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Morphological components of yield in sweet potato (Ipomoea batatas (L.) Lam.) Soenarto 2001

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MORPHOLOGICAL COMPONENTS OF YIELD IN SWEET POTATO (Ipomoea batatas (L.) Lam.) by SOENARTO B. Sc., Akademi Pertanian, Ciawi-Bogor, 1962 Ir., Universitas Cenderawasih, Manokwari, 1978 M . S., Institut Pertanian Bogor, Bogor, 1987 M . Sc., The University of British Columbia, Vancouver, 1994  A THESIS SUBMITTED IN P A R T I A L F U L F I L M E N T OF THE REQUIREMENTS FOR THE D E G R E E OF DOCTOR OF PHILOSOPHY in THE F A C U L T Y OF G R A D U A T E STUDIES (Department of Plant Science)  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH C O L U M B I A April, 2001 ©Soenarto, 2001  In presenting degree  this thesis  in partial fulfilment  of the requirements  for an advanced  at the University of British Columbia, I agree that the Library shall make it  freely available for reference  and study. I further  copying of this thesis for scholarly purposes department  or  by his or  her representatives.  agree that permission for extensive  may be granted It  is  by the head  understood  that  of my  copying or  publication of this thesis for financial gain shall not be allowed without my written permission.  Department of  PlA^F  JC<€£hiCGr  The University of British Columbia Vancouver, Canada Date  DE-6 (2/88)  -Mf<\\~2.J.  P-00\  u  Abstract Growth and productivity were analyzed in two cultivars of sweet potato (Ipomoea batatas (L.) Lam.): a bushy type (cv B O 44T3) and a spreading type (cv BO 129T9). Two main aims were to determine how tuberous root yield and aboveground morphological measures respond to population density in different growing seasons, and to identify morphological measures of aboveground plant parts that are indicators of high tuberous root yield. In addition, the study was used to compare several techniques of plant growth analysis. Two field experiments were performed using randomized complete block designs. One was repeated in 1995 and 1996 and involved a single final harvest after the cultivars were grown at three levels of plant population density. The second was carried out in 1996; it involved a sequence of harvests performed at different times during crop growth at a single population density. Five different techniques were used to analyze the experimental results: conventional plant growth analysis, inverse yield-density regression analysis, allometric analysis, path analysis and yield component analysis. These procedures offered complementary interpretations in that each provided new perspectives on plant performance. The two cultivars arrived at similar final tuberous root yields through different chronologies of growth. Increasing population density reduced tuberous root yield along with most other measures of growth. Responsiveness to population density, i. e., intraspecific competition, differed among the different plant measures and years, and the two cultivars did not always respond to density to the same degree. Where significant differences were found between years, the responsiveness was always higher in the year that was less favourable to growth (1996). Some effects of population density on tuberous root yield were direct, but indirect effects on yield via responses of  Ul  aboveground measures were stronger. Throughout growth, the addition and expansion of leaves were positively correlated with tuberous root growth. At the final harvest, variation in number of stems per plant was an important indicator of variation in tuberous root yield.  iv  Table of Contents  Abstract  ii  Table of Contents  iv  List of Tables  vi  List of Figures  viii  List of Appendices Abbreviations and Symbols Acknowledgements  x ...xiii xv  1  General Introduction 1.1 Sweet Potato 1.2 Background of the Study 1.3 Methods of Growth Analysis - A n Overview 1.4 Objectives, Experimental Approaches, and Outline of This Study  1 1 2 5 8  2  General Procedures 2.1 Experimental Site and Site Characteristics 2.2 Plant Material 2.2.1 Source of Plant Material 2.2.2 Transplants for the 1995 and 1996 Field Experiments 2.3 Experimental Design 2.3.1 Experiment 1 2.3.2 Experiment 2 2.4 Field and Plant Maintenance 2.5 Climate Observations 2.6 Harvests and Primary Measurements 2.6.1 Plot and Plant Samples 2.6.2 Primary Plant Measurements  3  Chronological Trends in Growth, and Primary Responses to Population Density, in Two Sweet Potato Cultivars 22 3.1 Introduction 22 3.2 Materials and Methods 25 3.2.1 Crop Culture and Experimental Details 25 3.2.2 Data Analysis 25 3.2.2.1 Conventional Plant Growth Analysis 25 3.2.2.2 Simple Linear Correlation 26  10 10 11 11 11 14 14 15 15 17 19 19 19  V  3.3  3.4  3.2.2.3 Analysis of Variance 3.2.2.4 Inverse Yield-Population Density Relationships Results 3.3.1 Chronology of Growth 3.3.1.1 Growth of Primary Measures 3.3.1.2 Indices of Growth Rates 3.3.1.3 Ratio Indices 3.3.1.4 Tuberous Root Growth Rate and Its Relationships with Indices of Aboveground Growth 3.3.2 Effects of Plant Population Density upon Primary Plant Measures 3.3.2.1 Analysis of Variance 3.3.2.2 Inverse Yield-Density Relationships Discussion 3.4.1 Growth Characteristics in cv BO 44T3 and BO 129T9 3.4.2 Effects of Plant Population Density on Primary Measures of Growth.  27 27 28 28 28 31 35 37 40 40 46 49 49 53  4  Relationships between Aboveground Plant Measures and Tuberous Roots 56 4.1 Introduction 56 4.2 Materials and Methods 58 4.2.1 Allometric Analysis 59 4.2.2 Path Analysis 61 4.2.3 Yield Component Analysis by Two-Dimensional Partitioning (TDP) 67 4.2.3.1 Choice of Yield Components 67 4.2.3.2 Regression and Analysis of Variance 68 4.3 Results 71 4.3.1 Allometric Relationships 71 4.3.2 Path Analysis 74 4.3.3 Two-Dimensional Partitioning of Yield Variation 78 4.4 Discussion 83  5  General Discussions 87 5.1 Yield Relationships in Sweet Potato 87 5.1.1 Productivity at the Aggasiz Study Site 87 5.1.2 Growth Chronology and Density-dependence 91 5.1.3 Relationships between Aboveground Parts and Tuberous Root Yield 93 5.2 Methods of Analyzing Sweet Potato Performance 99  6  General Conclusions  106  7  References  108  8  Appendices  115  vi  List of Tables Table 2.1 Some characteristics of the sweet potato cultivars used in this study  11  Table 2.2 Dates of harvests of observation blocks in Experiment 2  15  Table 2.3 Dates of application, the amount and dosage of fertilizers used in sweet potato experiments in 1995 and 1996 17 Table 2.4 Primary observations made on individual plants at each harvest  20  Table 3.1 Growth Indices (Conventional Plant Growth Analysis)  25  Table 3.2 Correlation coefficients between growth indices of aboveground plant measures and TGR at different growth periods in 1996 in sweet potato cultivars ' B O 44T3' and ' B O 129T9'  38  Table 3.3 Analysis of variance for data of the final harvests (1995): F values of the effects of plant population density and sweet potato cultivar on measures per plant 41 Table 3.4 Arithmetic means of measures per plant at the 1995 final harvests  42  Table 3.5 Analysis of variance for data of the final harvests (1996): F values of the effects of plant population density and sweet potato cultivar on measures per plant 43 Table 3.6 Arithmetic means of measures per plant at the 1996 final harvests  44  Table 3.7 Constants and coefficients from inverse yield-density regression, measuring the density-dependence of different primary plant measures in 1995 and 1996 for ' B O 44T3' and ' B O 129T9' sweet potatoes 47 Table 4.1 Regression coefficients and other statistics for simple allometric relationships: InTW = a + (31n(z) (Eqn 4.2). Observations pooled from both varieties and seasons 72 Table 4.2 Standard partial regression coefficients and other statistics for best subsets multiple regression models of the allometric relationships between T W and plant measures in sweet potato varieties. Allometric relationships for pooled observations from 1995 and 1996 studies 73 Table 4.3 Path analysis of the relationships among aboveground plant measures and T W in ' B O 44T3'. Partitioning of correlation coefficient (r) into direct and indirect effects 76  Vll  Table 4.4 Path analysis of the relationships among aboveground plant measures and T W in ' B O 129T9'. Partitioning of correlation coefficient (r) into direct and indirect effects 77 Table 4.5 Two-dimensional partitioning of sum of squares for T W per plant in sweet potatoes grown in 1995 and harvested at 130 days after planting  80  Table 4.6 Two-dimensional partitioning of sum of squares for T W per plant in sweet potato grown in 1996 and harvested at 123 days after planting  81  Vlll  List of Figures Figure 3.1 Time course of dry mass of the whole plant (W), dry mass of aboveground plant parts (VW) and dry mass of tuberous roots per plant (TW) in sweet potato cultivars: a) ' B O 44T3' and b) ' B O 129T9' in the 1996 growing season 29 Figure 3.2 Time course of per plant measures in sweet potato cultivars ' B O 44T3' and ' B O 129T9' in the 1996 growing season: (a) stem number (SN), (b) stem length (SL), (c) stem dry mass (SW), (d) Length per stem, (e) number of leaves (LN), (f) leaf area (LA), (g) leaf dry mass (WL), and (h) mean area per leaf 30 Figure 3.3 Time course of plant growth rates: (a) absolute growth rate (AGR), (b) relative growth rate (RGR) and (c) unit leaf area (ULR) in sweet potato cultivars ' B O 44T3' and ' B O 129T9' in the 1996 growing season  32  Figure 3.4 Time course of growth rates of stem and leaf measures: (a) leaf number growth rate (SNGR), (b) stem length growth rate (SLGR), (c) stem dry mass growth rate (SGR), (d) leaf number growth rate (LNGR), (e) leaf area growth rate (LAGR) and (f) leaf dry mass growth rate (LGR) in sweet potato cultivars ' B O 44T3' and ' B O 129T9' in the 1996 growing season 34 Figure 3.5 Time course of leaf characteristics and leaf properties: (a) leaf area index (LAI), (b) leaf weight ratio (LWR), (c) leaf area ratio (LAR) and (d) specific leaf area (SLA) in sweet potato cultivars ' B O 44T3' and ' B O 129T9' in the 1996 growing season. Arrows denote the optimum L A I 36 Figure 3.6 Time course of harvest index (H) in sweet potato cultivars BO 44T3 and BO 129T9 in the 1996 growing season 36 Figure 3.7 Time course of tuberous root growth rate in two sweet potato cultivars ' B O 44T3' and ' B O 129T9' in the 1996 growing season 37 Figure 3.8 Effects of plant population density on primary measures: (a) plant dry mass (W), (b) stem length (SL), (c) stem dry mass (SW), (d) leaf dry mass (WL) and (e) tuberous root dry mass (TW) in sweet potato cultivars ' B O 44T3' and ' B O 129T9' at the final harvests 45  ix  Figure 4.1 A path diagram for the linear relationships among plant population density (X), the above ground plant measures and tuberous root yield (TW) together with the residual (s). One-arrowhead lines indicate direct effect (p). Twoarrowhead lines denote simple correlation coefficient (r). The other simple correlation coefficients are not presented in this figure, i.e., all possible paths among SN, SL, SW, L N , LA.and W L exist. SN, SL and SW are number of stems, length of stems and dry mass of stems, respectively. L N , L A and L W are number of leaves, leaf area and dry mass of leaves, respectively 62  List of Appendices Appendix A l  Soil analysis for the 1995 field experiment at Agassiz, British Columbia 115  Appendix A 2  Long-term weather conditions. Mean values of air temperature, rainfall, and bright sunshine duration at Agassiz, British Columbia for the period 1889-1990 116  Appendix A3  Layout of Experiment 1 conducted from 9 May to 16 September 1995 at the Pacific Agricultural Research Centre, Agassiz, British Columbia 117  Appendix A 4  Layout of Experiment 1 and Experiment 2 conducted from 5 June to 25 October 1996 at the Pacific Agricultural Research Centre, Agassiz, British Columbia 119  Appendix A5  Mean values of air temperatures, total rainfall and total bright sunshine duration for 1995 and 1996 growing seasons 121  Appendix A 6  Mean values of soil temperature (at about 0.1m depth) for the period June-September 1995 and June-October 1996 122  Appendix A7  Estimated incident solar radiation for the 1995 and 1996 growing seasons at Agassiz, British Columbia  123  Appendix A8  Observations on growth of sweet potato cultivar ' B O 44T3' during the 1996 growing season 124  Appendix A9  Observations on growth of sweet potato cultivar ' B O 129T9' during the 1996 growing season 126  Appendix A10 Plant measures per land area at the final harvest in ' B O 44T3' and ' B O 129T9' grown at different plant population densities in 1995 and 1996. 128 Appendix A l 1 Analysis of variance for pooled data of the 1995 and 1996 final harvests:F values of the effects of year of planting, plant population density and sweet potato cultivar on plant measures per land area 130 Appendix A12 Arithmetic means of plant measures per 1.65 m land area at the 1995 and 1996 final harvests 131  XI  Appendix A13 Analysis of variance for data of the final harvests (1995): F values of the effects of plant population density and sweet potato cultivars on plant measures per land area 132 Appendix A14 Arithmetic means of plant measures per 1.65 m land area in 1995 ... 133 2  Appendix A15 Analysis of variance for data of the final harvests (1996): F values of the effects of plant population density and sweet potato cultivars on plant measures per land area 134 Appendix A16 Arithmetic means of plant measures per 1.65 m land area in 1996 ... 135 2  Appendix A17 Measures per plant at the final harvest in ' B O 44T3' and ' B O 129T9' grown at three different plant population densities in 1995 and 1996. 136 Appendix A l 8 Analysis of variance for pooled data of the 1995 and 1996 observations: F- values of the effects of years of planting, plant population density and sweet potato cultivars on measures per plant 138 Appendix A19 Arithmetic means of plant measures per plant at the 1995 and 1996 final harvests 139 Appendix A20 Regression coefficients of inverse yield-density regressions for different plant measures in 1995 and 1996 for sweet potato cultivars ' B O 44T3' and ' B O 129T9' 140 Appendix A21  Regression coefficients of inverse yield-density regression for different plant measures in sweet potato cultivars ' B O 44T3' and ' B O 129T9' for 1995 and 1996 141  Appendix B I  Regression coefficients for best subset multiple regression models of the allometric relationships between T W and other plant measures in sweet potato varieties. Allometric relationships are for pooled observations from the 1995 and 1996 studies 142  Appendix B2  Simple correlation coefficients among plant population density and various plant measures in cultivar ' B O 44T3' at the 1995 and 1996 final harvests 143  Appendix B3  Simple correlation coefficients among plant population density and various plant measures in cultivars ' B O 129T9' at the 1995 and 1996 final harvests 144  Appendix B4  Path analysis of the relationships among aboveground plant measures and T W in ' B O 44T3' in 1995 and 1996. Partitioning of correlation coefficient ( r ) into direct and indirect effects 145  XI1  Appendix B5  Path analysis of the relationships among aboveground plant measures and T W in ' B O 129T9' in 1995 and 1996. Partitioning of correlation coefficient ( r ) into direct and indirect effects 146  Appendix B6  Simple correlation coefficients among population density, yield components and yield in ' B O 44T3' at the 1995 and 1996 final harvests. 147  Appendix B7  Simple correlation coefficients among population density, yield components and yield in ' B O 129T9' at the 1995 and 1996 final harvests  148  Xlll  Abbreviations and Symbols  Abbreviation /Symbol a AGR b bi C Cp  DAP df F H  LA LAGR LAI LA/LN LAR LGR LN In LNGR LN/SL LWR MTW N n ns P P Q QA  R r RGR SGR SL SLA SLGR SL/SN 2  Definition Inverse of plant yield in the absence of competition Absolute growth rate per plant Index of mean plant responsiveness to change in population density Regression coefficient Centigrade or Celsius Mallow's Cp: an estimate of the standardized total squared error Days after planting Degree of freedom Variance ratio, a test of significance for a difference Harvest index Leaf area per plant LA growth rate Leaf area index Area per leaf Leaf area ratio Leaf growth rate Number of leaves per plant Natural logarithm LN growth rate Number of leaves per stem length Leaf mass ratio Dry mass of marketable tuberous roots per plant Day length Mean daily bright sunshine Not significant Probability Path coefficient Calculated incident radiation Total daily solar radiation at the top of the atmosphere Coefficient of determination Simple correlation coefficient Relative growth rate Stem growth rate Length of stems per plant Specific leaf area SL growth rate Length per stem  Units of measurement  Page of first reference 27  kg/day  25 27 63  116 73  day  19 41 41 25  m m /day 2  20  2  25 25  m m /kg kg/day 2  68  2  25 25 20 59  per day per m kg/kg kg hour hour  25 68 25 20 18 18 38 38 63  kJ/cm kJ/cm  2  18  2  18 48 62  per day kg/day m m /kg m/day m 2  25 25 20 25 25 68  (continued on following page)  xiv (Abbreviations and Symbols, continued)  Abbreviation /Symbol SN SNGR SP Sqrt SW t TDP TGR TW TW/LA ULR V VGR v:v VW W WL y X X/,  z  z  z  | l f } f i n 111 n n J-SCllIllllUIl  N u m b e r o f stems per plant S N growth rate Sum o f products Square root D r y mass o f stems per plant Y e a r o f planting Two-dimensional partitioning yield variation Tuberous root growth rate D r y mass o f tuberous roots per plant D r y mass o f tuberous roots per leaf area U n i t leaf rate Cultivar Growth rate o f the above ground plant parts V o l u m e ratio D r y mass o f the above ground plant parts per plant D r y mass o f the whole plant D r y mass o f leaves per plant Y i e l d per plant N u m b e r o f plants per land area The linear response o f a plant measure to increasing plant population densities The deviation from linear response o f a plant measure to increasing plant population densities A b o v e ground plant variable Standardized value o f the subscript variable  Unit of measurement  per day  kg  kg/day kg kg/m /day 2  kg/day kg kg kg kg plants/1.65 m  2  Page of first referred 20 25 79 76 20 59 67 25 20 68 25 27 25 11 20 20 20 27 27 27 27 59 63  a  The allometric coefficient  59  P  The allometric exponent The residual o f regression  59 59  Significant at P = 0.05 Significant at P = 0.01  41 41  E  * **  XV  Acknowledgements  M y study in the Faculty of Graduate Studies at the University of British Columbia has been funded by the Eastern Indonesia Universities Development Project of Simon Fraser University/CIDA (EIUDP), the University of British Columbia and by Cenderawasih University, to which I wish to express my gratefulness. I also wish to express my sincere gratitude to Dr. Peter A . Jolliffe and Dr. George W. Eaton of Faculty of Agricultural Sciences/the University of British Columbia and to Dr. Patricia A. Bowen of the Pacific Agriculture Research Centre (PARC) for their guidance during the development of this project. The counsel of the other members of my supervisory committee, Dr. Art A. Bomke of the Department of Soil Science and Dr. F. Brian Holl of the Faculty of Agricultural Sciences, is acknowledged with gratitude. M y appreciation is due to Mr. August Kafiar and Mr. Frans A . Wospakrik of Cenderawasih University, and to Dr. Barizi of Bogor Agricultural University (IPB), who encouraged me to study at the University of British Columbia. M y appreciation is also extended to Mr. Christopher J. Dagg, Ms. Mary Hehn, Ms. Chris Arnet and Mr. Roger Ross of EIUDP and to Mr. Frank Wang of International Student Service/the University of British Columbia for their support during the period of my study in Canada. I wish to express my appreciation to Dr. II Gin Mok of the International Potato Center, who kindly provided stem cuttings of eight sweet potato varieties for my field experiments. I also wish to extend my appreciation to the management of the Pacific Agriculture Research Centre at Agassiz, British Columbia, for the invaluable opportunity, which enabled me to carry out the field experiments and to use facilities at this research station. M y special thanks are extended to Mr. Sean Trehearne of Faculty of Agricultural Sciences, Mrs. Heidi Rempel, Mrs. Brenda Frey, Mr. Mark Gross, Mr. Wayne Johnson, Mr. Kevin Usher and to Mrs. Audrey Nadeline of the Pacific Agriculture Research Centre, Agassiz, for their wonderful contributions to my work. A special thank you is also due to Dr. Akhmad Fauzi of Institute of Fisheries Analysis/Simon Fraser University for sharing his computer expertise with me. A special word of thanks to Dr. Zainal Arifin, Dr. Agus Heri Purnomo, Mr. Yorianta Sasaerila and to Ms. Jeane Maria Casparin Linthin, Mr. Marlis Syamsuddin and Ms. Thea Hendrarto for their great support during my difficult time. Finally, I wish to express my sincere gratitude to my wife, Joedaningsih, and to my children, Santi, Ari and Annisa, for their spiritual support and patience, without which my studies in the University of British Columbia could not have been conducted.  1 1.1  General Introduction  Sweet Potato  Sweet potato (Ipomoea batatas (L.) Lam.) is a perennial root crop belonging to the Convolvulaceae. It is normally grown as an annual crop planted in lowland tropical areas at altitudes of up to 2000 meters. Sweet potatoes are cultivated at latitudes between 40° North and 40° South (Hahn, 1977b) in diverse environmental conditions (Kay, 1973). The plant is adapted to a wide range of soil conditions (Norman et al., 1995), and is able to produce a crop of tuberous roots even with minimum field maintenance. About 92% of the sweet potatoes grown in the world are produced in Asia, 6% in Africa, and the rest in other continents (FAO, 1996). In developing countries such as Papua New Guinea (Bourke, 1982) and Indonesia, particularly in the Baliem Valley in which sweet potato is the staple food (Soenarto and Rumawas, 1997), sweet potatoes are produced using traditional, low-input forms of agriculture (Onwueme and Charles, 1994). In developed countries such as Japan and the United States, sweet potato is produced commercially using modern technology, which requires relatively high-energy inputs. Sweet potato is not only important because its tuberous roots are consumed, but also for other useful characteristics. For example, in Japan the tuberous roots are an important raw material in the industrial production of ethanol. As a cash crop, the sweet potato also makes an important contribution to national economies of the Philippines, Solomon Islands, Tonga, Rwanda, Papua New Guinea and some Caribbean islands (Horton et al., 1989). Sweet potato also has potential as a food source for long-term manned space missions because of its horizontal growth habit, its nutritional qualities, and the edibility of its tuberous roots and foliage (Loretan et al., 1989).  2  1.2  Background of the Study  Various attempts have been made to understand and improve characteristics of sweet potato yield. Some studies showed that early stages in plant growth can affect eventual sweet potato production. For example, studies by Godfrey-Sam-Aggrey (1974) and Hall (1986) indicated that the yield of tuberous roots increases with an increase in either stem cutting length or transplant length. Tuberous roots are formed on stem nodes below the ground, but tuberous root yields of 'Red Jewel' and 'Georgia Jet' sweet potatoes were not affected by the number of underground nodes of a transplant (Hall, 1986). 'Georgia Jet' grown from cuttings without a primary shoot, produced greater lateral vines and dry mass of tuberous roots than those planted from cuttings with the shoot apex (Hall, 1987). Several studies have investigated the relationships between yield of tuberous roots and leaf area. Chapman and Cowling (1965) found that leaf distribution plays an important role in determining sweet potato yields in Trinidad. They showed that plants that were trained on wire produced a higher yield than those that were not grown on wire. Bourke (1984) indicated that for cultivars with a high leaf area index, the distribution of dry matter within the plant was an important factor influencing tuberous root production. However for cultivars with a low leaf area index, the yield of tuberous roots was determined more by leaf area per plant. In a more recent study, leaf removal during growth reduced fresh and dry masses of tuberous roots at the final harvests (David et al., 1995). Some general connections have been made between plant growth and tuberous root production. Dry mass of tuberous roots increases with an increase in growth in above ground plant parts (Austin et al, 1970). Sweet potato plants having the greatest growth of  3  above ground parts produce the highest tuberous root yields (Knavel, 1971). A greater dry mass of tuberous roots is obtained from plants having tuberous roots with the early enlargement characteristics grafted with plants having highest source capacity (Hozyo, 1970). The growth of tuberous roots is influenced by solar radiation, through effects on net assimilation rate and crop growth rate, when leaf area index is above an optimum value (Agata, 1982). Bouwkamp (1983) suggested that differences in vine growth patterns during the later part of the growing period might contribute to differences in final tuberous root yields. Further, he emphasized the importance of canopy management in efforts to obtain high yields. The proportion of assimilates partitioned into tuberous roots (harvest index) can also be important. Bhagsari and Ashley (1990) also reported that increases in harvest index and total plant biomass increased tuberous root yield. Bouwkamp and Hassam (1988) showed that the relationships between tuberous root yield and vine dry mass are inconsistent from one year to another, and vary among cultivars. Although other plant parts can be exploited by humans, the main harvested product of sweet potato is the tuberous root, which constitutes about 75% of the dry matter produced by a sweet potato plant (Jansson, 1978). Dry matter accumulation in tuberous roots is coincidental with the growth of the shoot. Consequently, a partitioning of assimilates occurs between the aboveground and below ground parts (Austin et al., 1970). This raises the possibility that the different parts may compete with one another as dry matter is allocated. The view that source-sink relationships are significant in determining the ability of sweet potato plants to produce high tuberous root yields was expressed by Hahn (1977b). Also, Watson (1952) suggested that tuberous root yield is  4  influenced by the rate of production and distribution of dry matter. Screening for high yield potential on the basis of high source activity, however, may not be an effective approach. Source activity is affected by many environmental factors, which makes screening for source potentials difficult (Hahn and Hozyo, 1984). It was found that both biomass and tuberous root yield of cultivars with high source efficiency did not significantly differ from that produced by cultivars with lower source efficiency (Hahn, 1982). Also, some studies have suggested that dry matter accumulation in tuberous roots is influenced more by the sink activity of tuberous roots than by the source activity of the shoot (Hahn, 1977a, Bouwkamp and Hassam, 1988, Bhagsari, 1990). Kays (1985) suggested that leaf distribution, photosynthate transport and the capacity of the tuberous root system are all of potential importance for sweet potato yield improvement. In previous studies, two terms, e.g., "tuber" and "storage root", were used to indicate the edible underground plant part. Since this underground plant part is formed from secondary thickened root (Artschwager, 1924), I used term "tuberous root" to indicate the edible underground plant part in this study. In summary, previous studies have suggested that various factors, including leaf distribution, leaf area, number of lateral vines, source capacity, sink capacity and the early enlargement of tuberous roots, may help to determine tuberous root yield. It is evident that an understanding of tuberous root production cannot be achieved by studying the roots alone, but must take into account the relationships between the tuberous roots and other plant parts, and those relationships may alter as the plant grows and responds to changing environmental conditions.  5  1.3  Methods of Growth Analysis - A n Overview  This study used five analytical techniques to explore tuberous root production and the quantitative relationships between tuberous root production and the growth of aboveground parts in sweet potato plants. These techniques characteristically began with simple primary observations of the sizes and numbers of plant parts. Subsequently, growth indices were formed from the primary measures, and statistical procedures were then used to describe and evaluate growth. These techniques are briefly described below in the order in which they were used in this thesis. (1) Conventional plant growth analysis commonly follows the chronology of growth, and growth is quantified using several indices of plant presence and performance: population density, growth rate, persistence of growth, and partitioning of dry matter (Hunt, 1982; Jolliffe et al., 1982). A central concern in conventional plant growth analysis is whether changes in (relative) growth rate are related to adjustments in the efficiency (net assimilation rate) and extent (leaf area ratio, leaf area index) of assimilatory systems. Some measures of plant proportions and dry matter partitioning (harvest index) are also considered in conventional plant growth analysis. Conventional plant growth analysis can be applied at the crop, organismal and suborganismal levels (Hunt, 1980; Jolliffe et al., 1982; Jolliffe and Courtney, 1984), and can be used to detect competition between plant organs during their growth. Conventional plant growth analysis originated shortly after the World War I, and has been widely used to assess physiological and ecological aspects of plant growth (Hunt, 1982). (2) Yield-density relationships. Crowding tends to reduce the size of individual plants, and the amount of growth reduction is an indicator of competitive interference. Yield-  density relationships (Shinozaki and Kira, 1956; Holliday, 1960; Willey and Heath 1969) are empirical relationships that account for the decline in plant or plant component and in size with increasing population density. Coefficients of inverse yield-density relationships are population-level measures of competitive response: the larger the coefficient, the more rapid the decline in size as plants are crowded. In the present study, inverse yield-density relationships will be used to evaluate within-species influences of crowding on different measures of plant growth. Since about 1980, inverse yield-density relationships have also been used to quantify within- and between-species influences in species mixtures (e. g., Spitters, 1983). (3) Allometric analysis explores the relationships that exist between different measures of an organism. Since the 1890s a simple power function has often been used to quantify such relationships in many different organisms (Gould, 1966). The power function was expanded by Jolliffe et al. (1988) to allow the use of multiple regression procedures to assess how allometric relationships respond to experimental treatments. (4) Path analysis (Li, 1975) analyses the magnitude and direction of the effect of one factor upon a correlated factor. Path analysis is therefore a potentially helpful procedure for interpreting the complex correlations that tend to exist between different plant measures. Path analysis began with the work of Wright (1921). Path analysis is used to partition the coefficient of simple correlation between two variables into components of direct and indirect effects using a standardized regression (Li, 1975). The direct effect is the effect of one factor upon another if these two factors are only connected by a single path with no other variables intervening to influence the second variable. The indirect effect is the effect of one factor upon another by way of one or more correlated factors.  This procedure can be used to identify plant organs that positively contribute to yield. Path analysis has been successfully used in plant breeding to determine selection indices in grain crops (Dewey and Lu, 1959; Dhagat et ai, 1977). Path analysis has also been used to study the impact of weed competition on yield in tomato (McGiffen et al, 1994). (5) Yield component analysis assesses the quantitative relationships that may exist between variations in morphological yield components and variation in yield. Formal yield component analysis began with the work of Engeldow and Wadham (1923), and the approach has been extensively used as an aid in crop improvement (e. g. Matsushima, 1970). Yield component analysis has exploited a variety of statistical techniques to evaluate the relationships among yield components, which are ratios of morphological measures, and variations in yield (Fraser and Eaton, 1983). One of these procedures, twodimensional partitioning of yield variation (TDP, Eaton et al., 1986), uses stepwise multiple regression and analysis of variance to subdivide the total sum of squares for yield into contributions made by individual yield components and experimental sources of variation. The specifics of these five techniques will be described in more detail later in this thesis. It should be noted that other methods of growth and yield analysis exist. For example, sub-organismal demographic analysis (Bazzaz and Harper, 1977) follows the origins ('births'), categories ('fates') and elimination ('deaths') of plant constituents. Sub-organismal demographic analysis is particularly useful in plants that repetitively produce large numbers of organs, such as leaves or flowers, during the course of growth. Sub-organismal demographic analysis was not used in the present studies since the present focus was not on the life cycles of plant parts. There is considerable overlap  8  among all of these techniques, which is necessarily the case because they often begin with similar input data. As shown by Jolliffe and Courtney (1984), conventional plant growth analysis, yield component analysis and sub-organismal demographic analysis all link with allometric analysis. Hence, they are not true alternatives to each other, but are interconnected branches of the general subject of the quantitative analysis of plant growth and yield. I know of no other single study, however, which has employed all five methods of analysis that are used here.  1.4  Objectives, Experimental Approaches, and Outline of This Study  The present study had three main objectives: 1)  to gain a better understanding of the growth and yield variation in sweet potato. In particular, this study aims to determine the responses of tuberous root yield, and the responses of aboveground morphological measures, to population density in two different sweet potato cultivars grown in different seasons,  2)  to identify morphological measures of aboveground plant parts that are positive indicators of high tuberous root yield in sweet potato  3)  to compare the capabilities of different methods of quantifying and analyzing crop performance.  At the outset, it was expected that in attaining the first two objectives this study would advance previous understanding of yield generation in sweet potato, and would provide measures that might be used to direct crop improvement. The third objective was expected to lead to a better understanding of the capabilities and limitations of different techniques of crop growth analysis.  9  To accomplish these objectives two field experiments, described in Chapter 2, were carried out using two sweet potato cultivars that have some contrasting morphological characteristics. In the first experiment, the two cultivars were grown at three different levels of plant population density, and yields and other plant characteristics were observed at the end of the growing season. Results from that experiment allowed the within-cultivar competitive responses to be evaluated using inverse yield-density relationships, as presented in Chapter 3. In the second experiment the two cultivars were grown at one population density, and the progress of crop growth was followed by making a succession of harvests throughout the growing season. The periodic harvests provided the input data for conventional plant growth analysis, which is also presented in Chapter 3. The first experiment also provided data for exploring the quantitative relationships between above ground plant parts and tuberous roots, using techniques of allometric analysis, path analysis, and yield component analysis, as described in Chapter 4. Chapter 5 provides a general discussion that relates the results from the three preceding chapters to the objectives of this study and to the external literature. Chapter 6 lists the main conclusions drawn from these investigations.  10  General Procedures In order to avoid repetition, this Chapter will describe general aspects of the experimental design and other methods that are applicable to the studies reported in both Chapters 3 and 4. In Chapters 3 and 4, you will find descriptions of additional procedures, including methods of statistical analysis, which are specific to those Chapters. As detailed in later sections, two field experiments provided the data that form the core of this thesis. Experiment 1 was repeated in 1995 and 1996, and it was used to evaluate population density-dependence, and the relationships among different measures of growth, in two sweet potato cultivars. Experiment 2 was only performed in 1996; it followed the progress of growth of the same two cultivars at a single population density. 2.1  Experimental Site and Site Characteristics  Field experiments on sweet potato were conducted at the Pacific Agriculture Research Centre (PARC), Agassiz, British Columbia (49° 15'N 121°46'W, altitude 15 m) in 1995 and 1996. The soil at the experimental site was a silt loam (Rego Humic Gleysol). Soil tests for the experimental site was conducted by Griffin Laboratories Corporation and results are presented in Appendix A l . Soil reaction was slightly acid. Soil of the experimental site was high in phosphorus, potassium and in magnesium. Calcium content was medium, but sulphate was low (Appendix A l ) . Long-term climate observations for Agassiz are presented in Appendix A2.  11  2.2 2.2.1  Plant Material Source of Plant Material  Two sweet potato cultivars with contrasting morphological characteristics were chosen for use in this study. A n erect type of sweet potato was represented by ' B O 44T3', which was characterized by its short stem. A spreading type of sweet potato was represented by ' B O 129T9', which had a long vine (Table 2.1). These two cultivars were selected Table 2.1 Some characteristics of the sweet potato cultivars used in this study Characteristic Shoot type Length of main vine Leaf shape Tuberous root shape Tuberous root colour: skin Tuberous root colour: flesh  'BO 44T3' Erect 0.75 m Lobed Long, oblong Pink White  2  'BO 129T9' Spreading >2.50m Triangular Long, elliptical Orange Orange  'Source: Huaman, Z. (ed.). 1991. from among eight sweet potato cultivars received from the International Potato Centre (CIP), Regional Office at Bogor, Indonesia. The eight sweet potato cultivars, each represented by ten 10 cm long stem cuttings, were sent from Indonesia via air courier, and were received in Vancouver on September 9, 1994.  2.2.2  Transplants for the 1995 and 1996 Field Experiments  Starting on September 14,1994, stem cuttings from the eight cultivars were rooted and grown in the plant nursery under warm and humid conditions in the greenhouse of the Department of Plant Science, the University of British Columbia. The cuttings were rooted in wooden flats of 0.50 x 0.25 x 0.10 rn. The medium for rooting was a mixture of peat moss and Perlite (50:50/v:v). The bottom part of each stem cutting was treated with  12  IBA rooting powder for softwood cuttings: Stim-Root N o . l (indole-3 butyric acid 0.01%) to stimulate root formation. Supplemental lighting in the nursery was provided by using two 400 Watt HPS lamps located approximately 1.75 m above the benches on which the wooden flats were placed. A 24-hour timer was used to control the lighting system, and day length was set for 16 hours. The temperature regime in the nursery was about 25 and 18C for day and night, respectively. Relative humidity was maintained at approximately 80% by spraying sweet potato leaves and nursery floor with water. On October 10, 1994 the young, rooted plants were transplanted to black plastic pots having a diameter of 0.26 m and a height of 0.3 m. Each pot contained 8 kg of sterilized loam soil mixed with 5 g of Osmocote fertilizer (14:14:14). Two plants of the same cultivar were planted in each pot, and there were five pots for each of the eight cultivars, providing a total of 10 plants per cultivar. From the five pots per cultivar, three were used to observe tuberous root development, and the remaining two were used as sources of stem cuttings for plant propagation. On December 5, 1994, each plant grown in the three pots was removed and the size and shape of their tuberous roots were observed. Cultivars having a capability for early tuberous root enlargement were selected. From the eight cultivars, only four formed tuberous roots under the nursery conditions. Based on their contrasting morphological characteristics (erect vs. spreading), and their capability for early tuberous root development, ' B O 44T3' and ' B O 129T9' were selected for subsequent selected for subsequent research. Using similar procedures and starting the first week of December 1994, stem cuttings of ' B O 44T3' and ' B O 129T9' were rooted for a period of four weeks, and  13  then the growing cuttings were removed from the wooden flats and planted into pots. Five transplants were grown in each pot, and those plants were used as sources of stem cuttings for plant propagation. This procedure was repeated several times in the ensuing months to multiply stem cuttings for the 1995 field experiment. In the first week of April 1995, about four weeks before planting in the field, transplants destined to be used for the 1995 field experiment (Experiment 1, first repetition) were obtained from terminal cuttings with shoot apex. On May 1, 1995, the transplants were moved to Agassiz and placed in cold frames. The transplants were then planted in the field on May 9, 1995. Plant material used for field experiments carried out in 1996 (Experiment 1, second repetition, and Experiment 2) were obtained from stem cuttings from the remaining field plants from Experiment 1 in 1995. On September 22, 1995, stem cuttings of both cultivars were rooted in wooden flats in the greenhouse of P A R C using the procedures described previously. Each cultivar was rooted in four wooden flats, and there were 30 stem cuttings per flat. On November 15, 1995, the young plants were moved to the greenhouse of the Department of Plant Science, the University of British Columbia where stem cuttings were multiplied using the procedures describe previously. Starting on April 1, 1996, transplants were obtained from rooted terminal cuttings (including shoot apex). On May 30, 1996, these transplants were moved to Agassiz and placed in cold frames. The transplants used for Experiment 1 in 1996 were planted in the field on June 5 and those used for Experiment 2 were planted in the field on June 10, 1996.  14 2.3 2.3.1  Experimental Design Experiment 1  In the two years that Experiment 1 was performed, it used similar split plot designs to examine the effects of plant population density on the two sweet potato cultivars. There were six treatment combinations involving the two cultivars ('BO 44T3' and ' B O 129T9') each grown separately at three levels of plant population density (24,242, 48,485 or 72,727 plants/ha). These densities correspond to 8, 16 or 24 plants within plots of size 3.0 m x 1.1m. Within the plots, plants were established in two rows, separated by 0.55 m, in a staggered system. Levels of plant population density were assigned to the main plots, while cultivars were assigned to the subplots. This was done partly for practical reasons and partly to improve the precision of the study in determining the effects of cultivars and the interaction between plant population density and cultivar. The main plots were replicated, in blocks, four times in 1995 and three times in 1996. In assigning the treatments to experimental plots, a two-stage randomization was conducted. In the first stage, levels of plant population density were randomized within each of the (four or three) experimental blocks followed by randomization of cultivar assignments to the subplots within each main plot. The layouts used for Experiment 1 are given in Appendices A3 and A4. In 1995, the two guard rows were also planted with ' B O 44T3' and ' B O 129T9'. The 1995 trial of Experiment 1 was conducted from May 9 to September 16. The 1996 trial was carried out from June 5 to October 6. The delayed planting in 1996 was due to greater rainfall (Appendix A5), which prevented the preparation of raised beds before early June.  15  2.3.2  Experiment 2  Experiment 2 was conducted from June 10 to October 25, 1996. It was carried out to provide descriptive information on the chronology of growth of the two sweet potato cultivars, ' B O 44T3' and ' B O 129T9', grown at the intermediate population density of 48,485 plants/ha. The experiment consisted of 15 observation blocks, each having two subplots (one per cultivar, assigned randomly, Appendix A4). Subplot size was 1.50 m x 1.10 m, and the distance between plots was 1.00 m. Each subplot contained eight sweet potato plants per 1.65 m in two rows growing in a staggered system. As detailed below, destructive harvests were carried out during the course of the growing period. For that purpose, different observation blocks were randomly chosen for harvests at different times (Table 2.2). Table 2.2 Dates of harvests of observation blocks in Experiment 2.  Date of harvest  2.4  Observation block harvested  July 10, 1996  4,11,15  July 31,1996  3,9  August 20, 1996  2,8,14  September 14, 1996  1,6,12,13  October 25, 1996  5,7,10  Field and Plant Maintenance  Compost, derived from mixed vegetation, was applied as a mulch to the experimental fields, at a rate of 10 tonnes/ha, in the fall of 1994. In March 1995, the soil was tilled and 24 m long raised beds were formed. After they were formed, the raised beds were covered with dark green plastic, in order to control weeds and to keep soil temperature  16  and moisture content high. The raised beds were 1.1m wide and 0.30 m high, and the distance between adjacent raised beds was 0.70 m. In both years, a thin colourless polyethylene plastic wall, 0.6 m high and supported by wooden canes, was erected in the middle of the spaces between the raised beds. This wall was used to prevent the sweet potato plants from growing into adjacent raised beds. Appendices A3 and A4 show the distribution of raised beds within the experimental arrays. Water status of the raised beds was monitored by tensiometers and plots were irrigated when the tensiometer reading fell below -250 kPa. Irrigation was applied using typhoon hose, placed in the middle of the raised beds under the plastic sheet. Fertilizer components were dissolved in 20 L of warm water, pH was adjusted to between 5.5 to 6.0 using NaOH, and the resulting solutions were applied though the irrigation system. Fertilizing was conducted three times during plant growth, at two, six and at nine weeks after planting. Rates of application were calculated on the basis of the surface areas of the raised beds, which were 106 and 210 m in 1995 and 1996, 2  respectively (Table 2.3). Two pest control sprays were applied in 1995. On June 2, plants were sprayed with Pirimor 50 DF (a.i.: primicarb) at 3.5 g in 7 L of water (corresponding to 330 g/ha in 660 L/ha of water) to prevent aphid infestation. On June 9, plants were treated with Ambush 500 E C (a.i.: permethrin) at 1.4 mL diluted in 10 L of water (corresponding to a dosage of 140 mL/ha) to control cutworms. In 1996, to control aphids, plants were sprayed with 200 mL Safer's insecticidal soap (a.i.: potassium salts of fatty acid, 50.5%) in 10 L of water or at a dosage of 10 mL in 500 mL of water on June 21. Since the aphids did not completed killed in the first treatment, then on June 25 the plants were treated  17  Table 2.3 Dates of application, the amount and dosage of fertilizers used in sweet potato experiments in 1995 and 1996. Date  1995 May 23  June 20  Fertilizer  NH4NO3 (34:0:0) KH2PO4 (0:53:34) Chelated micronutrient mixture KNO3 (13.75:0:46) M g S 0 (9.8% Mg) Chelated micronutrient mixture KCI (0:0:60) 4  July 11  Quantity (g)  z  Dosage (kg/ha)  710 360 16 528 50 16 529  68 34 1.5 50 25 1.5 50  1,421 1,665 32 1,050 239 . 32 699 239  68 79 1.5 50  1996  June 19  July 17  August 7  NH4NO3 (34:0:0) KH2PO4 (0:22.7:28.7) Chelated micronutrient mixture K N O 3 (13:0:37) MgSCU (9.8% Mg) Chelated micronutrient mixture KCI (0:0:60) MgSC-4 (9.8% Mg)  11.4  1.5 33.3 11.4  Chelated micronutrient mixtures were: E D T A (42%), Fe (5.0%), M n (2.0%), Zn (0.4%) and C u (0.10%) all on a w/w basis.  z  with 3.5 g Pirimor 50 DF in 7 L of water or at a dosage of 330 g/ha in 660 L/ha of water. To protect the sweet potato plants from loopers and cut worms, on August 7, the plants were sprayed with 40 mL Foray 48B (a.L: Bacillus thuringiensis, sub species Kursteki) in 10 L of water or at a dosage of 2 L/ha. 2.5  Climate Observations  Climate observations were made during both years primarily in order to provide background information on the environmental setting in which these field experiments took place. Solar radiation, air temperature and soil temperature were monitored at the experimental site during both years of the study, and the results of those observations are  18  compiled in Appendices A5 to A7. The duration of bright sunshine was measured by using Campbell-Stokes sunshine recorder. The incident solar radiation at the experimental field was calculated based on the daily duration of bright sunshine (in hours) using the following regression equation proposed by Angstrom (Chang, 1968): Q / Q A = 0.355 + 0.68(nM/)  (Eqn. 2.1)  where Q is the calculated incident radiation at the experimental field, QA is the total daily solar radiation at the top of the atmosphere at a latitude of 50° North (List, 1971), n is the mean daily bright sunshine at the experimental field and N is day length at a latitude of 50° North (List, 1971). The values of 0.355 and 0.68 are summer month constants for Canada (Chang, 1968). Air and soil temperatures were monitored using a data logging microprocessor connected to nine or 15 probes for the 1995 or 1996 experiments, respectively. Air and soil temperatures were recorded every hour, and the locations of the temperature probes are shown in Appendices A3 and A4. In 1995, three probes were used to monitor air temperature, while in 1996 six probes were used for that purpose. Those probes were suspended within a Styrofoam shield, about 0.60 m above the soil surface, in the middle of the experimental plots. Soil temperature probes were placed about 0.10 m below the raised bed surface, between the two plant rows. Temperatures recorded by different probes were pooled, and daily mean air temperatures and soil temperatures are presented in Appendix A5 and Appendix A6, respectively.  2.6  Harvests and Primary Measurements  2.6.1 Plot and Plant Samples In both experiments, destructive harvests were conducted to assess plant performance. For Experiment 1, the harvests were conducted at the ends of the growing seasons, on September 16, 1995 (130 days after planting (DAP)) and on October 6, 1996 (123 DAP). The plants harvested were located in the middle of the subplots, within an area of a subplot measuring 1.5 m x 1.1 m. Only plant material found within that area was collected; all stems and leaves crossing the perimeters of the area were cut at the border. /. e., it was assumed that the numbers of stems and leaves running out from a sampling area was equivalent to those entering into the area. For Experiment 2, sweet potato plants were harvested periodically during the growing season, at 31, 51, 71, 96 and at 137 DAP. The first harvest was carried out on July 10, and the last was on October 25, 1996. For each harvest, two to four blocks were randomly selected for observations (Table 2.2). In this case, four plants growing in the middle of each subplot were harvested. 2.6.2 Primary Plant Measurements Plants were severed at the soil surface (and in the case of Experiment 1 the aboveground parts were also severed at subplot boundaries as described above), and the aboveground plant material was quickly moved to the laboratory for further processing. There, leaves were removed and leaf area was measured using a LI-COR Portable Area Meter Model 3000. Tuberous roots were then collected and brought to the laboratory. Branches were separated from the main stems, and additional observations were taken on the harvested plant material, as listed in Table 2.4. In Experiment 1, mean values per plant were  20  calculated using the combined value for the plant material obtained from a 1.65 m  2  sampling area divided by the nominal plant population for that sampling area. In Experiment 2, data for individual plants were recorded separately. Dry mass of plant parts was measured after the parts were dried at 70C for 48 hours in an oven.  Table 2.4 Primary observations made on individual plants at each harvest Primary Plant Measures  Symbols and Units  Number of leaves per plant  LN  Leaf area per plant  LA, m  Dry mass of leaves per plant  WL, kg  Number of stems per plant  SN  Length of stems per plant  SL,m  Dry mass of stems per plant  SW, kg  Dry mass of the above ground plant parts per plant  VW,kg  Dry mass of tuberous roots per plant  TW, kg  Dry mass of marketable tuberous roots per plant  M T W , kg  Dry mass of the whole plant  W, kg  2  These primary data, and indices derived from the primary data, were subjected to several types of statistical analysis, as detailed in Chapters 3 and 4. It should be noted that in the present studies, the term "stem" indicates the collective of main above ground stem plus primary, secondary and tertiary branches. Number of stems per plant was the total number of the main stem plus all branches. Length of stems per plant comprised the length of the main stem plus the combined lengths of all branches. Similarly, dry mass of stems comprised the dry mass of the main stem plus the dry masses of all branches and dry mass of petioles. A marketable tuberous root was identified as one having a fresh  21  mass of 100 g or more. Total dry mass of the aboveground plant parts was the total dry mass of leaves, the main stem plus all branches and petioles. Dry mass of the whole plant was composed of the dry mass of the aboveground plant parts plus the dry mass of tuberous roots (marketable plus non-marketable). Non-tuberous root dry mass was not measured and therefore was not included in whole plant dry mass.  22  3  3.1  Chronological Trends in Growth, and Primary Responses to Population Density, in Two Sweet Potato Cultivars Introduction  Observations of the chronology of growth can be used to identify the timing of key events during growth and they allow us to explore plant responses to environmental condition and genetic manipulation. They can be used to follow several important aspects of plant functioning, including trends in the efficiency of leaves in producing dry matter and trends in the distribution of dry matter to various plant parts. Previous studies on sweet potato plant growth have indicated that different cultivars can differ in these features. For example, 'Centennial', 'Julian' and 'Nemagold' were found to differ in their leaf morphology and rate of growth (Austin et al., 1970). Stem growth was greater in 'Centennial' and 'Nemagold' than in 'Julian', while 'Julian' had greater proportional dry matter accumulation in tuberous roots compared to the other two cultivars. The greater partitioning of photosynthate into tuberous roots of 'Julian' was related to lower photosynthate allocation to stem development. The difference in the partitioning of dry matter accumulation into tuberous roots was not related to the differences in the leaf shapes or stem growth between the cultivars. High yielding sweet potato cultivars seem to be characterized by rapid tuberization. For example, high yielding cultivars 'Laloki No. 1', 'Laloki No. 2' and 'Milne Bay' accumulated tuberous root mass faster than the other, lower yielding, cultivars (Enyi, 1977). Tuberous root growth, however, seems to occur at least partly at the expense of aboveground growth. In addition to the works of Austin et al. (1970), other studies suggest an inverse relationship between aboveground and underground  growth. For example in sweet potato cultivar 'VSP-2', a bushy cultivar, dry matter accumulation in the tuberous roots was inversely related to dry matter accumulated in the stem and leaves (Pardales and Belmonte, 1989). In 'VSP-2' maximum vine growth was attained at about 10-12 weeks after planting, then the vine dry mass declined up to the final harvest, as tuberous roots expanded. By comparison cultivar 'BNAS-51', a spreading cultivar, accumulated a greater amount of dry matter in stem and leaves, but less in tuberous roots. The greater vine dry mass in ' B N A S - 5 1 ' was due to the gradual but steady increase in dry matter in stem and leaves up to the final harvest. Mean size per plant tends to diminish as plants are crowded, and observations of the density-dependence of plant growth are helpful in assessing competitive interference in plants (Spitters, 1983). Studies on the effects of plant population density on sweet potato have indicated that the growth of aboveground parts and tuberous roots both decline with increasing plant population density. For example in cultivar 'Jewel' many plant measures decreased with increasing plant population density, including total number of branches, total length of branches, total number of nodes, total number of leaves, and numbers of leaves on primary and on secondary branches (Somda and Kays, 1990b). Both fresh and dry masses of leaves of cultivar 'TT-55' decreased with higher population density when within-channel plant spacing was reduced from 0.25 to 0.13 m (Mortley et al., 1991). In earlier studies, Bouwkamp and Scott (1980) showed that the effect of plant population density was greater on the number than on the yield of tuberous roots per plot. Further, they found that responses of cultivars 'Redmar' and 'Centennial' to plant population density differed, particularly in their generation of tuberous roots per  24  plot. That study also indicated that the size distribution of tuberous roots, produced at a certain level of plant population density, differed between cultivars. It is difficult to make a formal comparison, but my impression is that characteristics of growth and yield are not as well documented for sweet potato as for some other important food crops, such as cereal grains. The present study was done to track the chronology and density-dependence of growth in sweet potato by observing a broader set of above- and underground features than has been done previously. It employed two sweet potato cultivars ' B O 44T3' and ' B O 129T9', which had some contrasting morphological characteristics. Sweet potato cultivar ' B O 44T3' is a partly erect type of sweet potato, having short stem. Sweet potato cultivar ' B O 129T9' is a more spreading or recumbent type, having a long vine (Table 2.1). The choice of these two cultivars was based on Wilson's hypothesis (1977) that a short stem bushy type cultivar would have a greater efficiency in tuberous root production. Support for this hypothesis was obtained in sweet potato cultivar 'VSP-2' in a study performed in the Philippines (Pardales and Belmonte, 1989). In this study, two field experiments were done to meet the following objectives: 1)  to compare the chronology of growth in two contrasting sweet potato cultivars, ' B O 44T3' a n d ' B O 129T9',  2)  to determine what measures of aboveground growth rate are positively or negatively correlated with the formation of tuberous roots in the two cultivars,  3)  to evaluate effects of plant population density on various primary measures of plant growth in the two cultivars, and  25  4)  to determine if the density-dependence is similar, between the two different growing seasons, for the different measures of plant growth.  3.2 3.2.1  Materials and Methods Crop Culture and Experimental Details  The experimental designs and primary observations were discussed in Chapter 2. 3.2.2  Data Analysis  3.2.2.1 Conventional Plant Growth Analysis Indices (Table 3.1) of conventional plant growth analysis (Hunt, 1982) were employed to  Table 3.1 Growth Indices (Conventional Plant Growth Analysis) Measure  Abbreviation  Units  Formula  Simple Growth Rates Absolute growth rate Growth rate of aboveground parts Leaf growth rate Leaf number growth rate Leaf area growth rate Stem growth rate SN growth rate SL growth rate Tuberous root growth rate  AGR VGR  kg/day kg/day  dW/dt dVW/dt  LGR LNGR LAGR SGR SNGR SLGR TGR  kg/day per day m /day kg/day per day m/day kg/day  dWL/dt dLWdt dLA/dt  2  dSN/dt dSL/dt dTW/dt  Compounded Growth Rates Relative growth rate Unit leaf rate  RGR ULR  g/g/day  kg/m /day 2  (l/W)x(Mrft)) (\/LA)x(dW/dt))  Ratios Leaf area index Leaf area ratio Leaf mass ratio Specific leaf area Harvest Index  LAI LAR LWR SLA H  2/  2  m Im  m /kg kg/kg m /kg 2  g/g  LA/A LA/W WL/W LA/WL TW/W  26  interpret the chronology of growth in the two sweet potato cultivars during one growing season, using the data obtained from Experiment 2. Cubic spline growth curves were fitted to each set of mean values of the primary measures obtained at the periodic harvests in Experiment 2. The procedure for this involved several steps. Mean values were first ln-tranformed so that the data conformed better to the assumption of normality. No tuberous roots were formed early in the growing season, and in those cases non-zero values of T W were created before lntransformation by adding 0.000001 kg to the observed mean values of TW. Before fitting the spline curves, cubic polynomials were fitted to the data using the computer program PROC G L M (SAS Institute, 1988) to determine the location of inflexion points. Once inflexion points were obtained, cubic spline functions were fitted to the data for each primary measure, using Maple V Release 3 (Waterloo Maple Software, 1995). First derivatives of the fitted spline functions provided the compounded growth rates (RGR, ULR). The fitted curves were anti-transformed to represent the primary measures of growth in their original scales of measurements. Ratios of the anti-transformed spline function provided the ratio indices. 3.2.2.2 Simple Linear Correlation Simple linear correlations between growth rate of tuberous root and growth rates of the other plant indices were computed using the computer program PROC G L M (SAS Institute, 1988). To know when growth rates of the other indices were positively related to the growth rate of tuberous roots, simple linear correlation analyses were done for three different growing periods, i.e., the whole, the earlier and the later periods. The whole period was period from 31 up to 137 DAP. The earlier period was from 31 D A P  27  until the day when the growth rate of a primary plant measure reached its maximum. The later period was the period from the maximum until the final harvest. 3.2.2.3  Analysis of Variance  The analysis of variance of the split plot design was used to evaluate the effects of plant population densities, cultivars and their interactions upon variations in aboveground primary plant measures and tuberous root yield. Computations for the analysis of variance were performed with the program PROC G L M (SAS Institute, 1988). Data used for this analysis were obtained from the final harvests carried out in 1995 and 1996. Two different error sources, the main plot and subplot errors, are provided in analysis of variance for split plot design. The main plot error was used to test the effects of blocks and plant population density upon each primary measure. The subplot error was used to test the effects of cultivar and the interaction between plant population density and cultivar upon each primary measure. A n orthogonal contrast procedure was employed to partition degrees of freedom into single degree of freedom comparison. The purpose of using the orthogonal contrast was to examine and to test the trends of effects of plant population density upon plant measures. Three levels of plant population density of equal interval provided two orthogonal comparisons that were tested, i.e., the linear response of a plant measure to increasing plant population densities (X/,) and the remainder or the deviation from the linear response 3.2.2.4  (XDL)-  Inverse Yield-Population Density Relationships  The relationship between plant performance and plant population density was evaluated using an inverse yield-density equation (Holliday 1960): y"' = a + bX  (Eqn. 4.1)  28  where y is the mean yield o f a plant and X is number o f plants per unit area. Parameter a is the inverse of plant yield in the absence of competition and b is an index of mean plant responsiveness to change i n population density; the larger the value of b, the more rapid is the decline in y with crowding. Yield-density relationships were evaluated each year using the same data that were used for analysis of variance and were fitted using SigmaStat 2.0 (Jandel Scientific Ltd.). Values of regression parameters were compared using Student's t (Zar, 1974).  3.3  Results  Part 3.3.1 will report the chronology of primary measures (3.3.1.1) and indices of growth and dry matter distribution (3.3.1.2 to 3.3.1.5). Then, Part 3.3.2 will report the densitydependence of primary measures. 3.3.1  Chronology of Growth  3.3.1.1 Growth of Primary Plant Measures Chronological trends in growth will be displayed using the cubic spline regressions. The two cultivars exhibited similar patterns of increase i n both total (W) and vegetative dry masses (VW) per plant (Fig. 3.1). During the first 60 days after planting (DAP), W and V W increased slowly, but later, the plant measures increased rapidly. After about 60 DAP, W in 'BO 129T9' was greater than i n 'BO 44T3'. Dry matter accumulation was still occurring late in the season; there was no indication that at the final harvest W and V W had reached their maxima, in either cultivar. Both cultivars started to form tuberous roots at about 38 DAP. The major increase in T W occurred between 80 and 120 D A P , in both cultivars. At the final harvest TW was essentially the same in the two cultivars.  29  a) 0.7 -1  0.6  -I  I  W  Days after planting  Figure 3.1 Time course of dry mass of the whole plant (W), dry mass of aboveground plant parts (VW) and dry mass of tuberous roots per plant (TW) in sweet potato cultivars: a) 'BO 44T3' and (b) 'BO 129T9'in the 1996 growing season.  30  Stem  0 -! 20  1  40  : 60  ! 80  Leaf  : 100  Days after planting  : 120  , 140  ^  0 -! 20  ! 40  ! 60 D  a  y  ! 80 s  a  ft  e r  1  1  100  120  I  140  planting  Figure 3.2 Time course of per plant measures in sweet potato cultivars ' B O 44T3' and ' B O 129T9' in the 1996 growing season: (a) stem number (SN), (b) stem length (SL), (c) stem dry mass (SW), (d) Length per stem, (e) number of leaves (LN), (f) leaf area (LA), (g) leaf dry mass (WL), and (h) mean area per leaf.  31  Two different types of growth trends were observed for the primary plant measures. Some primary measures, such as, SN, SL, SW, L N and WL, continued to grow throughout the experiment (Fig. 3.2). The magnitude of SN, L N , and possibly of W L , did not differ greatly between the two cultivars. However, SL and SW were greater in ' B O 129T9' than in ' B O 44T3'. Some other measures, such as, L A , length per stem (SL/SN), area per leaf (LA/LN) and TW, stopped increasing or even declined late in the experiment (Figs. 3.1 and 3.2). Length per stem, L A , area per leaf and T W (except at the end) were greater in ' B O 129T9' than in ' B O 44T3'. The largest differences between the two cultivars in stem characteristics were obtained for SL, SW and for length per stem. The differences between the two cultivars in leaf characteristics were not as large as for the stem characteristics.  3.3.1.2 Indices of Growth Rates The characteristics of sweet potato growth were further studied through indices of growth rate: A G R , R G R and U L R . These are based on W and L A , and the three growth indices exhibited different patterns of variation during growth (Fig. 3.3). AGR: In both cultivars, the absolute rate of dry matter accumulation increased at first, until maxima were reached at 108 and 101 D A P for ' B O 44T3' and ' B O 129T9', respectively (Fig. 3.3a). Thereafter, A G R o f ' B O 44T3' remained nearly constant while A G R of ' B O 129T9' continued to decrease until the final harvest. RGR: Relative growth rate is a measure of the rate of self-compounding (Evans 1972; Hunt, 1982). The R G R of both cultivars declined with increasing age (Fig. 3.3b). Before about 97 D A P , R G R was greater in ' B O 129T9' than in ' B O 44T3'. However,  32  a)  20  40  60  80  100  120  140  b)  0.1  I  0 ' 20  ! 40  : 60  1 80  : 100  : 120  • 140  C)  0.008  0 > 20  :  :  ,  1  1  40  60  80  100  120  r  140  Days after planting  Figure 3.3 Time course of plant growth rates: (a) absolute growth rate (AGR), (b) relative growth rate (RGR) and (c) unit leaf rate (ULR) in sweet potato cultivars ' B O 44T3' and ' B O 129T9' in the 1996-growing season.  33  after that time the ranking of the two cultivars was reversed. ULR: Unit leaf rate expresses the efficiency of leaves in accumulating dry matter (Evans, 1972). Both cultivars showed a similar trend of U L R (Fig. 3.3c). As growth proceeded, U L R increased steadily until maxima were reached at about 78 and 73 D A P for ' B O 44T3' and ' B O 129T9', respectively. Until about 105 D A P , U L R was greater in ' B O 129T9' than in ' B O 44T3'. After about 105 DAP, U L R o f ' B O 129T9' decreased rapidly and reached a minimum at about 134 DAP. In 'BO 44T3' after about 105 D A P , U L R decreased more gradually and reached a minimum at about 129 D A P . Stem and Leaf Growth Rates: Throughout the study there was a continuous increase in rates of growth of stem number and stem dry mass (Fig. 3.4 a and c), in both cultivars. There was also a continuous increase in rates of growth of stem length and leaf dry mass in ' B O 44T3' (Fig. 3.4 b and f). In all other cases, growth rates increased until about 90 to 100 days after planting and then declined. For SNGR, and for L N G R , the two cultivars did not differ in their growth trends (Fig. 3.4 a and d). On the other hand, SLGR, SGR, L A G R and L G R differed between the two cultivars (Fig. 3.4 b, c, e and f).  34  Stems  Leaves d)  Days after planting  Days after planting  Figure 3.4 Time course of growth rates of stem and leaf measures: a) leaf number growth rate (SNGR), b) stem length growth rate (SLGR), c) stem dry mass growth rate (SGR), (d) leaf number growth rate (LNGR), e) leaf area growth rate (LAGR) and leaf dry mass growth rate (LGR) in sweet potato cultivars ' B O 44T3' and ' B O 129T9' in the 1996 growing season.  35  3.3.1.3 Ratio Indices Ratios, such as L A I , LWR, L A R , S L A and H, express plant proportions, and results for these indices are presented in Figs. 3.5 and 3.6. LAI: This index indicates the foliage that a crop maintains above a unit area of land. L A I in both cultivars increased up to the final harvest (Fig. 3.5a), but the two cultivars differed in their trends of L A I increase. L A I of ' B O 129T9' reached a maximum of 8.02 at about 125 DAP. For ' B O 44T3', L A I was highest at the final harvest, having a value of 6.61 at that time. Throughout most of the study, L A I tended to be greater in ' B O 129X9' than in ' B O 44T3'. The two cultivars also differed in their L A I when A G R was at its optimum: ' B O 129T9' had a LAI of 6.20 at 101 DAP, while ' B O 44T3' had a L A I of 5.39 at 108 DAP. LAR, LWR and SLA: Leaf area ratio declined throughout the study (Fig. 3.5c) in both cultivars. L A R was marginally less in ' B O 129T9' than in ' B O 44T3'. i. e. ' B O 44T3' used less dry matter to construct the same area of leaves than did ' B O 129T9'. L A R is the arithmetic product of L W R and SLA. L W R expresses the proportion of dry matter that has been allocated to the leaves. Until about 72 DAP, allocation of dry matter to leaves (LWR) was higher in ' B O 129T9' than in ' B O 44T3' (Fig. 3.5b). Thereafter, the ranking was reversed. S L A is the ratio of leaf area to leaf dry mass. The two sweet potato cultivars differed in their S L A trends (Fig. 3.5d). Until about 95 D A P , the S L A of ' B O 44T3' was higher than in 'BO 129T9'. Thereafter, the ranking was reversed. Hence, while the L A R patterns for the two cultivars were similar, they exhibited different underlying patterns of L W R and SLA.  36 a) 10  b) 0.8  I  0' 20  1 40  , 60  , 80  1 100  , 120  , 140  j  0-! 20  D a y s after planting  1  ,  ,  40  60  80  ,  100  ,  120  ,  140  Days after planting  Figure 3.5 Time course of leaf characteristics and leaf properties: (a) leaf area index (LAI), (b) leaf weight ratio (LWR), (c) leaf area ratio (LAR) and (d) specific leaf area (SLA) in sweet potato cultivars ' B O 44T3' and 'B0129T9' in the 1996 growing season. Arrows denote the optimum L A I . 0.7  n  Days after planting  Figure 3.6 Time course of harvest index (H) in sweet potato cultivars ' B O 44T3' and ' B O 129T9' in the 1996 growing season.  37  H: H was higher in ' B O 44T3' than in ' B O 129T9', although the chronological patterns were similar for the two cultivars. H of 'BO 44T3' reached a maximum of 0.58 at about 117 DAP, while that of ' B O 129T9' reached a maximum of 0.52 at about 115 D A P . At the final harvest, H was 0.49 for ' B O 44T3' and 0.40 for ' B O 129T9'.  3.3.1.4  Tuberous Root Growth Rate and Its Relationships with Indices of Aboveground Growth  In both cultivars, the rate of dry matter accumulation in tuberous roots (TGR) increased until a maximum was reached at 105 and 103 D A P for 'B044T3' and ' B O 129T9', respectively (Fig 3.7).  20  40  60  80  100  120  140  Days after planting  Figure 3.7 Time course of tuberous root growth rate in two sweet potato cultivars ' B O 44T3' and ' B O 129T9' in the 1996-growing season.  Most indices of aboveground growth were correlated with T G R (Table 3.2), but the correlations changed at different periods of growth. Over the whole of plant growth, TGR was weakly and positively correlated with both L A I and V G R in both cultivars. In addition, there were weak positive correlations of TGR with SNGR, SLGR, L G R , L N G R , L A G R in both cultivars. However, stronger correlations occurred between SLGR,  38 Table 3.2 Correlation coefficients between growth indices of the aboveground plant measures and TGR at different growth periods in 1996 in sweet potato cultivars ' B O 4 4 T 3 ' a n d ' B O 129T9'.  Growth indices  5.  TGR Cultivar a  »  Z  The whole period  The earlier period  The later period  LAI  BO 44T3 BO 129T9  +0.65** +0.48**  +0.98** +0.98**  -0.96** -0.82**  VGR  BO 44T3 BO 129T9  +0.59** +0.61**  +0.95** +0.93**  -0.96** +0.25ns  SGR  BO 44T3 BO 129T9  +0.03ns +0.28**  +0.97** +0.97**  -0.92** -0.96**  SNGR  BO 44T3 BO 129T9  +0.46** +0.31**  +0.95** +0.94**  -0.98** -0.96**  SLGR  BO 44T3 BO 129T9  +0.61** +0.92**  +0.94** +0.93**  -0.96** +0.99**  LGR  BO 44T3 BO 129T9  +0.56** +0.80**  +0.95** +0.86**  -0.97** +0.99**  LNGR  BO 44T3 BO 129T9  +0.62** +0.69**  +0.68** +0.72**  +0.98** +0.99**  LAGR  BO 44T3 BO 129T9  +0.71** +0.72**  +0.81** +0.81**  +0.99** +0.99**  Z  T G R = Growth rate of tuberous roots. TGR in sweet potato cultivars ' B O 44T3' and ' B O 129T9'reached maxima at about 105 and 103 D A P , respectively.  y  L A I = Leaf area index, V G R = Growth rate of aboveground plant parts, SGR = Stem growth rate, SNGR = Growth rate of number of stems, SLGR = Growth rate of length of stems, L N G R = Growth rate of number of leaves, L A G R = Growth rate of leaf area, D A P = Days after planting. ns, ** = Not significant or significant at P = 0.01.  L G R and TGR in ' B O 129T9'. The correlation between TGR and SGR was weak in ' B O 129T9', and was not significant in ' B O 44T3'. In the earlier period of plant growth (until the maximum in TGR), correlations between TGR and aboveground plant measures were positive and mostly strong in both cultivars (Table 3.2). Later in growth, the correlations of TGR with L N G R , L A G R and TGR were positive, but TGR was negatively correlated with L A I , SGR, and with SNGR in both cultivars. Also later in growth, TGR was negatively correlated with V G R in ' B O 44T3', but in ' B O 129T9' the correlation was not significant. Also later in growth, the correlations between SLGR, L G R and TGR were positive in ' B O 129T9', but those were negative i n ' B O 44T3'.  40'  3.3.2 3.3.2.1  Effects of Plant Population Density upon Primary Plant Measures Analysis of Variance  Tuberous root yields per unit land area differed between the two years of planting and were significantly affected by population density (Appendices A l 1 and A12). Many measures of growth per unit land area differed between the two cultivars, but tuberous root yields did not (Appendices A l 1 and A12). It is more suitable to interpret the effects of population density on measures per plant than on measures per land area. Yield per land area, for example, is the product of yield per plant and plant population density. Hence, plant population density is not an independent variable in relation to yield per land area. The analysis of variance (Tables 3.3 to 3.6) indicated that significant declines occurred in all per plant measures with increasing plant population density. Some differences between the two cultivars were found. For example, variations in W, SN, SL, SW, L A and in W L differed between the two cultivars in 1995 (Table 3.3), but not in 1996 (Table 3.5). The mean of SN was greater in ' B O 44T3' than in ' B O 129T9' in 1995 (Table 3.4), but no significant difference was found in 1996 (Table 3.6). However, W, SL, SW, L A and of W L were smaller in ' B O 44T3' than in ' B O 129T9' in 1995 (Table 3.4), but not in 1996 (Table 3.6). Also, variation in W and SL both were influenced by XL x v in 1995 (Table 3.3), but not in 1996 (Table 3.5). Finally, tuberous root yields per plant (TW and M T W ) were reduced by increasing plant population density, but were not affected by cultivar (Tables 3.3 to 3.6). T W variation was affected by Significant density by cultivar interactions are illustrated in Fig. 3.8.  x v in 1995.  41  Table 3.3 Analysis of variance for data of the final harvests (1995): F values of the effects of plant population density and sweet potato cultivar on measures per plant. 2  o  u  r  c  e  o  variation Block X/,„ (Xi) X (X ) Error a Variety (v) X x\ ^ x v Error b Total e a r  remaMer  L  DL  x  df  W  3 1 1 6 1 1 1 9 23  1.46 80** 4.23"  y  ns  s  17** 16** 4.75 ns  SN  SL  2.2 l l * 0.42  0.36 61** 5.6"  6.2* 0.59 0.63  117** 24** 23** 12** 5.9* 5.1  ns  ns  ns  ns  ns  s  SW 1.9 28** 3.4 ns  ns  ns  LN  LA  WL  TW MTW  7.5* 99** 11*  5.2* 84** 12*  1.7 37** 5.0  0.96 90** 3.1  2.2 164** 5.1  4.8 0.93 1.9  22** 1.8 0.62  38** 5.8* 2.5  2.7 9.1* 1.8  0.17 3.1 0.58  ns  ns  ns  ns  ns  ns  ns  ns  ns  ns  ns  ns  ns  ns  ns  ns  ns  z  Values of measures per plant derived from values of plant measures per 1.65 m sample plots after being divided by number of plants planted in the sample plots.  y  Measures per plant: W = Plant dry mass (kg), SN = Number of stems, SL = Length of stems (m), SW = Dry mass of stems (kg), L N = Number of leaves, L A = Leaf area (m ), W L = Dry mass of leaves (kg), T W = Dry mass of tuberous roots (kg), M T W = Dry mass of marketable tuberous roots (kg).  2  2  x  Abbreviations and symbols: X = Plant population density (plants per 1.65 m ) , X i = The linear response of a plant measure to increasing population densities, X = Deviation from the linear response of a plant measure to increasing plant population densities, df— Degree of freedom, ns, *, ** = Not significant or significant at P = 0.05 or P = 0.01, respectively. 2  D L  The arithmethic means of measures per plant at the 1995 final harvests are presented in Table 3.4.  42  Table 3.4 Arithmetic means of measures per plant at the 1995 final harvests. 2  X  y  W  SN  SL  SW  LN  LA  WL  TW MTW  Mean response ofper plant measures to increasing plant population densities 4 8 12  0.896 0.496 0.324  Trend  Xi**  47 31 23  21 11 8  Xi*  Xi**  0.166 0.071 0.048  469 239 176  2.7 1.3 1.0 X *  0.062 0.031 0.024  0.668 0.398 0.251  0.605 0.343 0.204  X **  Xi**  Xi**  L  DL  Mean responses ofper plant measures to increasing plant population densities in sweet potato cultivars: BO 44T3 4 8 12 Mean  0.754 0.481  50 33 26 36  14 8 6 9  0.099 0.061 0.034  484 264 176  2.4 1.1 0.8  0.046 0.025 0.017  0.610 0.396 0.262  0.544 0.352 0.221  0.065  308  1.4  0.029  0.422  0.372  1.038 0.510 0.334 0.627  44 29 21  27 14 11  0.233 0.082 0.062  455 214 175  3.1 1.5 1.2  0.079 0.038 0.031  0.729 0.391 0.241  0.649 0.334 0.187  31  17  0.126  281  1.9  0.049  0.453  0.390  **  *  **  **  ns  **  **  ns  0.313 0.516  BO 129T9 4 8 12 Mean Mean difference z  ns  Measure per plant: W = Plant dry mass (kg), SN = Number of stems, SL = Length of stems (m), SW = Dry mass of stems (kg), L N = Number of leaves, L A = Leaf area (m ), WL = Dry mass of leaves (kg), TW = Dry mass of tuberous roots (kg), M T W = Dry mass of marketable tuberous roots (kg). 2  Abbreviations and symbols: X = Plant population density (plants per 1.65 m ) , X i - T h e linear response of measure per plant to increasing plant population densities, XDL Deviation from the linear response of measure per plant to increasing plant population densities, ns, *, ** = Not significant or significant at P = 0.05 or P = 0.01, respectively. 2  =  43  Table 3.5 Analysis of variance for data of the final harvests (1996): F values of the effects of plant population density and sweet potato cultivar on measures per plant. 2  Source of variation Block X / , „ r (XZ) ea  ^•nonlinear (X/J/J  Error a Variety (v) X x v XDL x v Error b Total L  w  2 1 1 4 1 1 1 6 17  y  §  N  §  1.02 100** 4 44  4.5  4.47 o.or 4.65  5.9 2.3 0.15  ns  ns  ns s  ns  ns  L  §  9.3*  1.3 8.0* 0.38  „s  4.8 2.1 0.87  r  ns  ns  ns  L  2.3 8.0* 0.087 ns  gg**  w  3  7  0.79 2.r  L  ns  3.5 69** 4.4  6.4 76** 5.2  6.4 52** 1.9  5.2 l 96** 1.8  3.8 0.82 1.6  0.40 0.03 0.64  0.95  0.37 0.65 10*  1.1™ 0.03 3.1  ns  ns  ns  A  5.4" 198** 21* s  ns  ns  s  ns  N  ns  ns  ns  ns  ns  ns  ns  ns  2 4  ns  ns  0.32  ns  ns  ns  ns  ns  n s  ns  ns  ns  z  Values of measures per plant derived from values of plant measures per 1.65 m sample plots after being divided by number of plants planted in the sample plots.  y  Measures per plant: W = Plant dry mass (kg), SN = Number of stems, SL = Length of stems (m), SW = Dry mass of stems (kg), L N = Number of leaves, L A = Leaf area (m ), W L = Dry mass of leaves (kg), T W = Dry mass of tuberous roots (kg), M T W = Dry mass of marketable tuberous roots (kg).  2  2  "Abbreviations and symbols: X = Plant population density (plants per 1.65 m ), X i = The linear response of a plant measure to increasing population densities, Xot = Deviation from the linear response of a plant measure to increasing plant population densities, df = Degree of freedom, ns, *, ** = Not significant or significant at P = 0.05 or P = 0.01, respectively. 2  The arithmetic means of measures per plant at the 1996 final harvests are presented in Table 3.6  44  Table 3.6 Arithmetic means of measures per plant at the 1996 final harvests. 2  X  W  y  SN  SL  SW  LN  LA  WL  TW  MTW  Mean response ofper plant measures to increasing plant population densities 4 8 12 Trend  0.397 0.248 0.178  77 42 31  X **  16 11 8 X*  L  L  0.063 0.039 0.028 X* L  342 160 110 ^ * *  2.4 1.2 0.8 +  X ** L  0.076 0.038 0.023  0.257 0.171 0.127  X **  X **  L  °-206 0.130 0.083 X **  L  L  Mean responses ofper plant measures to increasing plant population densities in sweet potato cultivars: BO 44T3 4 8 12  0.393 0.210 0.173  93 54 32  13 11 6  0.047 0.036 0.025  397 191 116  2.3 1.3 0.7  Mean  0.259  60  10  0.036  234  4 8 12  0.400 0.286 0.183  61 30 30  20 11 9  0.079 0.042 0.032  Mean  0.290  40  13  Mean difference  ns  ns  ns  0.275 0.136 0.131  1.4  0.071 0.037 0.018 0.042  0.181  0.210 0.102 0.083 0.132  288 131 104  2.6 1.2 0.8  0.081 0.039 0.029  0.240 0.205 0.123  0.203 0.158 0.083  0.051  174  1.5  0.050  0.189  0.148  ns  ns  ns  ns  ns  ns  BO 129T9  z  Measure per plant: W = Plant dry mass (kg), SN = Number of stems, SL = Length of stems (m), SW = Dry mass of stems (kg), L N = Number of leaves, L A = Leaf area (m ), W L = Dry mass of leaves (kg), TW = Dry mass of tuberous roots (kg), M T W = Dry mass of marketable tuberous roots (kg). 2  Abbreviations and symbols: X = Plant population density (plants per 1.65 m ) , X = The linear response of measure per plant to increasing plant population densities, XDL Deviation from the linear response of measure per plant to increasing plant population densities, ns, *, ** = Not significant or significant at P = 0.05 or P = 0.01, respectively. 2  t  =  45  Figure 3.8 Effects of plant population density on primary measures: (a) plant dry mass (W), (b) stem length (SL), (c) stem dry mass (SW), (d) leaf dry mass (WL) and (e) tuberous root dry mass (TW) in sweet potato cultivars ' B O 44T3' and ' B O 129T9' at the 1995 final harvests.  46  3.3.2.2  Inverse Yield-Density Relationships  Significant "deviation from linear" population density responses, as indicated by the analysis of variance results just presented, and the patterns seen in Fig. 3.8, suggest that an ordinary straight line will not adequately define the pattern of density-dependence. Inverse yield-density responses have proved suitable for this purpose (Willey and Heath 1969), and when applied to the present data significant relationships were usually obtained (Table 3.7). The constants (a) of the inverse yield-density relationships were mostly not significant (Table 3.7). Significant regression coefficients (b) quantify the responsiveness of each primary plant measure to changing plant population density. Since inverse relationships were formed, positive coefficients indicate that the primary plant measures declined with increasing plant population densities. The larger the magnitude of the regression coefficient, the more rapid was the decline in the mean value of a primary plant measure. Except for W and M T W in both cultivars, and L N and T W in ' B O 44T3', the magnitude of regression coefficients for a primary measure did not significantly differ between the two years (Appendix A20). Also, except for W L in both growing seasons, T W and M T W in 1995, and W in 1996, the magnitude of regression coefficient for each plant measure did not significantly differ between the two cultivars (Appendix A21).  47  Table 3.7 Constants and coefficients from inverse yield-density regression , measuring the density-dependence of different primary plant measures in 1995 and 1996 for ' B O 44T3' and ' B O 129T9' sweet potatoes. 2  Measure  W  y  Cultivar  vl v2  SN  vl v2  SL  vl v2  SW  vl v2  LN  vl v2  LA  vl v2  WL  vl v2  TW  vl v2  Year  Constant (a)  SE  t-test  Coefficient (b)  SE  t-test  R  2  1995 1996 1995 1996  0.360 1.110 -0.0241 0.841  0.176 0.578 0.147 0.562  ns ns ns ns  0.383 0.681 0.416 0.626  0.0337 0.110 0.0281 0.107  ** ** ** **  0.93** 0.85** 0.96** 0.83**  1995 1996 1995 1996  0.0147 0.000778 0.0132 0.0120  0.00789 0.00360 0.00655 0.00845  ns ns ns ns  0.00366 0.00415 0.00488 0.00353  0.00151 0.000687 0.00125 0.00161  * ** ** ns  0.37* 0.84** 0.60** 0.41ns  1995 1996 1995 1996  0.0187 0.0353 0.00929 0.0463  0.0169 0.0312 0.00777 0.0257  ns ns ns ns  0.0220 0.0179 0.0124 0.00903  0.00322 0.00597 0.00148 0.00491  ** * ** ns  0.82** 0.56* 0.87** 0.33ns  1995 1996 1995 1996  1.730 12.810 -0.109 5.928  3.308 6.076 1.571 10.519  ns ns ns ns  3.667 3.769 2.332 4.068  0.632 1.161 0.300 2.009  ** * ** ns  0.77** 0.60* 0.86** 0.37ns  1995 1996 1995 1996  0.000255 -0.000552 0.000856 0.00102  0.000873 0.00125 0.000929 0.00198  ns ns ns ns  0.000784 0.00130 0.000724 0.00129  0.000167 0.000240 0.000177 0.000378  ** ** ** *  0.69** 0.81** 0.63** 0.62**  1995 1996 1995 1996  0.0342 -0.108 0.129 0.0151  0.162 0.239 0.149 0.172  ns ns ns ns  0.177 0.223 0.107 0.168  0.0310 0.0456 0.0284 0.0328  ** ** ** **  0.77** 0.77** 0.59** 0.79**  •1995 1996 1995 1996  4.490 -10.478 6.465 2.424  3.932 13.114 5.313 6.367  ns ns ns ns  7.423 9.695 3.844 4.747  0.751 2.505 1.015 1.216  ** ** ** **  0.91** 0.68** 0.59** 0.69**  1995 1996 1995 1996  0.491 2.091 -0.0481 1.912  0.235 1.473 0.249 1.105  ns ns ns ns  0.453 0.889 0.572 0.826  0.0450 0.281 0.0475 0.211  ** * ** **  0.91** 0.59* 0.94** 0.69**  (continued on following page)  48  (Table 3.7, continued) Measure  Cultivar  MTW  vl v2  Constant  Year  (a)  1995 1996 1995 1996  0.382 1.476 -0.546 0.627  SE 0.375 1.539 0.612 2.235  t-test  Coefficient (b)  ns ns ns ns  0.564 1.557 0.812 1.572  SE 0.0715 0.294 0.117 0.427  t-test ** ** ** **  R  2  0.86** 0.80** 0.83** 0.66**  A11 relationships were of the form y" = a + bX, where y is a primary plant measure such as W, and X is species population density (plant-m" ). The larger the coefficient (b), the more rapid was the decline in the primary plant measure as species population density increased. The standard error of the parameter estimate (SE) and the test of significance for the coefficient being equal to zero according to a t-test are also given for each coefficient value, R = Coefficient of determination.  Z  2  2  Abbreviations and symbols: W = Plant dry mass (kg), SN = Number of stems, SL = Length of stems (m), SW = Dry mass of stems (kg), L N = Number of leaves, L A = leaf area (m ), W L = Dry mass of leaves (kg), T W = Dry mass of tuberous roots (kg), M T W = Dry mass of marketable tuberous roots (kg), v l = ' B O 44T3', v2 = ' B O 129T9', ns, *, ** = Not significant or significant at P = 0.05 or P = 0.01. 2  49  3.4  Discussion  3.4.1  Growth Characteristics in ' B O 44T3' and ' B O 129T9'  These results provide a more detailed description of the chronology of growth, and the population density-dependence of growth, than is available from previous studies with sweet potato. The two cultivars used in this study were chosen because of their contrasting growth habits: ' B O 44T3' is a shorter-stemmed, more bushy type than ' B O 129T9', a spreading type. Previous work with other sweet potato cultivars had found that a bushy cultivar 'VSP-2' was more productive than a spreading cultivar ' B N A S - 5 1 ' (Pardales and Belmonte, 1989). It was therefore expected that the present cultivars might also differ in their productivity. The present study, however, found no differences in final total or marketable tuberous root yields between the two cultivars. Perhaps my results differ from some findings of Pardales and Belmonte (1989) simply because I used different cultivars and there were different growing conditions for the two studies. Both studies showed that early in growth, there was little difference in the pattern of dry matter accumulation were between bushy and the spreading cultivars. However, later in their growth, the two type cultivars differed in their deposition of dry matter in tuberous roots. The two bushy type cultivars ('VSP-2' and ' B O 44T3') had greater dry matter accumulation in tuberous roots than did the spreading type cultivars ('BNAS-51' and ' B O 129T9'). The two spreading type cultivars had vigorous early growth but a smaller fraction of their total dry matter was accumulated in the tuberous roots. Both my studies and those of Pardales and Belmonte (1989) identified different chronological patterns of growth in different cultivars. For example, vine mass and  50  tuberous root dry mass in 'BNAS-51' continued to increase up to the final harvest, while those characteristics in 'VSP-2' reached maxima and then declined (Pardales and Belmonte, 1989). There was a greater final tuberous root yield in 'VSP-2' compared to 'BNAS-51', while in my study final yields were similar for my two cultivars. Given different chronological patterns of growth between cultivars, however, if the final harvest was performed at different dates, then the ranking of productivity for the different cultivars might be changed. For example, in my Experiment 2 the final harvest was conducted at 137 D A P , a time when my two cultivars had similar yields. Final yields would have been different, however, if the experiment was stopped at 120 D A P , when tuberous root yield was greater in ' B O 129T9' than in ' B O 44T3'. Final harvest time can be determined by crop maturity, and by factors that terminate a growing season, but it is also partly dependent on arbitrary decisions made by researchers on when to plant, how to grow, and when to observe. Most tuberous root mass accumulates following the photosynthetic assimilation of carbon by the shoot, so the performance of aboveground parts is physiologically relevant to tuberous root formation. For example, in my study the growth of tuberous roots (TGR) was strongly and positively correlated with the rates of addition (LNGR) and expansion of leaves (LAGR). Also, differences between cultivars in aboveground measures might contribute to differences in tuberous root growth. In the later period of growth, the correlations between SLGR, or LGR, and TGR were negative in ' B O 44T3', but these correlations were positive in ' B O 129T9'. In the two cultivars, there were different relationships between tuberous root development and the growth of length of stems (SL) and leaves (WL). As discussed in Section 3.3.1.3, the higher leafiness in ' B O 129T9'  51  may have resulted in greater self-shading, and this might have contributed to the slower accumulation of tuberous root dry mass in that cultivar. In addition to final yield, there were other similarities in growth of the two cultivars. Here, I will focus on chronological aspects, since density-dependence will be discussed later. The two cultivars exhibited similar trends of increase in vine dry mass, and the cultivars had similar numbers and rates of formation of stems and leaves, although the trends of these plant measures differed from one another. The biomass accumulation patterns found here (Fig. 3.1) resemble those observed in sweet potato 'Nemagold' (Bouwkamp, 1983). Finally, the two cultivars did not differ greatly in their leaf area ratios and their leaf weight ratios. Notwithstanding these similarities, the two cultivars exhibited numerous differences in their chronology of growth. Compared to 'BO 44T3', ' B O 129T9' exhibited more rapid stem elongation and stem dry mass accumulation. It had greater area per leaf formed, which resulted in higher leaf area per plant and higher leaf area index during much of the growing season. The ability of the assimilatory systems to generate biomass, as indicated by unit leaf rate, was initially higher in ' B O 129T9' than in ' B O 44T3'. Assuming that unit leaf rate largely reflects photosynthetic carbon accumulation by the leaves (Hunt, 1982), ' B O 129T9' not only had greater area of foliage, but also its foliage was more efficient in carbon assimilation early in growth. These traits were associated with initially higher absolute and relative growth rates in ' B O 129T9'. However, 'B0129T9' invested a smaller fraction of its accumulated biomass in the tuberous roots (i.e., its harvest index was lower than in ' B O 44T3').  52  A mid-season peak in unit leaf rate occurred with both cultivars. This may be due to the greater availability of solar radiation and more optimal environmental conditions for photosynthesis near mid-summer, compared to earlier and later dates. Despite having smaller leaves, the more compact form (shorter internode lengths) of ' B O 44T3' may have caused greater mutual shading by leaves to occur in that cultivar. This is a possible cause for its lower unit leaf rate through the first part of the growing season. This interpretation, however, is complicated by the possibility that the two cultivars may differ in the chronology of aging of the photosynthetic apparatus within cells (Salisbury and Ross, 1992). Indices of growth, such as relative growth rate, unit leaf rate and leaf area ratio, may assist in the interpretation of growth by simplifying the original primary data and by expressing performance in a physiologically meaningful way (Hunt, 1982). Also, i f tuberous root growth and yield are reliably correlated with growth indices, then such indices might be useful in selecting new sweet potato cultivars. It was for this reason that correlations between indices of aboveground growth and tuberous root growth were explored. Additional correlations, formed as part of path analysis, allometric analysis and yield component analysis, will be presented in the next chapter for tuberous root yield obtained at the final harvest only. Here, an interest was to determine i f correlations were strong and consistent in the two cultivars at different phases during growth. Aboveground indices of growth were commonly strongly correlated with tuberous root growth, the only exception being for V G R late in growth in ' B O 129T9' (Table 3.2). Such correlations do not prove the existence of functional relationships, but such relationships are to be expected from basic physiological knowledge and the strong  53  correlations highlight the importance of aboveground organs to tuberous root growth. Positive correlations predominated, except during the later period of growth, following the time of maximum growth rate, when some strong negative correlations occurred. For the majority of the indices (LAI, SGR, SNGR, L N G R and L A G R ) the direction and significance ofthe correlations were the same for the two cultivars. Differences between the cutivars were obtained in the direction or significance of the correlations of tuberous root growth with V G R , SLGR and LGR. Hence, the latter traits would not be a reliable indicator of tuberous root growth across cultivars. Similarly, L A I , SGR and SNGR changed from positive to negative correlation between the early and later stages of growth. Hence, these traits would not be a consistent indicator of tuberous root growth across different times during crop growth. Two indices, L A G R and L N G R , however, were similar in their direction of correlation across both cultivars and growth periods. O f these two, L N G R is the easiest to determine, although its correlations with tuberous root growth were lower than for L A G R . Either of these indices, however, might prove to be useful in selecting higher-yielding sweet potato cultivars. This possibility should be explored in future studies involving a greater diversity of cultivars.  3.4.2  Effects of Plant Population Density on Primary Measures of Growth  The next chapter will also explore density-dependence, using techniques of allometric analysis and yield component analysis. Here, the interpretation of population density results will be based on the A N O V A S and the inverse yield-density regressions. The A N O V A S detected significant population density responses in both years for all primary measures. Simple linear responses did not fully account for densitydependence, and inverse yield-density relationships were formed in order to describe the  54  form of density-dependence more completely. Inverse relationships have a long history for this purpose (Willey and Heath, 1969). They follow the decline in measures of plant size as plants are crowded. When transformed to a per unit land area basis, such relationships express an asymptotic trend. For monocultures, as is the case here, the inverse models have two parameters, and, as mentioned in the previous chapter, the constant (a) represents the inverse of plant size for plants grown in isolation. The coefficient (b) measures the decline in size with increasing population density. The latter is of particular interest as an indicator of intraspecific competition (interference) (Jolliffe, 1997). For this study, the inverse yield-density regressions were usually significant, with positive coefficients (b). i. e., crowding usually reduced primary measures, and the only exceptions to this were non-significant regressions for SN, SL and SW for ' B O 129T9' in 1996. It should be noted that the present results are from a field study, in which other environmental sources of variation may be prominent, and where the number and replication of density treatments were not large. Under these circumstances, the regular detection of density responses, with the majority of coefficients of determination exceeding 0.75, suggests the importance of density as a factor influencing plant performance. Other studies have also observed declines in primary plant measures in sweet potato in response to increasing population densities. For example, in 'Jewel', the total number and length of branches per plant decreased with increasing plant population densities (Somda and Kays, 1990a). Similarly, the number and area of leaves per plant (Somda and Kays, 1990b). In 'TI-500', fresh and dry masses of leaves per plant  55  decreased with reducing within-channel spacing from 0.25 to 0.13 m (Mortley et al, 1991). Also, the number and dry mass of tuberous roots declined linearly with reducing the distance between two channels from 0.38 to 0.13 m. However, yield per unit land area increases with the increase in plant population density (Bouwkamp and Scott, 1980). In the present study, differences in population density responsiveness, between cultivars (Appendix A21) and years (Appendix A20), were assessed by comparing regression coefficients using t-tests at P=0.10. In 5 out of 18 comparisons, cultivars differed in their density-dependence, although the ranking of the two cultivars was not constant for different primary measures. For example, in 1995 the response of T W to population density was greater in ' B O 129T9' than in ' B O 44T3', while for W L ' B O 44T3' was more responsive. Five primary measures differed in their population densitydependence between cultivars (Appendix A21). In three cases 'B044T3' was more responsive, while in two cases ' B O 129T9' was more responsive. Hence, it is not clear which cultivar is more subject to intraspecific competition, since the result seems to depend upon what primary measure is being observed. Where significant differences were found between years, coefficients were always higher in 1996 than in 1995. The difference in 1996 might be related to differences in soil temperatures, which were lower in September 1996 than in September 1995 (Appendix A6). The lower soil temperature in the last part of growing season resulted in slower growth that may also have aggravated intraspecific competition.  56  4  Relationships between Aboveground Plant Measures and Tuberous Roots  4.1  Introduction  In sweet potato, the leaves and young stems are sometimes used as vegetables, but the tuberous roots are the main harvested plant parts. Tuberous root production is influenced by a number of factors, including choice of cultivars (Levett, 1993), soil conditions (Norman et al., 1995), altitude (Ngeve et al., 1990), plant population density (Bouwkamp and Scott, 1980) and shade (Nkrumah et al., 1986). The production of aboveground plant parts is also affected by genetic and environmental factors. For example, the number of branches per plant is influenced by plant population density (Somda and Kays, 1990b), and frequency of branching is cultivar dependent (Yen, 1974). The preceding chapter provides further documentation of the effects of cultivar, growing season and population density on tuberous root and aboveground growth in sweet potato. It showed that several aboveground measures, such as leaf area and leaf number growth rates, were correlated with tuberous root growth. Other studies with sweet potato have shown that the number of lateral vines is positively related to the total dry mass of tuberous roots (Hall, 1987). The distribution of leaves on branches, and the size, shape and number of leaves, influence dry matter production per plant (Somda and Kays, 1990a and 1990b), and leaf distribution also affects dry mass of tuberous roots (Chapman and Cowling, 1965). Finally, some early research indicated that the development of tuberous roots competes with the growth of aboveground plant parts (Austin et al., 1970). Hence, the literature provides evidence that growth interrelationships exist between  57  different parts of the sweet potato plant, but it is sparse concerning quantitative details of those interrelationships. Three techniques available to explore such interrelationships are allometric analysis, path analysis and yield component analysis. Allometry assesses the proportional growth of different parts of an organism, or between a part and the entire organism (Huxley, 1932; Gould, 1966; Niklas, 1994). A simple power function has been used widely to quantify bivariate allometric relationships in plants and animals (Gould, 1966; Richards, 1969; Stanhill, 1977a and 1977b). Jolliffe et al. (1988) expanded the power function, allowing the direct effects of factors on yield (terms involving y) to be distinguished from the indirect effects of factors via allometric adjustments (terms involving P). Path analysis (Li, 1975) partitions the simple correlation coefficient between two measures, e. g., yield of tuberous roots and leaf area. This provides a way to determine the direct and indirect effects of other plant measures on variation in yield. Path analysis has been used in plant breeding to detect variables that highly influence yield of reproductive organs, such as grains (Dhagat et al., 1977). Path analysis has also been used to detect the impact of weeds on tomato yield components (McGiffen et al., 1994). Yield component analysis explores quantitative relationships between yield variation and variation in other morphological measures of a plant (Fraser and Eaton, 1983). Yield component studies in sweet potato have indicated that fresh tuberous root yield is related to both the number of tuberous roots per plant and fresh masses of individual tuberous roots (Lowe and Wilson, 1975; Kamara and Lahai, 1997). Many statistical procedures can be used for yield component analysis (Fraser and Eaton, 1983).  58  One of these, two-dimensional partitioning of yield variation (TDP), is able to assess treatment effects on both yield and yield component variations (Eaton et al., 1986). I have not found previous studies of allometry and path analysis in sweet potato and a thorough analysis of yield component relationships has not yet been done with this crop. In the present study, these three techniques were applied to the results from Experiment 1 in order to quantify and interpret the growth relationships between aboveground plant parts and tuberous roots. In that experiment, variations were potentially associated with three experimental factors: growing season, cultivar and population density. One interest in doing this study was to identify measures of aboveground plant performance that are strongly related to variation in tuberous root yield. Such measures are presumably be of value in future efforts to improve sweet potato productivity, and the analyses may lead to some inferences concerning mechanisms underlying the interrelationships. Another interest was to compare the interpretations gained from the three analytical procedures. That assessment will be considered in the next chapter, in conjunction with a general discussion of techniques of plant growth analysis.  4.2  Materials and Methods  The design of Experiment 1, and procedures for data collection in 1995 and 1996 were described in Chapter 2. Input variables used for the analyses were the primary plant measures at the final harvest.  59  4.2.1  Allometric Analysis  The power function used by Huxley (1932) to describe the allometric relationship between two per-plant measures, y and z, is: y = az  (Eqn. 4.1)  p  where parameters a and (3 are the allometric coefficient and exponent, respectively. This relationship is often dealt with in the In-transformed frame of reference: ln(y) = ln(a) + pin(z)  (Eqn. 4.2)  For an individual at a particular time, this relationship will exist without error, other than observational errors, so long as y and z co-exist. In a population of individuals, however, there may be allometric variations (i.e., a dispersion of values of a and P), as well as variation in y independent of z (represented by the residual s): ln(y) = ln(a) + pln(z) + ln(s)  (Eqn. 4.3)  The allometric coefficient, exponent and residual are subject to plant growth and treatment effects (Jolliffe et al., 1988). In order to detail the effects of experimental factors, such as time (t), cultivar (v) and plant population density (X), the allometric equation (4.3) can be expanded: ln(a) = ln(ao) + c^iln(ait) + <^ln(a2v) + ^ ln(a3X) + ^4ln(a tv) + 2  3  4  c; ln(a tX) + Celn(a vX) + <; ln(a tvX) 5  5  6  7  (Eqn. 4.4a)  7  which can be rewritten as: ln(a) = ln(ao) + £i[ln(a,) + ln(t)] + ^[ln(a ) + ln(v)] + £ [ln(a )+ ln(X)] + 2  3  3  Uln(a ) + lnftv)] + ; [ln(a ) + ln(tX)] + <; [ln(a ) + ln(vX)] + 4  £ [ln(a ) + ln(tvX)] 7  7  5  5  6  6  (Eqn. 4.4b)  60 P = po + Piln(t) + p ln(v) + p ln(X) + p ln(tv) + p ln(tX) + p ln(vX) + 2  3  4  5  6  p ln(tvX)  (Eqn. 4.5)  7  ln(s) = ln(so) + T)iln(sit) + r| ln(e v) + r^lnfoX) + ri4ln(s4tv) + 2  2  r)5ln(s5tX) + r) ln((£ vX) + Ti7ln(s tvX) 6  6  (Eqn. 4.6a)  7  which can be rewritten as: ln(s) = ln(s ) + Tn[ln(e,) + ln(t)] + n. [ln(e ) + ln(v)] + t|3[ln(8 ) + ln(X)] + 0  2  2  3  ri [ln(s ) + ln(tv)] + r) [ln(s ) + ln(tX)] + ri [ln(s ) + ln(vX)] + 4  4  5  5  6  6  ri [ln(8 ) + ln(tvX)] 7  (Eqn. 4.6b)  7  Some terms from Eqn. 4.4b and 4.6b can be rearranged and grouped into: ln(a') = ln(an) + ^iln(ai) + ^ hi(a2) + ^ln(a3) + <^4ln(a4) + <yna(oi5) + 2  ^ ln(a ) + (;7ln(a7) 6  (Eqn. 4.7)  6  ln(s') = ln(so) + r|iln(si) + n,2ln(e ) + r) ln(s3) + r| ln(s ) + ri ln(s ) + 2  3  4  4  5  5  r) ln(e ) + r\ \n(e ) 6  Tk = & + Tik  7  6  (Eqn. 4.8)  7  (where k = 1, 2,..., 7)  (Eqn. 4.9)  After grouping terms (Eqn.4.7 and 4.8) and incorporating the expanded parameter statements (Eqn. 4.4b, 4.6b and 4.9), the overall expanded model became: ln(y) = ln(a') + [p + Pit + p v + p X + p tv + p tX + p vX + p tvX]ln(z) + 0  2  3  4  5  6  7  Yiln(t) + y ln(v) + y ln(X) + y ln(tv) + y ln(tX) + y ln(vX) + y ln(tvX) + 2  ln(s')  3  4  5  6  7  (Eqn. 4.10)  The expanded allometric relationship (Eqn. 4.10) is a linear model that can be evaluated using regression procedures. In all cases, y was tuberous root dry mass per plant and z was some aboveground plant measure. In Eqn. 4.10, terms involving p express how  61  the proportionality of y and z (i.e., allometry) is potentially affected by experimental factors, while terms involving y express how y is affected by experimental factors independently of allometric responses of z. There is potential for structural multicollinearity among some of the 15 potential independent variables in Eqn. 4.10 [ln(z), tln(z), vln(z), Xln(z), tvln(z), tXln(z), vXln(z), tvXln(z), ln(t), ln(v), ln(X), ln(tv), ln(tX), ln(vX) and ln(tvX)]. i. e., inclusion of all ofthe independent variables may not be necessary. The expanded allometric relationships were therefore evaluated using a best subset multiple linear regression procedure (Daniel and Wood, 1971). Several criteria used to selecting the best subset model were: high R , low 2  Mallow's Cp, significant parameter estimates (according to t-test), and low variance inflation factor (VIF < 4.0) (Dixon et al, 1983). Pooled data ofthe 1995 and 1996 final harvests of Experiment 1 were used to explore allometric relationships, and the computations were performed with the program SigmaStat 2.0 (Jandel Scientific Inc.).  4.2.2  Path Analysis The path analysis was based on a path diagram (Fig. 4.1) that depicts the flow of  influence of plant population density (X) on TW, either directly or by way of aboveground measures. The diagram indicates that aboveground measures act either as paths for X to influence TW, as primary causes that influence TW, or as paths for other plant measures to affect TW. The path diagram also is meant to depict statistical relationships among plant population density, aboveground plant measures and tuberous root yield. L i (1975) simplified the computations required for path analysis by using the standardized regression equation to partition the correlation coefficient into direct and  62  indirect effects. Regression coefficients generated by path analysis are standardized partial regression coefficients. For that purpose I used regression equations for standardized density, Z , standardized aboveground plant parts (ZSN, X  , zT ) and WL  standardized tuberous root dry mass (ZTW).  Figure 4.1 A path diagram for the linear relationships among plant population density (X), the aboveground plant measures and tuberous root yield (TW) together with the residual (s). One-arrowhead lines indicate direct effect (p). Two-arrowhead lines denote simple correlation coefficient (r). The other simple correlation coefficients are not presented in this figure, i.e., all possible paths among SN, SL, SW, L N , L A , W L exist. SN, SL and SW are number of stems, length of stems (m) and dry mass of stems (kg), respectively. L N , L A and W L are number of leaves, leaf area (m ) and dry mass of leaves (kg), respectively. 2  A direct effect is a relationship between two variables connected by a single step. The path coefficient for a direct effect may equal to the magnitude of the simple  63  correlation coefficient for that step. However, it may not equal the simple correlation coefficient if there are also correlations with other variables. The direct effect of X upon T W was computed from a linear regression equation for standardized density (as independent variable) and standardized T W (as dependent variable). Similarly, the direct effects of X on each of the aboveground plant parts was computed from a linear regression equation for standardized X (as independent variable) and standardized aboveground plant parts (as dependent variables). The regression equations for standardized density and standardized plant measures were: Z N=b,Zx + s  1  (Eqn. 4.11)  Z  2  (Eqn. 4.12)  S  S L  =b Z +£ 2  x  Z w = b Zx + £3  (Eqn. 4.13)  Z  (Eqn. 4.14)  S  L N  3  =b Z +£ 4  x  Z A = b Zx + s L  5  4  (Eqn. 4.15)  5  ZWL = b Z + s  6  (Eqn. 4.16)  Z w = b Zx + £7  (Eqn. 4.17)  6  T  x  7  where Z was the standardized subscriptic plant measure, X was plant population density, SN, SL, SW, L N , L A , W L were the aboveground plant measures, T W was dry mass of tuberous roots, bi,  , b were regression coefficients, and e was the residual of a 7  regression. The regression coefficient (b) of the standardized plant measures is the path coefficient (p), which indicates the magnitude of the direct effect of one variable upon another (Dewey and Lu, 1959). The magnitude of p equals r when X and the aboveground plant measures, or X and TW, are connected by one single step.  64  Direct effects upon T W of the aboveground plant measures, which were intercorrelated, were computed from the following multiple regression equation: Z w = bgZsN + b Z L + bi Z w + b| [Z N + b\ Z T  9  S  0  S  L  2  LA  + bi Z L + e 3  W  (Eqn. 4.18)  where Z was the standardized subscriptic plant measure; SN, SL, SW, L N , L A , W L were the aboveground plant measures, T W was dry mass of tuberous roots; bg, ...., bn were partial regression coefficients and e was the residual of the multiple regression. The regression coefficients were the path coefficients for the relationship between T W and the aboveground plant measures (Dewey and Lu, 1959). The coefficient of determination of the multiple regression (R ), indicating the fraction of TW variation contributed by plant 2  measures, is computed from Eqn 4.18. A n indirect effect is an effect of one variable on another by way of other correlated variables. The value of the simple correlation coefficient is the sum of direct and indirect effects along all paths (Li, 1975). The value of the indirect effect of one variable on another is the sum of products of path coefficients and simple correlation coefficients for all possible paths connecting both variables. The indirect effects of X on TW were computed from the following equations:  T(X, TW)  =  P(TW, X) + [p(SN, X)  X  P(TW, SN)] + [P(SL, X) X P(TW, SL)] + [P(SW, X) X P(TW, SW)]  + [P(LN, X) X P(TW, LN)] + [P(LA, X)  X  P(TW, LA)] + [P(WL, X) X P(TW, WL)]  (Eqn.4.19) where r(xjw) was the simple correlation coefficient for the relationship between X and TW, and p was the path coefficient between the subscriptic variables. Here: [P(SN, X)  X  P(TW, SN)]  was the indirect effect of X on T W by way of SN,  [P(SL, x) x Pcrw, SL)] was the indirect effect of X on T W by way of S L ,  [P(sw, X) x p Tw, sw)] was the indirect effect of X on T W by way of S W , (  [P(LN, x) x p(xw, LN)] was the indirect effect of X on T W by way of L N , [P(LA, x) x pgw, LA)] was the indirect effect of X on T W by way of L A , [P(WL, X) x P(TW, WL)] was the indirect effect of X on T W by way of W L .  Indirect effects of the aboveground plant measures on T W were computed from: f(SN, TW)  =  P(TW, SN) + [P(TW, SL)  X  T(SN, SL)] + [P(TW, SW)  X  T(SN, SW)] +  [P(TW, LN) X T(SN, LN)] + [P(TW, LA) X T(SN, LA)] + LP(TW, WL)  x  r( N, WL)] S  (Eqn. 4.20) Here:  [P(TW, SL) T(SN, SL)] was the indirect effect of S N on T W by way of S L , X  [P(TW, sw) x T(SN, sw)] was the indirect effect of S N on T W by way of S W , [P(TW, LN) x  T(SN,  LN)] was the indirect effect of S N on T W by way of L N ,  [p(TW, LA) x T(SN, LA)] was the indirect effect of S N on T W by way of L A , [P(TW, WL) x T(SN, WL)] were the indirect effect of S N on T W by way of W L .  f(SL, TW) = P(TW, SL) + [P(TW, SN)  X  T(SN, SL)] + [P(TW, SW) X T(SL, SW)] +  [P(TW, LN) X T(SL, LN)] + [P(TW, LA)  x  r(SL, LA)] + [P(TW, WL) X T(SL, WL)]  (Eqn. 4.21) Here:  [P(TW, SN) T(SN, SL)] was the indirect effect of S L on T W by way of S N , X  [P(TW, sw) x T(SL, sw)] was the indirect effect of S L on T W by way of S W , [P(TW, LN) x r(SL, LN)] was the indirect effect of S L on T W by way of L N , [P(TW, LA) x T(SL, LA)] was the indirect effect of S L on T W by way of L A ,  [P(TW, WL)  X  was the indirect effect of SL on T W by way of WL.  T(SL, WL)]  f(SW, TW) = P(TW,SW) + [P(TW, SN) X r N, SW)] + [P(TW, SL) X f(SL, SW)] + (S  [P(TW, LN) X r w, LN)] + [P(TW, LA) X r W, LA)] + [P(TW, WL) X r W, WL)] (S  (S  (S  (Eqn. 4.22) [P(TW, SN) X T(SN, sw)] was the indirect effect of SW on T W by way of SN,  Here:  [P(TW, SL)  xr  [P(TW, LN)  x r w, LN)] was the indirect effect of SW on T W by way L N ,  [P(TW, LA)  (LN, TW)  =  L, sw)]  was the indirect effect of SW on T W by way of SL,  (S  x  [P(TW, WL)  R  (S  x  r(sw,  LA)]  r( w,  WL)]  S  was the indirect effect of S W on T W by way of L A , was the indirect effect of S W on T W by way of W L .  P(TW, LN) + [P(TW, SN) X T(SN, LN)] + [P(TW, SL) X T(SL, LN)] + [P(TW, SW)  x  r w, (S  LN)] + [P(TW, LA) X r N, LA)] + [P(TW, WL) X rrjLN, WL)] (L  (Eqn. 4.23) Here:  [pcrw, SN) T(SN, LN)] was the indirect effect of L N on T W by way of SN, X  [P(TW, SL)  x r(SL, LN)] was the indirect effect of L N on T W by way of SL,  [P(TW, sw)  x r(sw, LN)] was the indirect effect of L N on T W by way of SW,  [P(TW, LA)  x T(LN, LA)] was the indirect effect of L N on T W by way of L A ,  [P(TW, WL)  x T(LN, WL)] was the indirect effect of L N on T W by way of W L  r(LA, TW)  =  P(TW, LA) + [P(TW, SN) X T(SN, LA)] + [P(TW, SL) X T(SL, LA)] + [P(TW, SW) X T(sw, LA)] + [P(TW, LN)  X  T(LN, LA)] + [P(TW, WL) X T(LA, WL)]  (Eqn. 4.24) Here:  [P(TW, SN) X T(SN, LA)] was the indirect effect of L A on T W by way of SN,  67 [P(TW, SL)  x f(SL, LA)] was the indirect effect of L A on T W by way of SL,  [P(Tw, sw)  x r(sw, LA)] was the indirect effect of L A on T W by way of SW,  [P(TW, LN)  x rruM, LA)] was the indirect effect of L A on T W by way of L N ,  [P(TW, WL)  xr  (LA  , WL)] was the indirect effect of L A on T W by way of W L  f(WL, TW) = P(TW, WL) + [P(TW, SN) X T(SN, WL)] + [P(TW, SL) X r( L, WL)] + S  [P(TW, SW) X r W, WL)] + [P(TW, LN) X T( N, WL)] + [P(TW, LA) (S  L  x  r( A, WL)] L  (Eqn. 4 . 2 5 ) Here:  [P(TW, SN) X T(SN, WL)] was the indirect effect of W L on T W by way of SN, [P(TW, SL)  x T(SL, WL)] was the indirect effect of W L on T W by way of SL,  [P(TW, sw) x r(sw, WL)] was the indirect effect of W L on T W by way of SW, [P(TW, LN)  x T(LN, WL)] was the indirect effect of W L on T W by way of L N ,  [P(TW, LA)  x r(LA, WL)] was the indirect effect of W L on T W by way of L A .  Since path analysis is conducted using standardized variables, the direct and indirect effects of different aboveground measures can be compared to determine their relative influences on tuberous root yield. Path analysis was performed separately on data for the two sweet potato cultivars. The analysis was done separately for data of 1995 and 1996. The path analysis was performed with program PROC G L M (SAS Institute, 1988).  4.2.3  Yield Component Analysis by Two-Dimensional Partitioning (TDP)  4.2.3.1 Choice of Yield Components The major morphological subdivisions of the sweet potato plants observed in this study were the stems, the leaves and the tuberous roots. On that basis, a set of primary measures was selected to represent these parts: SN, SL, L N , L A and TW. A chronological sequence  68  was assumed for these measures, reflecting the order of events during plant growth. Progressing forward in time (forward analysis, Bowen and Eaton, 1983): plant stems are formed (SN) and elongate (SL), and these serve as a basis for leaf formation (LN). As leaves expand (LA), they generate photosynthetic products that support tuberous root growth (TW). This sequence can also be viewed retrospectively, from the most recent event to the most distant in past time (backward analysis, Bowen and Eaton, 1983). In constructing these chronologies, it is not required that one developmental step be complete before the next is initiated; the growth of stems and leaves and tuberous roots is partly concurrent during plant growth. The primary measures were then formed into ratios, i.e., yield components, whose mathematical product is tuberous root yield: TW = S N x SL/SN x LN/SL * L A / L N x T W / L A  (Eqn.4.26)  Which can be transformed to an additive system by ln-transformation: ln(TW) = ln(SN) + ln(SL/SN) + ln(LN/SL) + ln(LA/LN) + ln(TW/LA) (Eqn.4.27) As can be seen from Eqn. 4.26 or 4.27, tuberous root yield (TW) was assessed per plant, and the yield components used in this analysis expressed stem occurrence per plant (SN), length per stem (SL/SN), leaf occurrence per stem length (LN/SL), area per leaf (LA/LN) and tuberous root dry mass per unit leaf area (TW/LA). 4.2.3.2 Regression and Analysis of Variance In TDP, total yield (InTW) variation is partitioned in two dimensions (Eaton et al., 1986). As with path analysis, separate analyses were performed for data from the 1995  69  and 1996 harvests. The first dimension of the TDP analysis involved a stepwise multiple linear regression. Here, ln-transformed yield components were introduced into the multiple regression either in forward or backward chronological order, with ln(TW) being dependent variable and the ln-transformed yield components as independent variables, using the model of Eqn. 4.27. Increments in coefficient of determination were obtained for each step in the multiple regression procedure. The final regression had no residual (R = 1.00) because Eqn. 4.26 is a mathematical identity. The coefficients formed by this regression serve as multipliers that can convert ln-transformed values of the yield components into ln(TW). A n orthogonalization procedure (Winer, 1971) was then used to eliminate statistical correlations between the successive yield components. For example, Eqn. 4.27 may be rewritten as: ln(TW) = C i + C + C + C + C 2  3  4  (Eqn.4.28)  5  Set the first orthogonal term Ei equal to Ci and regress C on E i : 2  C = ao + a, Ei + E 2  (Eqn.4.29)  2  Hence, a new orthogonal term E (= C - (ao + aiEi)) is formed. Successive orthogonal 2  2  terms, E ... E 5 , are similarly formed from regressions of later ln-transformed yield 3  components ( C ... C 5 ) on the sum of previous orthogonal terms (e. g. C on Ei plus E ) . 3  3  2  The end result of this procedure, in the forward direction, is a relationship between ln(TW) and a set of orthogonal terms: ln(TW) = E , + E + E + E + E 2  3  4  5  (Eqn. 4.30)  In the backward direction, the procedure begins with ln(TW/LA) as the first orthogonal component, and the end result is:  70  ln(TW) = E + E + E + E + Ei 5  4  3  2  (Eqn. 4.31)  It should be noted that the quantities of corresponding orthogonal terms (e. g. E ) in Eqn. 5  4.30 and 4.31 will usually not be the same. In the second dimension of the TDP analysis, sources of variations in yield (ln(TW)) and in the orthogonalized yield components (Ei ... E5) were assessed by the analysis of variance, according to the split plot design discussed in the previous chapter (3.2.2.3). Here, two different sources of error, i.e., the main plot and the subplot errors, are available. The main plot error was used to test the effects of block and main plot treatments upon yield and yield component variations. The subplot error was used to test effects of subplot treatments upon yield and yield component variations (Steel and Torrie, 1980). Results of the TDP analyses were tabulated with results for yield and the orthogonalized yield components in separate columns, and sources of variation and error in separate rows. Columns were converted to the same units of measurement by multiplying their values by their respective multiple regression coefficients obtained when developing the first dimension of the TDP procedure. The TDP analysis was performed with the program PROC G L M (SAS Institute, 1988).  71  4.3 4.3.1  Results Allometric Relationships  When the simple ln-transformed allometric power function (Eqn 4.2) was used, significant allometric relationships were obtained between InTW and other plant measures, except for SN (Table 4.1). For the significant relationships, coefficients of determination varied widely, ranging from 0.13 for InWL to 0.95 for InW. When the expanded allometric relationships (Eqn. 4.10) were developed from the same data, however, significant relationships were obtained in all cases. For the expanded allometric relationships, the coefficients of determination ranged from 0.92 to 0.98 (Table 4.2, Appendix B l ) . Hence, a considerable improvement was usually achieved through addition of further independent variables in the expanded models, and those additional terms account for allometric (terms involving P i ... p ) and non-allometric (terms involving yi ... Y6) responses of InTW to 7  experimental factors. In Table 4.2, the relative contributions of the different independent variables is indicated by the magnitude of standard partial regression coefficients, and the direction of the relationship is given by the sign on the standard partial regression coefficients. Parameter p was significant, except for L N and L A , indicating the occurrence of simple 0  and positive allometry between T W and each of W, SN, SL, SW and W L . The highest coefficient of determination of determination in the expanded allometric models was obtained for the W relationship, which is unsurprising since TW was a large fraction of W (see Chapter 3). Simple allometry was the strongest factor for W, but the negative vln(W) term indicates that ' B O 129T9' had a smaller coefficient ( P ) for its allometric relationship between T W and W than did ' B O 44T3'.  72  Table 4.1 Regression coefficients and other statistics for simple allometric relationships: InTW = a + pin(z) (Eqn 4.2). Observations pooled from both varieties and seasons. Plant measure (z) W  SN  SL  SW  z  LN  LA  WL  Parameter a  -0.612  5.16  4.27  2.89  1.52  5.43  4.27  P  1.05  1.33  0.566  0.679  0.762  0.631  0.379  Residual mean square  0.0159  0.339  0.262  0.135  0.166  0.227  0.298  R  0.95**  0.01  0.24**  0.61**  0.52**  0.34**  0.13*  41  41  41  41  41  41  41  Statistics  2  df  ns  Plant measures, symbols and abbreviations: TW = Dry mass of tuberous roots per plant (kg), W = Biomass per plant (kg), SN = Number of stems per plant, SL = Length of stems per plant (m), S W = Dry mass of stems per plant (kg), L N = Number of leaves per plant, z  2  2  L A = Leaf area per plant (m ), W L = Dry mass of leaves per plant (kg), R = Coefficient of determination, df = Degree of freedom, ns, *, ** = Not significant, significant at P = 0.05 or P = 0.01, respectively.  73  Table 4.2 Standard partial regression coefficients and other statistics for best subsets multiple regression models of the allometric relationships between T W and plant measures in sweet potato varieties. Allometric relationships for pooled observations from the 1995 and 1996 studies. Potential Paraindependent meter variable y  ln(z) tln(z) vln(z) Xln(z) tvXln(z) ln(X) ln(tX) ln(vX) Statistic: Mallow Cp Residual mean square R df 2  Bo  Plant measure (z)  z  W  y  1.18**  Bi  fi fi  2  SL  SW  0.416**  0.666**  0.568**  -0.871**  -0.799**  -0.601** -0.767**  -0.542**  -0.481**  -0.489**  LN  LA  0.463** -0.259**  -0.934** -0.666** 0.175**  7  -0.809**  Y3  -1.17** 0.141*  Y5 Y6  WL  -0.253**  3  B  SN  0.213**  -0.295  9.47  3.54  2.54  5.15  9.88  7.01  0.008  0.027  0.028  0.030  0.027  0.027  0.021  0.98**  0.93**  0.92**  0.92**  0.93**  0.93**  0.94**  3,38  3,38  3, 38  3,38  2,39  3,38  4, 37  Plant measures, experimental factors and abbreviations: T W = Dry mass of tuberous roots per plant (kg), W = Biomass per plant (kg), SN = Number of stems per plant, SL = Length of stems per plant (m), SW = Dry mass of stems per plant (kg), L N = Number of leaves per plant, L A = Leaf area per plant (m ), W L = Dry mass of leaves per plant (kg), t = Year of planting (1995 = 1 and 1996 = 2), v = Cultivar ('BO 44T3' = 1 and ' B O 129T9' = 2), X = Plant population density (plants-per 1.65 m ), Cp = A n estimate of the standardized total squared error, R = Coefficient of multiple determination, df = Degree of freedom, *, ** = Significant at P = 0.05 or P = 0.01, respectively, ln = Natural logarithm. z  2  Potential independent variables that were never significant in any of the expanded allometric relationships were tvln(z), tXln(z), vXln(z), ln(t), ln(v), ln(tv) and ln(tvX).  y  74  For SN, SL, SW and WL, there were strong negative contributions by tln(z) and Xln(z). The tln(z) term was also negative and significant for L N and L A . Hence, allometric relationships between T W and these measures were decreased in the second growing season and (where Xln(z) was significant) at higher population densities. A complex positive interaction, tvXln(z), was the weakest term in the expanded allometric model for WL. In addition, non-allometric effects of factors on T W were significant for three of the relationships: W, L N and L A . In the relationships for W and L A , the interaction term ln(vX) was positive but was the weakest significant term in those models. Strong negative effects of ln(X) and ln(tX) were significant in the models for L A and L N . The occurrence of significant non-allometric terms (i.e. terms involving y) does not prove direct effects of experimental factors on TW. Such terms may be surrogates for experimental effects on allometric relationships between T W and another plant measure not included in the model. The best subset models for SN, SL, SW and W L did not include significant terms involving y. Several terms were never significant in the expanded relationships: tvlxi(z), tXln(z), vXln(z), ln(t), ln(v), ln(tv) and ln(tvX).  4.3.2  Path Analysis  The allometric analyses considered relationships between T W and other measures of plant growth (z) separately from one another. However, multiple relationships commonly exist among different plant measures, and path analysis allows one to quantify direct and indirect components throughout the entire set of these relationships. The present study evaluates two different types of relationships, the relationships between aboveground plant measures and TW, and the relationships between plant  75  population density and TW. Path analysis of the relationships between T W and aboveground plant measures is presented in Tables 4.3 and 4.4 for ' B O 44T3' and ' B O 129T9', respectively. These aboveground relationships, plus the direct and indirect plant population density effects on TW, are presented in Appendices B5 and B6. These appendices are used to evaluate the mode of relationships between aboveground plant measures and T W in different cultivars in different years of planting and will be discussed in the following chapter (Chapter 5). In Tables 4.3 and 4.4, the rows contain the correlation coefficients (r) and their subdivisions into direct and indirect effects, for the various plant measures. Note that the total indirect effect plus the direct effect sum to r within each column. The total indirect effect is broken down into indirect effects via other plant measures, within each column: The coefficient of multiple determination (R ) indicates the proportion of total T W 2  variation associated with variation in all aboveground plant measures as computed from Eqn. 4.18. The proportion of TW variation not determined by variations in aboveground measures equals (1-R ), and the square root of this value is the residual. Overall relationships between aboveground plant measures and T W were usually strong in both cultivars and years, as is indicated by R values of 95% or greater, except 2  for 1996 in ' B O 129T9' where the R value was 0.73 (Table 4.4). Residual values for 2  ' B O 44T3' were 0.22 and 0.10 for 1995 and 1996, respectively, and those for ' B O 129X9' ere 0.20 and 0.52 for 1995 and 1996, respectively. The higher residual (and W  corresponding lower R ) in 1996 for ' B O 129T9' suggested that in that case variation in 2  T W was influenced by other factors not included in the regression model.  76  Table 4.3 Path analysis of the relationships among aboveground plant measures and T W in ' B O 44T3' in 1995 and 1996. Partitioning of correlation coefficient (r) into direct and indirect effects. Plant measure SN  2  SL  SW  LN  LA  WL  0.921**  0.872**  0.842**  0.875**  0.940  0.284  0.890  -0.269  1.152  -0.797  -0.097  -0.134 0.214  -0.096 0.223 0.595  -0.090 0.247 0.581 -0.261  -0.109 0.257 0.748 -0.245 1.086  a. 1995 growing season r 0.783** Direct effect: -0.148 Indirect effect via: SN SL 0.188 SW 0.807 LN -0.176 LA 0.702 WL -0.590 Total 0.931  0.671 -0.212 0.996 -0.721 0.637  -0.180 0.752 -0.670 -0.018  1.115 -0.725 1.112  -0.752 -0.275  0.762*  0.631  1.737  Coefficient of multiple determination (R ) = 0.95 Residual = Sqrt (1 - R ) = 0.22 2  2  b. 1996 growing season r  0.558  ns  0.122  ns  0.450  ns  Direct effect: Indirect effect via: SN SL SW LN LA WL Total  ns  0.609"  3.666  0.782 0.050 -0.249 2.345 -5.832 -2.904  Coefficient of multiple determination (R ) = 0.99 Residual = Sqrt (1 - R ) = 0.10 2  Plant measures, symbols and abbreviations: T W = Dry mass of tuberous roots per plant (kg), SN - Number of stems per plant, SL = Length of stems per plant (m), SW = Dry mass of stems per plant (kg), L N = Number of leaves per plant, L A = Leaf area per plant (m ), W L = Dry mass of leaves per plant (kg), r = Simple correlation coefficient with TW, Sqrt = Square root; ns, *, ** = Not significant or significant at P = 0.05 or 0.01, respectively.  z  2  77  Table 4.4 Path analysis of the relationships among aboveground plant measures and T W in ' B O 129T9' in 1995 and 1996. Partitioning of correlation coefficient (r) into direct and indirect effects. Plant measure SN  2  SL  SW  LN  LA  WL  0.939**  0.892**  0.855**  0.822**  0.844**  0.697  0.496  0.492  -0.457  -0.374  0.117  0.135 0.574  0.131 0.566 0.470  0.127 0.549 0.464 0.489  0.123 0.599 0.466 0.458 -0.429  a. 1995 growing season r  0.836**  Direct effect: 0.161 Indirect effect via SN SL 0.506 SW 0.417 LN 0.400 LA -0.363 WL -0.286 0.674 Total  0.409 0.399 -0.360 -0.322 0.243  0.466 -0.428 -0.351 0.396  -0.455 -0.349 0.363  -0.351 1.278  1.217  Coefficient of multiple determination (R ) = 0.96 Residual = Sqrt (1 - R ) = 0.20 2  b. 1996 growing season r  0.483  ns  0.197  ns  0.331  ns  Direct effect: Indirect effect via: SN SL SW LN LA WL Total  0.443*  0.575  ns  0.547"  -2.663  -0.176 -0.538 0.832 4.506 -1.519 3.105  Coefficient of multiple determination (R ) = 0.73 Residual = Sqrt (1 - R ) = 0.52 2  Plant measures, symbols and abbreviations: T W = Dry mass of tuberous roots per plant (kg), SN = Number of stems per plant, SL = Length of stems per plant (m), SW = Dry mass of stems per plant (kg), L N = Number of leaves per plant, L A = Leaf area per plant (m ), W L = Dry mass of leaves per plant (kg), r = Simple correlation coefficient with TW, Sqrt = Square root; ns, *, ** = Not significant or significant at P = 0.05 or 0.01, respectively.  2  2  78 Correlation coefficients (r) were high and significant in 1995, for all relationships between aboveground measures and T W (Tables 4.3 and 4.4). In 1996, however, only L N was significantly correlated, in both cultivars. For ' B O 44T3', and where the correlation coefficients were significant, direct effects exceeded total indirect effects in three of seven possible cases: SW, L A in 1995 and L N in 1996. For ' B O 129T9', when correlations (r) were significant, direct effects also exceeded total indirect effects in three of seven possible cases: SL, SW and L N in 1995. Hence, the results were not consistent as to the balance of contributions by direct and indirect effects to significant values of r for different aboveground plant measures between different cultivars and years. For both cultivars, the highest total indirect effects were obtained for L N in 1996. Where indirect effects predominated, the size and direction of these effects were not always consistent between cultivars and years. For ' B O 44T3' the indirect effects via SL and L A were always positive while the indirect effect via W L was always negative (Table 4.3). For ' B O 129T9' the indirect effect via SW was always positive while the indirect effect via W L was always negative (Table 4.4). The indirect effects via the other aboveground measures, however, changed in their direction of contribution between the two years of the study. 4.3.3  Two-Dimensional Partitioning of Yield Variation  The two-dimensional partitioning (TDP) procedure explored how variation in Intransformed morphological yield components expressed as ratios was related to variation in per plant yield (InTW). Results from analyses for 1995 and 1996 are summarized in Tables 4.5 and 4.6, respectively. Total yield variation (i. e., total sum of squares of InTW) is expressed as 100%, and other table entries are percentages of the total yield variation  79  Table 4.5 Two-dimensional partitioning of sum of squares for T W per plant in sweet potatoes grown in 1995 and harvested at 130 days after planting 2  a. Forward analysis Source of variation Block Density ( X ) Error a Variety (v) X xv Error b Total  x  Yield component  5.  df  SN  SL/SN  3 2 6 1 2 9 23  12 2g** 13 2 0 3 58**  2 5** 1 ]2** 0 1 21*  LN/SL 2 1 1 0 0 0 5  LA/LN  TW/LA  1 0 0 1 0 1 5  3 2 2 0 1 3 12  SP -19 56 -15 -15 1 -6 0  Yield (TW) 2 92** 2 0 2* 2 100  b. Backward analysis Source of variation ' df Block Density ( X ) Error a Variety (v) X xv Error b Total  x  3 2 6 1 2 9 23  Yield component TW/LA 0 0 0 0 0 0 0  LA/LN 0 0 0 1 0 0 1  LN/SL  SL/SN  SN  3 0 2 0 1 3 8  4 4 6 0 0 3 17*  8 49** 14 0 1 2 74**  SP -13 38 -18 -1 -1 -5 0  Yield (TW) 2 92** 2 0 2* 2 100  Cells to the right of the df column are percentages of the total sum of squares for T W per plant; 0 denotes less than 0.5% of the total sum of squares. 2  Measures per plant: SN = Number of stems, SL = Length of stems (m), L N = Number of leaves, L A = Leaf area (m ), T W = Dry mass of tuberous roots (kg).  y  2  "Abbreviations and symbols: X = Plant population density (plants/1.65 m ), df = Degree of freedom, SP = Sum of products, *, ** = Significant at P = 0.05 or P = 0.01, respectively. 2  80  Table 4.6 Two-dimensional partitioning of sum of squares for T W per plant in sweet potatoes grown in 1996 and harvested at 123 days after planting. z  a. Forward analysis Yield component/  Source of variation Block Density ( X ) Error a Variety (v) Xxv Error b Total  x  df  SN  2 1 4 1 1 6 17  1 13 1 3 1 2 20  SL/SN 0 0 0 1 0 0 2  LN/SL  LA/LN 1 0 1 2 0 1 6  0 1 1 0 1 6 9  TW/LA  SP  24* 8* 4 0 10 16 63**  -10 43 -5 -5 -4 -19 0  Yield (TW) 16* 65** 2 1 o* 6 100  b. Backward analysis Yield component/  Source of variation Block Density ( X ) Error a Variety (v) Xxv Error b Total  x  df  TW/LA  LA/LN  2 1 4 1 1 6 17  0 0 0 0 0 0 1  0 0 0 2 0 0 2  LN/SL 10 3 8 1 1 4 27*  SL/SN 0 1 2 0 2 8 14  SN  SP  4 30* 5 0 1 17 56**  2 30 -13 -2 5 -22 0  Yield (TW) 16* 65** 2 1 g* 6 100  Cells to the right of the df column are percentages of the total sum of squares for T W per plant; 0 denotes less than 0.5% of the total sum of squares. z  Measures per plant: SN = Number of stems, SL = Length of stems (m), L N = Number of leaves, L A = Leaf area (m ), TW = Dry mass of tuberous roots (kg).  y  2  "Abbreviations and symbols: X = Plant population density (plants/1.65 m ), df = Degree of freedom, SP = Sum of products, *, ** = Significant at P = 0.05 or P = 0.01, respectively. 2  81  associated with individual yield components and experimental sources of variation. The rows for total in these Tables give the results of the first dimension of the analysis; columns of these Tables give the results of the second dimension of the analysis. Sums of products (SP), which represents compensation among other components, were also generated by the analysis, and these enable the TDP tables to sum horizontally as well as vertically. Focussing on the rows for total yield partitioning in Tables 4.5 and 4.6, several lntransformed yield components were found to make significant contributions to yield variation. In the forward analysis, SN and SL/SN were significant in 1995 (Table 4.5), while T W / L A was significant in 1996 (Table 4.6). The latter was the final term in the forward multiple regression; its effects on variation in InTW can be considered to be direct and independent, because contributions from all other yield components had already been included in the model. In the backward analysis, SL/SN and SN were significant in 1995 and LN/SL and SN were significant in 1996. The latter was the final term in the backward multiple regression; its effects on variation in InTW can be considered to be direct and independent, because contributions from all other yield components had already been included in the model. As reported in Chapter 3, the analysis of variance showed that plant population densities significantly affected TW. Here, density (X) and cultivar by density interactions (X x v) effects were also significant for InTW, as shown in the right hand columns of Tables 4.5 and 4.6. Significant direct effects of population density via direct-acting yield components, were identified for SN in both years and T W / L A in 1996. Those effects ranged in magnitude from 8% for T W / L A in 1996 to 49% for SN in 1995. There was also  82  a significant and direct block effect via T W / L A in 1996 (Table 4.6). The TDP analysis does not identify whether significant relationships for the intermediate yield components, SL/SN, LN/SL, and L A / L N involve direct or indirect effects. In these cases, contributions might not be detected since they may be attributed to yield components entered earlier into the multiple regressions. One of the intermediate yield components, L A / L N , was never significant in its total contributions to yield variation. In 1995, comparing the results from the forward and backward procedures, S N and to a lesser extent SL/SN, stand out as being the most important yield component contributors to yield variation. As already noted, SN made a direct and large contribution as shown by the backward analysis. In the backward analysis in 1995, the first three components entering the multiple regression T W / L A , L A / / L N and LN/SL, all had the opportunity to account for 99% or more of InTW variation, but none were significant. In the forward analysis, SL/SN was significant after the yield relationship with S N had been removed. Because the backward analysis has ruled out contributions by T W / L A , L A / / L N and LN/SL, I conclude that in 1995 SL/SN was also important, and it was the only yield component to exhibit a significant cultivar response, in both years. (The contribution of variety to total variation in SL/SN was significant in 1996. However, SL/SN did not contribute significantly to total TW variation in that case). In 1996, the results for intermediate yield components (SL/SN, LN/SL, and L A / L N ) resist interpretation (Table 4.6). For example, the importance of LN/SL is ambiguous because it was significant in its total contribution to yield variation in the backward analysis, but not in the forward analysis. It is not anomalous that T W / L A and SN are not significant when they are the first term in the regressions, since their  83  correlations with T W may be weakened by multiple correlations with other yield components. Once those multiple relationships have been eliminated, i. e., when T W / L A and SN are the final term in the regressions, their direct effects are detectable.  4.4  Discussion  The present study has analyzed relationships between aboveground plant measures and tuberous root yield using three different analytical techniques: allometric analysis, path analysis and yield component analysis. The capabilities of the three techniques will be discussed in Chapter 5. Here, I will focus on the interrelationships that were detected. In Chapter 3 it was shown that for this study (Experiment 1) T W significantly differed between years and population densities, but cultivar differences were not significant (Appendices A l 1 and A12). Here, significant cultivar by density interactions were detected when yield was analyzed as InTW (Tables 4.5 and 4.6), although effects of cultivar were still overshadowed by differences between years and population densities. A l l of the present analyses demonstrated numerous relationships between aboveground plant measures and yield (either as T W or InTW). Stronger relationships, however, were obtained in 1995, compared to 1996. This is indicated by the negative t terms in the best subset multiple regression models, and by the lack of simple correlations for most of the aboveground measures in the path analysis for 1996. In 1996, plant performance might have been more restricted by environmental stresses. In particular, soil temperature, which was lower in September 1996 than in September 1995 (Appendix A6). The possibility that stresses occurred more severely in 1996 is suggested by comparing the yields for the two years: T W averaged only 44% as high in 1996 as it did  84  in 1995 (Appendix A12). The significant direct effect of T W / L A in 1996 suggests that the abilities of leaves to support tuberous root growth were more important that year than in 1995. Whether this was due to the generation of assimilates, or their flow to tuberous roots, is not known. A similar case was indicated by TW/D (dry mass of tuberous roots per leaf-area duration), which was found to be the highest in a high yield sweet potato cultivar Laloki N o . l (Enyi, 1977). TW/D was considered as the efficiency of leaves to produce dry matter. It is not unusual or novel to detect relationships between aboveground and underground parts, which have often been found with other crops. For example, allometric studies found plant biomass and dry mass of leaf rosette to be good contributors to variation in tuberous root yield in carrots (Stanhill, 1997a, 1977b). Physiologically, one expects to find such relationships; carbon assimilation by aboveground plant parts is required for the growth of tuberous roots. The importance of the relationships between aboveground plant parts and tuberous root yield in sweet potato has been indicated in previous studies (Chapman and Cowling, 1965; Haynes et al., 1967; Lowe and Wilson, 1974; Enyi, 1977 and Hall, 1986). For example, leaf distribution plays an important role in determining sweet potato yield (Chapman and Cowling, 1965). The attainment of the optimum leaf area index was considered important for achieving maximum tuberous root yield (Haynes, et al, 1967). Another previous study indicated that sweet potato plants having an early vigorous growth of aboveground plant parts might cause a delay in tuberous root growth causing a lower tuberous root yield (Enyi, 1977).  85  The present study provides detailed information on the size, direction and variability of such relationships and leads to a clearer understanding of the relationships between aboveground plant measures and tuberous root yield in sweet potato plants. A l l of the analytical procedures highlighted differences between years, densities, and to a lesser extent, cultivars. Strong, positive relationships tended to exist between aboveground measures and tuberous root yield. For example, the expanded allometric models for SN, SL, SW and W L all demonstrated direct allometric relationships with TW. In the path analysis all significant simple correlations between aboveground measures and T W were positive. The results suggest that experimental sources of variation may have acted on yield largely via their influences on aboveground plant parts. In the allometric analyses, effects of year and population density tended to be more prominent in allometric terms (p), compared to non-allometric terms (y) in the expanded allometric models. There were large similarities in the input data utilized by the three different analytical procedures. For that reason, it would be expected that many of their findings would be similar. That was not always the case. In the yield component analysis, SN was highlighted as a significant and direct contributor to yield variation in both years of the study. In the simple allometric analysis and the path analysis, however, SN was not significant in terms of its simple correlation with T W in 1996, for both cultivars. Also, the path analysis found that, where the correlation coefficient was significant, indirect effects of SN were larger than direct effects. In this context, it should be noted that the path analysis technique does not involve a statistical test to compare the direct and indirect effects. The different path analysis and the yield component analysis results are  not necessarily contradictory. The TDP analysis was performed on the ln-transformed T W and SN, while the path analysis did not involve ln-transformation. Also, in the TDP analysis, the direct relationship between InTW and InSN was determined after contributions from other measures had been removed, while that was not the case for the path analysis. Finally, the allometric and TDP analyses were performed on the pooled data from the two cultivars, while the cultivars were analyzed separately in the path analysis. Because of the frequent occurrence of positive and significant relationships, many of the measures tested here might have potential as aboveground indicators of tuberous root yield. Of all of the measures tested, perhaps SN is the most helpful. Compared to other measures it is easy to determine, and it was identified as a direct contributor to yield variation in the yield component analysis. A previous study (Hall, 1986) showed that in 'Georgia Jet' sweet potato, increasing lateral vine seemed to increase tuberous root yield. The present study also indicated that SN mostly positively correlated with other aboveground measures, such as SL, L N and L A in both cultivars (Appendices B2 and B3). In 1996, where SN did not significantly correlate with SL, SN did not significantly correlate with T W in either cultivar. However, it may not be entirely reliable, because it lacked a significant simple correlation in 1996 in the path analysis, and further studies will have to be done to confirm the reliability of these relationships.  87  5  General Discussion  These studies explored tuberous root production and other morphological characteristics in sweet potato, and the results will be discussed in relation to two main themes. First, I was interested in measuring and better understanding the effects of experimental factors (different growing seasons, cultivars and population densities) on plant performance. In that context, I was particularly interested in assessing how aboveground plant measures were interrelated with variation in tuberous root yield. Second, I was also interested in assessing and comparing different methods for analyzing plant growth and yield in sweet potato.  5.1  Yield Relationships in Sweet Potato  5.1.1  Productivity at the Agassiz Study Site  In these experiments, final tuberous root yields and other measures of final plant size, were greater in 1995 than in 1996, and increasing plant population densities tended to reduce measures of growth and growth and yield per plant. Cultivars, however, did not differ in their tuberous root yields at the final harvest in Experiment 2 or in either year of Experiment 1. Nevertheless, the detailed analyses indicated many differences between cultivars, as well as between densities, growing seasons, and times of observation within a growing season. Worldwide, sweet potatoes are cultivated in diverse growing regions (Kay, 1973) between 40° North and 40° South (Hahn, 1977b). Previous studies have indicated that sweet potato plants flourish in an area with annual rainfall of about 1,600 mm, daily mean temperature of about 24C and the intensity of solar radiation between 12,600 and  88  15,100 kJ/m /day (Badillo-Feliciano and Lugo-Lopez, 1977). 2  The location of the present experiments, Agassiz, B C , is not a typical location for commercial sweet potato production. It is interesting to compare the present results with those I obtained in a previous study of sweet potato grown in a tropical mountain valley, the Baliem Valley of Indonesia where the indigenous people grow the crop using low inputs (e.g., fertilizers are not used). In that study I found final yields of 25 and 10 tonnes/ha/year, generated by wetland and dryland cultural systems, respectively (Soenarto and Rumawas, 1997). At Agassiz the average yield was 42 tonnes/ha/year. Hence Agassiz, while it is certainly not a center for sweet potato production, is by no means an inappropriate place to grow and study this crop, which is adaptable to many growing regions. The Baliem valley of Indonesia is located at an altitude between 1,500 and 2,500 m with an annual rainfall of 1,800 mm, 195 rainy days per year and a daily mean air temperature of about 19C (Soenarto and Rumawas, 1997). The average duration of daily bright sunshine in the Baliem valley is about 3.98 hr/day with an incident radiation averaging 13,800 kJ/m /day and a daily mean soil temperature of about 21C for the period June to September (Soenarto, 1987). Many of these conditions are quite different from those at Agassiz, BC. The Baliem Valley is frost-free, while in Agassiz the sweet potato growing season is curtailed by low temperatures; the first frost at Agassiz usually occurs in mid-November (Atmospheric Environment Service, 1990). Climate observations at the Agassiz experimental site showed that daily mean air temperatures were about 17C and 15C, for the 1995 and 1996 growing seasons, respectively. Mean monthly rainfalls were about 75 mm and 102 mm, and mean monthly rainy days were 16  89 and 17 days, for the 1995 and 1996 growing seasons, respectively. Mean monthly bright sunshine duration was about 223 and 184 hours (Appendix A5), and the estimated incident solar radiation was about 21,700 and 20,700 kJ/m /day for the 1995 and 1996 2  growing seasons, respectively (Appendix A7). The daily mean soil temperatures for the period June-September 1995 and June-October 1996 were about 20C for both years (Appendix A6). However, daily mean soil temperature in September 1996 was lower than that in 1995. At Agassiz, soil potassium content was high in the experimental plots (Appendix A l ) . This factor may have benefited the growth of the plants, since potassium has been shown to prolong leaf area duration and to enhance the development of tuberous roots in sweet potato (Tsuno, 1971). It is difficult, however, to interpret the growth and productivity of sweet potato, including the differences between growing seasons and growing regions, in terms of specific climate data. As discussed in Chapter 4, the 1996 season had greater environmental extremes compared to 1995, particularly in terms of rainfall variation, daily mean air and daily mean soil temperatures. It seems likely that these may have contributed to the poorer yields in 1996, but it is difficult to prove such a conjecture. In 1996, planting was delayed by high soil moisture, compared to 1995. By itself, this factor might have caused the reduced yield in 1996, and may have contributed to different patterns of growth between the two years. In 1996 there was less summer precipitation than in 1995, but because the crop was irrigated it seems unlikely that summer drought stress was a limiting major factor in 1996 (or in 1995). Leaf wilting was never observed during these experiments.  90  At the Agassiz study site the observed daily mean temperature for the period April to September in 1995 was higher than the long-term averages (Appendix A2). The daily mean air temperatures for September and October 1996 were lower than the longterm weather observations. The low air temperatures in September and October 1996, and low daily mean soil temperature in September 1996, stood out as deviations from the long term averages. They may well have been important in reducing yields in 1996. Sweet potato plants grown either at the Baliem Valley of Indonesia or at Agassiz were not aimed to reach the maximum potential yield possible with this plant species. At the Baliem Valley, tuberous roots were produced using local agricultural technique with a low population density, low energy input, and intercropped with vegetables and other food crops, such as taro, in a subsistence agricultural system (Soenarto and Rumawas, 1997). At Agassiz, productivity was probably limited by the relatively short growing season. There, the sweet potato plants were grown in beds covered with green plastic sheets to maintain high soil temperature and high soil moisture content. The beds were fertilized moderately and irrigated regularly. The finding that sweet potato can be successfully grown using irrigation and plastic mulch at Agassiz may encourage others to evaluate the commercial feasibility for sweet potato as a commercial niche crop in British Columbia.  91  5.1.2  Growth Chronology and Density-dependence  The developmental chronology of growth was recorded for only one population density in one growing season (1996, Experiment 2). The limited availability of plant material prevented that experiment from being replicated in 1995 and also prevented it from being enlarged to include other densities. Nevertheless, the chronological study was useful in revealing trends leading to final yield, and those trends often differed between the two cultivars. Compared to ' B O 44T3', ' B O 129T9' had greater stem length, length per stem, leaf area, and area and mass per leaf. Cultivar ' B O 129T9' had higher rates of dry matter production, and higher relative growth rate and unit leaf rate, particularly in the earlier period of growth. The two cultivars also differed in the timing of growth, such as when maximum growth occurred. For example, the maxima of L A , length per stem and of area per leaf were reached earlier by ' B O 129T9' than by ' B O 44T3'. Hence, while final tuberous root productivity tended to be similar, it was achieved through different chronological sequences in the two cultivars. The present study provides more detail on the formation and growth of plant parts in sweet potato than is currently available from the literature. The observed growth trends are consistent with those reported in previous research involving other cultivars. These similarities were evident for dry matter accumulation (Austin et al., 1970; Enyi, 1977; Bouwkamp, 1983; Pardales and Belmonte, 1989) and in numbers of branches and leaves (Somda and Kays, 1990b). Other previous studies indicated that early vigorous growth of aboveground plant parts might retard tuberous root growth (Lowe and Wilson, 1974) causing a lower yield of tuberous roots (Enyi, 1977). This may correspond to the present finding that the cultivar having more vigorous vegetative growth ('BO 129T9') had lower  92  early tuberous root dry matter accumulation. In the present study, the growing season was limited by the possibility of early autumn frost. Previous research has sometimes involved more lengthy growing seasons and have found that maximum dry mass of aboveground plant parts is reached about two to three weeks before the maximum development of tuberous roots (Austin et al, 1970). Vine dry mass tends to decline near the end the growing season. When that decline is gradual, the dry mass of tuberous roots was found to be higher than when the decline was rapid (Bouwkamp, 1983). These declines correspond with the final stages of tuberous root growth. The mobilization of shoot reserves in sweet potato, however, is not well understood. Further studies are needed to provide a better understanding of source and sink relationships in sweet potato throughout the growing season. Such studies may improve procedures for attaining high tuberous root yields. Density-dependence was evaluated in two growing seasons in Experiment 1. In accord with previous findings (Bouwkamp and Scott, 1980; Somda and Kays, 1990a, 1990b; Mortley et al, 1991), the present studies found that tuberous root yield and many other plant measures declined with increasing plant population density. Within growing seasons, the effects of plant population density on plant measures tended to be more prevalent and were larger than cultivar. differences. Of the two cultivars, ' B O 129T9' was more density-dependent, particularly in terms of tuberous root yields. The greater expanse of leaves and longer stems in ' B O 129T9' may have caused greater interference and competition for sunlight in that cultivar, especially at high population densities. Comparing the two growing seasons, there was greater responsiveness to plant population density in 1996 than in 1995 in both cultivars. This finding suggested that in both  •  93  cultivars responses to crowding of sweet potato were greater under the less favorable (1996) conditions. 5.1.3  Relationships between Aboveground Parts and Tuberous Root Yield  These relationships were explored using several different techniques. Results from Experiment 2, which documented the chronology of growth, were used to test the correlations between aboveground growth indices and tuberous root growth at different stages. Growth indices were usually strongly correlated with tuberous root growth rate. The correlations often changed their direction with time, however, moving from a positive correlation in the earlier period of growth to a negative correlation in the later period. This change was observed for six of eight indices in 'BO 44T3', and for three of eight indices in ' B O 129T9'. For the two growth indices L N G R and L A G R , however, strong positive correlations were found in both early and late stages of growth in both cultivars. This consistency suggests that these measures, particularly L N G R which is easy to observe, might be useful as non-invasive surrogates for tracking tuber growth. This possibility will have to be confirmed by future research. Other analyses of these relationships employed data from the end of season harvests in Experiment 1. Here, significant allometric relationships between aboveground plant measures and tuberous root yield were found when the expanded allometric models were used. The allometric relationships were broken down into contributions by allometric (P terms) and non-allometric components (y terms). The dominant contributions were provided by the allometric terms, and involved either simple allometry (Po), or allometric adjustments to experimental factors (Pi, p , P3 or P7). Among the 2  allometric terms, year of planting (tln(z)) and plant population density (Xln(z)) largely  94  and negatively contributed to the allometric relationships. Hence, allometry was significantly affected by growing season and population density, with cultivar having a smaller influence. In most of the best subset models (/'. e., except for the L A and L N models), non-allometric relationships were weak or absent, suggesting that the main effects of experimental factors on tuberous root yield were indirect, via allometric relationships with aboveground parts. Differences were found, however, between the best subset models for the different allometric relationships. Hence, there was some independence in how the different aboveground parts responded to experimental factors and how those responses were reflected in tuberous root yield. Multiple relationships were evaluated using path analysis to partition the correlation coefficient into direct and indirect components. In both cultivars, correlations between tuberous root yield and aboveground plant measures were significant in 1995. In 1996, however, only L N significantly was correlated with TW. Path analysis revealed that about 43% of the correlations were due to direct effects. For both cultivars, the highest total indirect effects were obtained for L N in 1996. In 1995, the contribution of indirect effects to the correlations of plant measures with T W differed between cultivars. For example, the indirect effects of SL and L A in ' B O 44T3' were always positive, while the indirect effect of W L was always negative. For ' B O 129T9', the indirect effect of SW was always positive, while the indirect effect of W L was always negative. Path analysis also indicated that the other indirect effects changed their direction contribution between the two years of planting. Hence, path analysis also showed that the relationships between aboveground plant measures and T W changed with year and cultivar.  95  In addition to the observed variations between years and cultivars, details of the path analysis (Appendices B2 to B5) suggest that considerable complexity exists in the relationships among different plant parts. For example, SN significantly and positively correlated with SL in 1995, but the correlation was not significant in 1996. Where S N significantly correlated with SL, SN also significantly and positively correlated with TW. Path analysis in 1995 indicated that in 'BO 44T3', when SN was significantly correlated with TW, SL as a path for SN to influence TW, provided a positive indirect effect on the correlation (Appendix B4). In 1996, when SN did not significantly correlate with TW, SL as a path provided a positive indirect effect with less magnitude (Appendix B4). S N significantly correlated with T W in 1995, as it did in ' B O 129T9', and SL as a path provided positive indirect effect on the correlation (Appendix B5). However, in 1996, when SN did not significantly correlate with TW, SL as a path provided a negative indirect effect on T W (Appendix B5). These results suggest that SN and SL might act together to improve the correlation between SN and T W in both cultivars, but their function was modified by the different growing conditions experienced in the two years of the study. The final procedure used to evaluate these relationships was sequential yield component analysis, which was performed on ln-transformed measures using the twodimensional partitioning procedure (Eaton et al., 1986). By comparing forward and backward analyses, SN (both years) and T W / L A (in 1996) were identified as yield components that directly contributed to variation in tuberous root yield. These directacting yield components were significantly affected by population density, but not by cultivar. Other yield component influences may have been indirect. This was the case for  96  mean length per stem (SL/SN) in 1995 and frequency of leaves per stem length (LN/SL) in 1996, and these yield components were not significantly affected by either population density or cultivar. Path analysis and yield component analysis have formed an extensive set of statistical relationships between aboveground plant measures and tuberous root yield, but they do not prove the mechanisms for such relationships. A n aboveground plant part might well function as a causal agent, which acts by some physiological mechanism(s) to promote or retard the development of tuberous roots. On the other hand, aboveground measures may show statistical relationships with tuberous root yields that are noncausative and represent relationships they may have with other, causative factors. Hence, identifying "direct" influences by path analysis and yield component analysis does not prove a cause and effect relationship. The relationship between population density (X) and tuberous root yield (TW) was well described by inverse regressions, and negative statistical correlations were accordingly found between T W and X . When the path analysis results are examined, it is notable that when aboveground measures served as indirect paths for the influence of population density (X) upon tuberous root yield (TW), they partly alleviated the negative effects of X on TW. i. e., the aboveground measures made positive indirect contributions (Appendices B4 and B5). In contrast, when aboveground plant measures were paths for the indirect influences of other aboveground plant measures upon TW, they reduced the positive correlations between the other aboveground plant measures and TW. i. e., here the aboveground measures made negative indirect contributions (Appendices B4 and B5). Together with the allometric analyses, which indicated that allometric influences  97  outweighed the direct effects of factors on InTW, these results highlight the importance of aboveground parts in regulating tuberous root yield. The results indicate that considerable flexibility exists in how aboveground plant parts contribute to tuberous root production in sweet potato. However, among all of the aboveground measures and indices observed at the final harvests, number of stems per plant (SN) was perhaps the most helpful as a positive indicator of tuberous root yield. As with most of the other measures, however, SN did not show a significant correlation with T W in 1996 (Appendices B4 and B5). Previous studies have also shown that an increase in number of branches increases tuberous root yield (Hall, 1987; Somda and Kays, 1990a). In part, SN may act via beneficial relationships with other aboveground plant measures. For example, the path analysis in 1995 showed that an increase in S N increased L N and L A , which positively correlated with T W (Appendix B2). Also as a path, L A consistently and positively contributed to correlations between the other plant measures and T W in 'BO 44T3' in both years (Appendices B4 and B5). In summary, the present study revealed that sweet potato cultivars ' B O 44T3', a bushy type, and ' B O 129T9', a spreading type, had similar tuberous root yields at the final harvests in 1995 and 1996. The present study also revealed that associations between aboveground plant measures and tuberous root yield existed in both cultivars. In the earlier period of growth, the developments of all aboveground measures strongly and positively contributed to tuberous root growth (TGR). Also, in the early and later period of growth, tuberous root development (TGR) was strongly and positively correlated with the addition (LNGR) and the expansion of leaves (LAGR) in both cultivars. However, for several indices of growth, such as SNGR, the direction of their correlations with TGR  98  might change in the later period of growth. The association between aboveground plant measures and tuberous root yield can also be seen from the relationship between aboveground primary measures and tuberous root yield. The relationships differed between years, densities and to a lesser extent, cultivars. Stronger relationships were obtained in 1995, compared to 1996. The present studies indicated that many of the measures had potential as aboveground indicators of tuberous root yield, such as SN and T W / L A . Among those measures, number of stems per plant (SN) was considered more significant as an indicator of tuberous root yield. For example, in allometric analysis, InSN strongly and directly associated with InTW; in path analysis, where SN significantly correlated with TW, indirect effects of SN were larger than direct effects. Also, in the yield component analysis, orthogonalized InSN was a significant and direct contributor to yield variation in both cultivars. In addition, S N is more helpful in its ease to be defined and observed. The present study also indicated that SN mostly positively correlated with other aboveground plant measures, such as SL, L N and L A in both cultivars. Most plant measures declined with the increase in plant population density. The responsiveness of plant measures to increasing crowded conditions tended to be more influenced by growing seasons than by cultivar differences. Greater responsiveness generally was found on sweet potato plants grown under less favorable growing conditions. In terms of tuberous root yields per plant (TW and MTW), ' B O 129T9' was more susceptible to crowded conditions than was ' B O 44T3'. This result likely related to the vigorous growth o f ' B O 129T9'.  99  5.2  Methods of Analyzing Sweet Potato Performance  In addition to the analysis of variance, I have used five different procedures to quantify and interpret sweet potato performance: conventional plant growth analysis, yield-density regression analysis, allometric analysis, path analysis and yield component analysis. I will comment on some of the characteristics of these approaches, focusing on methodology rather than the growth patterns of sweet potato. I am not aware of any other studies that have exploited such a broad range of analytical procedures to interpret plant growth and productivity. Two of these techniques, conventional plant growth analysis and yield component analysis, were previously used in a study by Jolliffe et al. (1982). Conventional plant growth analysis and sub-organismal demographic analysis were compared in a study by Hunt and Bazzaz (1980). In my studies, there was some necessary overlap in interpretation derived from these different procedures, since they often used the same input data. A l l of these procedures help to summarize and simplify the complexity that exists in the raw experimental results in order to facilitate the organization and understanding of the information generated by experimental observations. Conventional plant growth analysis (Hunt, 1982) describes and interprets the sequence of events during the course of plant growth. Previous studies with sweet potato have made limited use of conventional plant growth analysis to measure dry matter allocation into different plant parts (Austin and Aung, 1973; Enyi, 1977), to evaluate density dependence (Somda and Kays, 1990b), and to detect effects of shading on dry mass of tuberous roots (Soenarto, 1994). In the present study, conventional plant growth analysis was performed on data from Experiment 2. The spline growth curves were useful  100  in illustrating the timing of different events, such as the period of maximum growth rate and the relative responsiveness of different plant measures. Knowledge of the chronology of growth can be valuable, particularly in terms of comparing similarities between treatments. For example, at the final harvests in 1995 and 1996, there was no difference in tuberous root yield (TW) or leaf number (LN) per plant (Tables 3.3 and 3.5). However, when T W and L N were tracked during growth, the former was found to differ between cultivars (Fig. 3.1), while the latter did not (Fig. 3.2). Had additional densities been included in Experiment 2, it is possible that conventional plant growth analysis might have identified the timing and targets of density effects, as has been shown with other crops (e.g., Jolliffe and Gaye, 1995). In conventional plant growth analysis, primary measures are combined into growth indices, which express features such as the efficiency and the extent of assimilatory systems, and the partitioning of plant dry matter (Hunt, 1982). These indices can be helpful in suggesting the physiological origins of growth responses. For example, they led to the proposition that in ' B O 44T3' self-shading early in growth might have caused lower efficiency of dry matter assimilation compared to ' B O 129T9'. Although ' B O 129T9' had more efficient early assimilation, it eventually had less dry matter partitioning into tubers than did ' B O 44T3'. Conventional plant growth analysis traditionally uses a limited set of primary measures, which can limit its ability to interpret some details of plant growth. However, this may not be a significant limitation since it is possible to broaden the definition of some growth indices. For example, relative growth rate can be defined narrowly, as (l/W)(dW/dt), or more broadly as (l/V)(dV/dt), where V is any plant measure (Hunt,  101  1982). As already discussed, conventional plant growth analysis was extended in this study by including the correlations between growth indices and tuberous root production at different stages of growth. Conventional plant growth analysis is normally employed to interpret chronological changes, but some indices can be calculated from observations made at a single harvest. This is the case for all of the ratio indices such as leaf area ratio. In contrast, the other four analytical procedures were only applied to data from the final harvest. It is important to note, however, that these techniques are not restricted to such use. There is no reason why yield-density relationships, allometric analysis, path analysis and yield component analysis cannot be performed on results from more than one harvest. For example expanded allometric relationships were formed (Jolliffe et al., 1988), and inverse yield-density models were constructed (Turkington and Jolliffe, 1996), using data from several harvests. Although this approach requires considerably more effort, the benefits include identification of the timing of key events during growth and more thorough interpretation of differences in plant performance can be made. Inverse yield-density models have been used in studies on monocultures since the 1950s (Shinozaki and Kira, 1956; Holliday, 1960), and have since been extended to mixed species associations (e. g, Spitters, 1983; Jolliffe, 1997). Such models reflect the decline in (mean) size per individual plant (y) as competition and other forms of interference increase with increasing population density (X). When transformed to a yield per unit land area basis (Y), they describe a hyperbolic increase in Y toward an upper limit as X increases. Much of the older literature attempted to interpret yield-density relationships in terms of yield per unit land area. It is more appropriate to do this for yield  102  per plant, however, because yield per unit land area is not independent of X (/. e., Y = y X ; Willey and Heath, 1969). In my study, the inverse yield-density models usually had high coefficients of determination. This was particularly true for total dry mass and tuberous root dry mass. Both of these measures reflect overall extraction of environmental resources by the plants. Hence, the high coefficients of determination for these models are evidence for the importance of competition for resources. Inverse yield-density relationships for some other measures, such as stem number, had lower and sometimes non-significant coefficients of determination. Those measures may be somewhat buffered from the effects of external influences by processes of dry matter partitioning and by developmental controls. For any particular plant measure the strength of competition is measured by the size of the model coefficient, b. The inverse yield-density relationships showed that the strength of competition was not always constant, but sometimes differed between cultivars and years (Appendices A20 and A21). For example, for total and tuberous root dry masses the model coefficients were higher in 1996 than in 1995. As discussed earlier, 1996 seemed to be a more stressful growing season, and these results suggest that higher competition for resources may have partly contributed to such stresses. Other research has also suggested that competitive influences are not fixed, but may vary under different experimental circumstances (Jolliffe, 1997; Turkington and Jolliffe, 1996). The allometric power function has been used for more than a century to quantify bivariate relationships between different measures of an organism (Gould, 1966). The simple allometric power function, however, was usually much less effective in detailing  103 allometric relationships (Table 4.1) than was the expanded relationship (Tables 4.2). i. e., incorporating more experimental factors into the allometric analysis improved the description of the experimental results. Expanding the allometric models also proved useful in previous research on the density-dependence of mixed orchardgrass and timothy associations (Jolliffe et al., 1988). As in that study, the main influences of factors in my work were to modify allometry, rather than influence yield directly. This response seems to be consistent with the path analysis results, which indicated that effects of population density on T W were predominantly indirect, via other plant measures. It should be noted that the allometric models assumed independent effects of other plant measures on TW; the procedure lacks the ability to explore the collective relationships among many measures potentially acting on TW. Path analysis, however, does allow the evaluation of relationships among correlated plant measures and tuberous root yield (Li, 1975), although it has been used less often than the other techniques. Most studies using path analysis have dealt with relationships between measures of aboveground plant parts and grain yield (Dhagat et al., 1977). In forming the path diagram the analysis assumes, and does not separately test, a relationship between experimental factors such as X and TW. The path analysis measured direct and indirect statistical relationships contributing to correlations, and whether those relationships were positive or negative. The procedure does not provide a test, however, of the relative statistical significance of direct and indirect effects. Results from the path analysis highlighted the changing contributions made by different aboveground constituents in the different cultivars and years. For the 1996 results, path analysis suggested the importance of factors not included in the regression model for ' B O 129T9',  104 since the residual from the regression exceeded 50%. While formal yield component analysis has been performed since the 1920s (Engeldow and Wadham, 1923), the two-dimensional partitioning technique has only been available since 1986 (Eaton et ai, 1986). Yield component analysis is somewhat more complex than path analysis in that it tests relationships between ratios of plant measures, rather than the simple measures. It should be noted, however, that conventional plant growth analysis also makes extensive use of ratios (LAR, SLA, L W R , H , etc.), and allometry does the same (y/z = azP ). Yield component analysis is further complicated -1  by taking yield as the product, rather than the sum, of a set of components. Like allometric analysis, yield component analysis analyzes plant performance in the Intransformed frame of reference, and it is a demanding procedure to carry out because the orthogonalization step in the procedure is complex. The TDP procedure requires the analyst to assume a sequence of plant development, although many developmental steps actually overlap in time. Interpreting the TDP tables is complicated because the roles of intermediate yield components are conditional on their relationships with earlier and later terms entering the multiple regression. Inspecting correlation matrices can help to interpret intermediate yield components (Eaton and Kyte, 1976). This was not done in the present study because it was felt that correlations between aboveground parts and T W were more directly and simply assessed by path analysis. Nevertheless, there were some benefits from applying yield component analysis. Although the yield components were ratios in the ln-transformed frame of reference, they still represented potentially interesting features of growth. For example, two components were mean length per stem (SL/SN), and the frequency of leaves per stem (LN/SL). It  105  was possible that analyzing plant performance in terms of these new variables might reveal things that would not be obvious from simply analyzing the primary measures. In TDP, the contributions of yield components to yield variation are always positive as the computations in TDP are based on total sum of squares. In addition, TDP allows an evaluation ofthe contributions of experimental treatments upon yield components and on total yield variation. M y TDP analysis indicated that several components (SN and T W / L A in 1996) contributed directly to yield variation, and that these components were affected by population density. Past experience has shown that plant breeders and agronomists have found yield components to be useful as traits for breeding programs as well as for understanding plant behavior (e. g., Matsushima, 1970; Yoshida, 1972). I found that there was some overlap in the interpretation of sweet potato performance that I gained from using these different analytical techniques. This is to be expected because they often had the same basic input data. However, each technique also provided its own perspective. Results from the conventional plant growth analysis highlighted the value of tracking the chronological changes that occur during plant growth. As noted above, the other techniques can be used with data from different harvests. This would strengthen them all. Once appropriate data are obtained, the choice of which analytical technique should be used depends on the kind of question that a researcher is trying to ask of the data.  106  6  General Conclusions  Based on the objectives stated in Chapter 1, the following conclusions were reached: 1)  This research has advanced our understanding of sweet potato productivity by comparing two cultivars, a bushy type ('BO 44T3') and a spreading type ('BO 129T9'). The two cultivars arrived at similar final tuberous root yields through different chronologies of growth. Increasing plant population density significantly reduced tuberous root yields and most measures of aboveground plant parts. Responsiveness to population density differed among the different plant measures and years, and the two cultivars did not always respond to density to the same degree. Where significant differences in density responsiveness were found between cultivars, the ranking of responsiveness depended on the measure observed. Where significant differences were found between years, the responsiveness was always higher in the year that was less favourable to growth (1996).  2)  Significant relationships were found between measures of aboveground plant parts and tuberous root yield in both cultivars. Throughout growth, the rates of addition (LNGR) and expansion of leaves (LAGR) were positively correlated with TGR in both cultivars. At the final harvest, number of stems per plant (SN) was an important indicator of tuberous root yield. In allometric analysis, InSN was strongly and directly related to InTW. In path analysis, where SN was significantly correlated with T W in 1995, indirect effects of SN were larger than direct effects. In yield component analysis, orthogonalized InSN directly contributed to InTW variation. Further research will have to be done to confirm the reliability of L N , L A and S N as  107  predictors of tuberous root yield in other cultivars and under other growing conditions. Each of the analytical techniques used in this research made a useful and distinctive contribution to the quantification and interpretation of plant performance. Conventional plant growth analysis indicated that the two cultivars arrived at similar final yields in different ways. It is helpful to know the origins of final yield, so I believe it would also be useful to apply the other analytical techniques to data from a chronological series of harvests. The coefficients of inverse yield-density relationships quantified intraspecific competition (interference), and showed that competition had different impacts on different plant measures. Allometric analysis detected strong bivariate relationships between tuberous root yield and aboveground plant measures, plus some direct effects of experimental factors on yield. Multiple relationships were assessed through path analysis and yield component analysis. Path analysis was able to separate direct and indirect contributions to the correlations between aboveground parts and tuberous root yields. Yield component analysis identified orthogonalized InSN as a direct contributor to variation in InTW. Therefore, these different analytical techniques can complement one another in interpreting plant performance. In any study they do not all have to be applied, as was done here. I hope that these studies will have shown some of their capabilities, and that future researchers can select the techniques that are most suitable for their needs.  108  7  References  Agassiz Research Station. 1995. Recorded daily measurements (unpublished). Agassiz Research Station. 1996. 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Soil analysis for the 1995 field experiment at Agassiz, British Columbia z)  Property pH ( H 0 ) Organic matter Bulk density Salt Nitrate Phosphorus Potassium Magnesium Calcium Sodium Sulphate Boron Copper Iron Manganese Zinc  Code  Units  2  E.C N as N 0 " P K Mg Ca Na S as S 0 " B Cu Fe Mn Zn 3  2  4  % g/ml dS/m pg/L pg/L pg/L pg/L pg/L pg/L pg/L pg/L pg/L pg/L pg/L pg/L  Value 6.4 5.6 1.06 0.24 6 75 433 147 959 9 17.0 0.45 1.3 64.4 6.6 1.6  Category/Rating  y)  Slightly acid x) x) x) x)  High Very high High Medium Very low Low  z  Soil analysis was conducted by Griffin Laboratories Corporation. The following are soil analytical procedures used in 1995: Soil samples were taken on the first week of March 1995. No soil sample was taken for soil analysis in 1996.  y  Ratings came from Griffin Laboratories Corporation  "Organic matter, salt, nitrate and phosphorus contents in the soil are very time dependent. Organic matter, salt, nitrate and phosphorus leach during winter.  116  Appendix A2. Long-term weather conditions. Mean values of air temperature, rainfall, and bright sunshine duration at Agassiz, British Columbia for the period 1889-1990 . z  Air temperature (C) Month  January February March April May June July August September October November December z  Daily mean  Daily max.  Daily min.  2.1 4.6 6.8 9.5 12.9 15.7 17.9 18.1 15.5 10.7 5.9 2.7  4.9 8.0 10.9 14.1 17.8 20.7 23.6 23.8 20.6 14.9 8.8 5.3  -0.8 1.1 2.8 4.9 8.0 10.7 12.2 12.3 10.3 6.6 3.0 -0.1  Rainfall (mm/month)  Rainy days (per month)  Sunshine (hr/month)  195.2 162.2 145.8 117.7 97.4 82.0 60.4 57.4 100.0 174.0 234.6 213.4  16 16 18 17 15 13 9 9 12 17 20 18  50.3 78.0 119.5 144.8 185.6 192.7 248.3 229.1 176.2 115.5 59.6 46.9  Source: Atmospheric Environment Service. 1990.  117  Appendix A3. Layout of Experiment 1 conducted from 9 May to 16 September 1995 at the Pacific Agricultural Research Centre, Agassiz, British Columbia.  v&/Ai7/£r/£r/z  %7/A7/A7/AT/£>  I 2' A  \  I 2 B  1  1  1  VAW/AWA  II 1 B  1  II 1 A  i  Ay/zr/47/J7/Aj  /  I 1 A  I 3 B  1—K?l  l_R9  I 1 B  I 3 A VAWJET,  II 3 A  &•/&•/&VAW/AWJBMOWB>  T  •  t 1  II 3 B  i 1  1  I  i  II 2 B  1  Subplot  !  III 2 A  i  IV 3 A  IV 1 B  IV 3 B  IV 1 A  PAWAWJLvjy/jy/jr/JT/t  III 3 B  III 1 A  i—i  !  I_I  II 2 A '*v/£r/jr/Ayy*7/  1  1 1  1 i IV 2 A  1  i  III 1 B  III 3 A T/AT/A?. r/Ar/Axr/jy/JT/A  W/AV/AWA7/A7/A7/A7/A7/A&  Raised bed  r/A7y*r/J77*7/A\ VA7/A7,.  \  III 2 B  !  !  i  y/AWdWAWJT/A  %  Si  i  I  ZT/AT/A\  Block  The width of raised bed = 1.10 m Distance between adjacent raised beds = 0.70 m Subplot size for Experiment 1 = 3.00 m x 1.10 m = 3.30 m . 2  r/AWA7/A7/J7/JL r/Ayyjxfo/jtT'/a  IV 2 B /Avzam  Experimental design for Experiment 1: Split-Plot Main plot: Plant population density: 1 = 8 plants per 3.30 m (24,242 plants/ha) 2 = 16 plants per 3.30 m (48,485 plants/ha) 3 = 24 plants per 3.30 m (72,727 plants/ha) 2  2  2  Subplot: Sweet potato cultivar A = cv BO 44T3 B = c v B O 129T9 I = Block 1 II = Block 2  III = Block 3 IV = Block 4  • Location of a probe used to monitor soil temperature <g> Location of a probe used to monitor air temperature  119  Appendix A4. Layout of Experiment 1 and Experiment 2 conducted from 5 June to 25 October 1996 at the Pacific Agricultural Research Centre, Agassiz, British Columbia.  Al  BI  T 1 j  1 i  -  A2  B2  -t-  1  I 3 A  II  2 B  II 1 A  Q2H  -O-  -D-  I 3 B  II  II 1 B  2 A  A10  A14  BIO  B14  III  III 2 B  f P  •  A13  1 I  I  2 A  1 B -QS>-  A3 I  I  2 B  A  1  B3  I  II 3 A  III 1 B  m  III 1 A  in  -TJII 3 B  t  B13  A12  4-  B  7/3,.  B12  A4  B5  A6  B7  A8  B9  All  A 15  B4  A5  B6  A7  B8  A9  Bll  B 15  D2>  Raised bed  Subplot  Block  The width of raised bed = 1.10 m. Distance between adjacent raised beds = 0.70 m Subplot size for Experiment 1 - 3 r a x 1.10m = 3.30m Subplot size for Experiment 2 = 1.50 m x 1.10 m = 1.65 m 2  2  Experiment 1: Split-Plot Design Main plot: Plant population density 1 = 8 plants per 3.30 m (24,242 plants/ha) 2=16 plants per 3.30 m (48,485 plants/ha) 3 = 24 plants per 3.30 m (72,727 plants/ha) 2  2  2  Subplot: Sweet potato cultivar A = cv B O 44T3 B = cv B O 129T9 I = Block 1  II = Block 2  III = Block 3  Experiment 2: Plant growth observations A = cv B O 44T3 B = c v B O 129T9 Plant population density = 8 plants per 1.65 m (48,485 plants/ha) Each cultivar was grown on 15 subplots. Distance between subplots A and B was 1.00 m C Location of a probe used to monitor soil temperature ® Location of a probe used to monitor air temperature  121  Appendix A5. Mean values of air temperatures, total rainfall, total rainy days and total bright sunshine duration for 1995 and 1996 growing seasons. 2  Air temperature (C) Month  :  Daily Daily mean max.  Daily min.  Rainfall ( /ni nth) 0  Rainy days (days/month)  Sunshine (hr/month)  mm  1995 April May June July August September  10.7 15.9 19.2 19.8 17.7 19.4  16.0 22.6 26.8 27.0 25.2 27.9  5.4 9.2 11.6 12.6 10.3 11.0  78.2 32.2 86.2 98.1 83.6 53.0  15 10 15 15 25 13  195 282 230 220 178 232  10.6 11.5 16.0 19.5 17.9 13.8 12.9  14.8 15.9 23.5 27.3 26.1 21.1 18.1  6.4 7.2 9.5 12.1 11.4 7.6 8.2  167.5 152.4 33.5 43.3 73.5 147.4 255.5  27 25 14 7 10 18 18  122.2 145.9 217.1 315.4 234.7 157.9 96.5  1996 April May June July August September October Z  -Values of air temperature for April and May, rainfall, rainy days and of sunshine duration in 1995 were obtained from Agassiz Research Station (1995). -Values of air temperature for April and May, rainfall, rainy days and of sunshine duration in 1996 were obtained from Agassiz Research Station (1996). -Values of air temperature for the period June to September 1995 and June to October 1996 derived from field observations. -Values of air temperature for October 1996 were means temperatures recorded during the first week of October 1996.  122  Appendix A6. Mean values of soil temperature (at about 0.1 m depth) for the period June-September 1995 and June-October 1996.  Month  Soil temperature (C) Daily mean  Daily maximum  Daily minimum  23.0 21.6 18.1 18.7  27.1 23.7 19.6 20.4  18.9 19.4 16.7 16.9  23.6 24.8 20.0 15.7 14.4  28.7 29.3 21.6 18.7 19.9  18.6 20.3 18.4 12.7 8.8  1995 June July August September 1996 June July August September October  123  Appendix A7. Estimated incident solar radiation for the 1995 and 1996 growing seasons at Agassiz, British Columbia.  z  Month  N  April May June July August September October Mean  13.8 15.4  n  t\  z  VA  Q  1995  1996  1995  30,600  6.50  4.05  20,664  16,970  38,200  9.10  28,810  21,506  16.3  41,400  7.67  4.71 7.24  27,944  27,201  15.9  39,900  7.10  10.20  26,280  31,570  14.5  33,100  5.75  7.57  20,676  23,501  12.7  23,800  7.74  5.26  18,312  15,152  10.8  17,300  2.93  3.11  9,333  9,529  6.68  6.02  21,717  20,776  1996  Symbols designate: N = Daylength at latitude of 5 0 ° North, in hours (List, 1971), Q A = Total daily solar radiation at the top of the atmosphere at a latitude of 5 0 ° North, in kJ/m (List, 1971). n = Mean daily bright sunshine duration at Agassiz, British Columbia, in hours. Q = Incident solar radiation estimated using a regression equation proposed by Angstrom, in kJ/m (Eqn. 2 . 1 ; Chang, 1968). 2  2  124  Appendix A8 Observations on growth of sweet potato cultivar BO 44T3 during the 1996 growing season. 2  DAP SN y  SL  30 7 0.17 30 5 0.17 30 9 0.20 30 5 0.16 31 7 0.42 31 7 0.37 31 7 0.29 31 5 0.26 32 1 0.08 32 7 0.28 32 4 0.21 32 5 0.17 50 10 1.73 50 25 2.23 50 25 2.85 50 20 2.32 52 21 2.62 52 31 3.83 52 43 4.92 52 13 1.56 56 44 4.03 56 15 1.12 56 35 5.76 56 21 3.12 71 17 2.70 71 29 5.24 38 7.93 71 71 60 10.87 86 58 14.29 86 27 8.21 86 12 1.26 86 36 9.70 92 29 6.76 92 48 7.16 92 65 17.09 92 22 4.54 100 55 10.32 11 3.62 100 100 85 11.60 100 107 21.62 137 240 32.54 137 153 26.09 137 199 35.91  SW 0.00044 0.00050 0.00044 0.00040 0.0013 0.0010 0.00082 0.0011 0.00023 0.00048 0.00031 0.00029 0.0029 0.0067 0.0058 0.0043 0.0044 0.0096 0.0099 0.0029 0.0092 0.0026 0.0122 0.0067 0.0054 0.0123 0.0211 0.0292 0.0316 0.0219 0.0030 0.0257 0.0236 0.0029 0.0505 0.0122 0.0179 0.0087 0.0314 0.0191 0.102 0.0626 0.165  LN 31 24 38 45 31 40 34 18 30 24 31 12 132 199 185 161 177 229 287 111 292 135 341 216 180 253 355 505 466 302 47 388 284 333 620 170 421 113 488 793 534 525 630  LA 0.0373 0.0251 0.0428 0.0442 0.0560 0.0420 0.0375 0.0135 0.0270 0.0178 0.0236 0.0086 0.288 0.422 0.459 0.417 0.420 0.593 0.889 0.261 0.785 0.306 1.001 0.582 0.590 0.838 1.179 1.850 2.196 1.427 0.161 1.881 1.176 1.337 2.633 0.652 1.827 0.560 2.173 4.064 2.623 2.577 1.432  WL 0.0014 0.00083 0.0015 0.0016 0.0023 0.0016 0.0013 0.00049 0.00089 0.00057 0.00072 0.00026 0.0091 0.0132 0.0138 0.0134 0.0135 0.0184 0.0262 0.0088 0.0232 0.0088 0.0294 0.0161 0.0158 0.0247 0.0376 0.0545 0.0564 0.0337 0.0044 0.0534 0.0318 0.0525 0.0723 0.0193 0.0484 0.0149 0.0561 0.0861 0.122 0.102 0.254  PW  VW  TW  W  0~ 0.0019 0.00014 0.0019 0.00010 0.0014 0 0.0014 0.00021 0.0021 0 0.0021 0.00010 0.0021 0 0.0021 0.00017 0.0038 0 0.0038 0.00017 0.0027 0 0.0027 0.00013 0.0023 0 0.0023 0.00008 0.0016 0 0.0016 0.00000 0.0011 0 0.0011 0.00010 0.0012 0 0.0012 0.00009 0.0011 0 0.0011 0.00007 0.00062 0 0.00062 0.0022 0.0142 0.00059 0.0148 0.0036 0.0226 0.00044 0.0230 0.0044 0.0239 0.00022 0.0242 0.0035 0.0211 0.00032 0.0215 0.0040 0.0219 0.0087 0.0306 0.0068 0.0348 0.0053 0.0401 0.0088 0.0449 0.0076 0.0525 0.0025 0.0142 0.00025 0.0144 0.0081 0.0404 0.0017 0.0421 0.0022 0.0136 0.00034 0.0139 0.0106 0.0522 0.00052 0.0527 0.0069 0.0297 0.00009 0.0298 0.0070 0.0282 0.0359 0.0611 0.0108 0.0478 0.0048 0.0525 0.0210 0.0797 0.0156 0.0953 0.0312 0.1149 0.0435 0.158 0.0356 0.1235 0.264 0.140 0.0232 0.0788 0.230 0.152 0.0021 0.0095 0.0096 0.0191 0.0307 0.1097 0.306 0.196 0.0227 0.0781 0.0667 0.145 0.0236 0.0790 0.0695 0.149 0.0521 0.1748 0.309 0.134 0.0142 0.0457 0.0197 0.0653 0.0091 0.0754 0.284 0.208 0.0074 0.0310 0.0709 0.102 0.0348 0.122 0.312 0.190 0.0084 0.114 0.293 0.179 0.0233 0.247 0.565 0.318 0.0657 0.230 0.443 0.213 0.0274 0.447 0.521 0.213  125 z  Sweet potato plants were grown at population density of 48,484 plants/ha, this corresponds to 8 plants per 1.65 m .  Abbreviations: D A P = Days after planting, SN = Number of stems per plant, SL = Length of stems per plant (m), SW = Dry mass of stems per plant (kg), L N = Number of leaves per plant, L A = Leaf area per plant (m ), W L = Dry mass of leaves per plant (kg), P W = Dry mass of petioles per plant (kg), V W = Dry mass of vines per plant (kg), T W = Dry mass of tuberous roots per plant (kg), W = Dry mass of the whole plant (kg). 2  126  Appendix A9 Observations on growth of sweet potato cultivar BO 129T9 during the 1996 growing season. 2  DAP 30 30 30 30 31 31 31 31 32 32 32 32 50 50 50 50 52 52 52 52 56 56 56 56 71 71 71 71 86 86 86 86 92 92 92 92 100 100 100 100 137 137 137  y  SN SL 8 0.50 2 0.65 1 0.25 3 0.36 6 0.39 6 0.38 3 0.17 3 0.27 1 0.10 1 0.12 1 0.11 1 0.08 21 5.87 25 4.79 32 8.83 12 3.47 22 7.23 7 3.83 12 7.51 13 1.56 27 42.34 7 15.06 14 21.08 10 27.89 8.50 18 31 10.78 26 7.27 11 3.84 27 13.09 37 10.62 34 10.01 6 3.73 5.74 13 35 15.89 33 13.17 76 20.06 6 1.79 68 20.33 183 210.10 41 16.88 136 55.28 189 61.81 112 31.45  SW 0.00093 0.00033 0.00074 0.00053 0.00083 0.00049 0.00030 0.00067 0.00013 0.00015 0.00014 0.00011 0.0127 0.0096 0.0203 0.0093 0.0164 0.0092 0.0263 0.0200 0.0207 0.0084 0.0137 0.0100 0.0305 0.0337 0.0214 0.0122 0.0394 0.0344 0.0277 0.0091 0.0218 0.0242 0.0214 0.0271 0.0070 0.0808 0.184 0.0583 0.210 0.253 0.137  LN 22 18 29 36 19 35 22 12 9 9 9 8 149 172 231 120 203 107 281 297 246 95 143 84 232 263 185 85 286 229 234 99 154 284 349 349 33 415 1108 306 575 616 390  LA 0.0227 0.0261 0.0424 0.0621 0.0271 0.0485 0.0408 0.0111 0.0107 0.0058 0.0054 0.0085 0.709 0.587 1.016 0.673 0.901 0.485 1.292 1.328 1.181 0.673 1.073 0.670 2.145 1.398 1.010 0.504 1.653 1.359 1.546 0.530 1.453 2.049 3.239 2.848 0.338 3.518 7.923 2.423 3.449 3.695 0.583  WL 0.0092 0.0113 0.0178 0.0272 0.0120 0.0208 0.0183 0.0043 0.0037 0.0021 0.0018 0.0029 0.255 0.241 0.370 0.235 0.295 0.159 0.422 0.434 0.364 0.213 0.553 0.211 0.708 0.511 0.329 0.174 0.559 0.466 0.457 0.129 0.427 0.609 0.943 0.799 0.0973 0.864 2.124 0.560 1.499 1.342 0.880  PW 0.00008 0.00023 0.00000 0.00008 0.00007 0.00016 0.00004 0.00002 0.00000 0.00000 0.00000 0.00000 0.0076 0.0046 0.0096 0.0081 0.0092 0.0052 0.0140 0.0141 0.0011 0.00072 0.0014 0.00073 0.0311 0.0190 0.0127 0.0091 0.0249 0.0187 0.0208 0.0065 0.0188 0.0304 0.0452 0.0313 0.0051 0.0442 0.0890 0.0285 0.0657 0.0274 0.0338  VW TW 0.0019 0 0.0017 0 0.0025 0 0.0033 0 0.0021 0 0.0027 0 0.0022 0 0.0011 0 0.00050 0 0.00036 0 0.00032 0 0.00040 0 0.0458 0 0.0384 0.00019 0.0670 0.0031 0.0409 0.00016 0.0550 0.0011 0.0303 0.0050 0.0825 0.0096 0.0775 0.0217 0.0581 0.0206 0.0304 0.0146 0.0703 0.00000 0.0318 0.0231 0.132 0.0849 0.104 0.0540 0.0671 0.0339 0.0387 0.0214 0.120 0.0886 0.0997 0.0880 0.0941 0.114 0.0285 0.0190 0.0838 0.0905 0.116 0.190 0.161 0.407 0.138 0.177 0.0218 0.0459 0.211 0.216 0.486 0.339 0.143 0.227 0.425 0.299 0.415 0.305 0.259 0.0862  W 0.0019 0.0017 0.0025 0.0033 0.0021 0.0027 0.0022 0.0011 0.00050 0.00036 0.00032 0.00040 0.0458 0.0385 0.0700 0.0410 0.0561 0.0353 0.0921 0.0992 0.0788 0.0451 0.0703 0.0549 0.217 0.158 0.101 0.0602 0.209 0.188 0.208 0.0475 0.174 0.306 0.568 0.315 0.0677 0.428 0.825 0.370 0.724 0.719 0.345  127 z  Sweet potato plants were grown at population density of 48,484 plants/ha, this corresponds to 8 plants per 1.65 m .  Abbreviations: D A P = Days after planting, SN = Number of stems per plant, SL = Length of stems per plant (m), SW = Dry mass of stems per plant (kg), L N = Number of leaves per plant, L A = Leaf area per plant (m ), WL = Dry mass of leaves per plant (kg), PW = Dry mass of petioles per plant (kg), V W = Dry mass of vines per plant (kg), T W = Dry mass of tuberous roots per plant (kg), W = Dry mass of the whole plant (kg). 2  128 Appendix A10. Plant measures per land area at the final harvest in ' B O 44T3' and ' B O 129T9' grown at three different plant population densities in 1995 and 1996. 2  t  b  X  V  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2  l l l l l l  8 8 16 16 24 24 8 8 16 16 24 24 8 8 16 16 24 24 8 8 16 16 24 24 8 8 16 16 24 24 8 8 16 16 24 24 8 8 16 16 24 24  1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2  2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3  y  pin  W  SN  SL  SW  LN  LA  WL  TW MTW  4 4 8 8 12 12 4 4 8 8 12 12 4 4 8 8 12 12 4 4 8 8 12 12 4 4 8 8 12 12 4 4 8 8 12 12 4 4 8 8 12 12  2.49 3.56 3.90 3.97 4.00 3.76 3.48 5.43 4.17 3.97 3.36 4.35 3.39 4.11 3.67 4.61 4.01 4.23 2.70 3.50 3.65 3.77 3.65 3.70 1.39 1.54 1.82 1.86 1.72 2.27 1.75 1.65 1.64 2.24 2.26 2.48 1.58 1.62 1.55 2.77 2.27 1.84  120 134 269 267 283 274 299 265 395 330 286 264 209 162 140 177 396 250 162 139 248 148 252 213 496 208 575 215 420 388 344 239 395 336 336 359 274 280 317 163 397 325  52.4 85.6 65.2 99.2 73.1 147.0 59.2 118.0 56.8 110.0 56.4 106.0 61.2 130.0 51.7 110.0 61.7 112.0 51.4 105.0 94.5 120.0 80.0 137.0 61.7 106.0 152.0 97.7 75.2 104.0 35.1 34.6 64.5 60.8 78.1 115.0 53.6 96.7 51.7 105.0 59.8 113.0  0.224 0.963 0.330 0.606 0.410 0.677 0.585 0.139 0.688 0.673 0.453 0.798 0.450 0.861 0.484 0.804 0.381 0.785 0.319 0.506 0.441 0.537 0.397 0.722 0.209 0.362 0.414 0.371 0.296 0.474 0.137 0.146 0.263 0.218 0.291 0.468 0.222 0.442 0.189 0.424 0.298 0.214  2447 2122 2568 1927 2685 2505 2111 2178 2646 2081 2040 2265 1847 1679 1574 1794 2292 1935 1327 1296 1658 1063 1436 . 1730 1615 1264 2177 1144 1763 1060 1949 937 1142 1348 1254 1458 1199 1253 1258 650 1146 1223  11.52 14.96 10.67 14.24 11.64 17.15 9.31 14.57 9.40 14.14 8.57 15.00 10.31 11.99 6.66 12.30 11.22 12.99 6.58 7.90 8.83 6.97 7.08 11.62 10.28 10.80 16.00 10.51 9.80 8.80 11.82 10.29 7.33 11.58 7.20 11.70 5.77 9.96 7.38 6.38 6.74 9.94  0.183 0.324 0.181 0.272 0.222 0.420 0.199 0.381 0.240 0.333 0.218 0.352 0.217 0.376 0.174 0.402 0.184 0.328 0.134 0.181 0.196 0.192 0.201 0.400 0.328 0.349 0.463 0.345 0.316 0.405 0.351 0.337 0.206 0.391 0.182 0.313 0.168 0.289 0.212 0.193 0.147 0.313  2.09 2.28 3.39 3.09 3.37 2.66 2.70 3.65 3.24 2.96 2.69 3.20 2.72 2.88 3.01 3.41 3.44 3.12 2.25 2.82 3.01 3.04 3.95 2.58 0.851 0.824 0.944 1.14 1.11 1.39 1.26 1.16 1.18 1.63 1.79 1.70 1.19 0.888 1.15 2.15 1.82 1.32  1.89 1.86 2.97 2.39 2.82 1.64 2.28 3.34 3.13 2.60 2.20 2.66 2.50 2.62 2.92 2.79 3.04 2.49 2.04 2.56 2.25 2.90 2.54 2.17 0.696 0.791 0.833 0.775 0.765 0.786 0.907 0.971 0.863 1.29 1.06 1.30 0.916 0.671 0.754 1.74 1.16 0.906  129 z  Plant measures and abbreviations: W = Plant dry mass (kg), SN = Number of stems, SL = Length of stems (m), SW = Dry mass of stems (kg), L N = Number of leaves, L A = Leaf area (m ), W L = Dry mass of leaves (kg), T W = Dry mass of tuberous roots (kg), M T W = Dry mass of marketable tuberous roots (kg), t = Year of planting, b = Block or replication, v = Variety, X = Plant population density (plants/area, subplot area =3.3 m ), pin = Number of plants (plants/area, sample plot area = 1.65 m ). 2  2  y  Values of plant measures listed in the Table are those determined from the 1.65 m sample plots.  2  130  Appendix A l l . Analysis of variance for pooled data of the 1995 and 1996 final harvests: F values of the effects of year of planting, plant population density and sweet potato cultivar on plant measures per land area. z  Source of variation  Year (t) Block (R(t)) ^linear (X/.) X j / rcma  nc  er  (X ) txX,, txX Error a Variety (v) tx v X xv XDL x v txX xv t x XDL x v Error b Total  df  1 5 1 1  SN  W  y  SL  102**  7.7*  0.78  15.6** 4.1  8.0* 0.067™  4.5 0.24  1.5  0.23 0.17  0.44 0.60  ns  SW ns  ns  ns  LN  16*  5.7  ns  0.034™ 0.17  4.1 2.1  2.0 0.40  6.6" 0.054  ns  LA  WL  0.95  ns  0.63  ns  ns  0.39 0.19  ns  0.25 0.84  ns ns  ns  ns  TW  MTW  124**  103**  25** 8.9  1.4 9.5*  ns  ns  D i  D i  t  t  1 1 6 1 1 1 1 1 1 15 41  ns  o.4 r  s  10.2** 1.2 2.1 ns  o.or  2.2 3.2  ns  ns  s  ns  ns  13**  4.r  s  0.29 1.2 1.9™ 2.0 ns  ns  ns  ns  ns  2 ] ** 7.0* 0.25 3.9" 0.07 1.0™  ns  s  ns  ns  48** 14** 2.5 6.0* 0.94" 2.0 ns  ns  3.5  s  ns  6.2* 0.79 0.60 1.7 0.14 0.12  ns  ns  2.4 0.74  11** 3.5 0.70 0.93 0.018" 0.3 l  29** 3.5 1.5 2.0 0.28 0.67  ns  ns  ns  ns  ns  ns  ns  ns  n s  ns  ns  ns  ns  s  „s  2 9  ns  5  ns  ns  0.83" 2.2  0.36 1.6  s  ns  ns  ns  0.56 0.043 2.4 0.87 2.2 3.4 ns  ns  ns  ns  0.092 0.68 2.8 0.22  ns  ns  ns  ns  ns  2.4™  ns  '1.7™  z  Values of plant measures were obtained from the 1.65 m sample plots.  y  Measures per 1.65 m land area: W = Plant dry mass (kg), SN = Number of plants, SL = Length of stems (m), S W = Dry mass of stems (kg), L N = Number of leaves, L A = Leaf area (m ), W L = Dry mass of leaves (kg), T W =Dry mass of tuberous roots (kg), M T W = Dry mass of marketable tuberous roots (kg).  2  2  2  "Abbreviations and symbols: X = Plant population density (plants per 3.3 m ), X = The linear response of a plant measures to increasing plant population densities, X = Deviation from the linear response of a plant measure to increasing plant population densities, df = Degree of freedom, ns, *, ** = Not significant, significant at P = 0.05 or P = 0.01, respectively. 2  L  DL  The arithmetic means of plant measures per 1.65 m land area are presented in Appendix 12.  131  Appendix A12. Arithmetic means of plant measures per 1.65 m land area at the 1995 and 1996 final harvest. 2  W  SN  y  2  SL  SW  LN  LA  WL  1,967 1,324  11.1 9.57  0.263 0.295  TW  MTW  Means of plant measures in 1995 and 1996 1995 1996 Year mean difference  3.81 1-90  237 337  **  *  89.3 81.4 n s  0.551 0.302 *  n s  n s  n s  2.98 1.31  2.53 0.955  **  **  Mean responses of plant measures to increasing plant population densities 2.73 238 75.0 0.398 1,659 10.4 0.273 1.97 1.72 4 284 88.5 0.460 1,645 8 3.11 10.2 0.271 2.38 2.02 12 3.14 309 95.2 0.475 1,763 10.7 0.270 2.51 1.88 Y * x * Trend X/ ** ns ns ns ns ns X^ ** X  L  Means of plant measures in cvs BO 44T3 and BO 129T9 CVJ30  44T3  c v B 0 129T9  2.78  315  66.4  0.356  1,815  9.24  4.80  245  105  0.533  1,567  11.6  C^u.ltiv3r mc3.ii difference  H*  ^  ^^  0.225 0.328  2.25 2.28  1.84 1.87  **  ns  ns  Arithmetic means for responses of plant measures to increasing plant population densities and for plant measures per 1.65 m land area in cvs B O 44T3 and 129T9 were calculated from pooled data of the 1995 and 1996 final harvests. 2  y  Measures per 1.65 m land area: W = Plant dry mass (kg), SN = Number of stems, SL = Length of stems (m), S W = Dry mass of stems (kg), L N = Number of leaves, L A = Leaf area (m ), W L = Dry mass of leaves (kg), T W = Dry mass of tuberous roots (kg), M T W = Dry mass of marketable tuberous roots (kg). 2  2  "Abbreviations and symbols: X = Plant population density (plants per 3.3 m ), ns, *, ** = Not significant, significant at P = 0.05 or P = 0.01, respectively, X = The linear response of plant measure to increasing plant population densities, X = Deviation from the linear response of plant measure to increasing plant population densities. 2  L  DL  132  Appendix A13. Analysis of variance for data of the final harvests (1995): F values of the effects of plant population density and sweet potato cultivar on plant measures per land area. 2  Source of variation Block ^•linear ( X i ) " ^remainder  (X ) Error a Variety (v) Xixv X/x x v Error b Total Di  df  SN  W  SL  y  SW  3 1  2.32" 1.51  2.0 4.8  1  1.20  0.17"  0.027  0.5 l  12.6** 5.56* 2.06"  5.7* o.7 r 0.032  152** 0.13 2.0  39**  6 1 1 1 9 23  s  ns  ns  s  0.53 2.0  ns  3.5" i.r  ns  ns  s  s  ns  ns  ns  ns  3.6 5.1  ns  ns  LA  27** 5.4  s  ns  LN  ns  n s  0.83  ns  3.6 0.24 3.0 ns  ns  ns  WL  28** 4  jns  1.5 1.7  i.r  ns  ns  ns  ns  4 5  ns  0.049  0.60  3.4  8.8*  47**  0.24 5.8* 0.32  ns  2  ns  24** 0.86 0.22  s  MTW  3 ns  ns  5.2  TW  ns  ns  0.58 1.3  ns  ns  ns  0.15" 3.1 0.10  s  ns  ns  2  Values of plant measures were obtained from the 1.65 m sample plots.  y  Measures per 1.65 m land area: W = Plant dry mass (kg), SN = Number of plants, SL = Length of stems (m), SW = Dry mass of stems (kg), L N = Number of leaves, L A = Leaf area (m ), W L = Dry mass of leaves (kg), T W =Dry mass of tuberous roots (kg), M T W = Dry mass of marketable tuberous roots (kg).  2  2  2  "Abbreviations and symbols: X= Plant population density (plants per 3.3 m ), Xi = The linear response of plant measure to increasing plant population densities, X = Deviation from the linear response of plant measure to increasing plant population densities, df = Degree of freedom, ns, *, ** = Not significant, significant at P = 0.05 or P = 0.01, respectively. 2  DL  The arithmetic means of plant measures per 1.65 m land area in 1995 are presented in Appendix 14. 2  133  Appendix A14. Arithmetic means of plant measures per 1.65 m land area in 1995. 2  W  SN  Z  SL  SW  LN  LA  WL  TW  MTW  Mean responses of plant measures to increasing plant population densities 4 8 12 Trend y  3.58 3.96 3.88 ns  186 247 277 ns  83 88 97 ns  0.663 0.570 0.578 ns  1,876 1,914 2,111 ns  10.9 10.4 11.9 ns  0.249 0.249 0.291 ns  2.67 3.14 3.01 ns  2.42 2.74 2.45  0.196 0.330  2.91 2.97  2.55 2.50  **  ns  ns  v  *  Means of plant measures in cvs BO 44T3 and BO 129T9 c v B 0 44T3 c v B 0 129T9 Cultivar mean difference  3.54 4.08 _  55 218 *  2  64 115 **  0.430 0.777 **  2,053 1,881  9.3 12.8 **  Plant measures, abbreviations and symbols: W = Plant dry mass (kg), SN = Number of stems, SL = Length of stems (m), SW = Dry mass of stems (kg), L N = Number of leaves, L A = Leaf area (m ), W L = Dry mass of leaves (kg), T W = Dry mass of tuberous roots (kg), M T W = Dry mass of marketable tuberous roots (kg), X = Deviation from the linear response of plant measure to increasing plant population densities,. ns, *, ** = Not significant, significant at P = 0.05 or P = 0.01, respectively. z  2  DL  y  Plant population density (plants per 1.65 m2).  134  Appendix A15. Analysis of variance for data of the final harvests (1996): F values of the effects of plant population density and sweet potato cultivar on plant measures per land area. z  Source of variation  Block Xu„ (X/)" X j f (Xct) Error a Variety (v) X x v X xv Error b Total eor  rema  nc  er  A  DL  df  SN  W  SL  y  SW  2 1  2.46 18.8**  4.1 4.r  1  1.10  0.037  0.56  7.5* 0.98 1.6  3.6 0.14 2.1  ns  ns  4 1 2.85 1 0.79 jns 1 6 17 ns  ns  2  2  2.r 2.4  ns  s  ns  ns  ns  l.l" 1.7  s  ns  ns  ns  LA  WL  5.0 0.18  3.6 0.39  0.085  0.29  3.5 o.i r 0.47  3.6 0.42 0.23  s  ns  ns  ns  ns  LN  ns  ns  ,,s  0.16  0.13  0.87  0.48 0.15 0.85  3.5 l.l 0.96  0.81 0.020 7.8*  ns  ns  s  8.4* 20*  ns  ns  ns  ns  ns  ns  MTW  10* 0.57  ns  ns  TW  ns  ns  ns  ns  n s  ns  5.4 3.2  ns  ns  2.5  ns  ns  1.4 0.0098 3.5  ns  ns  ns  ns  ns  z  Values of plant measures were obtained from the 1.65 m sample plots.  y  Measures per 1.65 m land area: W = Plant dry mass (kg), SN = Number of plants, SL = Length of stems (m), SW = Dry mass of stems (kg), L N = Number of leaves, L A = Leaf area (m ), W L = Dry mass of leaves (kg), T W =Dry mass of tuberous roots (kg), M T W = Dry mass of marketable tuberous roots (kg).  2  2  2  "Abbreviations and symbols X = Plant population density (plants per 3.3 m ), X = The linear response of plant measure to increasing plant population densities, XDL = Deviation from the linear response of plant measure to increasing plant population densities, df = Degree of freedom, ns, * = Not significant and significant at P = 0.05, respectively. 2  L  The arithmetic means of plant measures per 1.65 m land area in 1996 are presented in Appendix 16. 2  135  Appendix A16. Arithmetic means of plant measures per 1.65 m land area in 1996. 2  w  SN  2  SL  SW  LN  LA  W L  T W  M T W  Mean responses of plant measures to increasing plan t population densities 4  y  1.59  307  65  0.253  1,370  9.8  0.304  1.03  0.825  8  1,98  334  89  0.313  1,287  9.9  0.301  1.37  1.04  12  2.14  371  91  0.340  1,317  9.0  0.179  1.52  0.997  ns  ns  ns  ns  ns  ns  Trend  X ** L  ns  XL*  Means of plant measures in cvs BO 44T3 and BO 129T9 c v B 0 44T3 cv B O 129T9 Cultivar mean difference  1.78 2.03  395 279 *  n s  70 93  0.258 0.347  ns  ns  1,500 1,149 ns  9.1 10.0 ns  0.264 0.326 ns  1.25 1.36  0.884 1.02  ns  ns  Measures per 1.65 m land area, abbreviations and symbols: W = Plant dry mass (kg), SN = Number of stems, SL = Length of stems (m), SW = Dry mass of stems (kg), L N = Number of leaves, L A = Leaf area (m ), W L = Dry mass of leaves (kg), T W = Dry mass of tuberous roots (kg), M T W = Dry mass of marketable tuberous roots (kg),. X = The linear response of plant measure to increasing plant population densities, ns, * = Not significant or significant at P = 0.05, respectively. z  2  2  L  y  Plant population density (plants per 1.65 m2).  136  Appendix A17. Measures per plant at the final harvest in ' B O 44T3' and ' B O 129T9' grown at three different plant population densities in 1995 and 1996. 2  t  b  X  V  pin  W  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2  l l l l l l 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3  8 8 16 16 24 24 8 8 16 16 24 24 8 8 16 16 24 24 8 8 16 16 24 24 8 8 16 16 24 24 8 8 16 16 24 24 8 8 16 16 24 24  1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2  4 4 8 8 12 12 4 4 8 8 12 12 4 4 8 8 12 12 4 4 8 8 12 12 4 4 8 8 12 12 4 4 8 8 12 12 4 4 8 8 12 12  0.6231 0.8905 0.4878 0.4965 0.3335 0.3130 0.8701 1.3570 0.5212 0.4961 0.2801 0.3622 0.8472 1.0283 0.4582 0.5767 0.3338 0.3528 0.6760 0.8755 0.4564 0.4708 0.3043 0.3082 0.3468 0.3837 0.2276 0.2323 0.1431 0.1895 0.4380 0.4118 0.2055 0.2793 0.1885 0.2067 0.3940 0.4048 0.1940 0.3465 0.1891 0.1536  SN  y  30 34 34 33 24 23 75 66 49 41 24 22 52 41 18 22 33 21 41 35 31 19 21 18 124 52 72 27 35 32 86 60 49 42 28 30 69 70 40 20 33 27  SL  SW  LN  LA  WL  TW  MTW  13.09 21.39 8.15 12.40 6.09 12.28 14.81 29.38 7.10 13.79 4.87 8.84 15.31 32.58 6.46 13.80 5.14 9.29 12.86 26.35 11.81 14.98 6.67 11.45 15.42 26.43 19.04 12.21 6.27 8.63 8.78 8.66 8.06 7.61 6.51 9.59 13.39 24.17 6.46 13.11 4.98 9.45  0.056 0.241 0.041 0.076 0.034 0.056 0.146 0.349 0.086 0.084 0.038 0.067 0.112 0.215 0.061 0.101 0.032 0.065 0.080 0.126 0.055 0.067 0.033 0.060 0.052 0.091 0.052 0.046 0.025 0.040 0.034 0.037 0.033 0.027 0.024 0.039 0.055 0.111 0.024 0.053 0.025 0.018  612 531 321 241 224 209 528 545 331 260 170 189 462 420 197 224 191 161 332 324 207 133 120 144 404 316 272 143 147 88 487 234 143 169 105 122 300 313 157 81 96 102  2.88 3.74 1.33 1.78 0.97 1.43 2.33 3.64 1.16 1.77 0.71 1.25 2.58 3.00 0.83 1.54 0.93 1.08 1.64 1.97 1.10 0.87 0.59 0.97 2.57 2.70 2.00 1.31 0.82 0.73 2.95 2.57 0.92 1.45 0.60 0.97 1.44 2.49 0.92 0.80 0.56 0.83  0.046 0.081 0.023 0.034 0.019 0.035 0.050 0.094 0.030 0.042 0.018 0.029 0.054 0.094 0.022 0.050 0.015 0.027 0.034 0.045 0.025 0.024 0.017 0.033 0.082 0.087 0.058 0.043 0.026 0.034 0.088 0.084 0.026 0.049 0.015 0.026 0.042 0.072 0.027 0.024 0.012 0.026  0.521 0.569 0.424 0.387 0.281 0.222 0.674 0.913 0.405 0.370 0.224 0.266 0.681 0.719 0.376 0.426 0.287 0.260 0.563 0.704 0.377 0.380 0.255 0.215 0.213 0.206 0.118 0.143 0.092 0.116 0.316 0.291 0.147 0.203 0.149 0.141 0.297 0.222 0.144 0.269 0.152 0.110  0.467 0.466 0.372 0.298 0.235 0.136 0.571 0.834 0.391 0.325 0.183 0.222 0.626 0.655 0.365 0.349 0.253 0.208 0.511 0.640 0.281 0.363 0.212 0.181 0.174 0.198 0.104 0.097 0.064 0.065 0.227 0.243 0.108 0.161 0.089 0.108 0.229 0.168 0.094 0.217 0.097 0.075  137 z  Values of measures per plant listed in the Table derived from measures per 1.65 m sample plot after being divided by number of plants planted in the sample plot.  2  Abbreviations: t = Year of planting, b = Block or replication, v = Variety, X = Plant population density (plants per 3.3m ), pin = Number of plants (plants per 1,65 m ), W = plant dry mass (kg), SN = Number of stems per plant, SL = Length of stems per plant (m), S W = Dry mass of stems per plant (kg), L N = Number of leaves per plant, L A = Leaf area per plant (m ), W L = Dry mass of leaves per plant (kg), T W = Dry mass of tuberous roots per plant (kg), M T W = Dry mass of marketable tuberous roots per plant (kg). 2  2  2  138  Appendix A18 Analysis of variance for pooled data of the 1995 and 1996 observations: F-values of the effects of years of planting, plant population density and sweet potato cultivars on measures per plant. z  Source of variation  df  w  SN  Year (t) Block (R(t))  i  59.9**  7.2*  u  Xij  l !  230.8**  78**  11.8**  1 1  40.1**  1 1 1 1 1 1 15 41  10.0** 2.6 6.2* 0.6 4.8* 3.4  (X/,)  mar  X. - ainder r(  m  txX txX Error a Variety (v) txv Xx v X xv tx X/, x v t xX x v Error b Total t  D i  L  DL  DL  2 4  ns  ns  ns  ns  SL  y  SW  LN  LA  WL  TW  0.95  94**  80**  MTW  11*  4.8  142**  227**  402**  216**  109**  133**  173**  5.4*  8.0*  24**  43**  22**  U**  4.6  4.5  8.8* 1.5  4.9 2.6  56** 9.3*  5.1* 0.60  o.or 0.83  8.1* 3.5 2.0 0.09  24**  ] 3**  3_ „s  3.8 6.2* 2.6 2.0 0.85"  5.8* 1.0  ns  ns  ns  „s  0.20  ns  ns  ns  3  ns  2 3  n s  ns  5.0* 3.0 0.62 0.1 l ns  n s  ns  ns  ns  s  0.30" 0.68 0.25  5  ns  2.9 0.00  ns  g o** 2.8 0.73 1.0 0.24 0.09" ns  ns  s  ns  2.4 0.66  2.2 2.5 1.7 0.03  ns  1.0 0.00  ns  jns ns  4  ns  ns  ns  ns  jns  0.10 6.1* 6.2*  ns  ns  40** 1.3  ns  25** 4  ns  31** 1.0  ns  ns  ns  ns  5  ns  ns  j pns  ns  ns  0.61  ns  3 4  „s  0.02 3.1 2.5  ns  ns  ns  ns  ns  z  Values of measures per plant derived from values of plant measures per 1.65 m sample plots after being divided by number of plants planted in the sample plots.  y  Measures per plant: W = Plant dry mass (kg), SN = Number of stems, SL = Length of stems (m), SW = Dry mass of stems (kg), L N = Number of leaves, L A = Leaf area (m ), W L = Dry mass of leaves (kg), T W = Dry mass of tuberous roots (kg), M T W = Dry mass of marketable tuberous roots (kg). 2  "Abbreviations and symbols: X = Plant population density (plants per 3.3 m ), X = The linear response of a plant measure to increasing population densities, X , = Deviation from the linear response of a plant measure to increasing plant population densities, df = Degree of freedom, ns, *, ** = Not significant or significant at P = 0.05 or P = 0.01, respectively. 2  £  DI  The arithmethic means of measures per plant at the 1995 and 1996 final harvests are presented in Appendix 19.  139  Appendix A19. Arithmetic means ; of measures per plant at the 1995 and 1996 final harvests. 2  W  SN  SL  y  SW  LN  LA  WL  TW  MTW  Means of measures per plant in 1995 and 1996 1995  0.57  34  13  0.096  295  1.7  0.039  0.438  0.381  1996  0.27  50  12  0.044  204  1.5  0.046  0.185  0.140  Year mean difference  **  *  ns  *  ns  ns  ns  **  **  Mean responses of measures per plant to increasing plant population densities 4 8 12 X  Trend  0.896 0.496 0.324 X i **  57 34 26 X/„ ** *  19 11 8  x ** t  A  D£  0.119 0.058 0.041 X/ ** Y  **  404 201 146 X i ** A  Di  2.5 1.2 0.9 X/,** Y A  iU  **  0.065 0.033 0.024 X i ** Y A  iU  **  0.510 0.308 0.202  0.452 0.261 0.158  Xi**  Xi**  Means of measures per plant in cvs BO 44T3 and BO 129T9 cv B O 44T3 cv B O 129T9 Cultivar mean difference  0.388 0.458  44  10  0.052  271  1.4  0.033  0.330  0.283  33  16  0.093  230  1.7  0.048  0.350  0.297  **  *  **  **  *  **  **  ns  ns  Arithmetic means for responses of measures per plant to increasing plant population densities and for measures per plant in cvs BO 44T3 and 129T9 were calculated from pooled data of the 1995 and 1996 observations. Measures per plant, abbreviations and symbols: SN = Number of stems, SL = Length of stems (m), S W = Dry mass of stems (kg), L N = Number of leaves, L A = Leaf area (m ), WL = Dry mass of leaves (kg), T W = Dry mass of tuberous roots (kg), M T W = Dry mass of marketable tuberous roots (kg), x = The linear response of plant measure to increasing plant population densities, XDL Deviation from the linear response of plant measure to increasing plant population densities.), ns, *, ** = Not significant, significant at P = 0.05 or P = 0.01, respectively  y  2  L  =  "Plant population density (plants per 1.65 m ). 2  140  Appendix A20 Regression coefficients of inverse yield-density regressions for different plant measures in 1995 and 1996 for sweet potato cultivars ' B O 44T3' and ' B O 129T9'.  „» .  Regression coefficient  P l a n t z  Cultivar  measure  .. . . <- '*< tes  y  1  9  9  5  ^  F = 0.10  W  BO 44T3 BO 129T9  0.383 0.416  0.681 0.626  SN  BO 44T3 BO 129T9  0.00366 0.00488  0.00415 0.00353  ns ns  SL  BO 44T3 BO 129T9  0.0220 0.0124  0.0179 0.00903  ns ns  SW  BO 44T3 BO 129T9  3.667 2.332  3.769 4.068  ns ns  LN  BO 44T3 BO 129T9  0.000784 0.000724  0.00130 0.00129  * ns  LA  BO 44T3 BO 129T9  0.177 0.107  0.223 0.168  ns ns  WL  BO 44T3 BO 129T9  7.423 3.844  9.695 4.747  ns ns  TW  BO 44T3 BO 129T9  0.453 0.572  0.889 0.826  * ns  MTW  BO 44T3 BO 129T9  0.564 0.812  1.557 1.572  Measures per plant: W = Plant dry mass (kg), SN = Number of stems, SL = Length of stems (m), SW = Dry mass of stems (kg), L N = Number of leaves, L A = Leaf area W L = Dry mass of leaves (kg), T W = Dry mass of tuberous roots (kg), M T W = Dry mass of marketable tuberous roots (kg).  z  y  P = Probability, ns, * = Not significant and significant at P = 0.10, respectively.  141  Appendix A21 Regression coefficients of inverse yield-density regression for different plant measures in sweet potato cultivars ' B O 44T3' and ' B O 129T9' for 1995 and 1996. Plant  Year of  measure  planting  Regression coefficient < 0 44T3' B  ' B O 129T9'  ^ p y =  a t  0  1  W  1995 1996  0.383 0.681  0.416 0.626  ns *  SN  1995 1996  0.00366 0.00415  0.00488 0.00353  ns ns  SL  1995 1996  0.0220 0.0179  0.0124 0.00903  ns ns  SW  1995 1996  3.667 3.769  2.332 4.068  ns ns  LN  1995 1996  0.000784 0.00130  0.000724 0.00129  ns ns  LA  1995 1996  0.177 0.223  0.107 0.168  ns ns  WL  1995 1996  7.423 9.695  3.844 4.747  TW  1995 1996  0.453 0.889  0.572 0.826  * ns  MTW  1995 1996  0.564 1.557  0.812 1.572  ns  °  Measures per plant: W = Plant dry mass (kg), SN = Number of stems, SL = Length of stems (m), SW = Dry mass of stems (kg), L N = Number of leaves, L A = Leaf area (m ), W L = Dry mass of leaves (kg), TW = Dry mass of tuberous roots (kg), M T W = Dry mass of marketable tuberous roots (kg).  z  2  y  P = Probability, ns, * = Not significant or significant at P = 0.10, respectively.  142  Appendix BI Regression coefficients for best subset multiple regression models of the allometric relationships between TW and other plant measures in sweet potato varieties. Allometric relationships are for pooled observations from the 1995 and 1996 studies.  Potential independent meter variable"  Plant measure (z)  2  Intercept ln(z) tln(z) vln(z) Xln(z) tvdln(z) ln(X) ln(tX) ln(vX)  w  SN  SL  SW  5.88 0.510 -0.230  5.79 0.777 -0.349  5.60 0.497 -0.21  -0.128  -0.185  -0.102  y  ln(a') -1.68 1.26 B B, -0.0453 B B B 0  LN  LA  7.58  6.63  -0.176  -0.182  WL 6.25 0.483 -0.260  2  3  -0.170 0.0103  7  -1.02  Y3  -1.18 0.142  Y5 Y6  0.213  Parameters according to Eqn. 4.10, ln is natural logarithm. y  Plant measures and experimental factors: T W = Dry mass of tuberous roots per plant (kg), W = Biomass per plant (kg), SN = Number of stems per plant, SL = Length of stems per plant (m), S W = Dry mass of stems per plant (kg), L N = Number of leaves per plant, L A = Leaf area per plant (m ), W L = Dry mass of leaves per plant (kg), t = Year of planting, v = Variety, X = Plant population density (plants per 1.65 m ). 2  2  "Potential independent variables that were never significant in many of the expanded allometric relationships were tvln(z), tXln(z), vXln(z), ln(v), ln(tv) and ln(tvX).  143  Appendix B2 Simple correlation coefficients among population density and various plant measures in cultivar ' B O 44T3' at the 1995 and 1996 final harvests. X  SN  SL  SW  LN  LA  WL  -0.63* -0.91** -0.77** -0.85** -0.86** -0.89** -0.95**  1.00 0.66* 0.91** 0.65* 0.61* 0.74** 0.78**  1.00 0.75** 0.79** 0.86** 0.90** 0.92**  1.00 0.67* 0.65* 0.84** 0.87**  1.00 0.97** 0.91** 0.84**  1.00 0.94** 0.88**  1.00 0.94**  -0.84** -0.36 -0.73* -0.87** -0.81** -0.81** -0.80**  1.00 0.53 0.77* 0.89** 0.90** 0.92** 0.56  1.00 0.76* 0.39 0.45 0.45 0.12  1.00 0.63 0.62 0.62 0.45  1.00 0.98** 0.98** 0.76*  1.00 0.99** 0.63  1.00 0.61  z  1995 SN SL SW LN LA WL TW 1996 SN SL SW LN LA WL TW z  n s  ns  ns  n s n s n s ns  n s ns  n s n s  n s  n s  Plant measures, abbreviations and symbols: X = Population density (plants per 1.65 m ), SN = Number of stems per plant, SL = Length of stems per plant (m), SW = Dry mass of stems per plant (kg), L N = Number of leaves per plant, L A = Leaf area per plant (m ), W L = Dry mass of leaves per plant (kg), T W = Dry mass of tuberous roots per plant (kg), ns, *, ** = Not significant or significant at P = 0.05 or P = 0.01, respectively. 2  2  144  Appendix B3 Simple correlation coefficients among population density and various plant measures in cultivar ' B O 129T9' at the 1995 and 1996 final harvests. X  SN  SL  SW  LN  LA  -0.70* -0.89** -0.78** -0.83** -0.81** -0.78** -0.92**  1.00 0.73** 0.84** 0.81* 0.79* 0.76** 0.84**  1.00 0.82** 0.81** 0.79** 0.86** 0.94**  1.00 0.95** 0.94** 0.94** 0.89**  1.00 0.99** 0.93** 0.85**  1.00 0.94** 0.82**  1.00 0.84**  -0.78* -0.59 -0.68* -0.86** -0.92** -0.90** -0.77*  1.00 0.51 0.63 0.91** 0.91** 0.88** 0.48  1.00 0.93** 0.76* 0.62 0.54 0.20  1.00 0.77* 0.65 0.58 0.33  1.00 0.97** 0.93** 0.44  1.00 0.98** 0.57  1.00 0.55  z  WL  1995 SN SL SW LN LA WL TW 1996 SN SL SW LN LA WL TW z  n s  n s n s  ns  n s  n s  n s  n s  n s  n s  n s  n s  n s  Plant measures, abbreviations and symbols: X = Population density (plant per 1.65 m ), SN = Number of stems per plant, SL = Length of stems per plant (m), SW = Dry mass of stems per plant (kg), L N = Number of leaves per plant, L A = Leaf area per plant (m ), W L = Dry mass of leaves per plant (kg), T W = Dry mass of tuberous roots per plant (kg), ns, *, ** = Not significant, or significant at P = 0.05 or P = 0.01, respectively. 2  2  145  Appendix B4 Path analysis of the relationships among aboveground plant measures and T W in ' B O 44T3' in 1995 and 1996. Partitioning of correlation coefficients ( r ) into direct and indirect effects. Plant measure X  SN  z  SL  SW  LN  LA  WL  a. 1995 growing season r -0.948** 0.783** 0.921** 0.872** 0.842** 0.875** 0.940** Direct effects: -0.046 -0.148 0.284 0.890 -0.269 1.152 -0.797 Indirect effects via: SN SL SW LN LA WL Total  0.093 -0.258 -0.683 0.228 -0.995 0.714 -0.902  -0.097 0.188 0.807 -0.176 0.702 -0.590 0.931  -0.134 0.214  0.671 -0.212 0.996 -0.721 0.637  -0.096 0.223 0.595  -0.180 0.752 -0.670 -0.018  1.115 -0.725 1.112  -0.090 0.247 0.581 -0.261  -0.109 0.257 0.748 -0.245 1.086  -0.752 -0.275  1.737  Coefficient of multiple determination (R ) = 0.95, Residual = Sqrt (1 - R ) = 0.22 2  2  b. 1996 growing season r -0.798** Direct effects: -0.014 Indirect effects via: SN SL SW LN LA WL Total  -0.743 -0.047 0.289 -3.195 -1.949 4.861 -0.784  0.558 0.883  ns  0.122 0.129  0.465 0.068 -0.303 3.246 2.161 -5.497 -0.325  -0.300 1.418 1.081 -2.671 -0.007  ns  0.450 -0.396  0.677 0.098 2.304 1.488 -3.720 0.847  ns  0.762* 3.666  0.631 2.400  0.782 0.050 -0.249  0.796 0.058 -0.245 3.581  2.345 -5.832 -2.904  -5.958 -1.768  ns  0.609 -5.980  ns  0.812 0.058 -0.246 3.575 2.391 6.590  Coefficient of multiple determination (R ) = 0.99 Residual = Sqrt (1 - R ) = 0.10 2  2  z  Plant measures, abbreviations and symbols: X = Population density (plants per 1.65 m ), SN = Number of stems per plant, SL = Length of stems per plant (m), SW = Dry mass of stems per plant (kg), L N = Number of leaves per plant, L A = Leaf area per plant (m ), W L = Dry mass of leaves per plant (kg), T W = Dry mass of tuberous roots per plant (kg), r = Simple correlation coefficient with TW,.Sqrt = Square root, ** = Significant at P = 0.01. 2  2  146  Appendix B5 Path analysis of the relationships among aboveground plant measures and T W in ' B O 129T9' in 1995 and 1996. Partitioning of correlation coefficients ( r ) into direct and indirect effects. Plant measure X  z  SN  SL  SW  LN  LA  WL  a. 1995 growing season r -0.919** Direct effects: -0.055 Indirect effects via: SN SL SW LN LA WL Total  -0.113 -0.620 -0.387 -0.407 0.371 0.293 -0.863  0.836* * 0.939** 0.892** 0.161 0.697 0.496  0.117 0.506 0.417 0.400 -0.363 -0.286 0.674  0.135 0.574  0.409 0.399 -0.360 -0.322 0.243  0.855** 0.822** 0.844* 0.492 -0.457 -0.374  0.131 0.566 0.470  0.466 -0.428 -0.351 0.396  0.127 0.549 0.464 0.489  -0.455 -0.349 0.363  -0.351 1.278  0.443* -2.663  0.575 4.666  -0.176 -0.538 0.832  -0.176 -0.441 0.703 -2.571  0.123 0.599 0.466 0.458 -0.429 1.217  Coefficient of multiple determination (R ) = 0.96 Residual = Sqrt (1 - R ) = 0.20 2  2  b. 1996 growing season r Direct effects: Indirect effects via: SN SL SW LN LA WL Total  -0.773"'* -0.087  0.483 -0.194  0.152 0.415 -0.731 2.297 -4.283 1.465 -0.686  -0.364 0.676 -2.415 4.226 -1.446 0.677  ns  0.197 -0.708  -0.100 1.009 -2.023 2.908 -0.890 0.904  ns  0.331 1.081  -0.121 -0.661 -2.048 3.033 -0.953 -0.750  ns  4.506 -1.519 3.105  -1.606 -4.091  ns  0.547 -1.636  ns  -0.171 -0.412 0.630 -2.472 4.581 2.156  Coefficient of multiple determination (R ) = 0.73 Residual = Sqrt (1 - R ) = 0.52 2  2  z  Plant measures, symbols and abbrevisions: X = Population density (plants per 1.65 m ), SN = Number of stems per plant, SL = Length of stems per plant (m), SW = Dry mass of stems per plant (kg), L N = Number of leaves per plant, L A = Leaf area per plant (m ), W L = Dry mass of leaves per plant (kg), TW = Dry mass of tuberous roots per plant (kg), r = Simple correlation coefficient with TW, Sqrt = Square root; ns, *, ** = Not significant or significant at P = 0.05 or 0.01, respectively. 2  2  147  Appendix B6 Simple correlation coefficients among population density, yield components and yield in cultivar ' B O 44T3' at the 1995 and 1996 final harvests. X  SN  z  SL/SN  LN/SL  LA/LN  TW/LA  1995 SN SL/SN LN/SL . LA/LN TW/LA TW  -0.63* -0.36" -0.13" -0.25 -0.40 -0.95**  1.00 -0.39" 0.22 ™ 0.02 -0.35 ™ 0.79**  1.00 -0.37" 0.47 -0.03 0.17"  -0.84** 0.41 -0.53 0.00  1.00 -0.38" 0.42 *" 0.28 -0.63 0.56  1.00 -0.72* 0.21 0.07 -0.50"  8  8  m  118  8  8  118 118  8  1.00 -0.62* -0.57" 0.12"  8  8  1.00 -0.16" 0.30"  8  8  1.00 -0.42  1,8  996 SN SL/SN LN/SL LA/LN TW/LA TW z  118  m  118  0.47 ™ 0.80**  8  118  n s ns  118 m  8  1.00 -0.12" -0.30" 0.70*  8  8  1.00 -0.57 -0.38  05 08  1.00 0.00  1,8  Plant measures, abrreviation and symbols: X = Population density (plants per 1.65 m ), SN = Number of stems per plant, SL = Length of stems per plant (m), SW = Dry mass of stems per plant (kg), L N = Number of leaves per plant, L A = Leaf area per plant (m ), W L = Dry mass of leaves per plant (kg), T W = Dry mass of tuberous roots per plant (kg), ns, *, ** = Not significant or significant at P = 0.05 or P = 0.01, respectively. 2  2  148  Appendix B7 Simple correlation coefficients among population density, yield components and yield in cultivar ' B O 129T9' at the 1995 and 1996 final harvests. X  SN  z  SL/SN  LN/SL  LA/LN  TW/LA  1995 SN SL/SN LN/SL LA/LN TW/LA TW  -0.71** -0.40" 0.00 -0.02 -0.23 -0.92**  1.00 -0.19" 0.24 0.08™ -0.11" 0.84**  1.00 -0.67* -0.27 0.54 0.29"  1.00 0.41 -0.76** -0.02  1.00 -0.57 -0.10"  -0.78* -0.06 -0.41 -0.44 0.30" -0.77*  1.00 -0.41 0.55" 0.07 -0.61 0.48  1.00 -0.80** -0.03 0.51 0.08  1.00 0.46 -0.43 0.42  1.00 0.30 0.72*  8  0 8  0 8  1,8  8  118  8  m  08  8  1,8  118  08  8  1.00 0.21  118  996 SN SL/SN LN/SL LA/LN TW/LA TW z  08 08 08 8  118 8  m  1,8  n s  118  n s  118  118 n s 1,8  n s  1.00 0.27  08  Plant measures, abrreviations and symbols: X = Population density (plants per 1.65 m ), SN = Number of stems per plant, SL = Length of stems per plant (m), SW = Dry mass of stems per plant (kg), L N = Number of leaves per plant, L A = Leaf area per plant (m ), W L = Dry mass of leaves per plant (kg), T W = Dry mass of tuberous roots per plant (kg), ns, *, ** = Not significant or significant at P = 0.05 or P = 0.01, respectively. 2  2  

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