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Ifiéq‘ '.¢.‘.". 5" ullllllllllll L A . 2 312.??? £12"; : 32:}; - - dissertation entitled Biomass Allocation in Ambrosia artemisiifolia L. presented by Scott Kinshelah Gleeson has been accepted towards fulfillment of the requirements for Ph.D. degree in Zoology ‘ )Qu‘:)r ‘Oég<1)‘\s ~ Major professor Date in“) 2?, (‘th MS U is an Affirmative Action/[q ual Opportunity Institution 0-12771 RETURNING MATERIALS: IV1£3I_] Place in EEOEhargp tof remove th s c ec out rom w your record. FINES will be charged if ESE-is returned after the date stamped below. nor ’35 1993 «“1. v.4, BIOMASS ALLOCATION IN AMBROSIA ARTEMISIIFOLIA L. By Scott Kinshelah Gleeson A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY W.K. Kellogg Biological Station and Department of Zoology 1986 ABSTRACT BIOMASS ALLOCATION IN AMBROSIA ARTEMISIIFOLIA L. By Scott Kinshelah Gleeson Two tapics in resource allocation are explored, the cost of height (stem) and the cost of sex (males). While quite different in many respects, these two problems share the uniquely Darwinian quality of advantage to the individual (relative fitness) at a cost to population productivity. The problem of optimal height is studied empirically, using the common ragweed Ambrosia artemisiifolia. Grown across a range of densities, Ambrosia shows a pattern of increasing height allocation (height/basal diameter ratio) with increasing competition (density of neighbors), consistent with theoretical predictions of increasing optimal height with increasing competition. This result, while statistically significant, leaves much variation in height allocation unexplained. Height allocation shows no evidence of directional selection (on reproductive output) and only weak stabilizing selection. Direct manipulation of height allocation with chemical growth regulators (gibberellin, B9) was used to test the game theory prediction that deviation from normal height allocation (in either direction) is generally deleterious to the individual, but depends also on neighbor allocation. While some of the results are consistent with the hypothesis, they could not be strongly distinguished from the alternative hypothesis of general deleterious effects of the chemicals. The cost of sex was studied in Ambrosia (a monoecious annual), as expressed in the assumption of a tradeoff between male and female function. Little evidence is found for a tradeoff in natural variation in reproductive allocation (no negative correlation of male and female output per gram). An experimental suppression of male output (emasculation), however, did result in an increase in female (seed) output, supporting the tradeoff assumption. The cost of sex in age-structured populations is explored theoretically, and it is concluded that the significance of the cost of sex for the evolution of life-histories and the evolution of sex depends on a known, the generation time of the life histories under consideration, and an unknown, the time scale of the benefits of sex. ACKNOWLEDGEMENTS Special thanks to Dave Wilson and Anne Clark for putting up with me all these years, and the rest of my guidance committee for their help - Deborah Goldberg, Sue Kalisz, Steve Tonsor, Earl Werner, and Pat Werner. Thanks also to my parents for motivation and encouragement. For help with the research I thank JoAnn Burkholder, Pam Carlton, Carmen Cid-Benevento, Claudia Jolls, and Mathew Leibold. Norm Lownds, Martin Bukovac, and Hans Kende made the growth regulator experiment possible. Tom Miller kept me in ragweed. Other members of the gang that kept me in soul food and stitches include (in rough order of appearance); Ann Hedrick, Jim Gilliam, Leni Wilsmann, Ron Gross, Don Hall, Tim Ehlinger, Robert Moeller, Alice Winn, Mike Coveney, Carol Folt, Dave Peart, Andy Sih, Marie-Sylvie Balthus, Kay Gross, Gary Mittelbach, Craig Osenberg, Rick Carlton, Rich Losee, Kathe Sharpe, Steve Kohler, Beth Kohler, Mark McPeek, Pat Crowley, and Jackie Brown. Special thanks to Wes Knollenberg for wide-ranging conversation, to Carmen for friendship, and to JoAnn for inspiration by example. Thanks also to Italy for sending Mariana. Thanks to George Lauff and the exceptional staff at Kellogg, especially John Gorentz, Steve Weiss, Carolyn Hammarskjold, Charlotte Adams, Alice Gillespie, Dolores Teller, Lou Alkema, Stu Bassett, Kath Wiest, Sandy Ford, and of course, Art Wiest. iv TABLE OF CONTENTS LIST OF TABLESOOOOOOOOOOOOOOOO0.0......OOOOOOOOQOOOOOOOOO LIST OF FIGURES.......OOOOOOOO......OOOOOOOOO0.0.0.0.0... INTRODUCTIONOO.........OOOOOOOOOOOOO......OOOOOOOCOOOOOOO CHAPTER 1. ALLOCATION TO GROWTH: AN EXPERIMENTAL STUDY OF OPTIMAL HEIGHT................... Materials and Methods................................ Density experiment............................... Chemical experiment.............................. Results.............................................. Biomass allocation............................... Height diameter ratios........................... Measurement of competition....................... Height behavior and competition.................. Natural selection on h/d ratio................... Chemical height manipulation..................... DisCUS310nooooooooooooooooooooo00000000000000.0000... CHAPTER 2. ALLOCATION TO REPRODUCTION: THE COST OF SEX IN RAGWEED............................ Materials and Methods................................ Results.............................................. DiSCUSSi-on...0.0.0.0000...I.00............OOOOIOCOOOO CHAPTER 3. THE COST OF SEX IN AGE-STRUCTURED POPULATIONS............................... The cost of sex with age structure................... Semelparity...................................... Iteroparity...................................... A more general approach.......................... The components of generation time................ D18C03810nooooooooooooooooooooo00000000000000.0000... SWYCCOOOOOOOOOOOOOOOO0....O..........OOOOOOOOOOOOOOOO APPENDIXOOOOOOOOOOOOOOO0.0.0.0000.........OOOOOOOOOOOOOOO LIST OF REFERENCESOOOOOO0.0.0000...O......OOOOOOOOOOOOOOO Page vi vii 1 ll ll 17 21 21 4O 43 51 56 58 63 69 73 76 88 92 94 96 97 99 103 110 118 120 124 Table Table Table Table Table LIST OF TABLES 1. Size distributions across time; skewness and kurt08180000...00......IO.........OOOOOOOOOOOOOCODO... 2. A) correlations of biomass allocation with biomass at each date. B) correlations of biomass allocation with date for each biomass class. (*=p<.05, **=p<.001, nssnot significant)................................... 3. Multiple regression of biomass allocation as a function of date and biomass. l correlations are significant (for all multiple r , p<.001, df-790)..... 4. Sex ratio correlations............................. 5. Results of emasculation experiments................ vi Page 23 37 39 82 87 LIST OF FIGURES Figure l. Biomass allocation decision hierarchy for a hemaphrOditic plant.......OOOOOOOOOOOO0.0.0.0...000...... Figure 2. Mean biomass per individual by date for weekly biomass harVEStSoooooooooooooooooooooooooooooooooooooooooo Figure 3. Mean biomass allocation as a function of date for weekly biomass harvests. A) root (R), leaf (L), stem (S), branch (B) and stem + branch (T) as a percent of total vegetative biomass B) male (M), female (F), and total (R) reproductive output per gram of vegetative biomass........ Figure 4. Mean biomass allocation as a function of biomass class (BIOAG) for weekly biomass harvests averaged across all dates. Class 0 = O-lg, class 2 - l-2g, ..., class 10- 10+g. A) root (R), leaf (L), stem (8), branch (B) and stem + branch (T) as a percent of total vegetative biomass B) male (M), female (F), and total (R) reproductive output per gram of vegetative biomass........ Figure 5. Mean biomass allocation as a function of date and biomass class (BIOAG), both absolute and relative allocation. A) root B) leaf C) stem D) branch E) male F) female (seed) G) total reproduction................... Figure 6. Mean height/diameter ratio as a function of date and biomass class for weekly biomass harvests............. Figure 7. Natural log of total plot biomass and mean biomass per individual as a function of 1n plot density for the nine density DIOCSOOOOOOOO......OOOOOOOOOOOOOOO0.00.0.0... Figure 8. Correlation between target plant biomass and numbers of neighbors within a circle of the prescribed radius, as a function of the radius for plants in the density plots. A) all plants from all plots B-J) for each plot separately in order of decreasing density....... Figure 9. Mean trajectories through time of nine density plots in height - basal diameter space. Trajectories are numbered in rank order of increasing plot density, and begin at the lower left on the first date................. vii Page 2 22 25 28 30 42 44 46 52 Figure 10. Mean height/diameter ratio (MHD) for each plot as a function of plot density (DEN).................. Figure 11. Mean height/diameter ratio (MHD) for each neighborhood density class (LOCLASS) as a function of naighborhOOd d8381ty C1888...oooooooooo0.0000000000000000. Figure 12. Regression estimate of stabilizing natural selection on mean height/diameter ratio for all plants in all plots. The curve is the best quadratic fit to reproductive output (male + female biomass - REP) as a function of mean height/diameter ratio (MHD) for each plantOOOOO......OOOOOOOOOO.........OOOOOOOOOOOOOOOOO...... Figure 13. Mean height, biomass, and reproductive output as a function of target treatment (averaged across neighbor treatments) for the chemical experiment. S ! short - B9, C - control, T 8 tall - gibberellin....................... Figure 14. Mean height, biomass, and reproductive output as a function of target and neighbor treatment. A) gibberellin and B) B9 (Alar) subsets of the chemical experiment. Points are target means, lines join points of same neighbor treatment. Asterisks refer to significant (*3 p<.05, ** - p<.001) target or neighbor treatment effECtSooooooooooooooooooooooooooooooo00000000000000.0000. Figure 15. Mean height, biomass, and reproductive output (yield per plant), as in Figure 14, for genetically selected height variants of rice from data given in Jennings and Aquino 1968.................................. Figure 16. Hypothetical relation between male and female reproductive output in a hermaphrodite (after Charnov et a1. 1979). Dotted line describes a perfect (linear) tradeoff, solid curve is the type of concavity required for stable hermaphroditism................................ Figure 17. Frequency histograms of sex ratio (Z seed) in Ambrosia artemisiifolia for two years A) 1981 B) 1984..... Figure 18. Correlation of male and female reproductive output in 1984 A) untransformed and B) natural log transformed... Figure 19. Sex ratio (2 seed) as a function of the natural log of individual biomass in 1984......................... Figure 20. Relation between female and male reproductive output per gram of vegetative tissue in 1984.............. Figure 21. Comparison of the seed output of all-female plants (points) with the seed output (regression line) of the hermaphrodites as a function of plant height in 1981...... viii 54 55 57 59 61 67 71 79 81 83 85 86 Figure 22. Two estimators of the cost of sex (cl, c ) plotted against generation time in years. Points are numerically calculated values for a sample of published life tables (Ballinger 1973; Charlesworth 1980a; Connell 1970; Eberhardt 1971; Hewer 1964; Hickey 1960; Murphy 1967; Organ 1961; Paris and Pitelka 1962; Perron 1983; Sinclair 1977; Watson 1970)........................................ 102 Figure 23. A) The sensitivity of generation time to perturbations in the age-specific survival (p ) and fecundity (m ) rates in a human life history {Charlesworth 1980a). B) The ”direct" (upper solid curves) and "indirect” (lower solid curves) components of total sensitivity (dashed curves)............................... 107 Figure 24. Results of greenhouse assays for chemical concentrations. GROWTH4 - height 4 weeks after treatment, chemical concentrations are in ug/liter. A) Assay #1, single doses. B) Assay #2, mixed doses. C) Assay #3, effects of B9. D) Assay #3, solid line - effects of B9 (as in C), dotted line - effects of B9 + GA........................................ 122 ix INTRODUCTION From an ecological point of view, all organisms are essentially resource gathering and transforming machines. The process of resource transformation into self and offspring is given an evolutionary interpretation by life history theory. In plant ecology, the study of this transformation process has been most thoroughly explored in the context of "resource allocation” or "biomass allocation", the _study of the allocation of the photosynthetic products to ‘various tissue types (roots, stems, leaves, seeds, etc.) This approach is based on the close correspondence between structure and function in plants, so that, for example, an increase in root tissue can be interpreted as an increase in the ability to gather soil resources. While plants are widely considered to be rather uniforni in their resource requirements (water, light, C02, nutrients), they vary greatly in their patterns of biomass allocation, both.‘within and between species. The study of this variation and its ecological and evolutionary significance is the study of biomass allocation. Figure 1 summarizes crudely the prevailing biomass allocation paradigm. Despite its huge simplifications, it is instructive in providing an overview of the ideas. The flow chart is designed to represent mutually exclusive allocation pathways as a hierarchy of 1 I I I / : Maintenance Shoot\ : \1’ / / ,___ I Resourcea\ \Leat 1 \\\\\\~ I \/Surplus I O 0 ~ I I I l l I I I I I '_ Vegetauve /Pollen \ / \ Reproducflon \ Sexual Number Seed sue ALLOCATION HIERARCHY Figure 1. Biomass allocation decision hierarchy for a hermaphroditic plant. decisions. Much of the literature is Specifically focused on one (or more) of the dichotomous choices; growth vs. reproduction, root vs. shoot, etc. Taken together the decisions form an instantaneous allocation "strategy”. One important consequence of this strategy is the acquisition of additional resources (dotted line in figure 1), which can in turn be allocated. Repetition of this process through time, initiated at seed germination, determines the plant's life history. While this integrated view underlies the research, most research has focused on particular pair-wise decisions. Useful reviews of a range of allocation topics are available in Mooney (1972), Harper (1977), Antonovics (1980), Soule and Werner (1981), Evenson (1983), Willson (1983), Lloyd and Bawa (1984), and Goldman and Willson(1986). The reproduction - growth decision has received the most intensive work, both theoretically (Williams 1966, Schaffer 1974, Schaffer and Gadgil 1975, and many others) and empirically (Harper and Ogden 1970, Gadgil and Solbrig 1972, Abrahamson and Gadgil 1973, Gaines .et a1. 1974, Ogden 1974, Abrahamson 1975a 1979, Hickman 1975, McNaughton 1975, Snell and Burch 1975, Abrahamson and Hershey 1977, Hickman 1977, Law et a1. 1977, Pitelka 1977, R003 and Quinn 1977, Sohn and Policansky 1977, Hawthorn and Cavers 1978, Newell and Tramer 1978, Reader 1978, Turkington and Cavers 1978, Weiss 1978, Brouillet and Simon 1979, Harrison 1979, Jaksic and Montenegro 1979, Law 1979, Primack 1979, Raynal 1979, Antonovics 1980, Grace 1980, Jolls 1980, Kawano and Masuda 1980, Soule and Werner 1981, Evenson 1983, Pritts and Hancock 1983, Samson and Werk 1986). Relatively less attention has been devoted to allocation to vegetative vs. sexual reproduction (Tripathi and Harper 1973, Ogden 1974, Abrahamson 1975b 1979, Holler and Abrahamson 1977, Law et a1. 1977 1979, Bostock and Benton 1979, Muller 1979, Grace 1980 ), number - size tradeoffs in seeds (Salisbury 1942, Johnson and Cook 1968, Janzen 1969, Harper et a1. 1970, Baker 1972, Smith and Fretwell 1974, Brockelman 1975, Schaffer and Gadgil 1975, Werner and Platt 1976, Harper 1977, Levin and Turner 1977, Wilbur 1977, Primack 1978) and root - shoot allocation (Monk 1966, Snell and Burch 1975, Orians and Solbrig 1977, Newell and Tramer 1978, Jaksic and Mbntenegro 1979, Tilman 1982, Bloom et a1. 1985). Virtually no work has been done on the surplus - maintenance decision, or on the decision hierachy as a whole, although there has been some desire expressed for a "whole plant" view in the recent literature (Mooney and Chiariello 1984, Givnish 1986). The research reported here concerns the two other decisions, the stem-leaf decision (chapter 1) and the male-female decision (chapters 2 and 3). These two decisions, while quite different in most respects, share one common element. From the point of view of population productivity, they can be seen as a significant cost in resources with no obvious direct benefit. For example, consider the allocation to stem in Figure 1. For allocation to leaf and root, the advantage to the plant is direct; the acquisition of additional resources. Likewise, the benefit of allocation to reproduction seems equally direct; the production of offspring. Allocation to stem, however, yields no direct advantage in growth or reproduction. Similarly, allocation to male reproductive effort can be viewed as wasteful for the population since resources spent on fertilization could potentially be used for the production of seeds (if fertilization is a problem, they could be produced asexually). Although allocation to stem has no clear direct benefit, its benefits may be indirect. The obvious indirect benefit would be increased height of the photosynthetic. surface to improve the light environment (or to reduce it for competitors). This idea has formed the basis for several recent theoretical explorations of the stem allocation issue (King and Loucks 1978, Givnish 1982, Iwasa et a1. 1984, Makela 1985). Givnish has called the problem one of “Optimal leaf height". The most general conclusion that emerges from these analyses is that optimal leaf height increases as competition increases. This intuitively reasonable prediction follows from the assumption that allocation to stem is a cost in terms of resources and. a ‘benefit in terms of increased light availability with increasing height. This positive relation between height and light availability is the result of a vertical gradient in light availability due to the interception of light by neighboring plants. The density and distribution of these neighbors determines the intensity of the gradient and thus the degree of benefit drived from an increment in height. Because this same allocation problem is faced by all plants in a stand, and the plants in the stand create the light environment, the predicted outcome must be thought of in terms of an evolutionarily stable strategy (ESS). While a particular height might be Optimal in a fixed environment, predicting what height behavior might have evolved in plants must involve defining that height behavior which when adopted by all members of the p0pu1ation is not invasible by an alternative height behavior. In chapter one, the question of optimal height is explored empirically in a study of the annual ragweed, Ambrosia artemisiifolia, In The prediction of changes in height behavior in response to competition is tested by manipulating the level of competition experienced by individual plants and observing their height response and its reproductive consequences (for an annual plant, reproductive output is the most relevant fitness measure). In addition, height behavior is manipulated directly by chemical growth regulators to examine the effects of deviations from normal height behavior. The general topic of male vs. female allocation in plants covers at least three areas; gametic allocation in hermaphrodites (Goldman and Willson 1986), offspring sex ratio in dioecious plants (Lloyd and Webb 1977, Opler and Bawa 1978), and comparative reproductive effort of males and females of a dioecious species (Putwain and Harper 1972, Lloyd and Webb 1977, Grant and Mitton 1979, Wallace and Rundel 1979, Givnish 1980, Hancock and Bringhurst 1980, Barrett and Helenrum 1981, Gross and Soule 1981). In chapter 2, the problem of male and female allocation in an annual hermaphrodite is addressed. Maynard Smith (1971) was the first to point out the relevance of Fisher's (1958) sexratio theory to male-female investment in a hermaphrodite. This prediction of equal allocation has been expanded to include situations of female bias (Hamilton 1967) and male bias (Clark 1978). Charnov (1979) presented a general graphical form which emphasizes the deviation from linearity of the male and female "gain curves". One plausible source of such deviations in plants is the degree of sex-biased sibling competition (probably due to differential dispersal of pollen and seeds) per unit cost. The important point is that unless rather special circumstances occur, roughly equal expenditure is expected on male and female function, and this prediction is independent of the level of male allocation required for pollination of the ovules. This means that competition between individual plants for reproductive success via male function can lead to substantial waste from the point of view of population productivity. This waste has been. called the ”cost of sex" (Maynard Smith 1971, Williams 1975). The most complete study of absolute allocation to male and female components in plants is Smith (1981), where a roughly equal overall allocation is reported. Other studies (Smith and Evenson 1978, Lovett Doust 1980, Gleeson 1982) suggest female-biased allocation. Several studies are consistent with the prediction (Hamilton 1967) that inbreeding (sibling pollen competition) would lead to female bias (Schemske 1978, Lemen 1980, Schoen 1982, Cruden 1977). In chapter two, the assumption that male reproductive allocation is gained at a cost in female reproductive output is tested in an annual plant. This is done by observation of natural variation and by direct manipulation of male allocation. It has been proposed (Waller and Green 1981) that the cost of sex is variable depending on the life history. Chapter three explores this proposal theoretically, and formalizes the basis and implications of this result. In summary, the research reported in this dissertation is concerned with the problem of resource allocation and fitness, concentrating on two allocation phenomena which share the peculiar and uniquely Darwinian characteristic of advantage to the individual at a cost to the p0pulation, the allocation to stem and the allocation to male reproduction. CHAPTER 1 ALLOCATION TO GROWTH: AN EXPERIMENTAL STUDY OF OPTIMAL HEIGHT. This chapter reports a study of the effects of competition on the allocation pattern of ragweed. The particular focus of study is the allocation to stems vs. leaves and its relation to competition, which has been formulated in the literature as the problem of "optimal leaf height” (Givnish 1982). The basic problem is to determine whether allocation to stem, which has no obvious direct benefit to the plant, has an indirect benefit as a result of competition with other plants. There have been several models developed which pertain to the stem-leaf tradeoff (King and Loucks 1978, Givnish 1982, Iwasa et a1. 1984, Makela 1985). While different in detail, they all are concerned with the importance of competition in controlling plant height, both proximately and ultimately. As Givnish has said, if it weren't for competition, the optimal plant would lay its leaves flat along the ground (accepting the other simplifications in the model). The reason for this claim is the basis for the height .9 10 models, that raising leaves above the ground incurs a cost in the production of stem tissue that must be repaid in improved light environment. Competition between plants for light is the factor which creates a gradient in light availability with height and the potential for an advantage to allocation to stem. The models share the prediction that increasing competition results in an increase in optimal plant height. The research reported here involves several steps relevant to the general problem. First, evidence is sought consistent with the predictions of the model with regard to the increase in allocation to height with increasing competition. The approach assumes that individual plants can vary their height behavior. Documenting this result requires both a measure of competition and a measure of height behavior. Second, variation in height behavior is examined in terms of its relation to reproductive output. Since reproduction is an important correlate of fitness, this is equivalent to measuring natural selection on height behavior (Endler 1986). Finally, height behavior is directly manipulated and its effect on competition and reproductive output measured. The important assumption in this sort of manipulation is that if plants are allocating to height in an Optimal fashion, forcing deviation from normal will result in reduced success. Two experiments are described, the first of which considers the effect of competition on height behavior by examining natural variation in the response of individuals to varying densities of neighbors. The second experiment attempts to manipulate the height behavior 11 of the plants directly using chemical growth regulators. MATERIALS AND METHODS. All data were collected in a first year old field, resulting from plowing and raking in the spring. The field is adjacent to the plant field laboratory at Kellogg Biological Station, Hickory Corners, Michigan. The first year fields are dominated by ragweed, Ambrosia artemisiifolia. The studies were conducted on pure stands of ragweed created by the removal of all other species. Density experiment. To study the effects of competition on biomass allocation, in 1984 nine 1m2 plots were established in a 3x3 grid spaced by 1m. All other species were weeded out by clipping at ground level with subsequent clipping of regrowth. Density treatments were assigned randomly to the plots. Densities were chosen to be high ‘natural density' (150 plants/m2,. three plots) and two plots each of successively lower density, approximately 120, 80, and 40 plants/m2. The densities were created by counting the plants in the plot and determining what proportion needed to be removed. Then, the plot was split into four sections by two diagonal markers and a path chosen through each section which included all the plants in that section. A thinning pattern was determined for each plot (for example, removing every third plant), and the plots thinned to the pre-determined density. One principal purpose of the plot-level 12 density treatments was to create a broader than natural range of neighborhood densities around each individual. Because of errors in counting and thinning, the final density of each plot was not exactly as intended. Thus the treatment could be seen as four or nine density treatments depending on the analysis desired. The resulting nine densities were 39, 41, 74, 87, 118, 132, 151, 154, and 155. Each individual was tagged at the base and its location mapped twice. The first map was made in the beginning of the season with a grid held above the seedlings, and the second map made on the tagged ”stumps" after the above ground harvest by covering each plot with a sheet of plastic and marking each plant on the plastic (later converted to coordinates). The second method was deemed more accurate because it avoided parallax problems, but the correspondence was very good between the two methods. All plants in the density plots were measured weekly through the growing season for basal diameter and height to the apical meristem. At the time of anthesis the length of all male inflorescences on each plant was measured. A sample of male inflorescences were harvested prior to anthesis, measured, dried and weighed individually. A regression of biomass on length was calculated for estimating the biomass of the measured male inflorescences. At the end of the season, each plant was clipped at ground level and placed individually in manila envelopes and 13 dried at 60°C and weighed. The plots were then excavated to 30 cm depth and the coarse roots separated from the soil, rinsed, placed individually in envelopes, and dried. Filled seeds were separated from the dried plant material by scraping across a number 18 (1 mm) sieve and weighed. All weights were taken to the nearest .0001 g. After each weekly measurement of the nine density plots, a nearby plot (.5 m2; .5x1 m) was harvested to 30 cm soil depth for biomass allocation measures. These plots were laid out in a 3x5 grid extending westward from the density plots, separated from each other by 1m and harvested in sequence, starting with the northern most plot nearest the density plots, harvesting that row southward and then repeating the sequence on the next row. The area surrounding the plot was hoed and the excavation begun by digging a trench surrounding the plot at a distance of 20cm. Plants were removed from this exposed core by gently tapping away the soil from the roots with a hammer and peeling each plant away from the core as it was exposed. This method was sufficient to collect the coarse roots, but underestimates total root allocation by an unknown degree. For each plant in the weekly harvest plots I measured basal diameter, height, number of nodes, length of root, length of longest leaf or branch (as a measure of horizontal extension), length of each male inflorescence (if any), and number of female flowers or seeds. A sample of flowers-seeds was obtained for 14 biomass estimate. The plants were then labeled, pressed and dried. The dried plants were separated into root, stem, branch, leaf, dead leaf, male and female components and weighed to the nearest .0001g. The term "female” is employed here to refer to female flowers or seeds, depending on the state of development. Seeds are considered female because, while they carry paternal genes, it is assumed that the purpose of allocation to seed by the maternal plant is primarily for the benefit of the maternal genes in the seed. This is an oversimplification if there is any degree of selfing or other population structure. Dead leaves remaining on the plant were separated and not included in the analysis (there is considerable leaf senescence as the season progresses). Dead leaves were excluded because while many remained temporarily on the plant, many also drOpped and could not be assigned to a particular individual. In addition, the leaves that remain on the plant wither and hang vertically adjacent to the stem and cannot be considered equivalent to a normal leaf even from the point of view of the shading of neighbors. The biomass of the plant is defined as the sum of vegetative parts, and the vegetative parts analysed as a percent of total vegetative biomass. The reproductive component is presented as grams of reproductive component per gram of vegetative tissue. The reason for choosing this convention among many possible is to see the relative amount of vegetative tissue types when compared to each other, independent of reproductive allocation. For example, if reproductive output were included and it increased with time, this would inevitably contribute to declines in all vegetative tissues. 15 Reproductive output is given per gram because of the strong effect of size on reproduction. This harvest was repeated weekly throughout the growing season for a period of fifteen weeks beginning on June 21, 1984. Each measurement/harvest involved approximately 20-30 hours and was concentrated in a 2-4 day period at weekly intervals. To assess the effects of competition on height behavior, it is necessary to first have a measure of competition. The treatment here follows the plant ecology convention of assuming that the principal effect of the presence of neighboring plants is a reduction in the growth rate and size (and ultimately survival and reproduction) of the individual of interest ("target"). There was virtually no mortality in these plots, so mortality was not considered. The density plots allow a conventional biomass-density analysis of competition, where final biomass of the plots and the mean individual biomass per plot 'are plotted against initial density (log transformed). While this approach shows the effects of competition clearly, it is a measure of mean response, and may not be the best approach when individual variation is the object of interest. One attempt to improve the resolution at this more detailed scale has been to use a restricted area around each plant and evaluate the effect of the density in this restricted area, what has been called ”neighborhood analysis” (Silander and Pacala 1985 and references 16 cited therein). A circle is drawn around each plant and a radius chosen which best explains the variation in some aspect of the target. This procedure assumes a priori that interaction is occurring. The mapping information was used in a computer program to determine a local neighborhood for each plant. To avoid circularity, final target biomass (rather than height index) was used to determine the local neighborhood. A linear correlation on untransformed biomass and local density was determined for a range of radii and the radius which produced the best fit to the data was used. Non-linear functions were not explored (although log transformation was found to not improve the correlations). Spatial distribution was also not incorporated into the function. This could potentialLy be a serious problem since plants at the edge of the plot were included in the analysis. The height and diameter data will be used to study the height allocation behavior of the plants. An ideal index would be both a good index of the cost and benefits of height (both in terms of allocation to. stem and of actual height per gram attained) and itself be independent of plant size. One index that has been used (Lechowicz 1984) is height per unit biomass. An alternative to this index, the height/diameter ratio, will be justified and employed here. Branch allocation presents a problem in this analysis. Firstly, the simple 'models in the literature do ‘not consider branching, and secondly, the contribution to height by branching 17 is ambiguous. Branches extend both outward and upward from the main axis and thus can be considered a structure for both lateral and vertical extension of the leaves and flowers. Because of this ambiguity, branch allocation will not be included in the analysis of height strategy presented here. Variation in height behavior was analysed for its effects on reproductive output. If there is individual variation in response to the same environmental conditions, it is in principle possible to deduce the fitness consequences of this variation. The method of Lande and Arnold (1983) was employed to estimate selection on height behavior (h/d ratio). In this method, some measure of fitness (here, reproductive output) is correlated with the character of interest (h/d ratio). A significant linear correlation suggests directional selection (larger or smaller values than the mean are favored), and a significant contribution of the squared value of the character in a multiple regression implies a degree of stabilizing/disruptive selection. Chemical experiment. This experiment involves the direct manipulation of plant height behavior by chemical growth regulators, and was conducted in 1985. Two chemicals were chosen, a height stimulator called GA. (gibberellic acid, GA3), and .a height inhibitor called B9 (also called Alar, Daminozide or butanedioic acid mono (2,2-dimethylhydrazide)). Both chemicals have been widely used in agronomy and horticulture to manipulate plant growth (Lang 1970).. The chemicals were applied to the 18 plants as 5 microliter droplets (dispensed with a variable volume Gilson micro-pipettor) to the apical meristem. The concentrations applied in the field were based on the results of greenhouse assays on potted seedlings gathered from the field. No surfactants were used since they have been shown to affect plant growth (N. Lownds, pers. comm.). There was a sequence of three greenhouse assays, each involving a range of concentrations of the two chemicals applied to potted seedlings collected from the field. In the first assay, there were ten replicates of each of six levels of GA (1, 5, 10, 20, 30, and 40 ug) and B9 (2.5, 15.5, 25, 50, 100, and 200 ug), and 48 replicates that were left untreated as controls. In the second assay, the same levels of CA were repeated (again with ten replications each) but each was also given a 50 ug dose of B9. The purpose of this was to find a combined dose that would be ”neutral" in its height effect to control for possible deleterious chemical effects unrelated to height behavior. In the third assay, the dosages of B9 were increased because of poor inhibition in the first assays, to a range of 0, 100, 200, 400, and 800 ug, with and without an additional dose of 10 ug GA (ten replications each - 100 plants). Plant height was recorded weekly on all seedlings for seven weeks and at final measurement basal diameter was also recorded. The chemicals were then applied to plants in the field based (n1 dosages determined from the greenhouse assays. 320 ‘plots 19 (.5x.5 m) were established in a 10x32 grid with 1m mowed alleys. The plots were weeded to monocultures of ragweed and the plants counted. The 20 plots of lowest density were discarded, 20 plots assigned to a separate staking treatment which will not be reported, and the remaining 280 plots assigned randomly to the experimental treatments. In each plot a central plant was chosen as the "target” and the remainder considered "neighbors”. There were three possible states of each target and each. group C/C > T/T > NC. The same sort of logic leads to prediction of the ranking for the B9 subset; C/S > S/S > C/C ) S/C. This is 21 similar to the GA predictions with a significant difference; the SIS treatment results in increased target success (because of reduced cost of height) relative to the control ESS. This is a key prediction because it is one where a treated target is expected to outperform an untreated target, thus contradicting the alternative hypothesis that the chemicals are merely damaging the plants in some way other than just affecting height behavior. RESULTS. Biomass allocation. Results of the weekly biomass harvests are presented in Figures 2-5. Figure 2 shows the overall mean biomass per plant for each week, and the curve is the best fit cubic equation to the points. The amount of scatter in the points may be due to a possible gradient of site quality in the field (plots harvested at weeks 1-2-3, 4-5-6, 7-8-9, 10-11-12, 13-14 were harvested along the same north-south gradient, as described in the ‘methods). Table 1 presents the analysis of the frequency distribution around the mean values, indicating that there is no significant trend in shifts in the skewness of the distribution through time. Figure 3 presents the biomass allocation as a function of date of harvest. Figure 3 shows that the percent root stays relatively constant throughout the season and that leaf allocation declines as stem and branch allocation increases. 22 mean biomass TOTBIO Oi DATE Figure 2. Mean biomass per individual by date for weekly biomass harvests. 23 Table 1. Size distributions across time; skewness and kurtosis. SKEW KURTOSIS date biomass ln biomass biomass 1n biomass 1 +1.62 -0.88 +3.14 +0.55 2 +0.56 -1.01 -0.83 +0.43 3 +1.26 -0.87 +1.88 +0.12 4 +1.38 -1.01 +3.04 +0.33 5 +1.18 -0.96 +1.16 +0.22 6 +1.35 -O.74 +1.40 +0.92 7 +1.61 —1.30 +3.20 +1.91 8 +0.94 -0.81 -0.05 -0.07 9 +4.06 -0.66 +21.00 -0.00 10 +1.61 -1.22 +2.95 +1.52 11 +0.88 -0.31 -0.09 -0.80 12 +1.21 -l.08 +0.87 +0.62 13 +0.42 -0.89 -O.48 -0.47 14 +0.86 -1.42 +0.55 +2.51 24 Figure 3. Mean biomass allocation as a function of date for weekly biomass harvests. A) root (R), leaf (L), stem (S), branch (B) and stem + branch (T) as a percent of total vegetative biomass B) male (M), female (F), and total (R) reproductive output per gram of vegetative biomass. 0.5-1 0.31 25 biomass allocation (BY DATE) 0.6‘E—M Ia’K ‘ \ Figure 3 A 0.3- 0.2-I 0.1‘ q "I J J n DATE reproductive allocation (BY DATE) est? Figure 3 B aa-dlp 26 Branch biomass does not appear until midseason. Reproductive biomass also does not begin until mid-season, when male infloresences begin to develop, followed later by female flowers which develop into seed. Together, reproductive biomass reaches 402 of vegetative plant weight at final harvest. Since plants are increasing in absolute size as the season progresses, the possibility arises that changes in allocation pattern are at least partly due to allometric changes relating to size rather than time of year. Plants were aggregated across all dates into 1 gram biomass classes (class 0 - 0-1 gram, class 2 = 1-2g, ..., class 10 - >10g), and biomass allocation plotted in Figure 4 as in Figure 3. Root, stem, and leaf patterns show similar trends in size as in time. Branch and reproductive components are present across all size classes, and increase with size. Trends in relation to size, however, are as confounded by time in this analysis (lumped across dates) as time with size. To separate the two factors, time and biomass class are plotted as two axes in Figure 5, showing absolute and proportional allocation. The trends by each date (against biomass) and biomass (against date) are described statistically in tables 2 and 3. Values in table 2a refer to the linear correlation of biomass allocation (2 root, etc.) with biomass at each date through the season. These are correlations of the raw data, but the relationships are related to the lines on the surface in Figure 5 27 Figure 4. Mean biomass allocation as a function of biomass class (BIOAG) for weekly biomass harvests averaged across all dates. Class 0 - O-lg, class 2 - 1-2g, ..., class 10= 10+g. A) root (R), leaf (L), stem (8), branch (B) and stem + branch (T) as a percent of total vegetative biomass B) male (M), female (F), and total (R) reproductive output per gram of vegetative biomass. 0.6a 28 biomass allocation (BY 8! 2E) Figure 4 A reproductive allocation (BY SIZE) maJ Ike~ /’ ~‘R ’/ 0 2+ ’R“~ // o l \ . I!” ‘R ..... R~~~~ R,»”’( 4 ”IR [I I l l 0.: x" 0.0 T l I 1 l T I F l l O 2 4 5 B 7 I I 10 IIOAB Figure 4 B 29 Figure 5. Mean biomass allocation as a function of date and biomass class (BIOAG), both absolute and relative allocation. A) root B) leaf C) stem D) branch E) male F) female (seed) G) total reproduction. l__ a O I'll" $4.11!? % LEAF .... / 7I_ a. . ~25, g ,. :2 E%KHK\ K/ ' BRANCH ’I ‘2 O s 73 BRANCH "73/ » li’l‘fi‘i‘y‘ 311' DATE h b.— REPRODUCTION ~ u 0‘ .. i H9: 0 REPRODUCTION per gram m 4"” "NV / # O i: h: “99" Table 2. d l 2 3 l; 5 6 7 8 9 10 11 12 13 14 io b 0 1 2 3 4 5 6 7 8 9 1 biomass class. ate Zroot +.04ns +.11ns -.03ns -.16ns .OOns +.29* -.11ns -.23ns +.10ns -.10ns -.31ns -.15ns -.09ns -.08ns Zroot -.05ns -.19* -.08ns -.03ns -.28ns -.27ns -.02ns -.25ns -.59ns -.74* 0 “.07118 Zstem +.03ns +.54** +.48** +.46** +.44** -.17ns +.23* +.01ns -.31* -.32* -.55** -.54** -.27ns -.59** Zstem +.76** +.79** +.75** +.61** +.29* -.09ns +.24ns +.31ns +.40ns -.66ns -.28ns 37 (*-p<.os, **-p<.001, ns-not significant). Zbranch +.56** +.78** +.55** +.85** +.90** +.75** +.82** +.85** +.69** +.87** Zbranch +.46** +.64** +.74** +.79** +.69** +.66** +.65** +.77* +.74* +.38ns +036n8 Table 2A Zst+br Zleaf +.03ns -.07ns +.54** -.62** +.48** -.46** +.46** -.35* +.49** -.50** +.22ns -.42* +.47** -.48** +.57** -.53** +.46** -.51** +.13ns -.05ns +.44* -.27ns +.23ns -.20ns +.52** -.44* -.08ns +.10ns Table 28 Zst+br Zleaf +.77* -.74** +.82** -.80** +.82** -.82** +.78** -.76** +.62** -.56** +.59* -.50* +.58* -.60* +.69* -.66* +.68* -.59ns -.49ns +.62ns +.19ns -.l6ns male/g seed/g rep/g +.33* +.19ns +.05ns +.20ns +.63** +.28ns +.31* +.44* +.22ns +.13ns -.04ns male/g +.78** +.85** +.84** +.85** +.83** +.83** +.80** +.59* +.86** +.04ns +.29ns +.46* +.07ns +.27* +.16ns -.24ns -.31* +.06ns seed/g +.68** +.62** +.59** +.73** +.83** +.78** +.80** +.76* +.81* +.79* +.75** +.33* +.19ns +.05ns +.20ns +.64** +.27ns +.32* +.43* +.07ns -.13ns +.01ns rep/g +.79** +.85** +.86** +.90** +.92** +.94** +.92** +.82** +.92* +.82* +.69** A) correlations of biomass allocation with biomass at each date. B) correlations of biomass allocation with date for each N 80 62 75 59 68 50 84 43 49 61 38 43 42 41 292 151 130 60 48 28 23 14 ll 26 38 originating at each date and traversing the surface across biomass classes. Table 2b consists of the correlations of biomass allocation with date at each size class. These analyses suggest that the trend of increasing Zstem with time applies primarily to the smaller size classes and thus results mainly from an increase early in the growing season (when there are no large plants) that levels off later. Percent leaf biomass decreases both across time and with increasing size, although the time effect is more pronounced. The percent allocation to branch is the most striking pattern, showing both an increase with time (indicating a developmental process) and also a strong increase with plant size. The apparent increase in reproductive output per gram with size disappears, and it is.clear that the effect is due almost entirely to time. Large plants are not disproportionately more successful per gram, although they are more successful absolutely. .Multiple regression of the raw data is related to the shape of the surfaces. Here, biomass allocation (2 root, etc.) is considered the dependent variable in a step-wise multiple linear regression with size and time acting as independent variables. Thus each plant contributes a value at some size and date. The stepping process first enters the independent variable which alone explains the most variance in the dependent variable. The criterion for inclusion of the second variable was that it result in a significant (p=.05) increase in the overall variance explained. Table 3 presents the results of this analysis, giving 2 the r resulting from the first step, the r2 resulting from both Table 3. Tissue Zroot Zstem Zbranch Zst+br Zleaf male/g seed/g rep/g 39 Multiple regression of biomass allocation as a function of date and bioma 8. All correlations are significant (for all multiple r , p<.001, df=790). var date date bio date date date date date r 2 1 .023 .475 .575 .636 .607 .658 .462 .736 var 2 bio date bio bio bio bio bio .667 .678 .643 .674 .468 .739 .005 .091 .042 .036 .017 .006 .003 SIOpel lepe2 int -.001 +.021 +.010 +.025 -.024 +.018 +.012 +.030 -0001 +.004 +.009 -.008 +.004 -.002 +.002 +.17 +.23 -.03 +.21 +.62 -.06 -.05 -010 40 variables (if both used), the change in r2 resulting from adding the second variable, and the slopes and intercept of the fitted surface. Given statistical significance, the slope is the informative parameter in describing trends. Only for Zstem is there no trend with biomass. Percent root, Zleaf, and seed/g decline with size, others increase with size. All parameters except Zroot and Zleaf increase with time. Height diameter ratios. This section describes the results used to justify the use of the height-diameter ratio as an index of height behavior. A relevant fact is that both height and diameter are highly correlated with biomass, and non-linearly. The highest correlations are obtained by linear regression with the cube root 1/3 of biomass (for biomass with height, r2-.75 df=794 p<.001, for diameter r2-.94 df=794 p<.001). This has several implications. First, note that diameter is more highly correlated with biomass than height is with biomass. In fact a stepwise multiple 1/3 regression of biomass with both diameter and height shows that 1/3 height adds 22 to the variance in biomass explained by diameter alone (r2=.96 df=794 p<.001). Second, since both 'height and diameter are correlated with biomass, neither alone will provide an adequate index of height strategy. Third, since height is 1,3, the index of height per unit biomass is proportional to (biomassl/3)/biomass, or biomass-2’3. I have proportional to biomass found from experience that this index can lead to many apparent 41 patterns that derive entirely from the necessary inverse correlation of the index with plant size. The simple ratio of height/diameter avoids the problem of dimensionality, and also incorporates the concept of height per unit size because of the very high correlation of diameter and biomass. It can be thought of as close to height/(biomassl/a) with the advantage of being obtained non-destructively. Figure 6 plots the mean height-diameter ratio for each date and size class. The surface suggests that while h/d increases with time, it is relatively independent of biomass. To explore this statistically, linear correlation of h/d and‘date shows a positive correlation (r2 = .50, df=794, p<.001) and correlation of h/d with biomass shows a very slight positive value (r2=.03, df=794, p<.001). Using a multiple linear regression with h/d as the dependent variable and date and biomass as independent variables, the positive effect on date is reaffirmed, but biomass now adds a new small negative component, while explaining only an additional 1% of the overall variance (r2=.51 df-794 p<.001, h/d - 1.01xdate -.13xbio + 5.0). In addition, the h/d ratio is positively related to percent allocation to stem overall (r2-.'53, df-794, p<.001). Because of the relative independence from plant size of the h/d ratio and its correlation with stem allocation, the problem of height strategy will be analysed using h/d as the index of plant height behavior. /\ a \ /v o 1N 14 3 I 2 11 N 1 42 HEIGHT / DIAMETER \ Qx’f‘v‘r l/ \ ‘M.’ .2... N ll. .' ‘7 . .0. s P III’ 1 Figure 6. Mean height/diameter ratio as a function of date an d biomass class for weekly biomass harvests. 43 7 Measurement of competition. Total biomass per plot was independent of density, despite a more than three-fold range of densities (Figure 7). However, the mean individual plant biomass is negatively correlated with plot density (r2-.93, df=8, p<.001, slope= -.99). While the log of plot density explains 932 of the variation in log of mean plant biomass, a correlation of plot density with all individual biomasses produces an r2 of only .16 (df-926, p<.001), implying that tere is a great deal of variation in biomass among plants within la plot. This result is for untransformed variables. When log-transformed, the correlation declines 3:111 further (r2-.05, df=926, p<.001). Figures 8 shows the results of neighborhood analyses. When this analysis was performed for all nine plots at once, an interesting result occurred. As shown in Figure 8a, as the radius was increased, the strength of the correlation between individual biomass and local neighborhood density improved (became increasingly negative) to a local minimum at 24 cm. But then as the radius continued to increase, after a short period of increase, the correlation again began to decline and in fact reached a minimum at a much greater radius (90 cm). At the maximum radius (approximately 142 cm, the length of the diagonal of a square meter plot), the correlation reduces to that of plot density, which« is actually a better correlate than the local 44 an 37 on g .2 ° . .o o o o. O O 01 O 2 2 r = ns 2.. . '2=.93 > ‘\ .2 1'Ii “‘~‘ _ ... ‘~‘ - slope — —1 0 \ ‘~~ .9. ~‘\ .0 ‘.‘s‘ 01 “~‘~ o . ‘~‘ - C ‘s‘ C u. r I I .l 1.6 1.8 2 242 log density Figure 7. Natural log of total plot biomass and mean biomass per individual as a function of In plot density for the nine density plots. 45 Figure 8. Correlation between target plant biomass and numbers of neighbors within a circle of the prescribed radius, as a function of the radius for plants in the density plots. A) all plants from all plots B-J) for each plot separately in order of decreasing density. ‘46 neighborhood size COR -°.°‘° ‘ .000“ " -D.133‘ -0.179- -0.2714 -0.SB4-I AJLLnimmmnm.‘ ‘-L:::.rv1vvvvvvrv 1 r I I I I I l I I i I I I I 0 to 20 30 40 50 80 70 so so 100 110 120 :30 140 180 RADIUS Figure 8 A neighborhood size PLOT DENSITY - 151 0.000J -o.o:ed ~o.osa- ~o.ose- -o.077e -o.oee- -o.1:s~ $.13!“ ~o.1544 -o.173J -0.192d -o.212- ~o.aai- -0.250 0 10 20 30 40 50 DO 70 DO 90 100 110 120 180 140 Figure 8 B o.ooo+ -o.o:s« -o.oaed -o.osa- -o.ov7+ -o.oss] -0.il!« ~o.Ias- -o.154< -o.173- -o.ssz. -o.aia- -0.231' -D 250‘ I Figure 8 C 47 neighborhood size PLOT DENSITY I 151 l I T I I 70 DO 90 100 110 120 130 140 neighborhood size PLDT DENSITY I 150 Figure 8 D I l I l l I 70 IO 90 100 110 120 130 140 d d 48 neighborhood size PLOT DENSITY - 124 0.1000‘ 0.0543“ 0.00..“ -0.0I29' .00"... ‘ -O.I743‘ -O 2200‘ O I 1 I I l I I l l I I I I I o to 20 30 40 50 so 70 no 90 100 110 120 130 140 Figure 8 E mmns neighborhood size PLOT DENSITY - 114 C09 AAAAA -O.340' I I I r I l l l I I I I l I 0 IO 20 30 40 50 60 70 DO 90 100 110 320 I30 140 Figure 8 F 49 neighborhood size PLOT DENSITY - O7 COR 0J4- -o&aa +—¥/7—+ -mmc+ ' j\\\‘ -0.114\’ ”I I I I‘ I I I I I I r’ ”“r""‘T“"'“T o to 20 so 40 so so 70 no no 100 110 120 130 140 Figure 8 G neighborhood size PLOT DENSITY - 7O COR 0.000 -0.0dl -0.007 -0.145 -0.193 -0.242 I I I I II I I I I ‘II I I I I I o to 20 30 40 so so 70 no 90 too 110 120 :30 :40 moms Figure 8 H ' -o.2:s~ con 0.314 0.2a- 0.2:- o.:a- 0.x:- o.osj o.o:« -o.04- -0.00~ -0.144 5() neighborhood size PLOT DENSITY - 40 W» Figure 8 I COR 0.000- -0.047q -0.0944 -0.!41j -o.:oaJ -0.202- -0.329‘ -0.370~ -0.4234 d I -o.47o I I I I I I I I I I 50 60 7o 60 90 100 110 $20 130 140 RADIUS neighborhood size PLOT DENSITY - 39 —+—-+ Figure 8 J -1 d d _ '1 q l 1 T I T 40 50 60 70 DO 90 100 110 120 130 140 51 minimum at 24cm. Suspecting that the local minimum reflected a neighborhood effect and the larger one a plot effect, each plot was examined independently for Optimal radius. As shown in Figure 8(b-j), individual plots showed, in general, the anticipated pattern, with a single minimum radius range and poor correlation at small and large radii. The mean of these best neighborhood sizes, weighted by plot (each plot value weighted equally) or individual (each plot value weighted by plot density), was approximately 18cm, and this was the value chosen as the measure of local competition. Height behavior and competition. The effects of plot density can be seen by plotting the trajectories of the mean plant in each plot in height-diameter space (Figure 9). The trajectories are labeled by numbers which correspond to the rank order of density for each plot (1- lowest density,etc.). Trajectories begin at the lower left on the first date and extend upward through the season. The upward curvature of each trajectory reflects the increase in h/d ratio with time found in the biomass allocation data. There is some indication of an. effect of’ density' on the trajectory, with plants at lower density putting on diameter at a faster rate for a given height than plants at higher density, but the pattern is not completely clean. In particular there seems to be a limit to variation in response, where above a certain density (roughly 75 plants/m2), the trajectories are similar. Height (cm) - 52 5C>- 3 ‘40- :30- 2C}- 10-4 Basal Diameter (mm) Figure 9. Mean trajectories through time of nine density plots in height - basal diameter space. Trajectories are numbered in rank order of increasing plot density, and begin at the lower left on the first date. 53 To analyse the height-diameter in relation to competition I decided to aggregate the weekly h-d into an overall h/d ratio for each individual. This has the advantage of integrating the h-d information throughout the season and also minimizing the effects of errors in measurement on any given date. This average was taken in two ways, as the ratio of the average height over the average diameter, and the average of the height/diameter ratios. These two measures turn out to be essentially identical (and both are well correlated with h/d at the end of the season), and the measure used was the mean of h/d ratios for each individual. This mean individual h/d ratio (across the season) will be referred to simply as the individual h/d ratio). The individual h/d ratio was used in two ways to analyse the effects of density on height behavior. First, using plot density as the index of competition, individual h/d ratio was correlated with plot density, yielding r-.l3 (df-953, p<.001). This relationship is illustrated in Figure 10, with. the ‘h/d ratio averaged for each plot. Second, The individual h/d index was correlated with local density as determined from the map analysis. The correlation of h/d ratio and neighborhood density is r'.l7 (df8952, p<.001). The trends are plotted in aggregated form (density classes in steps of ZS/mz) in Figure 11 to make the relationship more apparent. Neighborhood competition is given in units of plants/m2. The trend with local density is somewhat smoother than plot density, and theme is some indication of an 12 11 10 54 h/d and plot density I I I I I I I I I I I I 40 50 60 70 BO 90 100 1 10 120 130 140 150 DEN Figure 10. Mean height/diameter ratio (MHD) for each plot as a function of plot density (DEN). - T 180 I n A L L A A A__L_ n_l‘m A kl A g; 1 55 h/d and local density 'W‘W'Trrlfi m‘ 1'I-rrvarrr'1-rrrr1-rrrrrrn-fi'n-r‘rT-I'I-I'fi-I-ITITI TI 1' [’1 I rrnw f'l‘T‘TfiT 2 3 4 5 B 7 O 9 10 LDCLASS Figure 11. Mean height/diameter ratio (MHD) for each neighborhood density class (LOCLASS) as a function of neighborhood density class. 56 upper threshold. Natural Selection on h/d ratio. This section examines evidence that variation in h/d ratio is related to variation in reproductive output. This is essentially asking, is there phenotypic selection (directional or stabilizing) on height behavior? Using reproductive output (sum of male and female biomass) as a measure of success, one can apply the method of Lande and Arnold (1983) to these results. This simple method assumes that directional selection is revealed by a linear regression of relative fitness on a measure of the character, and that stabilizing/disruptive selection is indicated by a significant quadratic term in a multiple regression. This definition of stabilizing selection is based on changes in the variance only (some prefer to call this variance selection, Endler 1986). Thus, a population can be undergoing both stabilizing and directional selection simultaneously. For the data as a whole (lumping across plots) the regression analysis shows that there seems to be no significant directional selection but some degree of stabilizing selection (in multiple correlation, r-.l9, df-876, p-.006). This trend is illustrated in figure 12. However, breaking the data down by density treatments (four density levels, approximately 40, 80, 120, ISO/m2), there is again no evidence for directional selection at any density level, but in addition there is no significant evidence for stabilizing selection at any density level. It seems likely that this is due to the reduced 57 reproduction by h/d Figure 12. Regression estimate of stabilizing natural selection on mean height/diameter ratio for all plants in all plots. The curve is the best quadratic fit to reproductive output (male + female biomass - REP) as a function of mean height/diameter ratio (MED) for each plant. 58 sample size at each density level, and suggests that the overall result is probably weak. This analysis was performed separately on male and female reproductive output both overall and for each density level and the pattern was the same for each as for the sum of both, no directional selection and significant stabilizing selection only for the data as a whole (for seeds, r=.l8, p<.001, df=897, and for males, r=.20, p<.001, df=892). Chemical height manipulation. The results of the greenhouse assays are given in the Appendix. The results of the field experiment are sumarized in Fig 13. The overall effect on the target shows that the treatments were effective, the GA. and 39 plants being taller (F=ZS.9, df=l75, p<.001) and shorter (F=23.l, df=l76, ‘p<.001), respectively, than the control. The B9 plants were also lower in biomass than the control (F=10.2, df=l72, p=.002) and the GA plants not significantly different from the control (F=0.62, df=l78, p=.431). Reproductive output (sum of male and female) was lower for both chemical treatments, significantly so for B9 (F814.8, df=l77, p<.001) but not for CA (F-2I9, df-l77, p-.092). The effect of the neighbor treatments is analysed by analysis of variance on two subsets of the experiment in Figure 14. The subsets were chosen because in a sense two separate experiments were done, one on the effect of GA and one on the effect of 89. For the GA relations, we see that it is still true that treated targets are significantly taller (F=18.8, df-135, p<.001) and in 59 Ragweed - Target Response height(cm) biomass(g) reproduction(g) 5°‘ #- 8‘ + + 4i + r'l- 6' 3- r . '" 4- 2- +' + m 2' 14 s c I s o T s c T Treatment (Short, Control, Tall) Figure 13. Mean height, biomass, and reproductive output as a function of target treatment (averaged across neighbor treatments) for the chemical experiment. S . short - B9, C - control, T - tall - gibberellin. 60 Figure 14. Mean height, biomass, and reproductive output as a function of target and neighbor treatment. A) gibberellin and B) B9 (Alar) subsets of the chemical experiment. Points are target means, lines join points of same neighbor treatment. Asterisks refer to significant (*= p<.05, ** - p<.001) target or neighbor treatment effects. 61 Ragweed - Gibberellin height(cm) biomass(g) reproduction(g) 60W 50" T \ ”K 74 \T 3‘ 40- C 5‘ 24 C I I T l l 1 Control. Tall C T C * T ' it if Target Figure 14 A Ragweed - Alar (inhibitor) height(cm) biomass(g) reproduction(g) 84 4_ 4o 6- 3. 30" S C C j . 4 2 S ' c é C I Control Short 4‘ §<¥ i6 *6 Target Figure 14 B 62 this case also significantly lower in reproduction (F84.12, df=137, p-.044) and non-significantly lower in biomass (F=I.9l, df=138, p-.169) than controls. If the neighbors are treated, the target is significantly taller (F=8.5, df=135, p-.004) and non-significantly larger in size (F-l.46, df=138, p-.229) and reproductive output (F-1.00, df=137, p=.3l9). In the B9 analysis, again the treated targets are significantly shorter (F819.3, df=136, p<.001), lower in biomass (F-S.7, df=133, p=.018)and lower in reproduction (F88.4, df=137, p-.004) than controls irrespective of neighbor treatment, and neighbors had no significant effects. There were no significant interactions in these analyses. The ranking of reproductive output was as predicted for the GA subset (3.92 > 2.87 > 2.55 > 2.07) but not for the B9 subset of the experiment (3.7 > 1.9 not > 3.1 > 2.3). Most notably, the case where the treated target was expected to exceed the untreated target (S/S > C/C) was not produced. Finally, a characteristic was noted on some of the plants during data collection which consisted of a greying of the apical meristem and lack of growth. Suspecting an adverse chemical effect, the trait was noted and later checked for treatment. It turned out that of 30 plants recorded as ”tip grey", one was a GA treatment, 29 were B9 treatments, and none were controls. This suggests a deleterious effect of B9 on meristem growth, at least in some plants. 63 DISCUSSION The seasonal growth pattern of Ambrosia is described by the biomass allocation results. After germination there is a period of vegetative growth which consists of the addition of segments of stem (internodes) with leaves at each node. When most of the height of the plant is attained at mid-season, branching may occur at each node. This branching is quickly followed by the initiation and development of male inflorescences and eventually female flowers and seeds. The absolute amount of any tissue type in a plant, including reproductive structures, is strongly and positively determined by plant size. The relative amount of each tissue type, however, is relatively independent of plant size, with one notable exception; branches. Not only does the absolute amount of branch biomass increase with plant size, but the proportional amount also increases. 'Lf it is assumed that size reflects competitive status in a plot, this result suggests that dominant plants in a stand allocate their above-ground biomass differently than suppressed plants, showing lower height per unit biomass. This result indicates that Ambrosia may be capable of altering its growth form in response to ‘competition in an adaptively plastic way consistent with the theoretical predictions of Givnish (1982) and Iwasa et a1. (1984). The goal of this study was to determine whether plants adjust their allocation to stem (i.e. height) in response to competition 64 in a way that can be interpreted as advantageous to the individual plant. Three results were relevant to this problem, and will be discussed in turn. First, as predicted by theory, plants tended to be taller for a given biomass when grown at higher densities. This result was consistent with the theoretical expectation, but it must be noted that the effect was not dramatic, or at least there was a huge amount of variation in the measure of growth form (mean height/diameter ratio) left unexplained. This could suggest that either the theory is relatively unimportant in understanding growth form, that Ambrosia lacks adaptive plasticity in this character, or that the measures of growth form and/or competition were flawed. Second, the consequences of this variation in growth form to reproductive output was assessed. This analysis suggests that there is no evidence that types that deviate from the average type reproduce more that the mean type (no directional selection). This fact could mean either that the population is at an optimum, that there is opposing directional selection on another correlated character, or that there is no directional selection on the character. The significant non-linear term in the analysis, however, is consistent with the hypothesis that the p0pu1ation is behaving optimally, since the extreme types reproduce less than the more average types (stabilizing selection). However, when broken down by density treatment, there was no evidence for 65 stabilizing selection. Overall, the main problem with this result even if considered statistically significant is that it does not provide a causal test, since both characters (growth form and reproductive output) could be controlled by' some lather, unmeasured, character (Lande and Arnold 1983 discuss this and other problems). Third, because of the uncertainties of this approach, height behavior was directly manipulated and its reproductive consequences measured. It was found that plants that were forced to grow either taller or shorter than they would have without manipulation, reproduced less than 'unmanipulated plants. While consistent with the prediction of Optimality, this result is also consistent with the hypothesis that the chemical treatments had some general deleterious effect beyond control of height behavior. In fact, there was direct evidence that the inhibitor, B9, did have detrimental effects on the meristem. This deleterious effect meant the loss of a crucial treatment, where a chemically treated plant was predicted to do better than an untreated control. Looking only at the GA subset of the experiment, the results were consistent with the hypothesis in terms of the ranking of the reproductive success, but the neighbor effects were much weaker than the target effects. As a result, the overall conclusion must be that while the null hypothesis of no treatment effect is rejected, the important alternative hypothesis of deleterious chemical effects could not be decisively ruled out. 66 The problem of reduced reproduction resulting from allocation to stem tissue has been an important one to agronomists for some time, and is in fact a significant aspect Of the ”green revolution" (see Donald and Hamblin 1985 for a recent discussion), where, in addition to the benefits of irrigation and fertilization, plants were bred with the conscious intent of producing individual plants that would perform well as a group when grown at high density in monoculture. 30 called ”ideotypes” were conceived for' each. species, a frequent characteristic: of which was shorter stature. An example of this line of research is that Of Jennings on tropical rice, from which the results in Figure 15 derive (Jennings and Aquino 1968). In this experiment, the short line was produced genetically by artificial selection rather than chemically, and the plants grown in a checkerboard designs Otherwise, the experiment is directly comparable to the B9 portion of the design presented here, and the results support the Optimal height hypothesis. The term ”yield" here refers to the seed output of the target plant (which is equivalent to a yield because each plant occupies a fixed area). The highest yields are produced by the tall plants growing ‘withi short neighbors, as expected, but the highest yield of a monoculture was found to be short plants growing together. It cannot be stressed enough how difficult it is to produce and maintain maximally productive monocultures, since individual selection is constantly Operating to undermine the maximization of group productivity. A breeder, for example, that simply takes seed from the most productive plant in the field, a seemingly rational behavior, will utterly fail to 67 Rice - Selection (Jennings and Aquino 1967) height(cm) biomaSS(g/SQM) grain Yield (tlha) 200- 2000' 10. \ s \ s 150‘ 1000‘ 5. T T S 100' T 0-! ‘ 0- | [*~ I I l ' Tall Short T S T 3 Target Figure 15. Mean height, biomass, and reproductive output (yield per plant), as in Figure 14, for genetically selected height variants of rice from data given in Jennings and Aquino 1968. 68 select for the Optimal type for total yield. Of course, for some crops, like sugar cane and trees, stem tissue is the Object to be maximized. Interestingly, this is one crop which is routinely subjected to spraying with gibberellins. CHAPTER 2 ALLOCATION TO REPRODUCTION: THE COST OF SEX IN RAGWEED. Interest in the sex ratio of dioecious species extends at least from Fisher's (1958) insight that if the cost of an offspring is independent of its sex, then the primary sex ratio will evolve to 1:1. Interest in the investment to the male and female functions in hermaphrodites began relatively recently when Maynard-Smith (1971) noticed that the same principles apply. Hermaphrodites provide a particularly valuable subject of study in this regard because variation in sex, or gender, allocation is unlikely to be constrained by chromosomal sex determining mechanisms. The issue of sex ratio is inextricably bound up with that of the ”cost of sex" (Maynard-Smith 1971), which is the reduced fecundity of a sexual p0pu1ation or lineage relative to an Otherwise similar asexual species. This cost is due to the expenditure by the population on male reproductive output, the pursuit of fertilization. When the population sex ratio is 1:1 this is a 502. reduction in potential fecundity. An important 69 70 assumption here is that there is a perfect tradeoff between the male and female reproductive output (either to Offspring of different sexes or to gametes in a hermaphrodite). If the tradeoff is not perfect then different expectations arise. The nature of the tradeoff between male and female output is particularly important to examine in hermaphrodites because sex ratio theory predicts that hermaphrodites should evolve only when the tradeoff is not perfect (Charnov et a1. 1979). The condition required for the evolution of hermaphroditism is depicted graphically in Figure 16 (taken from Charnov et al. 1979). Here male and female reproductive output of a hypothetical individual are plotted as Opposing axes. The assumption of a complete tradeoff between the two leads to a linear constraint curve connecting the points of maximum male (zero female) and female (zero male) output. The intuitively reasonable theoretical result is that for hermaphrodites to be more than neutrally stable invaders of a dioecious population, the constraint curve must have some degree of outward bowing (downward concavity), so that the total potential reproductive output (sum of male and female) is greater for the hermaphrodite than for either single sex, at least over some range of reproductive output. This framework ignores an important aSpect of reproduction in plants, the size dependence of reproductive output. Since larger plants can produce both more male and female Output, one might expect that, contrary to the hypothesis of Charnov et al. (1979), 71 THEIX FEMALE 0 max MALE Figure 16. Hypothetical relation between male and female reproductive output in a hermaphrodite (after Charnov et al. 1979). Dotted line describes a perfect (linear) tradeoff, solid curve is the type Of concavity required for stable hermaphroditism. 72 there should be a positive correlation of male and female output. The simplest way to resolve this difficultly is to restrict the application of the hypothesis to plants of the same size, i.e., to control for size effects in the analysis. An additional dimension of the problem is thus raised; is there an effect of size on the relative allocation to 'male and female output, or, does size effect sex allocation? Any pattern of this sort could potentially interfere with the detection of a tradeoff between male and female output if for some reason this relationship were to vary with plant size. This tOpic has recently received a detailed review and theoretical analysis (Lloyd and Bawa 1984). This study was directed at two aspects of the problem of sex allocation. First, is there a pattern in variation of sex allocation with size and second, is there evidence for a tradeoff between male and female function as assumed by the theory? Evidence for the tradeoff assumption is sought both in natural variation in allocation and with an experimental manipulation of allocation (emasculation). The reduction of allocation to one sex might be expected to result in an increase in the other sex if reallocation of resources is possible. Ambrosia artemisiifolia is a relatively good subject for the study of sex allocation since it is an annual, monoecious, wind-pollinated plant.‘ This means that the lifetime reproductive output of male and female functions can be measured. Problems of survival-fecundity tradeoffs, sexually ambiguous structures 73 (nectar, eg.), pollinator behaviors, not to mention all the difficulties of measuring investment in animals, can be minimized. MATERIALS AND METHODS All data were collected in a first year old field adjacent to the plant field laboratory at Kellogg Biological Station, Hickory Corners, Michigan. The fields are created by plowing and raking each spring, and are dominated by annuals, particularly Ambrosia artemisiifolia. The work was done on pure stands of A, artemisiifolia created by removing all other species early in the season. The goals of the methods presented here are to measure male and female reproductive allocation, to examine the relation of reproductive allocation to other plant and plot characteristics, and to manipulate allocation to male function and measure the resulting effect on female allocation. All biomass estimates refer to dry weights. Male output was defined as the total biomass of male inflorescences, which was measured non-destructively by measuring the length of each inflorescence and calculating biomass by a length - biomass conversion factor. This factor was calculated in two years (1981, 1985) by harvesting a sample of male inflorescences just prior to anthesis, measuring length, placing individually in plasticine envelopes, drying, and weighing to the 74 nearest .0001g. Female output was defined as the total biomass of filled seeds at final harvest. One problem in measuring seeds due to the temporal variation in seed production. Seeds are initiated and matured at different times and rates, both within a plant and between plants. It is necessary to choose one date for seed harvest, leading 11) a possible underestimate of seed production due to pre-harvest seed drop or post-harvest seed maturation. The adequacy of the harvesting method was checked by marking paired branches on a sample of plants, bagging one branch and harvesting the other. This was done for the pre-harvest seed loss by bagging after anthesis but before significant seed development and harvesting bagged and unbagged branches at the time of harvest. For the post-harvest loss, one of a pair of branches was bagged at the time of harvest of the adjacent branch and left on the plant for an additional month. Comparison of seed production of the bagged and unbagged branches indicates if all 'potentially developing seeds were counted. Whole plant reproductive output was measured in two samples. One sample is Of 313 plants from 1981 measured for height and reproductive output in a single belt transect .5m x 4m. The other is of 870 plants from 1984 grown in a range of densities in nine 2 1m plots (plants from the density experiments described in chapter 1). 75 Natural variation in sex allocation was investigated for evidence of a tradeoff between male and female function. Since both male and female output are highly correlated with total plant biomass (see results), male and female Output per gram of plant were tested for a relationship. This could only be done with the 1984 data since biomass was not measured in 1981. A multiple regression of seed, male, and biomass was also done. In addition, there is a small fraction of plants which are entirely female, a trait which has been demonstrated to have a genetic component (Gebben 1965). The seed output of a collected sample (n=8) of these very rare types was obtained from a systematic search of the field in 1981, and compared with the production in the p0pu1ation as a whole. The existence of a tradeoff between male and female reproductive output was tested experimentally by exploiting the fact that male production occurs prior to female production, since pollination precedes seed development. In two years (1982, 1983), male inflorescences were removed (by pinching) in the bud stage (and checked weekly) to prevent allocation to ‘male function. Since this allocation occurs prior to seed development, prevention of male allocation potentially releases resources that can be used to increase seed production. 1&1 the first year (1982), this experiment was done in two versions 1)the ”paired branch” and 2) the "whole plant” removal. In the paired branch removal, pairs of adjacent branches were selected and one branch emasculated and the other unaltered. In the whole plant removal, plants were randomly 76 assigned as control plants or emasculated plants from which all male buds were removed. Seed production was measured at harvest for both treatments. In the second year (1983), the experiment was repeated with larger sample sizes and a third treatment was added to the whole plant experiment. This was an additional emasculation treatment done after the male inflorescences developed but before pollen was shed. RESULTS The male conversion factors were comparable between the two years (1981 and 1985). The factor used was the mean biomass per unit length (g/cm). The values obtained were .01 g/cm (1981, sd==.005, n=169) and .01 g/cm (1985, sd=-.002, n-76). The value used here to estimate male allocation in 1981 and 1984 is .01 g/cm. The test for pre-harvest drop indicated that underestimate of seed production probably does occur, since bagged branches yielded significantly greater number (mean(sd) of 28.4(18.4) vs. 19.1(13.7), n=66, F=10.8, p=.001) and biomass (mean(sd) of .12(.07)g vs. .08(.06)g, n=66, F=l4.8, p=.000) of seeds than unbagged branches. Post-harvest drOp, however, did not seem to be a serious source of error, since bagged branches did not show significantly greater numbers (mean(sd) of 18.5(15.8) vs. 18.8(17.8)) or biomass (mean(sd) .06(.05)g vs. .06(.06)g) of seeds by one-way ANOVA (N=88). Measures of reprduction presented here 77 have not been altered to compensate for these errors, but if desired, modified sex ratio can be calculated as follows; if seed production is multiplied by a factor x, then the new sex ratio is given by x/(l + (sex ratio)(x-1)). Figure 17 shows the distribution of sex ratio (defined here as the percent of reproductive biomass allocated to seed) for the two samples. The distributions are rather similar, with means of .43 and .37 and standard deviations of .19 and .16. For the 1984 data it is possible to examine the relation of sex ratio and aspects of plant size and density. First note that there is a strong positive relationship between plant size and male and female reproductive output (for seed and biomass, r=.92, p<.001, df=889, and for male and biomass, r=.92, p<.001, df=882). As a result of this relationship, there is a strong positive correlation of male and female output for the p0pu1ation as a whole, as illustrated in Figure 18 (r=.85, p<.001, df=876, seed = .75 x male + .006; log transformed, r=.90, p<.001, df=826, 1n seed = 1.13 x ln male - .44). Chapter 1 documented the negative relationship of plant density and individual biomass. Analysis of the density plot data (see Table 4) shows sex ratio (2 seed) to be correlated negatively ‘with plot density’ and with neighborhood density and positively with individual biomass, diameter, height, and the across-season mean h/d ratio. The relation of sex ratio and In biomass is plotted in Figure 19. The data from 1981, however, show no significant relation of sex ratio and height. 78 Figure 17. Frequency histograms of sex ratio (Z seed) in Ambrosia artemisiifolia for two years A) 1981 B) 1984. 1901 79 dexxflxamflyfiua .usafiufluNufic ). . . .L./ ..x ...... I. - . ..). . I a. \.a . l . V .I I K n yxsuvrnyyzaxgyw, ;.www.xxt ruNVDKV.NWVAVvKDUNV,.§: a . UhYLNKu 1984 ~‘ A“ I ‘A ”M ‘ "H I n“ «u . / . I C& . I a. , . o u. I . I u I H \. . x , N\.4H;I.l\-(¢LI\ ”If. \ 11(\ IIIKHK ./\ \u.l..\\.,,-KII.' .A . \ Y . "%wwmwmvwkfiw...ukwtunia.x PFEM NIDPOINT sex ratio (7. seed) FREOUENCY 7O 50 40 0.05 0.15 0.25 0.35 0.45 0.55 0.05 0.75 0.55 0.05 PFEN NIDPOINT Figure 17 A sex ratio (3% seed) FHEOUENCY 18‘s .‘T‘vi. 1'11.“ I-‘I‘II 111111-11] 300 o o :- 100 0.05 0.15 0.25 0.35 0.45 0.55 0.55 0.75 0.05 0.95 Figure 17 B 80 Figure 18. Correlation of male and female reproductive output in 1984 A) untransformed and B) natural log transformed. 81 seed vs. male seen 9- + 8" 7. 6-. + + 5‘ + + * + 4‘ + + + + * + + "+ + + ... 34 + * + ... '7: 4» 4+4. +1 + + + i +T++++* + + a + + + + + rtwfifigt + + 1 + +¢++1 + + .. + + '4' £4- + + + ++ o fiWWMTm-mm'fi‘ "1'fi11meW‘TT‘T‘V—T—rmT o 1 2 3 4 5 s 7 5 MALE Figure 18 A In seed vs. 1n male LNSEED 3. 3' + +/ " I o. -1- -2- _3- -4« + -6- -6‘ + —7 I l l I l I l l 1 fi' -7 -s -s —4 -3 —2 —1 o 1 a LNMALE Figure 18 B 82 Table 4. Sex ratio correlations. variable .5 £- g£_ slope intercept 1984 local density -.12 (.001 869 -.0003 .403 biomass .32 (.001 863 .0089 .324 ln biomass .50 (.001 863 .0619 .312 diameter .41 (.001 853 .0465 .213 height .42 (.001 868 .0038 .216 h/d .15 (.001 869 .0100 .262 1981 height -.07 n.s. 311 - - £33 sex ratio vs. size SEXRATIO 1.0+ + 0.91 . - + + + o a + + + 0.7‘ + ++ 44' ‘t + +r$++ '7'?“ + o_54 + 4'? 4+ .19, + # / +‘H-+ 4.41:. + ‘3‘ - “PF“- / + 005-4 + +H +% +-- .3!“ *aj'.' ’:+ + + -i”~'jgdyu'!‘*:?- ++gpt o 4. + +3 + .. limit: .m'g‘dw " . ++ .+* . . ‘ + nix. '-"(A' ' ‘ m ++ + ... 4: e + #- '+*‘ -2\n' 4+ 0 24 +¥¥pu¢ + ++t++++fifi ; ++ + ++ ++++ o 14 +4.: ++$+ ++ + on. +mHmHunsi++flhfi I U I l T -5 -4 -3 -2 -1 o 1 2 3 4 5 LNBIO Figure 19. Sex ratio (2 seed) as a function of the natural log of individual biomass in 1984. 84 Evidence for a tradeoff of male and female output was sought by plotting male and female output per gram of plant for the 1984 data in Figure 20. There is no significant linear relation between allocation to male and female output, but there is a significant quadratic relation (r=.21, df=869, p<.001). To analyse the seed output of the sample of all-female plants in 1981, first note that there is a positive correlation of seed output and height, the only measure of plant size in that year, for the population as a whole (the correlation of seed output and height is significant for the pOpulation, r-.69, df=365, p<.001, the equation is ln(seed biomass)= .073 x height - 5.52). Comparing the seed output of the all-female plants with the rest of the population (Figure 21), there is no clear tendency for differences. All-female plants show no tendency to produce more seeds that the general hermaphroditic population. The results of the emasculation experiments are shown in Table 5. In 1982, in the paired branch experiment, emasculation significantly increased seed number and size, but in the whole plant experiment only seed size increased. This pattern was not replicated in 1983 with larger sample sizes, with total seed Output increasing in both the paired branch and whole plant removals, and the increase apparently coming entirely from an increase in seed number (seed size did not change). The late emasculation was intermediate between the control and early 85 female/g vs. male/g rm 0..” + ... ... ... 0.1142 + + T + + +++++++ “T, ++ + t + ‘9' + + «t 0.103 ++ 4’ *Ifl- ++-'- + + 411'" I + !$#*+ + + +. . » , .1 . f + + + + +44. _ #€:* &£ ++ +* 0.145 iii-1.5: +V:- - t 4* + +7" + + .. I.' .- ’4 -" T + * + ' .l ’ .0 + - “gist 4L“ + * + + + 44 +1 '0 + + II- t + ++ + 0.040 Jet. 4’ ++¢+W$M+ 7‘1}... + {’1 + + t *1 ‘- +¢++*t++: ++ + .. ... ¢++++++f§3+ 1, :+ +4- + + + 0.000 ++ 4+4:- 4++H++I+ 4» «III flwfin +* + T— T T I I 0.000 0.047 0.093 0.140 0.107 0.233 0.1300 0.327 0.973 0.420 Figure 20. Relation between female and male reproductive output per gram of vegetative tissue in 1984. Ln TOTAL SEED BIOMASS 86 PLANT HEIGHT (cm) Figure 21. Comparison of the seed output of all-female plants (points) with the seed output (regression line) of the hermaphrodites as a function of plant height in 1981. 87 Table 5. Results of emasculation experiments. seed no. biomass wgt/seed 1982 Paired branch Control(n=26) 16.8 .05 .0030 Emasc.(26) 27.4 .09 .0034 P .002 .001 .015 ‘Whole plant Control(42) 196.7 .67 .0034 Emasc.(46) 210.3 .83 .0039 P n.s. n.s. .012 1983 Paired branch Control(108) 41.2 .140 .0031 Emasc.(108) 60.1 .212 .0031 P .002 .006 n.s. Whole plant Control(93) 149.6 .479 .0030 Emasc.(67) 280.0 .794 .0029 P .0001 .001 n.s. Late emasc.(70) 239.3 .726 .0031 P (vs cont) .001 .005 n.s. P (vs emasc) n.s. n.s. n.s. 88 emasculation, but significantly different only from the control. DISCUSSION Ambrosia artemisiifolia shows considerable variation in sex allocation within populations. It is likely that this measured variation has a number of sources, such as various artifacts and errors of measurement, the uncertainties of pollination, and fluctuations in conditions between the times of male and female allocation. However, the data from 1984 do suggest there may be one intrinsic source of variation, the effect of plant size, with larger (as measured by biomass, diameter, and height) plants tending to show increased relative allocation to seed production. Effects of competition (density) are significant but weaker and negative, suggesting that its effect is an indirect one, resulting from the effects Of competition on size. It is difficult to dismiss this result , but it must be considered a tentative one, since another substantial sample from a different year (1981) shows no relationship between sex ratio and size (as measured by height). Other studies of this genus show similar overall lack of ordered pattern to sex allocation pattern. McKone and Tonkyn (1986) found for Ambrosia artemisiifolia that height was positively correlated with maleness, the opposite of that found in this study, in some but not all of their experiments. Abdul-Fatih and Bazzaz (1979) found that the percent of plants with male 89 flowers declines at high density in Ambrosia trifida. This result is widely cited as evidence that sex ratio shifts with competition or size. In fact, without the parallel seed data, no such conclusion is justified (nor do the authors claim it). Lloyd and Bawa (1984) have recently thoroughly reviewed and analysed the problem of the relation of plant size (or ”status", a word which also incorporates the element of competition, or relative size) and sex allocation in hermaphrodites. Their paper contains a detailed review of data across a broad range of taxa, but just as importantly it contains the first quantitative models of the problem. Their basic theoretical result is summarized as follows, "Our models show that a difference in the costs of pollen grains and seeds does not in itself select for the conditional modification of gender. The production of many, largely independent, flowers and fruits generally allows plants that are rich or poor in resources to function equally well as maternal or paternal parents, or both. The amounts of pollen and seeds produced can simply' be 'varied in parallel. with the available resources. The reproductive status of a plant affects the selection of gender only if it differentially alters the production or utilization of pollen or seeds.” They emphasize this result because it contradicts a widely held view that since seeds are generally more expensive (larger) than pollen grains, then smaller or stressed plants would find it ”easier” to be male. They have debunked this erroneous intuition. While acknowleging that there is some data which suggests a pattern of increasing 90 femaleness with status, they conclude that ...on the contrary, the. limited data available at present suggest that a lack of correlation between status and gender may be the ‘most common pattern in cosexual seed plants. The pattern can be explained by the models ... which predict that gender is independent of status whenever the relative fitness rewards from the two parental modes do not change with status or when such changes cannot be evaluated by the plants." Using natural variation among individuals within a population, there is little evidence of a tradeoff for the plant in investment in sexual alternatives. There is no evidence for a negative correlation of male and female output per gram, except possibly the slight non-linear relationship (a possible downward turning of the relation at high levels of male production). The lack of higher seed output of the all-female plants also does not support the idea of a tradeoff. Natural variation can be deceptive in this sort of analysis, since unmeasured characters could be the causal factor. For example, if it was not suspected that plant size was an important confounding factor, it might have been concluded that there was strong evidence for a positive relationship between male and female output. It may be that a plant in a good site might be expected to have both high male and female output, even per gram, if for example relatively less resources are allocated to root tissue. The emasculation experiment circumvents this problem by 91 directly manipulating allocation and reveals strong evidence for a tradeoff in the stimulation of female output in response to reduced male allocation. An alternative explanation. of this treatment effect might be related to some sort of stimulation caused by the damage at male bud removal. This is difficult to rule out, but a leaf removal experiment not reported here failed to show any stimulatory effect. The results say little about the shape of the tradeoff curve, predicted by theory to be concave downward. The quadratic relationship in the natural variation is hard to interpret in this light since it is not expressed in the context of an overall negative relationship (the curve bends down at low as well as high levels of male output). The fact that while seed output increased but did not double with male removal might be argued to be consistent with the idea of a non-linear relationship, but it seems more likely that physiological constraints would prevent the complete translocation of male resources into seed even if the underlying tradeoff were linear. It is thus possible to conclude that although the natural variation fails to reveal signs of a tradeoff between male and female function, the experimental results show’ that for each individual plant, the tradeoff is real. The shape of the tradeoff remains unmeasured, and might be best studied experimentally, perhaps with a graded series of partial male removals. CHAPTER 3 THE COST OF SEX IN AGE-STRUCTURED POPULATIONS The adaptive function of sex has long been of interest to evolutionists, but only recently has its substantial fitness cost come under close scrutiny. The cost of sex is the reduced productivity of a sexual population, or lineage, relative to an asexual pOpulation that results from the existence of males (Weissman 1889, Maynard Smith 1971). As Williams (1975) puts it, "the primary task for anyone wishing to show favorable selection of sex is to find a previously unsuspected 502 advantage to balance the 50% cost of meiosis” (p 11). In his search for this favorable selection, Williams argues that certain life histories benefit more from sex than others, in particular that long-lived low fecundity equilibrium populations gain the least from sex. Noting that it is in these sorts of organisms that sex is most well established, Williams is led to the dilemma that the presumed benefits of sex predict a pattern in the taxonomic distribution of sexuality Opposite to that observed. He concludes that ...in these forms sexuality is a maladaptive feature, dating from a piscine or even protochordate ancestor, for which they lack the preadaptations for ridding themselves” (p 102). The unstated assumption here is that while the benefits vary, the cost of sex 92 93 is independent of the life history. Recently, Waller and Green (1981) have argued that this view needs to be modified, that the cost of sex is not independent of the life history. They compare, in the manner of Cole (1954), the effect of the cost of sex in three simple life histories '- annuals, biennials, and perennials, and show that asexual reproduction is more strongly favored in annuals than biennials and perennials. They conclude that the negative effect of sex on the growth rate declines as generation time increases. If this is true, it is an important result. It. suggests that the ‘very organisms which may benefit least from sex may in fact experience the lowest cost, offering a way out of William's dilemma. In addition, if patterns in the cost of sex can be related to patterns in the distribution of sexuality, then we might begin to quantify the selective advantage of sexual reproduction. The purpose of this chapter is to examine Waller and Green's conclusion by evaluating the cost of sex for the general case of age-structured populations. The relevant results from life history theory are presented, and indicate an inverse relationship between the cost of sex and generation time. However, the reader should be forewarned that while the solution to the problem is straightforward, its interpretation and significance are not. The very simple general result reveals a serious problem; the absolute magnitude of the cost of sex becomes a function of the time scale chosen to measure generation time. In particular, if the effect of 94 sex on the life history is measured in units of generation time, then the cost of sex is invariant across life histories. This issue of time scale must be resolved before any conclusions can be drawn concerning the distribution of sexuality. Most of the paper makes the implicit assumption that the cost of sex can be investigated without direct consideration of the possible benefits of sex. This seems reasonable, particularly in view of the fact that there is no agreement as to what those benefits are. It is the principal conclusion of this paper, however, that the ambiguity due to time scale that appears in the interpretation of the cost cannot be resolved without knowledge of the time scale of the benefits. unfortunately, this is just the information which we do not have; it is generally considered a measure of the depth of our ignorance that we do not even know whether the adaptive benefits (if any) of sexual reproduction are short or long term (Williams 1975, Maynard-Smith 1978, Bell 1982). As a consequence, the value of the theoretical results presented here must remain uncertain. For simplicity, the results are presented for the most part without qualification, and the question of their significance is left for the discussion. THE COST OF SEX WITH AGE STRUCTURE Most versions of the cost of sex begin with a sexual population in which an asexual mutant appears. This mutant has an altered rate of increase relative to the general pOpulation, and the magnitude of this difference is the cost Of sex. The reason 95 for this altered rate of increase is that the asexual ‘mutant produces only 'daughters', each of which can then produce daughters. If the sex ratio is 1:1, then the rate of daughter production of the mutant is double that of the sexual population (Maynard-Smith 1971). Alternatively, this can be expressed as the doubling of the maternal genome in each offspring (Williams 1975). In either case, the asexual mutant can be considered equivalent to a mutant with doubled fecundity. We wish to evaluate the effect of this increased fecundity on the fitness of the mutant in an age-structured population. Following Fisher (1958), in age structured models the fitness of a type is proportional to the population growth rate at stable age distribution and is given by the solution for >\ in the well known Euler-Lotka equation co 1 = ;:.>:x1 m (l) where lx is surviv’o'rshipxté age x and Inx fecundity at age x, a newborn is age 0 and 1 =1.0 (Charlesworth 1980a). The cost of sex 0 can then be evaluated by determining the effect of a given change in fecundity on A. The following results could all be developed in terms of a general multiple of fecundity. For simplicity, though, we will consider the case of a fully viable asexual mutant, and will levy the full cost of sex by doubling its fecundity at all reproductive ages. We then seek the solution for >\' in the equation 1 -:(>')-xlx(2mx) (2) where 1x and Inx are the life history schedules Of the sexual 96 population and )0 the rate Of increase of the mutant. We will define the cost of sex as the portion of the maximum growth rate (that of the ideal asexual. mutant) that. a sexual population fails to achieve. For example, the usual term ”50% cost" means that the fitness of the sexual population is 502 less than asexuality could attain. Defining the increase in fitness of the mutant ass) (>\'=>+A)I), the cost of sex (c) can be expressed as c = -------- . (3) >+Ak Equations (1) and (2) have no exact analytical solution, but there are some existing results in life history theory which give insight into the solution of (3). First, exact solutions of (3) will be obtained for two special cases of semelparity and iteroparity used by Waller and Green (1981). These are followed by two approximations of (3) for the general case. Semelparity Semelparous species are those, such as annuals and biennials, that undergo only a single bout of reproduction in a lifetime. The growth rate of a single cohort can be expressed as >~=(1m)l/a , (4) a a where a is the age of maturity. From (4) we can obtain the cost of sex by doubling ma, since )0 = 21/8(1ama)1/3 = 21/8)» and C =1 _ 2-(1/8) . (5) In this case the cost of sex is determined completely by the age 97 of first reproduction. When a=1 (i.e. for an annual) the cost of sex is 502, and it decreases as the age of first reproduction increases. As a simple numerical example, consider an annual vs. a biennial. If the annual has a survivorship to age 1 (11) of .25 and fecundity (m1) of 8, it will have a growth rate of 2. A biennial with l -.25 and m 2 2 fecundity will double the growth rate of the annual to 4 (c=.5) =16 will also have >F2. Doubling the but only increase the growth rate of the biennial by a factor of 21/2 to 2.83 (c=.293). Iteroparity The cost of sex with iteroparity is more complicated than semelparity because of the mOre intricate interaction between survival and fecundity in determining the growth rate. The semelparous cohort grows in cycles of increase and decrease, corresponding to periods of mortality and reproduction. With iteroparity, population growth is a mixture of yearly adult reproduction and the survival of individuals from one year to the next. Consider the iteroparous model used by Waller and Green, which derives from Charnov and Schaffer (1973). This assumes maturity at age 1, constant juvenile and. adult survival, and constant annual adult fecundity; m1=M, pi-P, for all #0. This model has the advantage of an explicit solution for ), since the adults at any time t are equal to the sum of the adults and newborns surviving from time t-1, so that at stable age distribution, >~=P+poM. (6) 98 When all fecundities are doubled, >~' = P + p02M, so A) = pOM, and the cost of sex can be exactly calculated, 1 c = . (7) P 2 + ---- POM The cost of sex will be increased by increases in fecundity, increases in juvenile survival, and decreases in adult survival. It is at a maximum of .5 when P=0, which, as in semelparity, is an annual. Any degree of perenniality will have a reduced cost of sex relative to an annual. If we interperet poM as ”effective fecundity", the offspring surviving to adulthood (age 1), the cost of sex can be considered to depend on the ratio of adult survival and effective fecundity. Whatis the magnitude of P/pOM? Since the growth rate is dependent on the sum of P and p0“’ conversely, we can say that the ratio is dependent on the growth rate. In particular, for a given level of adult survival, higher growth rates require increased effective fecundity and thus increase the cost of sex. Clearly, the highest ratios, and thus the lowest cost, are found in long-lived (high P), low fecundity, equilibrium populations, the very life histories for which Williams despairs of explaining the function of sex. These two special cases have given exact expressions for the cost of sex, and have supported the assertion that the cost varies with changes in the life history. However, the two cases differ substantially in what aspects of the life history control the cost. The following section derives a more general relationship 99 ‘which clarifies the underlying identity Of these results; the role of generation time. A More General Approach Hamilton (1966) first treated the problem of the effect on growth rate of changes in single age specific fecundities, and subsequently Caswell and Hastings (1980) considered the problem of a fixed change in fecundity across all ages. Their approaches assume changes of small magnitude and the potential doubling of fecundity inherent in a switch to asexuality constitutes a gene of large effect. However, accepting the approximate nature of the method, it is worth developing the expression for the sensitivity of growth rate to the doubling of all fecundities. Following Hamilton (1966), the effect on growth rate of fecundity perturbations at a single age x is given by d)\ )\ lx -- = - -- (8) x dmx T )\ where a: mix). 1:1me , (9) a common measure of generation time (the mean age of mothers of a newborn cohort). Following the method of Caswell and Hastings (1980) the effect on >. of doubling all fecundities (5 mx - ZmX-mx 8 mx) is approximated by ~°i d>. >\ A >\ . Amx -- - --- . (10) *‘0 dm T This result contains the information we need to produce an 100 estimator (cl) of the cost of sex, cl - ------- , (11) which is at a maximum (502) when T=1, again, for an annual. As generation time increases, the cost of sex declines. For the actual computation of the cost of sex, expression (11) is little help since the value of the growth rate is required to obtain T; whatever method is used to calculate T could as easily solve the cost of sex directly and more exactly from (1) and (2). The value of (11) is that it defines the cost of sex in an intuitively useful way. The importance of generation time in result (11) suggests an alternate estimator of the cost of sex. The relation between net reproductive rate, R0, and growth rate is often given as no - >3 . (12) 00 Since R -21 m , doubling of all fecundities has the effect of 0 X'-O x 7: '° exactly doubling the net reproductive rate; RO' =3; 1x2mx a 2R0. Therefore, doubling fecundity also doubles )F. Since 2)? = 1/T r l/T (2 >0 , then )0 - 2 >\ provided we assume that doubling fecundity does not change generation time (discussed later). From this, we can derive a second estimator of the cost of sex, 1 c = 1 - --- - . (13) 2 217T Again, the cost is at a maximum of .5 when T is at its minimum of 1, and decreases with increasing 'T. The two estimators are plotted together in figure 22, with numerically calculated 101 (equations 1&2) costs of sex and generation times for a sample of life histories. The relation of these results to the two special cases considered earlier can be readily seen. For a semelparous species the generation time is identical with the age of reproduction, a-T, and the estimator c gives an exact result. In this case, 2 generation time is completely insensitive to changes in fecundity or survivorship, and is determined entirely by age Of first reproduction. For the simple iteroparous life history (6), 1x=pon-l, and mx=M, so that from (9) ca poM “' P x . = -----2x(---) . .... P )\ X'eO This can be simplified by noting that for any non-negative Q(1 and oo oo 90 integer 1“;ka - cum-<1)2 (since (142).;ka = ‘— c1k - cum-0)). ‘ :0 LA and given (6), then P T = l + ----- . (15) P0” Comparing (15) with (7) we see that in this life history, c=1/(1+T), so that in this case, c1 (11) is an exact measure of the cost of sex. Growth rate is a linear function of fecundity in this life history (6), which was the assumption required to generate the estimator. We have seen that in the simple iteroparous life history, the cost of sex depends on the relative values of adult and juvenile survival and fecundity. (hi the other hand, for the semelparous Cost of Sex 102 . 5 .1 ...—_— Annual Isopod Squirrel ,4 - Barnacle Sheep Lizard Sardine .3 " Deer Conus Wildebeest Salamander .2- / C l ,// Atrican 30(1an _ Grey Seal J i / Human \ _I. 0 I I I I l l 5 10 15 20 25 Generation Time T in years Figure 22. Two estimators of the cost of sex (c , c ) plotted against generation time in years. Points are numerically calculated values for a sample of published life tables (Ballinger 1973; Charlesworth 1980a; Connell 1970; Eberhardt 1971; Hewer 1964; Hickey 1960; Murphy 1967; Organ 1961; Paris and Pitelka 1962; Perron 1983; Sinclair 1977; Watson 1970). 103 life history, survival and fecundity are irrelevant, and only age of first reproduction determines the cost Of sex. The general result, however, makes it clear that the effect of these life history components are in a sense an indirect result of their effect on generation time. Since the rate of increase is doubled by an asexual mutant across a period of a single generation, the growth rate per year is increased only by a factor of 1/T. Because growth is exponential, the shorter the generation time, the more frequently the doubling is compounded. If sex constitutes a waste of resources at each reproductive episode, the generation time can be seen as a measure of the frequency with which this cost is incurred. Waller and Green refer to this as the ”rate of gene dilution". The Components of Generation Time The generation time is the crucial aspect of a life history that determines the cost of sex. Understanding how elements of the life history contribute to the cost of sex, then, requires knowing how those elements contribute) to the generation time. Based on the special cases considered above, we expect that increases in age at first reproduction, decreases in fecundity, decreases in juvenile survivorship and increases in adult survival may all tend to increase generation time. The question of how changes in life history parameters affect the generation time can be approached more generally in a manner identical to the sensitivity analysis of growth rate. Implicit differentiation of the generation time (equation 9) with respect to age specific 104 survival (px) and fecundity (mx) gives dT 3T 2T d>\ - -- + -- -- -- (l6) dpx 9px 9% d1)x dT 9T 9T d>( -- - -- + -- -— (17) dmx gmx 2) dmx where 3T 1 93— _t 9px px 2:... .BT -x ..- = x >, 1x (19) 9111,, 9 T 1 00 - . _- - - - 2: .2). tltmt (20) 2 >\ >\ (7.0 d) >. °" -.. - --- E: >Ctltmt (21) dpx pr {$1.40 d). )I _ .. - - x xlx (22) dmx T Expressions (16) and (17) reflect that the overall effect on generation time of a change in a single px or tax can be separated into the "direct” effect of the change on T (18,19) and the "indirect" effect on T resulting from the change in growth rate (20). Expressions (21) and (22) were first derived by Hamilton (1966), who showed that they are both positive functions that decline as age x increases. By inspection, (20) is a constant with negative sign. Therefore the indirect effects of life 105 history perturbations on generation time must be of the Opposite sign as the perturbation, and begin at some minimum value and increase with age. That is, increases in growth rate reduce generation time and so also do increases in age specific survival and fecundity in so far as they affect growth rate. The direct effect of changes in px (18) are positive and decreasing with age, while the direct effect of changes in mx (19) is always non-negative. Thus the direct and indirect effects are of opposite sign and the total sensitivity of generation time will be the net result of these opposing effects. Values for these expressions were calculated for illustration in figure 23a,b using a human life table (Charlesworth 1980a). While life histories will differ in specifics, most iteroparous life histories show similar qualitative pattern. Both dT/dpx and dT/dmx are negative for early ages and become positive later, with dT/dmx monotonically increasing and dT/dpx approaching zero. Thus boosts in fecundity and survival in early ages tend to decrease generation time and increase it in later ages. This corresponds roughly to our eXpectations based on the simple models considered earlier. The distinction between ”juvenile" and ”adult” is still important, but only precise if defined in terms of the sensitivities. The age at which dT/dmx switches from negative to positive, which we will call xm,can be obtained from (17), - t: t2>.-tltmt m _ T X . _ (23) The age where dT/dpx = 0 can be obtained similarly from (16). It 106 Figure 23. A) The sensitivity of generation time to perturbations in the age-specific survival (p ) and fecundity (m ) rates in a human life history (Charlesworth 19803). B) THe ”direct" (upper solid curves) and "indirect" (lower solid curves) components of total sensitivity (dashed curves). 0 -l >— t > -2 E 17) Z LU ‘9 -3 -4 -5 -6 Figure 23 A 107 3'1 (iF5(\\\\‘IL \él dmx 10 20 AGE 30 4O 50 SENSITIVITY Figure 23 B ID 108 20 AGE 30 ‘40 50 109 is clear from the example that these ages are not necessarily equivalent to each other or to the age of first reproduction (10), peak reproductive value (20), or to generation time (25.9). The simpler model made no distinction between early and late fecundity, but predicted that an increase in all tax will tend to decrease generation time (15). This is confirmed in general by noting first that an increase in all IIIx is equivalent in its effect on T to the same increase in only p0. For a doubling of mx, dT dT E-Amx =-' g-Apo = T-xm e (2") mx p0 ,v AT D48 0 x= It 2?“ be shown that T-xm g 0 which is equivalent (using 23) to T2$22t2>ttltmt. That is, the square of the mean age of mothers of a newborn cohort (T2) is less than or equal to the mean of the squared ages of mothers. The proof involves showing first that under semelparity these quantities are equal, and then that any small increment of iteroparity will produce the inequality. Therefore, an increase in pO will decrease generation time, except in the case of semelparity, and so also will an overall increase in fecundity. In summary, we can say in general that increases in early fecundity and survival decrease generation time and increases later increase generation time, where "early" and ”late” are defined for each particular life history. Altering the age of first reproduction will have a direct effect on generation time, but can be more exactly conceived as a change in the fecundity 110 schedule. In the case of semelparity, however, age of reproduction is the only determinant of generation time. These results provide some rules of thumb for evaluating and comparing the cost of sex in different life histories. One interesting implication here is that the cost of sex will also vary between populations of the same species since fecundity and survival schedules will vary. DISCUSSION The cost of sex in age structured populations has been treated as a straight-forward application of life history theory. Assuming fitness is directly related to growth rate, the cost of sex varies inversely with generation time. This seems to confirm Waller and Green's (1981) conclusion that the cost of sex is lower in long-lived organisms. It is an exciting possibility because it may help explain the broad relation between generation time and sexuality across taxa that forms the basis of William's dilemma. There is, however, another way to interpret this result. The ”absolute” cost of sex is dependent on the time scale chosen to measure growth rate and is in that sense arbitrary. In particular, if one measures the growth rate of a species as a rate of increase per generation, then, since T-1.0, it follows (from equations 11 and 13) that the cost of sex must be 502. That is, in any life history, an asexual mutant would achieve a rate of increase per generation (equivalent to the net reproductive rate R0) double that of a sexual population. If fitness is defined as 111 the rate of increase Of a type per generation, then no particular pattern in reproductive mode is expected. The problem then has been recast: what is the pmoper time scale by which to evaluate the cost of sex? This issue is a more general one in life history theory, as discussed by Stearns (1977). He compares the reproductive value curves of two barnacles, and finds that when measured on a scale of years they have very different curves, but when plotted on a scale of generations the curves are strikingly similar. When comparing the fitnesses of various hypothetical life histories, the task of much life history theory, an absolute time scale is a logical standard. However, when comparing very different life histories, e.g. elephants vs. Daphnia, a more relativistic scaling such as generation time can seem desirable. The remainder of the paper is concerned with this ambiguity. Two alternative perspectives will be explored with the hOpe of by-passing the problem of time scale. These are first, variation in the relative importance Of survival and fecundity, and second the probability of survival of a rare mutant. Finally, it is concluded that the issue of time scale cannot be satisfactorily resolved without explicit consideration of the benefits of sex. The present study began with the intuitive notion that if life histories are an investment of resources (energy, time, etc.) into survival and reproduction, and since the cost of sex is the waste of half of that reproductive investment, then life histories which 112 achieve their fitness with relatively less reproductive allocation should experience a lower cost of sex. While some of the models discussed here seem to capture this idea, it has been shown to be imprecise and misleading; survival and reproduction are not simple additive components of fitness. A way to pose this idea more formally is to ask by what factor (zp) must all age-specific survivals (px) be increased to have the same effect on fitness as a doubling of all fecundities. The smaller the factor is, the less important is fecundity as a component of fitness. Goodman (1971) has shown that ‘multiplying all px by the same factor results in an increase in the growth rate by that same factor. This can be seen by noting that an increase of all px by a constant factor (2 ) leads to a new survivorship function 1' , (t4) x where l'x'lex, since ltI—ITp (10=1.0). When l'x is substituted x20 in (1), we see that we must also multiply X-x by z- X x to retain the equality, which is equivalent to (90-x. Thus the new growth rate, >', must satisfy )x' = 2% . This allows us to say that A)?(zp-l)>‘ which when substituted into (10) gives (21)-1)) - NT, or zp-(1+T)/T. For long-lived organisms (large T), the effect of a doubling of annual fecundity can be matched by a much smaller increment in annual survival than for short-lived organisms. This may be a reason for supposing that long-lived organisms are less susceptible to an asexual mutant. Further, one might suggest that in long-lived organisms, any survival benefits of sexuality are more likely to repay the fecundity cost. While an intriguing point of view, there are several problems. First, this cannot be treated like an allocation problem. The loss in fecundity of 113 sexuality does not free up resources for increased survival since it is all consumed in male reproductive effort. Some other survival benefit must be invoked. Moreover, as survival rates become high, further increases may be more difficult to achieve (if only because all zppx must be less than one). Finally, the relationship still depends on generation time and so the original problem of time scale remains. Ultimately what we would like to determine is the effect of variation in the life history on the likelihood that an asexual mutant will appear and replace a sexual population. Do life histories differ in their "resistance” to asexuality? This is the prOperty that could produce cost-determined patterns in the distribution of sexuality across life histories. In addition to growth rate, another measure of this sort is that of the probability of survival of a rare mutant. Charlesworth (1980b) has applied this standard to a closely related problem, that of the cost of sex with alternation of generations. There he points out that in populations in which generations are only intermittently sexual, the effect of sex on the growth. rate declines as increasing numbers of asexual generations intervene between sexual generations. This makes intuitive sense, at least in the extreme case of no sexuality which would have no cost. But the same ambiguity applies- sex is uniformly costly in terms of growth rate when scaled by the time between sexual generations. Charlesworth argues that the probability of survival of a rare gene, a dimensionless quantity, is independent of the time scale 114 employed and thus avoids the problem. He then shows that this probability also declines and concludes that the cost of sex is reduced. For age-structured populations, Charlesworth and Williamson (1975) have shown that the survival probability of a mutant is directly related to its growth rate. This conclusion, along with the results on the alternation of generations, encourages the expectation that increasing generation time, which lowers the effect of asexuality on the growth rate, may reduce the survival probability of an asexual mutant. One helpful special case assumes a population near equilibrium ()FI) and a mutant of small effect (Charlesworth and Williamson 1975, Charlesworth 1980a). In this case U32r12T12/V12 where U is the probability of survival of the mutant, r12 the intrinsic Site of increase of the heterozygote, T the generation time (nglxmx), and V the variance of lifetime offspring production. FOIlowing the same procedure as in equations 8-10 and noting that reln )gwe conclude that when fecundity is doubled, r-T‘l. Since the population as a whole is growing at rll-O, r12- rll+ Ar - T-l, which gives U c'2/V12 (since Rel, both T's are equivalent). The implication is that, contrary to expectation, the probability of survival of a rare asexual mutant is independent of generation time. While there is a close analogy between the growth of an organism and the growth of a clone of cells during an asexual generation, Charlesworth argues that the crucial difference is the independence of the cells. Thus under two standard criteria of relative fitness, the rate of 115 increase per generation (R0) and the probability of survival of a mutant allele, the cost of sex is independent of the life history. It remains true, however, that on an absolute time scale ()0, life histories can differ dramatically in the relative success of an asexual mutant. Is there a good case to be made for the use of an absolute time scale? One general problem with conceiving of the cost of sex on an absolute time scale is that it makes an implicit assumption about the benefits of sex. For example, consider the following argument for the use of an absolute time scale. The rate of increase per generation (R0) and the probability of survival of a rare mutant (U) are concepts of fitness that derive from population genetics, and as a result assume a population in ecological isolation. In fact, a mutant type must not only survive and increase relative to its ancestral population but also relative to all other species with which it competes. This imposes an absolute fitness criterion. In the case discussed earlier of annuals versus biennials, for example, the asexual mutant of an annual will have a higher growth rate than the biennial asexual mutant as well as both sexual parent species (which were assumed of equal fitness). Ecological competition Of this sort could lead to higher frequencies of asexuality in species with short generation times. A major flaw in this argument, however, is that while increasing the generation time reduces the rate of compounding of the cost, it also reduces the rate of compounding of any benefits - provided that those benefits accrue to each sexual generation. The net 116 effect of changes in benefit and cost suggest no pattern of reproductive mode across life histories. The bulk of this paper has explored the problem of the cost of sex independently of its possible benefits. As stated earlier, the lack of even general agreement about the nature of the benefits of sex made this a not only reasonable but necessary approach. However, it is now clear that to make an evaluation of the cost in any useful way, the time scale (at least) of the benefits must be taken into account. This is because the net effect of both the costs and benefits depend not only on their magnitudes, but the rates at which they apply, as in the compounding of interest. If the benefits of sex are determined somehow independently of the life history and accumulate on an absolute scale, this would be a strong argument for using an absolute scale for comparing the cost. If the benefits of sex are long-term (see Bell 1982 for a review), they are potentially in this class; environmental (abiotic or biotic) fluctuations that occur independently of the reproductive mode could impose such a scheduling of selection. Short-term benefits are more likely to be generated at a rate proportional to generation time. The problem of time scale that arises on considering the cost is unresolvable while uncertainty still remains about the suprisingly complementary problem of the time scale of the benefits. Stretching the argument a bit further; if a pattern exists in the relation of generation time and the frequency of sexual reproduction, and this pattern is consistent with that predicted 117 by assessing cost on an absolute time scale, one might then infer that the benefits of sex are long-term. An exploration of this approach would involve explicit assumptions about benefits, and will not be attempted here. While a consideration of the time scale of the benefits of sex may be the only effective argument in favor of the use of an absolute time scale, it is a potentially important one which should not be discounted. In summary, Waller and Green (1981) argued that the cost of sex is not fixed at 502 but varies with the life history, that as generation time increases the cost of sex declines. This result is derived for the general case of age-structured populations. Its intuitive basis is that since growth rate (fitness) is a geometrical process the fecundity advantage of asexuality is compounded at a rate controlled by the generation time. This result has the potential to explain a broad trend of increasing obligate sexuality with increasing generation time, but is undermined by a problem of time scale. While the result holds on an absolute time scale, on a scale of generations the cost of sex is invariant. It is concluded that this ambiguity can not be resolved independently of a strikingly analogous problem - whether the benefits of sex are short-term or long-term. SUMMARY Two tOpics in resource allocation are explored, the cost of height (stem) and the cost of sex (males). While quite different in many respects, these two problems share the uniquely Darwinian quality of advantage to the individual (relative fitness) at a cost to population productivity. The problem of Optimal height is studied empirically, using the common ragweed Ambrosia artemisiifolia. Grown across a range of densities, Ambrosia shows a pattern of increasing height allocation (height/basal diameter ratio) with increasing competition (density of neighbors), consistent with theoretical predictions of increasing Optimal height with increasing competition. This result, while statistically significant, leaves much variation in height allocation unexplained. Height allocation shows no evidence of directional selection (on reproductive output) and only weak stabilizing selection. Direct manipulation of height allocation with chemical growth regulators (gibberellin, B9) was used to test the game theory prediction that deviation from normal height allocation (in either direction) is generally deleterious to the individual, but depends also on neighbor allocation. While some of the results are consistent with the hypothesis, they could not be strongly distinguished from the alternative hypothesis of general deleterious effects of the chemicals. 118 119 The cost of sex was studied in Ambrosia (a. monoecious annual), as expressed in the assumption of a tradeoff between male and female function. Little evidence is found for a tradeoff in natural variation in reproductive allocation (no negative correlation of male and female output per gram of vegetative biomass). An experimental suppression ' of male Output (emasculation), however, did result in. an increase in female (seed) output, supporting the tradeoff assumption. The cost of sex in age-structured populations was explored theoretically, and it is concluded that the significance of the cost of sex for the evolution of life histories and the evolution of sex depends on a known, the generation time of the life histories under consideration, and an unknown, the time scale of the benefits of 88X. APPENDIX APPENDIX The results of the greenhouse assays are summarized in Figure 24. In assay #1, the GA treatments'show the typical increasing effect with dosage up to a threshold, but the B9 treatments do not have a noticable effect until the highest levels. When applied in combination in assay #2, the effect of GA entirely swamps that of B9 at those doses. In assay #3 the higher B9 doses have a more noticeable effect and perhaps even some tendency to threshold, although again the GA completely swamps the effect of B9. Because of uncertainties about the effectiveness of the chemicals in the field and on larger plants, high doses were chosen for the field experiments (40 and 20 ug GA and 800 ug B9) and applied twice (not shown in the figures is that the effect of the chemicals on weekly height increment tends to be unnoticeable by the fifth week). 120 121 Figure 24. Results of greenhouse assays for chemical concentrations. 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