.092 2 0.66 0.001 DR* 0.088310.002 0.002110.0001 0.001410.0001 1.457 2 0.62 0.001 W* 0.003210.001 0.001510.0001 0.001110.0001 1.328 2 0.72 0.001 * Beets variable, other variables apply to beans. 4.4 Yield advantages in crop mixtures The combined yield per unit land area was evaluated using equations (3.3) and (3.4) for predicted (computed using inverse yield-density models) and observed (computed using yield data) values respectively (Table 4.6). Differences between predicted and observed LER were negligible. In all cases, LER values were approximately equal to 1.0, indicating little total yield advantage or disadvantage due to intercropping bean and beet. In both predicted and observed combined LERs, the contribution of bean was always lower than that of beet for all the variables 53 evaluated, i.e. any yield advantage experienced by beet in the mixtures was approximately offset by yield disadvantage experienced by bean. Table 4.6 Predicted and observed LERs for different yield variables at mixture population densities (D) of 10 and 20 plants m"2 and component species population densities of 5 and 10 plants m"2 Predicted LER Observed LER Density Bean Beet combined Bean Beet combined Variable (D) component component component component LA 10 049 051 1.00 0.34 0.63 0.97 WL 10 0.39 0.54 0.93 0.42 0.61 1.03 WPFAVRF 10 0.50 0.53 1.03 0.49 0.53 1.02 WPDAVRD 10 0.47 0.48 0.95 0.45 0.54 0.99 W 10 0.41 0.51 0.92 0.47 0.54 1.02 LA 20 0.48 0.51 0.99 0.37 0.66 1.03 WL 20 0.35 0.55 0.90 0.40 0.59 0.99 WPFAVRF 20 0.50 0.53 1.03 0.50 0.53 1.03 WPDAVRD 20 0.45 0.48 0.93 0.49 0.53 1.02 W 20 0.38 0.51 0.89 0.47 0.54 1.01 4.5 Light absorption-density regression Regression analysis indicated that light absorption increased with increasing population densities of both species and time (weeks) of measurement except for the third week where absorption due to beet density was similar to that at the second week (Table 4.7). At equivalent densities there was greater absorption due to bean than to beet (i.e. cn>C22), always by more than 26%. 54 Table 4.7 Model (Equation 3.5) coefficient values for the effect of species population densities on light absorption Week cli C22 C l l / C 22 d.f R 2 P l 0.0336±0.002 0.0253+0.002 1.328 2 0.80 0.001 2 0.0373+0.003 0.0295+0.003 1.264 2 0.79 0.001 3 0.0378+0.003 0.0293+0.003 1.290 2 0.77 0.001 Cn and C22 due to bean and beet respectively. 5. DISCUSSION 55 Intercropping systems have been reported to be more productive than sole crops grown on the same land (e.g. Davis etal. 1981; Francis etal. 1982; Potdar, 1986; Harris etal, 1987; Jolliffe, 1988; Mchaina, 1991). This advantage has been attributed to partial complementary use of resources (Pilbeam et al, 1994) in either time or space, and thus more efficient use of resources. In order to maximize this complementarity, the combined species should be different in aspects such as morphology, nutritional requirements and time taken to reach physiological maturity. This complementarity has been achieved in intercropping between cereals and legumes, mainly maize-bean intercrops (Rezende & Ramalho, 1994), whereby the two species exploit different sources of nitrogen. Those two crops also have different durations of growth, so that when grown together, bean utilize resources earlier than maize. The present study pertains to intercropping of beans and beets viewed under three broad aspects: physiology (i.e. growth and productivity), ecology (i.e. competitive balance) of the two species, and agricultural productivity. 5.1 Physiology (growth and productivity) Beet seedlings were variable in their dates of emergence. This was attributed to variation in depth of planting and also to variation in soil compaction. During the early stages of stand establishment, plants for the two species and for all density treatments showed similar progress in growth. At about four weeks following the emergence of bean, differences in plant size and growth vigour were noticed among different treatments, with plants in higher densities being smaller than those at lower densities. This could be due to competitive interference because of density effects. Some variation was also observed within the individual subplots and this could be associated with variation in soil depth, some pockets of compacted soil and/or non-uniformity in irrigation water coverage. 56 Mchaina (1991) found bean to be more competitive than beet, which differs from the present experiment. In her study, however, bean and beet were planted at the same time. Here, beet was planted in advance of bean, to compensate for the slower emergence of beet. This offset in planting may have caused the difference in relative competitive abilities between this study and that of Mchaina (1991). The plants in the shaded plots were observed to be taller than those in unshaded plots, and the bean foliage was darker green, indicating the ability of the beans to withstand shading as was later revealed by yield-density regressions. The shade treatment was also found to retain soil moisture more than the sun treatment, probably because of reduced evapotranspiration, higher humidity and lower temperatures and probably better nutrient uptake.. In accordance with the available literature on plant response to interference, crop yield was strongly affected by the population densities of both species (Holliday, 1960; Willey & Heath, 1969;Potdar, 1986; Gaye, 1990; Mchaina, 1991). ANOVA results indicated that almost all the primary measures of growth and growth indices responded strongly to population density. This response may be mainly due to competitive interference, although other forms of interference cannot be ruled out. Partitioning of the treatment degrees of freedom and sum of squares to orthogonal contrasts of linear, quadratic and deviation revealed that all primary measures and growth indices of beet exhibited a linear response. Linear trends were shown by bean, but quadratic terms were also significant for some of the variables. Significant population density effects indicated a reduction in mean yield per plant with increase in each species' population density. This would be expected if competition for resources occurred as proximity among neighbours increased. These results were also reported by previous researchers (Potdar, 1986; Jolliffe, 1988; Gaye, 1990; Mchaina, 1991). The two species differed in their responses to shade, with beets responding more than beans in terms of the number of variables involved. Where the shade effect was significant, the result was an decrease in mean yield per plant under shade compared to full sun. This was presumably the result of reduced photosynthetic activity under shade. The reduction in beet yield under shade implies that beet may not be a good intercop with a tall cereal such as maize which is a major component of intercropping practices in tropical agriculture. Plant population density has been reported to affect dry-matter partitioning. The proportion of ear in corn has been reported to decrease with increasing plant population density (Harper, 1983). In this study, increase in bean density led to increase in dry matter allocation to stems and a decrease in allocation to pods This means that increasing bean population density in monocultures results in a greater fraction of biological yield at the expense of economic yield. Beet density significantly influenced dry matter allocation to leaves, stems and pods. The allocation to leaves decreased with increasing beet density but the rate of decrease was lower above the density of 10 plants m". More dry matter was allocated to stems than to any other part, irrespective of population density increases for either species. This may be a protective measure against lodging as plant size is reduced as a result of interference as will be discussed later. Dry-matter partitioning for beets was observed to respond to bean population density but not to beet population density. This was surprising given that beet primary measures of growth had indicated that both intra-and interspecific competition were stronger for beet was for bean. Beet seems to have a better allocation pattern for photosynthates than bean because more is allocated to storage roots, the product of interest to the grower. 5.2. Crop ecology As indicated by Spitters (1983), at low densities plants grow as if they are in isolation, and as the density increases interference intensifies. This yield density response was defined using reciprocal models chosen because of their biological basis (Jolliffe, 1988) and also because their parameters are useful indices of plant interference. Reciprocal models describe well the relationship between yield per plant and population density, which is inverse in nature. Model 58 parameter a measures species performance in the absence of competition. This parameter is not necessarily well-estimated from data obtained from experimental plots where competition has regulated crop performance. This problem may explain, for example the negative values of a obtained in some of the regressions. The model parameter (b), can however, be used to characterize the competitive patterns in mixtures. The b22 values for beet LA, WL, and WP were greater than b 2 i values indicating greater intra-than interspecific competition. The b 2 2 values were also greater that the corresponding bn values. These values indicate that beet was a stronger competitor than bean and also to itself. These results differ from those obtained by Mchaina (1991), who found bean to be more competitive than beet. As indicated earlier, this discrepancy may be because in the present study beets were planted 10 days before beans while in Mchaina (1991) the species were planted at the same time. As shown by b 2 2 /b 2 i values for WRF, WRD, DR and W*, the competitive ability of beet was modified by the presence of shade. It indicated greater competitiveness in full sun than under shade, but the yield of an isolated plant was better estimated under shade than in full sun as indicated by parameter a values for DR and W*. Storage root fresh and dry weights under shade registered negative intercepts in the inverse yield-density models, implying that the model failed to estimate the yield of the isolated plants. This could be, as indicated earlier, due to the fact that the model best describes interference at high population densities and thus would not provide a good estimate of yield of an isolated plant (Mchaina, 1991). The same reason can be advanced to explain the occurrence of low R2 for the yield-density regression. This, could also be attributed to non-treatment sources of yield variation, because higher variability could visually be observed within the plots. Several sources of this variation can be suggested: variation in soil depth, soil compaction in some parts of the plots, and differential covering of the plots by irrigation water. At equivalent densities, bean was found to intercept light more effectively than beet. 59 The difference in interception ability may be because of differences in canopy architecture (Loomis & Connor, 1992). Bean has a tendency towards more horizontal leaf display than beet, and horizontal leaves are more effective in light interception (Leopold & Kriedemann, 1975). Because light interception is also related to LAI, bean requires less LAI than beet to intercept the same amount of radiation. Both species showed an initial increase in light interception with density and time but a few days before harvesting (week 3), this trend was reversed for beet and the rate of increase for bean declined. This may be as a result of some leaf loss through abscission, and opening up of the bean canopy as the number and size of pods increased. It was surprising to observe that the superior species in light interception was a weaker competitor especially at higher light intensity. Several reasons pertaining to this observation can be advanced. The light measurements were taken near noon and this favoured high interception by bean because of the position of the sun at that time of the day. Due to the nature of leaf arrangement in bean, their lower leaves may have received light which was spectrally altered and therefore the efficiency of light utilization was impaired. Also, because of higher leaf temperatures under full sun situation than under shade condition, beans may have experienced respiration losses and were thus outcompeted by beets. Although beet intercepted light less efficiently than beans, beets may be more efficient in utilizing light than beans. This reason can be supported by the fact that beet had thicker leaves and therefore had an effect on k. 5.3 Agricultural productivity Yield advantage in crop mixtures is evaluated through comparison of the performance of crop mixtures in relation to monocultures. Direct and predicted land equivalent ratios were used to evaluate existence of yield advantages in beans and beets mixtures. Many crop mixture studies have reported overyielding for mixtures as opposed to monocultures (Potdar, 1986; Jolliffe, 1988; Mchaina, 1991). In this study, only total population densities of 10 and 20 plants m' were used to determine relative performance of bean and beet monocultures and mixtures. 60 The other population density combinations could not be used because of unavailability of equivalent monoculture population densities. Contrary to expectations, the predicted and observed LERs for all growth measures were similar, and approximately equal to 1.0. This indicates that neither overyielding nor underyielding occurred. This could be because densities used for this evaluation were low and the plants did not interact strongly enough agronomically. In all cases, and in both predicted and observed LERs, the bean contribution to the combined land equivalent ratio was always lower than that of beets. This confirms that beet was a stronger competitor than beans. As suggested by de Wit (1960) (cited by Willey & Osiru, 1972), the advantage of mixing two species is particularly likely to occur when the individual species utilizes slightly different parts of the environment. In this way a mixture utilizes a greater total amount of the environmental resources. This is not the case in this study since the two species were similar in many aspects including: height, rooting depths, optimum densities and time to maturity. There exists a general belief that, the larger the difference between life cycles of the species involved in intercropping, the less the competition and greater the efficacy of the system (Willey, 1979). 61 6. CONCLUSIONS 6.1 For both bean and beet, yield per plant for all the primary measures of growth decreased with increasing density of the competing species. The same result was caused by increasing density of the test species except for stem dry weight and leaf dry weight for bean and beet respectively. 6.2 Parameters of inverse yield density models indicated that in full sun, but not in shade beet was a stronger competitor both to itself and to bean. 6.3 Population density treatments altered patterns of dry-matter allocation in both plant species. Bean dry matter allocation to stems and pods was also reduced with increasing bean and beet densities, but allocation to leaves was not affected by bean density. Beet density did not affect its dry matter allocation, but bean density resulted in a significant reduction of allocation to storage root and increase on the allocation to petioles.. 6.4 Shade treatment was found to affect beet more than bean. Shade treatment reduced per plant yield for storage root fresh weight, storage root dry weight, storage root diameter and shoot dry weight in beet. 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(a) Plot of studentized residuals (RLA) against predicted values (PLA) (b) Plot of studentized residuals (RLGLA) against predicted values (PLGLA) for loge transformed data Appendix 8.2 70 (a) » BO 6 » «« " • MAC »K 0* « » 0 B DOOM C *A£OC ECS CC 1 « so m* Ft—fi u ' oc o a " < t*J 1 M l i*AA C " N ca » u * • a 11 t * U A l t * e A i« c * • CXU I * * O f 00* » » B B * U ~o~n 0.V3 on too i.» , , s * , rs i.» i.rs i.oo ncwi Homogeneity of variance test for bean leaf dry weight data. (a) Plot of studentized residuals (RWL) against predicted values (PWL) (b) Plot of studentized residuals (RLGWL) against predicted values (PLGWL) for loge transformed data 71 Appendix 8.3 a,) t i l » M Homogeneity of variance test for pod dry weight data (a) Plot of studentized residuals (RWPD) against predicted values (PWPD) (b) Plot of studentized residuals (RLGWPD) against predicted values (PLGWPD) for loge transformed data Appendix 8.4 72 (OL) AA a » W i l u g « a i » A , AA* s * * *A t • ao <u ASC «XFA EEACSCA * i e> un CCA A/ BAA « AAAA AAAOA ASA CS« AA DCAA A 1 AAAAA * A AACB AAA OCA A A A A A A AA A BBS* • CA A 1 AA OB A CBAAAJhB I AA AA ABBA > AA 8 AAA AS I (fe) Homogeneity of variance test for bean shoot dry weight data (a) Plot of studentized residuals (RW) against predicted values (PW) (b) Plot, of studentized residuals (RLGW) against predicted values (PLGW) for loge transformed data 73 Appendix 8.5 if 0.1 oz! o.i4 o.nl 0>> « oi w * i i a i i 00 Cl« 1 U C 1 u: u i Homogeneity of variance test for beet leaf area data (a) Plot of studentized residuals (RLA) against predicted values (PLA) (b) Plot of studentized residuals (RLGLA) against predicted values (PLGLA) for loge transformed data Appendix 8.6 74 {a) ' it B u i i ( t i C A SCA S A B u i A S I A AC AS AH AA « A OA A I A S 1 A A BSAC ASC OA SS A A AC A A t * A A o s oooee c A AS * A a A U E D O E C B C C A A C S A L C B C A B SO BA FCBSFA S A A C A * i» i SA C C U FCSAS AA SA a S t • Homogeneity of variance test for beet leaf dry weight data (a) Plot of studentized residuals (RWL) against predicted values (PWL) (b) Plot.of studentized residuals (RLGWL) against predicted values (PLGWL) for loge transformed data Appendix 8.7 75 (f t) *• * • • A * • • C C A * » o • • a* AABl AA a 8 » * " » * A " a r * * t.n Homogeneity of variance test for storage root dry weight data (a) Plot of studentized residuals (RWRD) against predicted values (PWRD) (b) Plot of studentized residuals (RLGWRD) against predicted values (PLGWRD) for loge transformed data Appendix 8.8 76 BAB IO BOC ti A AO BCD f CBA BB OT CSA BA 6 CT DBA C B BB AOS BBC 1 •AC BB BO OA* • Bi u ig i i Cf I 11 M * B A B B a 2.0 J.I ' -0 J.* 1.4 i.« n.cw Homogeneity of variance test for beet shoot dry weight data (a) Plot of studentized residuals (RW) against predicted values (PW) (b) Plot of studentized residuals (RLGW) against predicted values (PLGW) for loge transformed data 7 7 Appendix 8.9 Analysis of variance for loge transformed bean leaf area data Source of df Sum of Mean Square F value Probabili variation squares Total 47 3.506 Blk 1 0.033 0.033 6.57 0.2368 S 1 0.013 0.013 2.70 0.3480 Error 1 1 0.005 0.005 x, 2 0.242 0.121 4.89 0.0175 X 2 3 0.125 0.708 28.62 0.0001 S*Xj 2 0.002 0.001 0.04 0.9582 S*X2 3 0.058 0.019 0.78 0.5163 X,*X2 6 0.199 0.033 1.34 0.2820 S*Xj*X 2 6 0.283 0.047 1.91 0.1248 Error 2 22 0.544 0.025 R 2 = 0.82 C V = 28.33 Appendix 8.10 Analysis of variance for loge transformed bean leaf dry weight data Source of df Sum of Mean Square F value Probability variation squares Total 47 123.880 Blk 1 0.001 0.001 0.000 0.9842 S 1 7.723 7.723 4.07 0.2928 Error 1 1 1.089 1.089 X, 2 14.736 7.368 4.22 0.0280 X 2 3 105.705 35.235 20.20 0.0001 S*Xx 2 0.039 0.020 0.01 0.9888 S*X 2 3 0.756 0.252 0.14 0.9321 x,*x2 6 6.042 1.007 0.58 0.7442 S*Xi*X 2 6 7.134 1.189 0.68 0.6661 Error 2 22 23.106 1.050 R 2 = 0.80 C V = 19.71 Appendix 8.11 Analysis of variance for loge transformed bean stem dry weight data Source of variation df Sum of squares Mean Square F value Probability Total 47 94.236 2.005 Blk 1 0.854 0.854 0.41 0.6373 S 1 8.992 8.992 4.32 0.2854 Error 1 1 1.545 1.545 Xj 2 6.505 3.253 2.83 0.0807 x 2 3 60.857 20.286 17.64 0.001 S*X! 2 0.375 0.188 0.16 0.5472 s*x2 3 2.505 0.835 0.73 0.6311 X ! * X 2 6 5.032 0.839 0.73 0.3429 S * X ! * X 2 6 8.283 1.380 1.20 Error 2 22 18.476 0.840 R 2 = 0.78 C.V = 13.56 Appendix 8.12 Analysis of variance for loge transformed pod fresh weight data Source of d.f Sum of Mean Square F value Probability variation squares Total 47 115.746 Blk 1 0.748 0.748 0.55 0.5932 S 1 10.465 10.465 7.73 0.2198 Error 1 1 1.308 1.308 Xj 2 22.803 11.401 11.96 0.0003 X 2 3 42.635 14.212 14.91 0.0001 S*X! 2 0.417 0.208 0.22 0.8054 s*x2 3 3.463 1.154 1.21 0.3289 Xi*X 2 6 8.993 1.499 1.57 0.2020 S*Xj*X2 6 7.210 1.201 1.26 0.3150 Error 2 22 20.178 0.917 R 2 = 0.77 C.V = 6.49 79 Appendix 8.13 Analysis of variance for loge transformed pod dry weight data Source of df Sum of Mean Square F value Probability variation squares Total 47 90.330 Blk 1 3.634 3.634 3.29 0.3208 S 1 17.351 17.351 15.70 0.1574 Error 1 1 0.655 0.655 X i 2 21.082 10.541 13.69 0.0001 x2 3 48.924 16.308 21.18 0.0001 S*Xj 2 0.288 0.144 0.19 0.8306 s*x2 3 0.727 0.242 0.31 0.8144 X j * X 2 6 7.198 1.199 1.56 0.2064 S * X j * X 2 6 5.808 0.968 1.26 0.3168 Error 2 22 11.306 0.514 R2 = 0.78 C V = 15.38 Appendix 8.14 Analysis of variance for loge transformed number of pods data Source of variation .df Sum of squares Mean Square F value Probability Total 47 58.482 Blk 1 0.169 0.169 5.68 0.2529 S 1 7.778 7.778 262.03 0.093 Error 1 1 0.022 0.022 X! 2 15.218 7.609 14.94 0.0001 x2 3 24.106 8.035 15.78 0.0001 S*Xx 2 0.349 0.175 0.34 0.7134 S*X2 3 0.834 0.278 0.55 0.6563 X!*X2 6 3.847 0.641 1.26 0.3160 S*X!*X2 6 3.3217 0.539 1.06 0.4167 Error 2 22 9.519 0.433 R2 = 0.66 C V = 10.45 Appendix 8.15 Analysis of variance for loge transformed marketable number of pods data Source of df Sum of Mean Square F value Probability variation squares Total 47 78.354 Blk 1 1.331 1.331 0.99 0.5013 s 1 18.175 18.175 13.54 0.1689 Error 1 1 0.931 0.931 X , 2 18.728 9.364 13.07 0.0002 x2 3 29.291 9.764 13.63 0.0001 S*Xj 2 1.666 0.833 1.16 0.3311 s*x2 3 2.309 0.769 1.07 0.3803 X i * X 2 6 4.995 0.833 1.16 0.3614 S * X i * X 2 6 3.795 0.632 0.88 0.5236 Error 2 22 11.827 0.538 R 2 = 0.71 C.V = 13.63 Appendix 8.16 Analysis of variance for loge transformed bean shoot dry weight data Source of -df Sum of Mean Square F value Probability variation squares Total 47 115.956 Blk 1 0.055 0.055 0.03 0.8826 s 1 10.855 10.855 6.93 0.2312 Error 1 1 1.360 1.360 X i 2 12.997 6.499 6.04 0.0081 x2 3 66.327 22.109 20.54 0.0001 s*x, 2 0.125 0.062 0.06 0.9439 s*x2 3 1.029 0.343 0.32 0.8115 x,*x2 6 5.554 0.925 0.86 0.5389 S * X i * X 2 6 6.731 1.122 1.04 0.4253 Error 2 22 20.592 0.936 R 2 = 0.82 C.V = 8.47 81 Appendix 8.17 Analysis of variance for loge transformed beet leaf area data Source of variation df Sum of squares Mean Square F value Probability Total 47 0.813 Blk 2 0.001 0.001 0.28 0.6903 S 2 0.019 0.019 0.94 0.2971 Error 1 1 0.005 0.005 x, 2 0.440 0.220 61.77 0.0001 x2 3 0.166 0.055 15.56 0.0001 S*Xj 2 0.015 0.008 2.12 0.1439 s*x2 3 0.004 0.001 0.41 0.7488 Xi*X 2 6 0.067 0.011 3.14 0.0224 S*Xi*X 2 6 0.017 0.003 0.78 0.5944 Error 2 22 0.078 0.004 R2 = 0.72 C V = 23.02 Appendix 8.18 Analysis of variance for loge transformed beet leaf dry weight data Source of df Sum of Mean Square F value Probability variation squares Total 47 98.706 Blk 1 0.233 0.233 2.82 0.3420 S 1 4.367 4.367 52.80 0.0871 Error 1 1 0.083 0.083 X , 2 46.369 23.184 91.51 0.0001 x2 3 33.137 11.046 43.60 0.0001 S*Xi 2 1.103 0.552 2.18 0.1371 s*x2 3 0.179 0.060 0.24 0.8700 X ! * X 2 6 5.551 0.925 3.65 0.0115 S*X!*X 2 6 2.109 0.351 1.39 0.2636 Error 2 22 5.574 0.253 R2 = 0.77 C V = 16.72 82 Appendix 8.19 Analysis of variance for loge transformed petiole dry weight data Source of df Sum of Mean Square F value Probability variation squares Total 47 56.389 > Blk 1 0.029 0.029 1.04 0.4940 S 1 0.210 0.210 7.51 0.2227 Error 1 1 0.028 0.028 2 32.449 16.224 52.36 0.0001 x2 3 9.325 3.108 10.03 0.0002 S*Xj 2 2.760 1.380 4.45 0.0238 s*x2 3 0.724 0.241 0.78 0.5183 Xj*X 2 6 3.214 0.539 1.74 0.1588 s*x,*x2 6 0.813 0.135 0.44 0.8461 Error 2 22 6.816 0.310 R2 = 0.58 C.V = 22.09 Appendix 8.20 Analysis of variance for loge transformed storage root fresh weight data Source of -df Sum of Mean Square F value Probability variation squares Total 47 197.805 Blk 1 0.239 0.239 2.34 0.3684 S 1 24.708 24.708 242.51 0.0408 Error 1 1 0.102 0.102 X, 2 73.211 36.305 52.35 0.0001 x2 3 67.712 22.571 32.28 0.0001 s*xx 2 0.927 0.463 0.66 0.5255 s*x2 3 3.055 1.018 1.46 0.2536 Xj*X 2 6 9.191 1.532 2.19 0.0830 S*X!*X2 6 3.279 0.547 0.78 0.5932 Error 2 22 15.382 0.699 R2 = 0.86 C.V = 5.47 Appendix 8.21 8 3 0.87 C V Source of variation df Sum of squares Mean Square F value Probability Total 47 193.421 Blk 1 0.150 0.150 1.33 0.4545 S 1 36.937 36.937 327.28 0.0352 Error 1 1 0.113 0.113 2 51.719 25.859 28.05 0.0001 x2 3 23.582 25.58 25.05 0.0001 S*Xj 2 0.931 0.465 0.50 0.6105 s*x2 3 1.718 0.573 0.62 0.6089 Xi*X 2 6 6.787 1.131 1.23 0.3305 s*x,*x2 6 4.035 0.672 0.73 0.6310 Error 2 22 20.285 0.922 8.76 Appendix 8.22 Analysis of variance for loge transformed storage root diamete datar Source of variation df Sum of squares Mean Square F value Probabili Total 47 22.093 Blk 1 0.150 0.150 9.13 0.2034 S 1 36.937 36.937 1003.46 0.0201 Error 1 1 0.003 0.003 x, 2 51.719 25.859 36.51 0.0001 x2 3 70.747 23.582 25.04 0.0001 s*x. 2 0.9307 0.465 0.32 0.324 s*x2 3 1.7175 0.573 1.12 0.3620 X!*X 2 6 6.7868 1.131 1.56 0.2047 S*Xj*X2 6 4.035 0.672 0.69 0.6633 Error 2 22 2.240 0.102 R 2 = 0.82 C V = 5.59 84 Appendix 8.23 Analysis of variance for loge transformed beet shoot dry weight data Source of variation df Sum of squares Mean Square F value Probability Total 47 133.731 Blk 1 0.078 0.078 2.94 0.3359 s 1 18.249 18.249 686.94 0.0243 Error 1 1 0.027 0.027 2 47.153 23.576 54.74 0.0001 x2 3 48.601 16.200 37.62 0.0001 S*Xj 2 1.223 0.611 1.42 0.2631 s*x2 3 0.729 0.243 0.56 0.6440 Xi*X 2 6 6.202 1.034 2.40 0.0617 S*X,*X 2 6 1.994 0.332 0.77 0.6003 Error 2 22 9.475 0.431 R 2 = 0.87 C.V = 6.34 Appendix 8.24 85 Response of stem dry weight to bean and beet population densities Appendix 8.25 8 6 Beet Stty(P'*ms Response of pod fresh weight to bean and beet population densities Appendix 8.26 Response of pod dry weight to bean and beet population densities Appendix 8.27 88 Response of petiole dry weight to beet and bean population densities 

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