Competition for pollination and the evolution of flowering time
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Authors Waser, Nickolas Merritt, 1948-
Publisher The University of Arizona.
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Link to Item http://hdl.handle.net/10150/565376 COMPETITION FOR POLLINATION AND THE
EVOLUTION OF FLOWERING TIME
bY Nickolas Merritt Waser
A Dissertation Submitted to the Faculty of the
DEPARTMENT OF ECOLOGY AND EVOLUTIONARY BIOLOGY
In. Partial Fulfillment of the Requirements For the Degree of
DOCTOR OF PHILOSOPHY WITH A MAJOR IN BIOLOGY
In the Graduate College
THE UNIVERSITY OF ARIZONA
19.77 THE UNIVERSITY OF ARIZONA
GRADUATE COLLEGE
I hereby recommend that this dissertation prepared under my direction by Nicholas Merritt Waser______entitled COMPETITION FOR POLLINATION AND THE EVOLUTION OF
FLOWERING TIME be accepted as fulfilling the dissertation requirement for the degree of Doctor of Philosophy______
. uLrrt f 2 / fy\o-y^ i Dissertation Director Date
As members of the Final Examination Committee, we certify that we have read this dissertation and agree that it may be presented for final defense.
.2/ , ^ / f z z
t fll&YoL ^ ? 4-
______/ f a / ___ ^ C c jJ jlr____ ^ Mn-J____
Final approval and acceptance of this dissertation is contingent on the candidate's adequate performance and defense thereof at the final oral examination. STATEMENT BY AUTHOR
This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library.
Brief quotations from this dissertation are allow able without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manu script in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.
f SIGNED: t U l
My professional growth and the completion of this dissertation have depended on the help of many people.
First and foremost, I wish to thank my major advisor, Dr.
H. R. Pulliam, who has freely shared his time and energies as well as his insight into all areas of ecology. Among other things, I am indebted to Dr. W. A. Calder for intro ducing me to hummingbirds and their pollination of flowers.
The other members of my doctoral committee. Dr s. G." G. Ward,
W. B. Heed, and A. C. Gibson, have been an essential source of critical input. In addition, Dr. J. H. Brown has served as a very valuable unofficial committee, member during the last two years of my research. Finally, I wish to thank my graduate student colleagues at Arizona, and most es pecially M. V. Price, for many stimulating conversations and for constant encouragement.
This research was supported in part by grants from the Frank M« Chapman Memorial Fund, Sigma Xi, and The
University of Arizona Foundation. TABLE OF CONTENTS
Page
LIST OF TABLES « . , « . « . , « « . «. « . . » . « . vi
LIST OF ILLUSTRATIONS . . „ . 0 . . . „ . , „ vii
, ^3 'J*'RAC o 0 o 0 O 0 o 0 O 0 O- O O 0 O 0 0.0" O 0 o o o 1 2C
INTRODUCTION . » . o . , . « « = . , . » o « . , . , „ I
POLLINATOR SHARING, COEXISTENCE, AND COMPETITIVE DIVERGENCE AMONG CO-OCCURRING PLANT SPECIES ...... ' 3 The Basie Model © © © © © © ■ © © © © © © © © © © © © . 4 Rapid Fixation of the Common Species ....©„ 5 - Insight into Possible Mechanisms of Competition © © © © © © © © © © © © © © © © © 8 Computer Simulations . © . © . © . © . . . . . © © 9 The Simulation Programs © . . . © © © . © . © © 10 Pollinator Movements Limiting to Reproduction © © ■© © © © © © © © © © © © © © 13 Movements and Stigmatic Surfaces Both Limiting © 15 Amounts of Pollen Limiting .».©««,»'.. 16 Effects of Refugia . © .=.©..© © ... © 16 Pollen and Seed Flow between Separate Populations ©©©© ©« ©©©© © ©©©©©© 2 2 Discussion © © © ©■ © © © © © © e o o o . © © © © © © 2 7
COMPETITION FOR POLLINATION AND SEQUENTIAL FLOWERING IN COLORADO WILDFLOWERS ..•.©.©.,.© 37
^^2czz1 d,s © © © © © © © © © © © © © © © © © © © ©*o © 38 Results © © © © © © © © © © © © © © © © © © © © © © 46 Visitation and Pollination of D. nelsoni and I © aggregata ©.© © © © © © © © © © © © © 46 Pollen-Transfer by Hummingbirds in Situations of Flowering Overlap between D© nelsoni and I© aggregata ..... 56
IV, V
TABLE OF CONTENTS (Continued)
Page Seed Set Depression in Natural and Synthetic Situations of Flowering Overlap * o @ « « o «. ©« ® © © © 67 Discussion © © © © © © © © © © © © © © 75 APPENDIX A: FORTRAN PROGRAMS FOR SIMULATING THE POLLINATION OF TWO CO-OCCURRING PLANT SPECIES © © © '. © . © © © © © . © © , 86
APPENDIX Bs TESTS OF NORMALITY AND HOMOGENEITY OF
VARIANCES OF SELECTED SEED SET DATA . © 100
APPENDIX C; COMPARISONS OF MEAN NUMBERS OF FLOWERS PER PLANT IN SYNTHETIC POPULATIONS,
1976 © © © © © © © © © © © © © © © © © . 103
LITERATURE CITED © 105 LIST OF TABLES
Table Page
1. Flower species visited by broad-tailed hummingbirds at RMBL, 1975-1976 ...... 49.
2. Summary of pollen collected from humming birds and bees, 1975-1976 ...... 51
3. Visitors to flowers of D „ nelsoni and I. aggregata at RMBL, 1975-1976 . 55
4. Seed sets per flower from pollinator exclusion experiments, 1975 ...... 57
5. Nectar productions and standing crops in flowers of D. nelsoni and I_. aggregata in the- study meadow at RMBL, 1975-1976 . . . „ . 62
6. Seed sets as a function of flowering time in the natural study meadow at RMBL, 1975—1976 ." . . « ...... « . . . '. = = . 68
7. Seed sets in synthetic populations, 1975—1976 o o o o « e o o o e o e o o o e o o o e o 71
8. Seed sets from the hand pollination experiment, 1976 , ...... , . « « . . . 74
vi LIST OF ILLUSTRATIONS
Figure Page 1. The frequency of an initially common flower species, pn# as a function of the number of generations’, n ...... 7 2 . The. effect of varying the number of polli nator movements per generation on the number of generations to. fixation of one plant species ...... 14
3.o The effect of varying the initial pollen supply in anthers on the number of genera tions to fixation of one plant species ..... 17
4. The effect of size of refugial areas on the number of generations to fixation of one plant species, with one (A) and two (B) seed choices per refugial loca tion * ...... 20
5 o The effect of size of refugial areas on the number of generations to fixation of one plant species, with two (A) and four (B) seed choices per refugial location ..... 21
6. The effect of pollen flow on coexistence .... 24
7- The effect of combined seed and pollen flow on coexistence ...... 26
8. A diagram of synthetic populations of D. nelsoni and I_. a g g r e g a t a ...... 42
9. Plants and flowers of D. nelsoni and ]C. aggregata ...... 47 10. Cross—sectional drawings of flowers, with a broad-tailed hummingbird shown to the same scale ...... 53
11. Flowering phenology of D. nelsoni and I. aggregata in the study meadow at RMBL, 1975-1976 ...... 59 vii viii LIST OF ILLUSTRATIONS (Continued)
Figure, Page
12. Foraging movements of hummingbirds in meadows, 1976 ...... 60 13. Foraging movements of hummingbirds in synthetic populations, 1976 ...... 64 14. Stigmas and pollen grains of D. nelsoni and I. aggregata drawn to common scales . . . . 66
15. The sexual composition of the D. nelsoni population in the study meadow in 1976 .... . 70 ABSTRACT
Separation of flowering time among morphologically similar flower types represents one form of evolutionary divergence which may result from competition for a shared pollinatoro In this dissertation, I use computer simula tions based on a deterministic model of pollination of two plant species to examine mechanisms and consequences of competition for pollination. Competitive exclusion of one of the two species occurs in all simulations except those which introduce partial barriers to gene flow between dif ferent sections of a mixed plant population. From this general result, I predict that separation in flowering time or habitat will commonly allow coexistence between po tential competitors. I next describe empirical research designed to explore whether competition for hummingbird pollination is sufficient to explain the sequential flowering of two wildflowers in Colorado. Experiments and observations on natural and synthetic populations of
Delphinium nelsoni and Ipomopsis aggregata indicate that individuals of each species suffer a reproductive loss when they flower synchronously in mixed stands. This reduction in fitness can be attributed to interspecific pollen trans fer by hummingbirds. These findings support the
ix . X interpretation that patterns of flowering time as well as those of floral morphology often represent character displacement as a result of competition for pollination in which pollen, pollinators, stigmatic surfaces or some combination of these limit reproduction.
V INTRODUCTION
Because of their central role in the sexual repro duction of many plants, animal pollinators should strongly influence the flowering response of species they visit.
The striking diversity of floral morphologies and of floral attractant and reward characteristics, and the matching diversity in pollinator types, have been interpreted as a primary outcome of this evolutionary interaction (e.g.,
Muller 1883, Clements and Long 1923, Kugler 1930, Grant
1949, Straw 1955, Sprague 1962, Baker 1963, Ramirez 1970,
Dodson 1975, Heinrich 1975a). A corresponding expectation is that the timing of flowering of plant species will evolve toward coincidence with periods of abundance of appropriate pollinators. Within such periods, however, the pollination actually realized by any species will greatly depend on how pollinator foraging behavior is influenced by the presence of other plant species with similar pol linator affinities. If the behavior of a shared pollinator leads to a reproductive loss to those plant species which it simultaneously services, competition for pollination can be said to occur. Such competition could constitute a potent evolutionary force promoting divergence in flowering times of sympatric plant species (Robertson 1895, 1924, Lewis 1961, Levin and Anderson 1970). Although sequential flowering patterns have recently been reported which are inferred to result from competition for animal pollinators (e.g., Frankie, Baker and Opler 1974, Heithaus
1974, Stiles 1975, Heinrich 1975b, Feinsinger 1976), I am aware of no previous studies which have experimentally investigated mechanisms of competition for pollination or the causal link between such competition and observed flowering patterns in nature.
My intention in this dissertation is to show how competition for pollination among morphologically similar flowers may lead to and maintain divergence in their flowering times. In the first section, I use computer simulations of a pollinator visiting two co-occurring plant species to gain.insight into likely mechanisms of competi tion for pollination and into its probable evolutionary effect on flowering times. In the second section, I discuss the results of field experiments which indicate that competition for hummingbird pollination is a cause sufficient to maintain the observed sequential flowering of two species of wildflower in the Rocky Mountains of
Colorado. POLLINATOR SHARING, COEXISTENCE, AND COMPETITIVE DIVERGENCE AMONG CO-OCCURRING PLANT SPECIES
At least as early as the writings of Robertson
(1895, 1924), competition for pollination among flowering plants was envisioned as a force sufficient to lead to their evolutionary divergence in characteristics which reduced sharing of pollinators. Robertson (1895:100) reasoned that in order to avoid competition, co-occurring species should alter their habitat or pollinator affinities or ". . . separate their times of blooming so that they will not have to compete with a great many similar flowers for the atten tion of the same kinds of insects." More recently, the impact of competition for pollination on the temporal, spatial, and morphological structure of plant communities has received general attention from Grant (1950), Macior
(1970), Mosguin (1971), Levin (1972), Heinrich (1975b),
Stiles (1975), Feinsinger (1976), and others. In addition,
Lewis (1961), Levin and Anderson (1970), and Straw (1972) have initiated the discussion of mechanisms by which sharing of pollinators may lead to a competitive interaction between plant species.
When two or more cb-occurring species partly overlap in their time of flowering and attract pollinators in common, a reproductive disadvantage may accrue to indi^ viduaIs of each species which flower in the presence of the other species, relative to those which do not. In this section of the dissertation, I first examine a de terministic model of pollinator visitation to two plant species growing together. This examination suggests several mechanisms which might cause a reproductive loss from sharing and competing for pollinators. I next discuss the results of computer simulations which relax many of the simplifying assumptions of the basic model. Results of simulations generally support those from the basic model concerning the mechanics and outcome of competition, and they also indicate situations in which coexistence may be achieved between two competitors.
The Basic Model
Imagine two plant species, A and B, which grow randomly intermingled and are visited without preference by shared pollinators. Generations are discrete, non overlapping, and identical for the two species, and mature plants of each species produce only one flower. Frequencies of visits to flowers of the two species are pn and qn , which are respectively the proportions of A and B in the mixed population in any generation n (pn + qn = 1). If pollen picked up at any flower is completely deposited on the next flower visited (i.e., no "pollen carryover"), then pollination events consist entirely of A-to-A polli- 2 nator movements, which occur with frequency pn , and of B-to-B movements, which occur with frequency q^ 2 . Movements between dissimilar flowers (A-to-B and B-to-A) occur with frequency 2pnqn . Finally, assume that the proportions of
A and B in generation n+1 are solely determined by the frequencies of pollination events in generation n. This simplifying assumption is meant to imply, among other things, that amounts of pollen produced and mechanics of its pickup, transfer, and deposition by pollinators are functionally identical for the two plant species.
In this analysis, I normalize the frequency of pollination events to either species against the frequency of all effective pollination events in generation n, in order to obtain the proportions of A and B in the coming generation:
n+1 Pn +qn
Several conclusions arise from this basic model.
Rapid Fixation of the Common Species
In any case other than pn = qn = 0,5, the initially common plant species will increase in frequency through successive generations until it reaches fixation in the population. This can be seen by deriving an expression 6 for'Ap , the change in frequency of species A between generation n and n+l„ From the previous equation, it follows that
Rearranging terms, and recalling that pn + q^ + 1, this oecomes
APn = h W a l ■ P n +9n
Inspection of the numerator of equation (1) shows that the condition for Apn>0 is Pn>(3n / in other words, species A will go to fixation if it is initially even slightly more common than B» The trajectory toward fixation is sigmoidal in shape (Figure 1), as can also be seen by examining the numerator of equation (1). When pn = q^, it follows that (pn - qn ) = 0 and thus that Ap^ is small. The same holds true of the terms Pn<2n when either species is near fixation, since in this case Pn<3n = 0. The highest value of Ap comes at the intermediate value of pn = 0.75.
Notice also that pn = qn = 0.5 is an unstable equilibrium point, and that the two plant species can be maintained at this equilibrium in the basic model only because polli nators are assumed to visit flowers of A and B in these frequencies absolutely without sampling error. 7
1.0 -i • •
0.9 -
0.8 -
0.7 -
0.6 -
B • 0.5 -5 • • • • ■-- P0 = 0.51 • -- P0 = 0.501 0.0 -j-— i— i— i— i— |— i— i— i— i— j— i— i— i— i— | 0 5 10 15 n
Figure 1. The frequency of an initially common flower species, p , as a function of the number of genera tions , n.
Open circles: p (initial frequency of the common species) = 0.51; solid circles: pQ = 0.501. Insicjht into Possible Mechanisms of Competition
The second conclusion I derive from consideration of the basic model concerns the reasons for the disadvantage of rareness just discussed. The per-individual probability of effective pollination events to the rare species is 2 2 q /q = q, and to the common species is p /p = p, where q
Although these, effects follow directly from the restrictive assumptions of the model, they lend insight into mechanisms of competition for pollination which may apply in real biological systems. If it is true in nature that individuals of rare species receive relatively high proportions of interspecific and low proportions of effec tive pollination, then they can be expected to suffer a disproportionate reproductive loss. The exact magnitude of this loss in the basic model is dependent on the stipu lation that there is no pollen carryover, which is inaccurate for -many real systems„ If any interspecific pollen transfer occurs in natural systems, however, and if the avail ability of pollen is limiting to reproduction, plants of a rare species may suffer a disproportionate reproductive loss from pollinator movements which transfer their pollen to dissimilar flowers. Conversely, a disadvantage to plants of a rare species may follow from pollinator movements which bring pollen from a dissimilar flower, if the area of receptive stigmatic surfaces is limiting to reproduction.
Finally, a disadvantage to a rare species may follow if the availability of pollinators themselves, or of the floral rewards which induce their visitation, are limiting.
Computer Simulations
The basic model of competition for pollination uses the implicit simplifying assumption that populations of flowers and of seeds are effectively infinite, so that there is no sampling error in pollinator choice of flowers or in the constitution of each generation from seeds produced in the previous generation. The model also makes no attempt to distinguish explicitly competitive mechanisms due to pollinators, pollen, or stigmatic surfaces. A series of
FORTRAN computer programs were written (Appendix A), which retain much of the framework of the basic model while allowing for a more realistic simulation of the effects of pollinator visitation to a finite population of two plant species„ With the results from simulations, I wish to examine more rigorously the conclusion that sharing a pollinator leads to extinction of one plant species, and to explore conditions under which indefinite coexistence may be attained in natural situations. >
The Simulation Programs
The basic program, called COMPOL, simulates the progress of a pollinator moving through a population con taining two plant species, A and B. In all cases reported here, the population is represented by a 10 by 10 array of locations, each of which may contain only a single plant.
Plants of each species are considered to produce only one flower and to live for one generation. A pollination bout begins at a random flower in the array, and progresses in randomly determined unit movements from flower to flower until a movement causes the pollinator to leave the array.
At this point, a new bout is initiated. This process is repeated within a single computer generation until a specified total number of pollinator movements has accumu lated. Diagonal movements between points in the array are not allowed, and probabilities of moving in each of the four possible directions upon leaving a flower are equal.
Flowers of species A and B are initially assigned an equal number of pollen grains in their anthers. Each visit by a pollinator depletes this supply by a set amount 11 until it is exhausted. The pollinator carries no pollen on its body at the beginning of a bout, but picks up a set load from the first flower visited and from each suc cessive flower whose pollen supply is not exhausted. At each flower visited, the pollinator also deposits a set number of pollen grains chosen randomly and without re placement for the supply on its body. No deposition is made on the first flower of a bout, since the pollinator arrives without pollen on its body. Pollen deposits on flowers accumulate on a stigma of limited capacity, and each pollen grain of the proper species which is deposited on an unsaturated stigma is considered to give rise to a viable seed of that species. The plants constituting the first generation in the array are chosen at random and without replacement from an initial pool of 1000 seeds of each species; such that the initial frequencies of species
A and B are close to 0.5. The plants constituting each subsequent generation are chosen in the same way from finite seed pools resulting from pollination in the im mediately preceding generation.
In order to explore effects of pollen and seed flow between adjacent patches of flowers, I wrote a second main program called PATPOL. This'extends COMPOL by simu lating pollination in a 3 by 3 array of plant populations, each of which consists of a 10 by 10 mixture of species A 12 and R, Different amounts of. pollen and seed flow are allowed to occur between these populations. Once again, the plants constituting the first generation are chosen from initial pools of 1000 seeds for each species in each population.
Separate subroutines of the main COMPOL and PATPOL programs are used to specify the rules by which identities of flowers are chosen at the beginning of each computer genera tion, as well as those governing pickup, transfer, and deposit of pollen. In the sections which follow, I discuss the results of COMPOL simulations with two alternative subroutines determining the choice of flower identity; and two determining the competitive interaction of pollen grains on flower stigmas. I then discuss results from PATPOL simulations, with two alternative subroutines determining flower identity.
I verified the performance of the COMPOL and PATPOL programs and of their subroutines with the aid of sub routines called CHECK and PCHECK respectively, which list the sequence of flowers Visited in a generation, their locations in the array or arrays, and the pollen contents of their stigmas. From this information, the proportions of. A and B seeds produced in any generation were calculated by hand and compared with the proportions produced as final output of that simulation. 13 Pollinator Movements Limiting to Reproduction '
Pollinator movements will be limiting to the repro ductive output of both species in a mixed population if the number of movements allowed in each computer generation mul tiplied by the number of pollen grains deposited per movement is small relative to the total number of fertilization events possible in the population. Figure 2A shows the num ber of generations to fixation of one species from sets of
20 replicate simulations with 25, 100, and 400 movements per generation and with three pollen grains deposited per move ment. In all cases, there were 500 possible fertilizations per generation, because for each of 100 flowers a stigmatic surface was specified which could accept five pollen grains.
Heterospecific pollen grains were not counted toward this! total of five (STIG1 subroutine). Initial pollen loads in anthers were not limiting (100 grains), nor were the pollen loads picked up during each pollinator visit to a flower (10 grains). Under these conditions, the shortest mean duration of coexistence of species A and B occurred with 25 movements per generation. Coexistence was extended by about three generations with 100 movements per generation; and by a further three with 400 movements per generation. Without the constraints of limited pollen or stigmatic surface areas, further increases in the number of movements per generation should eventually lead to total fertilization of 14
2 0 - A. WITHOUT STIGMATIC COMPETITION
< 15- X
10- e CO z o 5 - cr LU z 0 “1 1 1------LU O B. WITH STIGMATIC COMPETITION U_ 10- o cr UJ CD 5 - s 3 l Z 0 “i r- 25 100 400
MOVEMENTS PER GENERATION
Figure 2. The effect of varying the number of pollinator movements per generation on the number of genera tions to fixation of one plant species. Simulations are without (A) and with (B) interspecific competition of pollen grains on stigmatic surfaces. Each bar graph represents a set of 20 replicate simulation runs and indicates mean (horizontal' line), ± two standard errors of the mean (solid bar), and range (narrow line). 15 both A and B„ At this point, the composition of the mixed population would depend on sampling error in the choice of the 100 seeds which constitute each generation.
Movements and Stigmatic Surfaces Both Limiting
In order to explore the effect of limited stigmatic surface areas on the duration of coexistence of A and B,
I ran a second set of simulations which were identical to those just discussed except for the replacement of the STIG1 subroutine by STIG2. STIG2 counts all pollen grains falling on a stigma toward the total of five grains which saturate its surface, and thereby allows heterospecific pollen reaching the stigma to block fertilization by con- specific grains deposited in 'a subsequent pollinator visitation. The effect of this additional competitive mechanism is seen in Figure 2B. With 25 movements per generation, the mean duration of coexistence was equivalent to that without competition on the stigmatic surface.
However, coexistence was extended by only about two genera tions at 100 movements per generation, and by only an additional fraction of a generation at 400 movements per generation. This suggests that an asymptote was being approached at which the effect of competition at the stig matic surface dominated in determining fixation of the common species, and at which additional increments in the 16 number of pollinator movements per generation would not ensure longer periods of coexistence.
Amounts of Pollen Limiting
If the initial supply of pollen in the anthers of flowers is small relative to the total number of possible fertilization events in the population, the loss of pollen in interspecific pollination movements may limit reproduc tion even in the absence of competition for limited pol linator movements or stigmatic surfaces. I investigated this prediction in simulations with 100 movements per generation, with pollen loads of 10 grains picked up per flower visit, and with the STIG1 subroutine to eliminate stigmatic competition. Figure 3 shows the results for initial pollen supplies in anthers of 100, 10, and 3 grains.
An appreciable decrease in the duration of coexistence appeared only below 10 grains per flower, suggesting that amounts of pollen are not limiting above this value given
500 possible fertilization events in the population.
Effects of Refugia
In simulations discussed to this point, plants which colonized all locations in the 10 by 10 array at the onset of any computer generation were chosen without re placement from the seed pool that resulted from pollination in the immediately preceding generation (IDEN1 subroutine). 17
CO o s tr UJ z P 10 H UJ < o X Ll o C 5^ a: 2 UJ CD s n ~ 3 3 10 100 Z INITIAL POLLEN SUPPLY
Figure 3. The effect of varying the initial pollen supply in anthers on the number of generations to fixation of one plant species.
Each bar graph represents a set of 20 replicate simulation runs with 100 pollinator movements per generation and with out stigmatic competition. Such a procedure can be interpreted to mean that each of the competitors grows equally well at all locations in the population. This suggests that the outcome of rapid com petitive exclusion in simulations might be altered by introduction of refugia for each of the plant species, in which the competitor has either a reduced chance or no chance at all of growing. The establishment of refugia of varying sizes was accomplished by replacing the 1DEN1 subroutine with IDEN2, which sets aside a certain number of columns in the array for occupation by each species.
At each of the refugial locations in these columns f a variable number of choices are made from the seed pool of the previous generation. If any of these seeds is of the proper species for that refugium, it is considered to germinate. If none of the seeds chosen is the proper species, the IDEN2 subroutine either specifies that no plant colonize that array location, or that one of the seeds of the improper species do so. These alternative stipulations can be taken in the first case to imply an absolute edaphic barrier to germination of improper seeds within each refugium, and in the second case a strong barrier to seedling establishment which is conditional on the presence of competition from a seedling of the proper species. The simulations do not count pollinator movements to empty refugial locations toward the total number of 19 pollinator movements in each generation. The STIG2 sub routine is used in all cases to allow stigmatic competition.
The results from simulations with these treatments appear in Figures 4 and 5. Figure 4A shows the distribu tion of the number of generations to fixation of one species from simulations with 100 pollinator movements per genera tion and refugial areas for each species of one to four columns of the array, or 10% to 40% of all array locations.
In all cases, there was a single seed chosen to colonize each refugial location, and the choice of a seed of the improper species lead to an empty refugial location during that generation. With refugial areas of 10%, the mean duration of coexistence did not differ appreciably from that achieved with the same number of movements per genera tion and values of other parameters, but without refugia
(Figure 2B). Coexistence was extended slightly with re fugial areas of 20% and 40%. Figure 4B shows the results of choosing two seeds as potential colonists for each refugial location, again considering that seeds of the improper species have no chance of germination. This pro- cedure seems more realistic than the choice of a single seed, since the seed pool from which colonists are drawn in most natural plant populations is probably much larger than the number of spots available for colonization in any generation. With two seed choices, there was an increase 20
15 -i A. ONE SEED CHOICE
10 -
5 -
B. TWO SEED CHOICES
Ll 10 -
CD
10% 20% 30% 40% REFUGIAL AREAS
Figure 4. The effect of size of refugial areas on the number of generations to fixation of one plant species, with one (A) and two (B) seed choices per refugial location.
Seeds of the improper species have no chance of germination at a refugial location. Each bar graph represents a set of 20 replicate simulation runs with 100 movements per genera tion and with stigmatic competition. 21
15 - O A. TWO SEED CHOICES
s 10 - X Ll
e 5 - CO 0 I I I < B. FOUR SEED CHOICES LJ 15- z LU CD Li_ O 10- or UJ CD 5 -
T T T 10% 20% 30% 40% REFUGIAL AREAS
Figure 5. The effect of size of refugial areas on the number of generations to fixation of one plant species, with two (A) and four (B) seed choices per refugial location.
Seeds of the improper species will germinate at a refugial location if no seed of the proper species has been chosen. Each bar graph represents a set of 20 replicate simulation runs with 100 movements per generation and with stigmatic competition. 22 in the mean duration of coexistence of about two genera tions as refugial areas were increased from 10% to 40% for each species„ Figure 5 shows the effect of variation of refugial areas, with two and four seed choices per refugial location and with the new condition that germina tion of seeds of the improper species occurs if no seed of the proper species has been chosen. With two seed choices (Figure 5A), an increase in refugial areas from
10% to 40% caused only a very slight increase in the mean duration of coexistence. With four seed choices (Figure
5B), coexistence was extended by about one generation with refugia of all sizes, relative to the case with two seed choices, In all simulations with refugia, coexistence appears to be sensitive to refugial area and to the degree to which seed exchange can occur between refugia for the two species. Coexistence is longest with large refugia, with a large number of seed choices per location, and without the possibility of germination of seeds of the im proper species in refugial locations.
Pollen and Seed Flow between Separate Populations
The simulations discussed to this point have dealt with effects of pollen flow within single mixed popula tions of species A and B, I now wish to introduce the possibility of pollinator flight and of seed dispersal between populations, using the PATPOL program. The simula tions reported here consider a 3 by 3 array of populations, each of which consists of a 10 by 10 array of plants of species A and B. in the course of a computer generation, at least one pollination bout is initiated in each of the nine populations. If the pollinator moves beyond the edge of any population array during a bout and has not left the overall array of populations, there is a specified prob ability that it will travel and carry pollen to the nearest flower in the adjacent population. The alternative to such flight between populations is initiation of a new bout in the population which the pollinator has just left.
I first wish to explore the effect of pollen flow between populations on the global outcome of competition for pollination, in .cases where seeds, are dispersed only within and never between populations (PIDEN1 subroutine).
Figure 6 shows frequency distributions of the number of populations out of nine which reached fixation for species
A, in sets of 10 replicate simulations with probabilities of pollinator flight between adjacent populations of 0.1 and 0.9. In both Cases, global coexistence of A and B was obtained, in the sense that several populations always reached fixation for each of the two species. With in creased pollen flow between populations, there was an increase in variance in the number of populations going to 24
A. POLLEN FLOW = 0. X = 4.90 > 5 — S = 1.45 o z LU 3 O i— r T T UJ B. POLLEN FLOW = 0 .9 cc X = 4.70 Ll 5 — S = 2.00
JBL T 0 I 2 3 4 5 6 7 8 POPULATIONS FIXED FOR SPECIES A
Figure 6. The effect of pollen flow on coexistence.
Simulations specify probabilities of pollinator flight between adjacent populations ("Pollen Flow") of 0.1 (A) and 0.9 (B). Global coexistence is indicated by the number of populations out of nine which reached fixation of species A. Each set of histograms represents 10 replicate simulations. In all cases, there were a total of 900 pollinator movements per generation. 25 fixation for either species» Once adjacent populations have diverged in species composition, however, pollen flow is no longer a possible means of gene exchange between them. For this reason, species compositions in the nine populations remained constant once fixation was reached.
An opposite extreme to absolute restriction on seed exchange between populations is the derivation of some por tion of the plants in each population during each generation from a seed pool representative of the proportions of species A and B in the overall array of populations. This is achieved with the PIDEN2 subroutine of PATPOL which in troduces a specified probability of making each seed choice from an overall seed pool. Seeds which are not chosen in this way are derived as before from the seed pools produced within each individual population during the previous genera tion. The choice of seeds from the overall pool therefore represents an event of seed dispersal over the whole array of populations. Figure 7 shows frequency distributions of the number of populations put of nine which reached or ap proached within 20% of fixation of species A after 15 com puter generations, from sets of 10 replicate simulations.
In Figures 7A and 7B, the probabilities of choosing seeds in each population from the overall seed pool ("seed flow") are 0.1 and 0.2, while that of pollinator flight between adjacent populations ("pollen flow") is 0.1. These choices 26 1 0 -i A. X = 4.10 POLLEN FLOW = 0.1 ’ S = 2.02 SEED FLOW = 0.1 5 -
JZ3L
B. X = 4.40 POLLEN FLOW = 0.1 5 - S =2.72 SEED FLOW = 0.2
> O z LU ZD C. X = 2.40 a io - POLLEN FLOW = 0.9 LU " S = 3.24 SEED FLOW = 0.1 or 54
JML r-r T D.."x= 2.70 POLLEN FLOW = 0.9 10 S = 4.35 SEED FLOW = 0.2
5 - i 1 1— I 1 1-- 1-- 1-- 1— T 0 1 23456789 POPULATIONS FIXED OR NEAR FIXATION FOR SPECIES A
Figure 7. The effect of combined seed and pollen flow on coexistence.
Simulations specify different probabilities of choosing seeds from a common pool ("Seed Flow") along with different probabilities of pollinator flight between adjacent popu lations ("Pollen Flow"). Coexistence is indicated by the number of populations out of nine which reached or approached within 20% of fixation of species A. Each set of histograms represents 10 replicate simulations. In all cases, there were a total of 900 pollinator movements per generation. 27 are meant to reflect the short distances of pollen and seed dispersal often found in natural plant populations (e.g..
Levin and Kerster 1974 and references therein). Small amounts of pollen and seed exchange seem to be tolerated in the simulations, without leading to global fixation for one species. However, increase in the seed flow term from
0.1 to 0.2 clearly increased the tendency toward such an outcome. In Figures 7C and 7D, the values of seed flow are again set at 0.1 and 0.2, while pollen flow is 0.9. Under this condition of higher pollen flow between populations, the tendency toward global fixation was greatly increased.
Because seed exchange remains an effective means of gene flow even between populations that have progressed to fixa tion of different species, the species compositions of the nine neighboring populations were still fluctuating at the end of 15 generations in cases where global fixation had not resulted.
Discussion
The results of my basic model of competition for pollination suggest that two plant species which share pollinators and identical mechanics of pollination will not coexist indefinitely, and that interspecific transfer of pollen may form the basis of a series of mechanisms of competition. Levin and Anderson (1970) reached analogous 28 conclusions after exploring frequency independent and positive frequency dependent flower preference of polli nators (or "constancy") with a similar deterministic model.
In contrast, the formulation of competition for pollination by Straw (1972) leads to a prediction of indefinite co existence of two competitors, unless pollinator constancy for one species is introduced. This result derives from a fundamental assumption by Straw that a pollen load of either competitor which the pollinator picks up at the beginning of a foraging bout will suffice to completely pollinate all further plants of that species visited during the bout.
This ih:effect supposes that the amounts of pollen produced by flowers and carried by pollinators and the receptive areas of stigmatic surfaces are very large relative to the number of possible fertilization events in the plant popu lation, so that interspecific transfer of pollen has no effect on reproduction. Straw’s conclusions cannot be applied to any situation in which these conditions are not met.
The general outcome of competitive exclusion from my deterministic model and from that of Levin and Anderson
(1970) is obtained again in my computer simulations of pollination within a single mixed population of two plant species. Fixation of one species occurs in any case where pollinator movements or amounts of pollen flowing in the 29 system are chosen to be limiting relative to the total number of possible fertilization events; or in simulations stipulating competition for space on limited stigmatic surfaces between conspecific and heterospecific pollen grains. When these different competitive mechanisms act in combination in simulations, fixation of one species is relatively accelerated. With the rules specified in the
COMPOL program, however, fixation is rapid in all cases, usually occurring within 10 computer generations.
Although,pollination within a single plant popula tion always leads to fixation of one competitor in my simu lations , the duration of coexistence is extended slightly by the introduction, of refugia for each species' between which seed flow is restricted. This effect is carried to an extreme in simulations which consider plants to grow in a series of separate populations. With little or no seed exchange between populations, global coexistence of two competitors is obtained because each competitor is fixed in several populations. This outcome is more sensitive to an increase in seed exchange than it is to an increase in pollen exchange between populations.
The rules of pollen flow that are stipulated in simulations are. an attempt to retain simplicity and economy in programming without straying from biological realism.
For example, the fundamental assumption of random pollinator visitation of flowers is an approximation of the behavior
Of many pollinator types which exhibit little or no flower constancy - These include bumblebees and some solitary bees
(e.g., Clements and Long 1923, Grant 1950, Free 1970a,
Macior 19701, lepidopterans (e.g.. Levin 1968, Levin and
Berube 1972, Kislev, Rfaviz''and' Lordh ;'1S72)V' and hummingbirds
(e.g., Grant and Grant 1968). Pollen picked up by the pollinator at successive flowers is added to a common pool on its body, from which grains are drawn without replace ment for deposit on stigmas.. This process approximates the case in which pollinators are liable to brush the sexual parts of flowers with a large area of their body so that pollen grains picked up at any flower have an essentially random chance of contacting the stigma of the next flower visited. The simulations also stipulate that each successive visit to a flower depletes its initial pollen supply by a set amount, rather than that depletion is somehow positively related to the pollen remaining on the flower. There seems to be no data on this process
from natural systems, so that I chose between the alterna
tive sets of rules solely on the basis of simplicity.
The stipulation of equal probabilities of pollinator flight
in any of four directions on leaving a flower is a conscious oversimplification, since directionality in foraging move ments has been described for pollinators and other animals 31 (e.g.-/ Pyke 1974) . I do not expect that lack of direction ality in simulations has had any qualitative effect on the outcome, of simulations> however, since the sequence of
flowers encountered in the randomly mixed populations is close to random with respect to species identity regardless of directionality.
The small values chosen in simulations for the number of pollen grains flowing in the plant population may have led to sampling error and to rates of competitive exclusion which are overestimates for real systems„
However, the choices of ratios of pollen involved in dif ferent phases of pollination are biologically reasonable ones. For example, the ratio of the initial pollen in anthers to the number of grains picked up by each polli nator visit is 10:1 in most simulations. This is in good agreement with the ratio reported by Levin and Berube
(1972) for butterfly pollination of two species of Phlox.
The 10:3 ratio of the number of pollen grains picked up to the number deposited in each pollinator visit is
similarly reasonable (Levin and Berube 1972) ... Most simu
lations use a 20:1.ratio of initial pollen production in
anthers to the pollen capacity of stigmas, which agrees with some natural systems (Levin and Berube 1972, Ornduff
1975a), but underestimates pollen production in others
(Ornduff 1971, 1975b, Cruden 1972). Since simulations 32 do not allow for pollen loss between anthers and stigma, however, the initial pollen supply stipulated for flowers can be taken to represent only pollen which will potentially reach a stigma and which is fertile. These conditions may be met by only a small portion of all pollen in many systems.
For example, about 52% of Phlox glabberima pollen is lost during transport by Colias butterflies, about 90% of what remains is lost during deposit on the stigma, and 10% of all pollen is infertile. Therefore, only about 4% of all pollen is potentially involved in fertilization (Levin
1968, Levin and Berube 1972). With a suitable correction for pollen.loss, the 20:1 ratio of pollen production to pollen capacity of stigmas, and even the 3:5 ratio used in investigating pollen limitation, fall within the range of all the systems studied by Levin, Ornduff, and others.
Finally, the pollen capacity of stigmas exceeds the number of grains deposited in a single pollinator visit, such that multiple visitation is necessary for full pollination.
This is surely the case for many plant species (Cruden et al. 1976 and references therein). . To this point, I have emphasized animal pollinators in my treatment Of competition for pollination, and my simulations are explicit attempts to model competition in a system with animal mediated pollen flow. However, my basic conceptualization of competition might also apply 33 to some wind pollinated systems. The necessary condition for competition in such cases is for interspecific pollen flow in the presence of a competitor to cause a loss of pollen or a covering of stigmatic surface which would otherwise Contribute to a fertilization event. The covering of stigmatic surface seems the more likely of the two mechanisms for wind pollinated plants.
The outcome of global coexistence obtained in simulations which consider plants to grow in separate sub- populations immediately can be interpreted to mean that spatial subdivision of a meadow into partly isolated patches can allow coexistence of potential competitors in real biological systems. This will occur if each plant species goes to fixation in somh habitats. The size of habitat patches in nature and. the physical distances separating patches containing potential competitors might be on the order of only meters or tens of meters, given the short distances over which biotic and abiotic vectors disperse the majority of pollen grains and seeds in many systems
(e.g., Bateman 1947, Bradshaw 1972, Linhart 1973, Levin and Kerster 1974 and references therein)'. Pollinators which defend or return to distinct foraging areas that remain fairly stable during the receptive period of single flowers or plants may play an important role in subdividing initially homogeneous mixtures of competing plant species, J .. . 34 although the exact location of foraging areas will normally change from year to year. Temperate hummingbirds often defend small feeding territories on the order of 0.1 ha or less (e.g., Armitage 1955z Grant and Grant 1968, Stiles
1971, Lyon 1973) , and bumblebees may also work small patches of meadow covering a few square meters over periods of several days or longer (e.g., Grant 1950, Free ,1966 and references therein. Free 1970b and references therein).
A second possible interpretation of global co existence within an array of plant populations is that separation of flowering times of two species also allows coexistence and can be one evolutionary outcome of compe tition for pollination. This follows despite the fact that the dynamics of divergence in continuous time are not addressed in the simulations. If other selective forces acting on flowering time are relatively weak, individual plants Whose single or multiple flowers are receptive during a period distinct from flowering times of competitors should displace conspecifics whose flowering times more or less overlap those of competitors. The simulations can thus be taken to depict the division of a flowering season into time Slots which overlap each other slightly or not . at all, each of which is eventually relegated to one of several species sharing a common pollinator. Alternatively, they might depict the division of each day into separate 35 periods during which each of several competitors is sexually receptive and produces floral rewards attractant to polli nators (cf9 Synge 1947, Percival 1955, Gilbert 1975)« This process of temporal divergence requires only some original individual variation in flowering overlap with competitors upon which selection can act. The degree to which complete temporal divergence is achieved in nature should depend on what other forces bear on the evolution of flowering time, and on the degree to which the proximal cues available to individual plants for the timing of flowering are accurate predictors of the flowering state of competitors«
Several sorts of selective forces might counteract the reproductive advantage to competitors of divergence in flowering times, Divergence implies a decrease in overall flower densities relative to a situation of complete flowering synchrony between competitors« If densities are reduced beyond a certain point which should depend largely on pollinator foraging energetics and sensory abilities, the expected per-flower visitation rate by pollinators can be expected to fall. An equilibrium separation of flowering times may result at which the positive effect of density on pollination of individuals, and the negative effect of interspecific pollen transfer, are exactly balanced. A completely analogous case is that in which predators of 36 flowers or fruits are swamped at the high densities involved in overlap situations (of. Rolling 1959).
It appears that those simulations which analyze the effects of pollination in a series of partially isolated plant populations provide the most interesting insight into potential evolutionary effects of competition for pollination. Only these simulations directly reduce polli nator sharing and pollen flow between flowers of two com petitors, and thus reduce the reproductive cost of these events to the individual. I conclude that separation in flowering habitat or in. flowering times will be eventual and common outcomes where pollinators are shared, if the reproduction of any of the plant species involved is limited by the availability.of pollinators, pollen, or stigmatic surfaces. COMPETITION FOR POLLINATION AND SEQUENTIAL ; , ^ FLOWERING IN COLORADO WlLDFLOWERS
In the first section of this dissertation, I have shown how the sharing of a pollinator by two co-occurring , plant species may lead to a reproductive loss to both, as a result of mechanisms involving pollinator movement and pollen transfer between dissimilar flowers (see also Levin and Anderson 1970). Selection in such a system is ex pected to act within both species to reduce their sharing of the common pollinator, and one result may be the pro duction and maintenance of sequential flowering times.
In the Elk Mountains of west-central Colorado* hummingbirds are frequent visitors to a series of herbaceous species that flower consecutively in subalpine meadows»
In order of appearance, these are Delphinium nelsoni,
Ipomopsis aggregate* and.D. barbeyi. The first two of these species correspond closely in the habitats in which they grow. Their flowering times are strikingly sequential, with an overlap of one week or less out of total flowering periods of about one month for each species. In this section of the dissertation, I explore whether competition for pollination is implicated as.a selective force promoting the sequential flowering of D. nelsoni and I. aggregata*
■' 37 38 by asking the following questions. (1) Do hummingbirds
(or other animal visitors) pollinate both D. nelsoni and
I. aggregata? (2) If so, do such common pollinators fly
between flowers of the two species and. cause interspecific
pollen transfer? (3) Finally, does interspecific pollen
transfer result in a significant reproductive disadvantage
. to individuals of D. nelsoni and I_. aggregata which flower
together, relative to those separated in time or location of
flowering?
Methods
I studied pollination and flowering of D. nelsoni
and I_. aggregata during the summers of 1975 and 1976 at
the Rocky Mountain Biological Laboratory (hereafter RMBL),
' elevation 2900 m in the Elk Mountains, Gunnison County,
Colorado. RMBL lies at the confluence of two streams,
one to two km distant from ridges which rise to 3700 m.
Stands Of aspen (Populus tremuloides) grow on dry hillsides
around the field station, whereas spruce (Picea engelmanni)
and occasional fir (Abies lasiocarpa) predominate in
riparian situations. Interspersed in aspen forest are
patches of dry meadow in which D. nelsoni and I_. aggregata
are abundant. I chose a relatively homogeneous patch of dry meadow
covering about 0.2 ha for studies of natural populations of /
39 D. nelsoni and I_. aggregata, as follows. (1) To obtain
flowering phenology, I counted flowers of the two 2 species within six permanent 4 m plots scattered through
the study meadow. (2) To explore the relative contribu
tions of different animal visitors to the natural pollina tion of flowers, I chose 15 D. nelsoni plants and 12 aggregata plants for pollinator exclusion experiments.
While still in bud stage, one-third of these plants (five
D. nelsoni and four aggregata) were covered with a cage of window screen with mesh about 1 mm x 1 mm, to exclude
all flying visitors ("hummingbirds and bees excluded").
A further set. of five D. nelsoni and four aggregata were
treated in a similar way with cages of chicken wire with mesh about 6 cm x 6 cm, to exclude only large, visitors such as hummingbirds ("hummingbirds excluded").
My observations indicate that queens of even the largest bumblebee species at RMBL enter such cages. The remaining plants were left uncaged ("open pollinated"). Seed sets
of flowers from these three treatments were compared.
(3) To determine how the presence of a potential competitor
for pollination influences the reproductive success of plants
in nature, I tagged receptive flowers of each species at
times when the other species was and was not also in
flower, and later compared seed sets under these different
conditions. (4) As an indication of the major floral 40 reward offered to hummingbirds and many insect visitors to
D« nelsoni and aggregata, I measured the nectar contents in flowers of each species using 10 ul or 20 pi calibrated microcapillary tubes. When possible, I then determined the equivalent sucrose concentration of nectar samples with a hand reftachometer. This provides an accurate expression of caloric value of nectars of flowers such as those of
D. nelsoni and I. aggregata, which contain primarily sucrose and monosaccharides such as glucose and fructose (Percival
1961, Watt, Hoch and Mills 1974). With these methods, I measured standing crops of nectar in flowers, and estimated rates of nectar production in flowers bagged with fine- mesh nylon netting to exclude all visitors. Because of their long and constricted corollas, I was forced to pick and dissect flowers of D. nelsoni and T. aggregata while extracting nectar. Therefore, I was unable to empty flowers used for nectar production estimates before bagging them, and production values include standing crops contained in flowers at the time of bagging. To minimize this error,
1 usually bagged flowers at dusk, when I have found standing crops to be lowest (about. 0.2 #1 for D. nelsoni and 0.8 ul for I. aggregata).
To supplement studies with natural populations,
I constructed synthetic populations using transplanted .
D. nelsoni and I . aggregata. Flowering times of these species are largely separate at RMBL. However, it is pos sible to collect individuals of the two species whose flowering times completely overlap, by locating populations of To aggregata at an elevation where seasonal timing is appropriately advanced relative to populations at the field station. In 1975 and 1976, I transplanted budding aggregata individuals from a site at 2400 m elevation and
40 km down the valley below RMBL into 13 cm by 13 cm paper flower pots. On the same days, I transplanted budding individuals from populations of D. nelsoni near RMBL. I kept transplants inside unheated laboratory buildings for one to two days after they were collected, and watered them frequently. They then were used in the following experiments. (1) To assess the effects on reproductive success of simultaneous flowering of D. nelsoni and I. aggregata, I exposed different mixtures of transplants to natural pollination in a meadow which was separated by about 100 m from the nearest natural populations of either species. In 1975, I constructed one plot in this meadow, containing eight individuals of each species alternated in 2 a square grid covering 4 m ? and two "control" plots of the same arrangement containing 16 individuals of each species alone (Figure 8). I matched transplants used in control and competition plots as closely as possible ac cording to size and number of buds, and placed control plots 42
• • • • • = D. nelsoni • • • • o = _[. oggreqato ZK
5 to C\J
N/ o o o o o o o o o o o o o o o o 2 0 - 2 5 M. 2 0 - 2 5 M. /K 2 M. 2 to CM
o o o o o o o o
Figure 8. A diagram of synthetic populations of D. nelsoni and aggregata.
Control plots of 16 individuals (1975 and 1976 replicates) and/or eight individuals (1976 replicates) of either species alone are separated by 20-25 m from a central mixed competi tion plot. 20 m to either side of the competition plot. The densities
of each species in experimental plots approximate their
natural densities around RMBL. I watered transplants
once a day, and measured seed sets of both species in all plots after the end of flowering. (2) I repeated this
experiment twice in 1976, with slight modifications. The
first replicate contained control plots of eight rather
than 16 individuals, each arranged in the same pattern as
the eight individuals of that same species in the mixed
competition plot. The second replicate contained two
controls of eight and two of 16 individuals, arranged around a central competition plot (Figure.8). In both replicates,
I increased the separation between control and competi
tion plots to about 25 m . ' I watered plants once a day and
counted flowers every other day. Controls of 16 individuals
were meant, to duplicate the overall density of plants (and
thus, roughly, of floral rewards) in the competition plot,
and those of eight individuals were meant to duplicate the
density of each species by itself in the competition plot.
In both 1976 replicates, late season snow and frost caused
plant mortality and damage in one or more control plots
which substantially exceeded that in competition plots.
Both controls of eight individuals in the second replicate
were so affected, along with the Ipomopsis control plot
in the first replicate. I do not consider the results from these plots. (3) Finally, I attempted to duplicate
effects of natural pollination by keeping 10 potted trans
plants of each species inside a laboratory building during
1976, and hand pollinating them with a mummified specimen
of a male broad-tailed hummingbird (Selasphorus platycercus).
I set aside five individuals of each species as controls,
and combined the remainder to form a competition mixture of
10 plants. I matched the plants chosen for these two
treatments as closely as possible according to size and
number of buds. During hand pollination, I moved the
hummingbird specimen so as to contact about 80% of the
flowers on each plant before switching to the next plant, which approximates the intensity of visitation I observed
in natural populations around RMBL. The ratio of inter-*
to intraspecific movements between plants in the competi
tion mixture was 1:1, and all movements in control groups
were intraspecific. Each plant was hand pollinated nine
times over a period of 10 days in which flowers of all
individuals were receptive. I measured seed sets of each
species resulting from the two treatments.
I used t-tests for small unequal samples for paired
comparison of seed set samples and other data, and two-
way ANOVAs for comparison of samples from more than two
treatments. Before performing these tests, I confirmed 45 the normality and homogeneity of variance of representative data samples (Sokal and Rohlf 1969) (Appendix B).
Concurrently with studies of flowers, I monitored potential pollinators to jD. nelsoni and X_. aggregata. I made observations by eye or with binoculars of hummingbird and insect visitation to these two species, and of humming bird visitation to other flowers. With the aid of a port able cassette tape recorder, I obtained sequences of flower visits of hummingbirds foraging in natural and synthetic populations. I captured representative insect visitors at flowers of both species, collected pollen from their bodies and corbiculae (in the case of bumblebees), and mounted and stained these collections in fuchsin glycerin gel
(Wodehouse 1935), I mist-netted hummingbirds in meadows or at sugar-water feeders hung from laboratory buildings, arid mounted and stained pollen collected from their facial plumage and mandibles. I also measured the length of the upper mandible to the nearest 0.5 mm on all captured hummingbirds. Finally, I collected stigmas of D„ nelsoni and aggregata which had been exposed to natural and synthetic conditions of flowering overlap with each other.
In all cases, I combined the pollen from groups of three to four stigmas in preparing pollen slides. I was able to identify almost all pollen to genus, by microscopic 46 comparison to reference slides I prepared in 1975 directly from common flowers around EMBL. .
Results
Visitation and Pollination of D. nelsoni and 1^. aggregata
. Delphinium nelsoni (Ranunculaceae), the low lark
spur, is an herbaceous perennial which produces about two to ten blue or blue-purple flowers on a racemous inflores cence (Figure 9), Its flowers are strongly zygomorphic, with a long spur composed of two nectariferous petals covered by the top-most of five petaloid sepals. The numerous stamens and (usually) three simple pistils arise from below, the opening to the spur, and are covered by the remaining two petals. The sexual parts are erect in turn as they mature, thereby obstructing entrance to the spur and the nectaries. The flowers are protandrous, and their position on the inflorescence indicates relative age and
sexual condition, with older, pistillate flowers lower on the plant (cf» Epling and Lewis 1952). .
Ipomopsis aggregata (Polemoniaoeae), the scarlet
gilia,.is a common biennial herb of western montane regions, whose flowers exhibit geographical diversity in color and
shape (Wherry 1961, Grant and Grant 1965). Populations
at RMBL produce numerous scarlet flowers on paniculate-
racemose inflorescences (Figure 9). Flowers are I cm.
I. aggregate
D. nelson!
Figure 9. Plants and flowers of D. nelson! and I_. aggregata
Flowers of the two species are drawn to a common scale, as shown. 48 actinomorphic, and nectaries are positioned at the base of a long, narrow corolla tube. The. five stamens are attached radially just inside the opening to the tube. The three carpels fuse to produce a single style with a three-lobed stigma, which is exserted after the anthers dehisce.
These two species are among the four which are very abundant around RMBL as well as highly attractive to humming birds (Table 1). For this reason, they are among the major nectar sources of broad-tailed hummingbirds (Selasphorus platycercus) which are resident in the area. Female broad-tails initiate nesting around RMBL in early June, soon after the appearance of D. nelsoni flowers (Waser
1976). At the same time, males establish large breeding territories (sensu Stiles 1972) which include dense patches of P.. nelsoni, and which foraging females often enter.
These territories usually persist until early-or mid-July, past the end of flowering of D. nelsoni and into that of
I,. aggregata in the same meadows. At this time, southward migrating rufous hummingbirds (£5 = rufus) appear around
RMBL. Rufous males often displace broad-'tails, in the process partitioning the large territories of the latter into much smaller feeding territories (cf. Feinsinger and
Chaplin 1975).
Nectaries of D. nelsoni and aggregata are re cessed such that their access is limited to visitors with Table Iv Flower species visited by broad-tailed hummingbirds at RMBL, 1975-1976.
(1) R = rare, C = common. (2) Values are in mm and are expressed as means ± one standard error, with sample sizes in parentheses. U — unknown? NA = not applicable. (3) Values are in % sucrose equivalents by weight, and are expressed in the same way as corolla lengths. U = unknown. (4) - species which are both abundant and frequently visited, and are therefore considered the major nectar sources of hummingbirds at RMBL.
Abundance Frequency of Corolla Tube or Nectar Concen- Flower Species at RMBL (1) Visitation (1) Spur Length (2) tration (3)
Mertensia fusiformes CR u U
Mo ciliata C R 14 o 8 ± 0.25(8) U
Delphinium nelsoni (4) CC 21.8 ± 0.15(77) 51.2 ± 0.70(121)
D. barbeyi (4) C C 17.5 ± 0.18(11) 41.6 ± 1.33(22)
Lonicera involucrata R C 18.8 ± 0.22(15) 24.5 ± 0.93(6)
Hydrophyllum fendleri C R U U
Frasera speciosa R CNA U
Ipomopsis aggregate (4) c ' . . C 26.6 ± 0.29(76) 24.7 ± 0.37(202)
Iris missouriensis R R U U
Pedicularis bracteosa R C 21.8 ± 0.33 (20) 42.5 ± 9.50(2)
Castilleja miniata (4) C C 23.1 ± 0.26(13) 32.5 ± 0.50(2)
C. sulphurea C R 18.7 ± 0.20(12) 19.9 ± 1.41(4)
Aquilegia elegantula R . C 28.7 ± 1.43(13) 35.3 ± 2.33(10)
A, coerulea C R UU 50 relatively long tongues„ Both broad-tailed and rufous hummingbirds should be able to extract nectar from these flowers, since they can extend their tongues to probe corollas which are up to about twice as deep as the length of their bills (of. Hainsworth 1973, Stiles 1975). In so doing, the mandibles and facial plumage of the birds contact, the sexual parts of the flowers, such that they carry both
D. nelsoni and 31. aggregata pollen on -their chins and lower mandibles, and 3E. aggregata pollen on their foreheads and upper mandibles as well (Table 2, Figure 10). Delphinium nelsoni also is visited commonly by nectar-foraging queens
Of three bumblebee species which are resident around RMBL.
Bombus appositus, with the longest proboscis, and B . flavifrons, with an intermediate length proboscis, both insert their heads completely or partly into the opening to the corolla spur in order to reach the nectaries (cf.
Macior 1975). Bombus occidentalis, with a short proboscis, robs the nectaries by biting directly through the spur without contacting the sexual parts of the flower. Queens of the fourth resident species at RMBL, B. bifarius, rarely visit D. nelsoni. With their short proboscises, they may be unable to reach the nectar or to extract it efficiently (cf. Brian 1957, Hobbs, Nummi and Virostek
1961). Long tongued swallowtail butterflies (Papilio rutulus) are able to reach the nectaries of I. aggregata. Table 2» Summary of pollen collected--from hummingbirds and bees, 1975-1976.
(1) BT = broad-tailed hummingbird, RUF = rufous hummingbird, (m) = male, (F) = female. No species is listed for females whose identity was ambiguous. (2) B.a. = Bombus apposifcus,.B.b. = B. bifarius, B.f. = B. flavifrons, B,o. = B„ occidentalis, H."A" = Halictus sp. "A", H."B" = Halictus sp. "B". All bumblebees are queens. Col lections from Halictus sp. "B" contain about 20% Compositae pollen in addition to that of D. nelsoni. All other visitors carried es sentially pure loads of D. nelsoni, r. aggregate, or both together, with occasional conifer and Compositae grains constituting 5% or less of all pollen.
Pollen Carried D. nelsoni + D. nelsoni I. aggregate I. aggregate None
Hummingbirds (1) (Period of Capture)
D. nelsoni flowering, 1975 1 BT(M), 3 BT (M) 3 BT(F)
D. nelsoni + 4 BT(M), 3 RUF (M) 2 RUF (M) 1 BT (M) I. aggregate 1 RUF (M) 2 (F) flowering, 1975
I. aggregate — 2 RUF (M) — — flowering, 1975
D. nelsoni flowering, 1976 1 BT(M) — — mm mm — —
D. nelsoni + — — 4 BT(F), 1 BT(F) 1 BT (M) I. aggregate 1 BT (M) flowering, 1976 Table 2. (Continued)
______Pollen Carried______D. nelsoni + D . nelsoni I aggregate I. aggregate None
I. aggregate 1(F) flowering, 1976
Bees (2) (Place of Capture)
D. nelsoni flowers. 1975 1 B.a. -- —
D. nelsoni flowers. 1976 2 B.a. , 1 B.o. 2 B.f., 1 B.b. , 2 H. "B"
I. aggregate — — 1 H."A" 1 B.a., — — flowers, 1976 1 H."A" 53
D. 11 el so ni
#»
I. aggregata S. plotycereus d1
I cm
Figure 10. Cross-sectional drawings of flowers, with a broad-tailed hummingbird shown to the same scale. 54 and I have occasionally seen them visit these flowers.
During some summers (but not in 1975 or 1976), hawkmoths
(Kyles lineata) have appeared for brief periods in the
RMBL area, where they foraged intensively at IE. aggregata.
Bumblebees and solitary bees also visit both flowering species in apparent search of pollen alone, which may be obtained by short as well as long tongued species.
One small solitary bee (Halictus sp. "A") crawls completely into the narrow corolla of aggregata to reach the anthers, and I captured one individual in a synthetic competition plot in 1976 carrying D. nelsoni pollen in addition to that of I. aggregata (Table 2). A second, larger species
(Halictus sp. "B") is a fairly common visitor to D. nelsoni.
My pollen collections from flower visitors indicate that all bumblebees visiting D. nelsoni (with the exception of
B. occidentalis). collect and transfer some pollen, as do occasional B. appositus queens which probe aggregata flowers when these first appear (Table 2).
These observations of potential pollinators Of
D. nelsoni and aggregata are summarized in Table 3. They agree with those reported by Watt et al« (1974) for this same area in Other years; by Grant and Grant (1965) for
][. aggregata in other areas; ahd by Clements and Long
(1923) and Macior (1975) for other species of Delphinium in eastern Colorado and the midwest. Hummingbirds in Table 3, Visitors to flowers of D„ nelsoni and aggregata at RMBL, 1975-1976.
(1) M = male, F = female, Q = queen. (2) Values are in mm and are expressed as in Table 1. Those for Bombus spp. (= prementum + glossa) are from eastern Colorado (Macior1974)? those for Halictus spp. are estimates based on European species (Knuth 1906). (3) Visi- tation scored as C (= common) R (= rare), or U (= unknown); pollen carrying scored as + (= pollen collected from individuals visiting flowers or otherwise captured during flowering of appropriate species), (= no pollen), or U (= unknown).
Sex/ Culmen/ Delphinium nelsoni (3) Ipomopsis aggregata Caste Proboscis Visita Pollen Visita Pollen Visitor (1) (2) tion Carrying tion Carrying
Hummingbirds
Selasphorus platycercus M 17„OiOoll(29) C + C 4*
S. platycercus F 18•5i0*19 (35) C + C 4*
S. rufus M 15o9±0.16(16) R 4* C +
So rufus F 16.510.16(17) R + C 4-
Bees
Bombus appositus Q 12.810.05(50) C + R 4-
B « flavifrons Q 10.210o10(50) C > ; UU
B. bifarius Q 8 o41 0 o06(50) R 4* U U
B. occidentalis Q 0.310.04(49) R -U U
Halictus sp„ 81 A” F <6 R 4* U U
Halictus sp» 11B” F <6 R + R +
Butterflies
Papilio rutulus u u U U R u 56 particular visit both D. nelsoni and I. aggregata, and may be expected to transfer pollen between the two species
in situations where they overlap in their flowering.
The pollinator exclusion experiments conducted in
1975 provide additional evidence for the important role of hummingbirds in pollination of D„ nelsoni and I . aggregata
(Table 4). Flowers of both species exposed to hummingbirds in addition to smaller visitors ("open pollinated”) had significantly higher mean seed sets than those from which hummingbirds were selectively excluded ("hummingbirds excluded") . In addition, D. nelsoni set few and aggregate set no seed in the absence of visitors ("humming birds and bees excluded")o This suggests that protandry in both species largely prevents self pollination within
flowers, and that seeds produced in nature are the result of pollinator visitation. Delphinium nelsoni is potentially
self compatible, as shown by the fact that self pollination by hand yields about 65% of the seed set per fruit obtained with outcrossing pollination by hand (Price and Waser 1976) .
Pollen Transfer by Hummingbirds in Situations of Flowering Overlap between D. nelsoni and I,» aggregata
D. nelsoni and 1. aggregata grow together in dry meadows around RMBL, but their flowering times are largely distinct. Delphinium nelsoni flowers after snowmelt in
late May or early June, appearing first on steep slopes and 57 Table 4« Seed sets, per flower from pollinator exclusion experiments, 1975.
Values are means ± 1 standard error, with sample sizes (number of fruits) in parentheses; values of t-statistics and associated probabilities are also shown (one-tailed tests).
Hummingbirds Hummingbirds and Pollinated Excluded Bees Excluded
Ipomopsis aggregate
10.17 ± 0.59 (59) 7.94 ± 0.70 (31) Aborted (26)
t = 2.43 t = 10.26 s s .02 Delphinium nelsoni 49.54 ± 2.35 (28) 30.83 ± 3.02 (18) 1.07 ± 0.51 (28) t = 4.92 t = 11.94 p <.001 p <.001 58 later in level patches of meadow. Ipomopsis aggregata fol lows this same flowering progression, appearing about four weeks after D„ nelsoni at any given spot. This means that the flowering of the two species is broadly overlapping in the RMBL area as'a whole, but that overlap is limited to one week or less within small patches of meadow on the order of 0.1-0.5 ha. Figure 11 shows the flowering phenology of D. nelsoni and 1_. aggregata in my study meadow during 1975 and 1976. For comparison, I also show the phenology of these species along with that of the other two major hummingbird nectar sources, Delphinium barbeyi and Castil- 2 leja miniata, from 1973 counts in 20 4 m plots spread throughout the RMBL area„ Despite differences between years of one to two weeks in overall seasonal timing, D. nelsoni and 1^ aggregata retained their sequential flowering pattern. The greatest flowering overlap came in years of late showmelt which shortened the summer growing period and compressed flowering seasons. This is seen in 1975 and in 1973 (the large area over which I counted flowers in 1973 also contributes to an apparently longer overlap period). During the brief flowering overlap in any meadow, I have often noticed broad-tailed hummingbirds flying between plants of D. nelsoni and I. aggregata. Figure 12 59 40 n 3 0 - 0. nelsoni °....L oggregofa o 20 - borbtyi 10 - N A....C. miniofo 5 10 15 20 25 30 5 10 15 20 25 31 5 10 15 20 25 1975 ae 30 - o 20- u bias 5 10 15 20 25 30 5 10 15 20 25 31 5 10 15 20 25 1976 50 -i 4 0 - W 30- 20 - 10 - v 111111 j 111111 5 10 15 20 25 30 5 10 15 20 25 31 5 10 15 20 25 JUNE ------II------JULY II---- AUGUST 1 9 7 3 Figure 11.• Flowering phenology of D. nelsoni and I. aggregate in the study meadow at RMBL, 1975-1976. Also shown is the phenology of these species along with that of D. barbeyi and C. miniata in 1973. Notice that the 1976 season is earlier than the others, and that flowering overlap of D. nelsoni and aggregate is shorter. 60 FROM TO D. nelsoni I, aggregate o 23 .04 D. nelsoni (.26) (.02) . .05 . 68 . I . aggregate (.02) (.70) Figure 12. Foraging movements of hummingbirds in meadows, 1976. Data are from 7 male, and 5 female broad-tails foraging during natural flowering overlap of D. nelsoni and aggregate. Values in parentheses are frequencies of flower-to-flower movements (n = 529); those without parentheses are frequencies of plant-to-plant movements (n = 211). summarizes my observations of inter- and intraspecific movements in foraging bouts from 1976. Because flowers of the two species were spatially separated on a fine scale during their short temporal overlap, and because most plant-to-plant movements were to neighbors (Price and Waser 1976) , hummingbirds fed at long series of flowers of either species before encountering patches of the other. This partly explains why only 9% of all plant-to-plant movements and 4% of all flower-to-flower movements were between species.. Also, the high frequency of Ipomopsis-Ipomopsis movements reflects an apparent preference for this species, whose flowers produce about five times the nectar volume of D. nelsoni flowers during a 24 h period, and contain up to five times the expected standing crop as well (Table 5). These discrepancies are partly offset by the fact that D. nelsoni nectar is slightly over twice as concentrated as that of aggregata (Table 1) . However, the rate of nectar extraction by hummingbirds declines at sugar con centrations above about 25% sucrose equivalents by weight, because of a rapid increase in viscosity (Hainsworth 1973, Baker 1975). Despite the lower expected standing crops in D. nelsoni flowers, my 1975 observations indicate that it took broad-tailed hummingbirds just as long to extract nectar from, them as from those of aggregata (0.87 flowers/sec during 10 bouts by males and females at 185 Table 5. Nectar productions and standing crops in flowers of D „ nelsoni and I_. aggregata in the study meadow at RMBL, 1975-1976» Values are means ± one standard error, and are expressed first as ul liquid and underneath (in parentheses) as mg sucrose-equivalent sugars„ Sample sizes are shown in parentheses following ul values. Nectar pro duction values include standing crops contained in flowers at the beginning of the 24 h production period. P. nelsoni i.” aggregata Date Standing Crop 24 h Production Standing Crop 24 h Production 6/20/75 0.20±0.OSyl (54) 0.70±0.ISyl(45) -- ■ (0.11±0..03mg) (0.40+0.08mg) 7/9/75 0.50 + 0.09yl (18) 1.50±0.38yl(10) 2.50±0.41yl(17) 6.50+0.38yl(37) (0.23±0.04mg) (0.68±0.17mg) (0,47+0.OSmg) (0.99±0.06mg) 7/18/75 0. 60±0.;02yl (20) 1.10±0.41yl(10) -- - -- (0. 22±0 . Olmg) (0.40+0.15mg) 7/19/75 -- 1. 20±0.25yl(48) 5.80±0.24yl(67) (0.26+0.02mg) (1.28+0.OSmg) 6/8/76 0.16+0.04yl(21) — — — — -— • • • — — (0.08+0.02mg) 6/12/76 0.15+0.03yl(34) 0.72±0,15yl(22) ——— ------(0.06±0.Olmg) (0.38+0.08mg) 6/21/76 0. 03±0.Olyl(12) 0.48±0.10yl(15) 0.12±0.03yl(10) 3.42±0.33yl (26) (0.02+0.Olmg) (0.26±0,05mg) (0.03+0.Olmg) (0.90+0.07mg) 7/15/76 ------—— 0.91+0.18yl(26) 2.32±0.27yl(28) (0.23 + 0. 05mg) (0.54+0.07mg) 63 D. nelson! flowers versus 0.85 flowers/sec during five bouts by males and females at 137 1. aggregata flowers). This suggests that the expected reward per unit foraging time at aggregata is often about two times that for D. nelsoni. The synthetic competition mixtures of transplanted D. nelsoni and aggregata achieved a maximum degree of spatial and temporal flowering overlap. Interspecific movements by broad-tailed hummingbirds foraging in these mixtures constituted 44% of all plant-to-plant and 14% of all flower-to-flower movements (Figure 13). These fre quencies exceed those in natural meadows, where overlap is low. If hummingbirds chose plants totally without pref erence while foraging, the expected frequency of each of the four classes of plant-to-plant movements would be 25%, whereas the. actual frequency between plants of I_. aggregata was 43% and between plants of D. nelsoni was 13%. These 2 deviations from expectation are highly significant (X = 27.64, d.f. = 1, p <.001, using actual movement fre quencies), and they again suggest a strong preference . for I. aggregata. The interspecific movements of hummingbirds effec tively transfer pollen between dissimilar flowers. During periods of flowering overlap of D. nelsoni and I_. aggregata in meadows in 1,975 and 1976, I captured both broad-tailed 64 FROM TO Do nelsoni I. aggregata .13 .18 Do nelsoni (.28) (.07) .26 .43 lo aggregata (.07) (.58) Figure 13» Foraging movements of hummingbirds in synthetic populations, 1976, Data are from 19 male and one female broad-tails foraging in competition plots containing D= nelsoni and aggre gata. Values in parentheses are frequencies of flower-to- flower movements (n = 256)? those without parentheses are frequencies of plant-to-plant movements (n = 88). 65 and rufous hummingbirds with pollen of the two species mixed on their chins and lower mandibles (Table 3). In addition, all 10 pollen preparations from stigmas of the two species collected in natural and synthetic conditions of flowering overlap contained pollen of both species. These prepara tions included three of D„ nelsoni and four of aggregata pollen from natural populations, arid one of D. nelsoni and two of I_. aggregata pollen from competition plots. In contrast, single preparations from stigmas collected during the riatural flowering of each species alone, and from stigmas collected from control plots of each species, con tained only pure loads. The movement of pollinators between dissimilar flowers, and the interspecific pollen transfer which follows from it, are central factors in mechanisms proposed to lead to competition between species sharing a pollinator (Sec tion 1 of this dissertation). One such mechanism involves the deposition of foreign pollen on stigmas whose receptive surface area is limiting to reproduction. Under a dis secting microscope, I estimated the receptive surfaces of the stigmas of D. nelsoni and I_. aggregata at 0.036 rnm^ 2 and 0.309 mm respectively, a ratio of 1:8.6 (Figure 14). The corresponding cross-sectional areas of pollen grains 2 2 are about 0.0003 mm and 0.0020 mm , a ratio of 1:6.3. From these estimates, I calculate that it would require 66 o 3 © © © D. n e I s o n i 0.2 m m 0.0 5 mm. I. V ■> v- I. aggregate Figure 14. Stigmas and pollen grains of D . nelsoni and I. aggregata drawn to common scales. 67 on the order of 900-1000 grains of D„ nelsoni pollen to completely coyer the single stigma of an aggregata flower, and only on the order of 45-75 aggregata grains to cover the three stigmas of a D. nelsoni flower. Seed Set Depression in Natural and Synthetic Situations of Flowering Overlap Delphinium nelsoni and Ipomopsis aggregata share hummingbird pollinators, which fly between flowers of the two species when these occur together in synthetic competi tion mixtures and during a brief period of overlap in natural meadows. Individuals of both species should suffer a reproductive loss in these situations, if mixing of pollen on stigmas or any other competitive mechanism in volving interspecific pollinator movements is acting. Similarly, a reproductive loss may appear in mixtures of transplants exposed to hand pollination, which simulates the mixing of pollen caused by natural interspecific move ments . A significant depression in the mean seed set of ! both D. nelsoni and It. aggregata flowers occurred during the period of their natural overlap in my study meadow at RMBL. Table 6 summarizes these, results from 1975 and 1976 (no fruits of IE. aggregata Were collected in 1975 in the study meadow). In both years, seed sets of flowers receptive Table 6. Seed sets as a function of flowering time in the natural study meadow at RMBL, 1975-1976. (A) Seed sets of aggregate flowers receptive during ("overlap") and after ("non-overlap") the flowering of D. nelson! in 1976. Values are expressed as in Table 4. (B) Corresponding results for D. nelsoni flowers in 1975 and 1976, with results from an ANOVA with the raw data. Non-overlap Overlap (A) Ipomopsis aggregate (1976) 14.4210.82 (26) 10.00 + 0.88 (21) ts = 3.67 p <.001 (B) Delphinium nelsoni (1975) 49.54+2.35(28) 26.6913.01 (16) Source of Variation d.f, F< (1976) 41.99+1.82 (43) 29.62 + 1.53 (55) Subgroups (Plots) 3 Years 1 2..06 .15 n.s, Treatments 1 58.76 <.001 Interaction 1 5.64 .02 Error 138 69 during overlap periods were about 30%. to 45% below those of flowers receptive before or after overlap periods. The seed set depression in natural populations of D. nelsoni corresponds with the end of flowering of this species as well as with the presence of I. aggregate flowers. Since D. nelsoni is strongly protandrous, I attempted to determine whether some abrupt decline in the proportion of staminate flowers at the end of the flowering period, and thus in the pollen available per pistillate flower, is a proximate cause of the reproductive effect. At least during 1976, this appears not to have been the case. The sexual composition of the population did not •change distinctly or significantly over the period in which flowers were receptive whose seed sets were later compared (Figure 15). The reproductive loss to both species in natural meadows was paralleled by that in synthetic populations of potted transplants in 1975 and 1976 (Table 7). In three replicates with D . nelsoni and two with I_. aggregate, seed sets in competition plots were reduced by about 25% to 50% below those in corresponding control plots. Seed sets within both treatments also differed by about 25% between the two 1976 replicates with D. nelsoni. The replicate with a control of eight individuals was initiated about 10 days later in the summer than that with a control 70 q 40-, 30- fO r 30 >■ m ro to o 2 0 - Z C L -5 Z C O m < o: » 10- S ^ di - 0*~p~ J Li. w 20 25 30 JUNE Figure 15. The sexual composition of the D. nelsoni population in the study meadow in 1976. Histograms show the percent pistillate flowers in the popu lation before and during the period of flowering overlap with ly aggregata, as indicated by plots of flowering phenology. The numbers of flowers sampled for sexual con dition on different dates are indicated above histograms. The two periods over which samples were taken (left and right groups of histograms) correspond to those from which D. nelsoni seeds were drawn for comparison of seed sets before and during flowering overlap with aggregata. There is no significant overall heterogeneity among indi vidual samples in the frequency of pistillate flowers (X2 = 1.61, d.f. = 10, p >.99 n. s.) . Table 7. Seed sets in synthetic populations, 1975-1976. (A) Seed sets of I* aggregate from three replicate sets of competi tion and control plots. Values are expressed as in Tables 4 and 8. (B) Corresponding results for D„ nelsoni from three replicates with control plots of 16 individuals„ (C) Results for D. nelsoni from one replicate with a control plot of eight individuals„ Control Competition Plots Plots (A) Ipomopsis aggregate (1975) 8„77±0.89 (14) 5.6911.00 (13) Source of F Variation d.f, (1976) 13.67+0.66(42) . 9.00+0.43(77) Subgroups (Plots) 3 Years 1 23.34 <.001 Treatments 1 43.34 <.001 Interaction 1 0.90 .35 n.s. Error 141 (B) Delphinium nelsoni (1975) 39.52 + 1.83 (35) 30.94+1.49(31) Source of Variation d.f, P (1976) 41.48+2.69(21) 25.85 + 3.92 (13) Subgroups (Plots) 3 Years 1 0.40 .53 n.s. Treatments 1 21.93 <.001 Interaction 1 1.69 .20 n.s Error 96 Table 7o. (Continued) Control Competition Plots Plots (C) Delphinium nelsoni (1976) 29.1712.81 (18) 18.2012.50 (15) tg = 2.86 .OOKpc.Ol K) 73 of 16 individuals, and was probably exposed to a substan tially different regime of natural pollination. In all synthetic populations, seed sets in competition and control plots were only slightly lower than those from natural Situations of flowering overlap and non-overlap of the two species (see Table 6). My 1976 counts of the number of flowers per plant throughout the flowering in each replicate yielded no significant differences between individuals in competition and control plots (Willcoxon's signed-rank test, Appendix C) . Because of this, I take seed set., results to indicate a reproductive loss in competition plots to individual plants as well as to single flowers, at least during 1976. Finally, Table 8 summarizes results from the hand pollination experiment of 1976. A significant depression in mean seed set of about 25% appeared in those 1. aggregate flowers exposed to pollen mixtures, relative to those not so exposed. The corresponding difference in the small sample of D. nelsoni flowers was slightly in the opposite direction, although it was not significant. These results are counter to the expectation that D. nelsoni will be more strongly influenced than I_. aggregata by interspecific pollen transfer, because of the small cross-sectional area of its pollen grains and the small area of its stig ma tic surfaces. On the other hand, competitive ability 74 Table 8. Seed sets from the hand pollination experiment, 1976. Values are expressed as in Table 4. Control Individuals Competition Individuals Ipomopsis aggregata 9.8710.94 (23) 7.5010.54 (32) ts = 2.33 .02 Delphinium nelsoni 11.8013.03 (15) 13.9413.06 (16) t = 0.46 s p>.50 n.s. ' ' ^ 75 may be influenced by things other than the simple size of pollen relative to that of stigmas? such as differential pollen production, differential ability of pollen to adhere to pollinators and stigmatic surfaces, or complicated mechanisms of excluding competing pollen grains from Stig matic surfaces. - Discussion In this dissertation, I stress mechanisms of com petition for pollination in which a reproductive loss to co-occurring plant species follows from pollen exchange between them. This conceptualization is very broad. In addition to competitive mechanisms which are specific to animal pollinated systems (e.g., pollinator foraging move ments or floral rewards limiting to plant reproduction), it includes those which could occur in wind pollinated as well as animal pollinated systems (e.g., amounts of pollen or of receptive stigmatic surface limiting to reproduction). These competitive mechanisms apply equally between indi viduals belonging to distantly and to closely related faxa, one formal difference being that in the latter case, interspecific pollen exchange resulting in hybrids of even a low fertility may represent only a partial rather than a total loss of gametes. The interactions I have outlined above are distinct from another form of competition for pollination, in which ■■■ - "■ ' 76 one plant species partially or completely draws away pol linators from another and in which interspecific pollinator movements are presumably not the sole cause of observed reproductive effects. Such competition has been reported in situations involving introduced plants or pollinators (e«,g. , Linsley and MacSwain 1947, Free 1968 and 1970b, Hocking 1968), where it may result because plant and pollinator population densities have not been allowed to equilibrate relative to one another„ If pollinator popula tion density is limited only by the food supply provided in flowers, it should eventually increase such that all co-occurring plant species are visited in proportion-to the floral rewards they offer (cf. Heinrich 1975c, 1976). This may not happen if pollinator population density is limited by other factors, or if behavioral or nutrient constraints keep pollinators from selecting flowers or foraging microhabitats simply on the basis of maximizing their rate of caloric intake (cf, MacArthur and Pianka 1966, MaeArthur 1972, Pulliam 1976). Although I have not directly explored this, my observations of foraging in natural meadows and in synthetic populations suggest that flowers of I. aggregate are always more attractive to hummingbirds than those of D. nelsoni. Therefore, com petition involving pollen mixing between these species may 77 be combined with some form of competition for hummingbird visits themselves. Models of competition for pollination involving interspecific pollen transfer imply that the less common of two competitors will always suffer extinction if it is not separated along some dimension which effectively re duces sharing of pollen vectors (see first section of this dissertation and Levin and Anderson 1970). If these models are at least qualitatively accurate, the outcome of com petition in plant communities may be to produce divergence I in characteristics such as flowering time on a seasonal or daily basis, habitat affinity, and the morphology of floral parts which dictate pollinator affinity by determining which visitors will gain access to nectar and pollen and how anthers and stigmas will contact their bodies as they do. Divergence of plant species in any of these char acteristics erects an effective barrier to pollen flow between them (Grant 1950). Divergence in flowering time may be an especially rapid outcome of competition for pollination, judging from the speed with which natural and artificial selection can act on this trait. For example, Stanford, Laude and Booysen (1962) found that the date of first flowering in three populations of clover was advanced by an average of 12.7 days after three generations of cultivation in California, relative to first flowering in the parental Idaho stocks„ Similarly, Akemine and Kikuchi (in Allard and Hansche 1964) found that only four generations of selection in natural environments in the north and south of Japan produced a heritable difference in mean flowering time of about 60 days between two populations of cultivated rice. By artificial selection against hybrids of two varieties of maize, Paterniati (1969) was able to reduce crossing between them from about 40% to 4% in six genera tions. This reduction was mostly the result of a change in peak flowering times on the varieties from original syn chrony to an asynchrony of one week. Other evidence for divergence under different artificial selective regimes comes from Snaydon (1963 a,b), who found heritable dif ferences in flowering times in populations of Anthoxanthum odpratum which had been subjected to different fertilizer treatments over a period of about 100 years. Similarly, McNeilly and Antonovics (1968) found that populations of A. odoratum and Agrostis tenuis growing on'tailings of mines which had been in operation on the order of 100 years flowered asynchronously with respect to populations in adjacent fields. Differences in flowering times within each species were especially striking at the boundaries between tailings and normal soil, suggesting that popula tions have diverged so as to reduce pollen exchange and the consequent formation of maladapted hybrids. - ' ' 79 In my three replicate experiments at RMBL with syn thetic populations of D» nelsoni, and two with ]C«, aggregata, individuals exposed to interspecific pollen flow in com petition plots suffered reduced seed sets relative to controls. Analogous reductions occurred during natural overlap of the two species in 1975 and 1976 for D. nelsoni, and in 1976 for I. aggregata, and also in the 1976 hand pollination experiment for I. aggregata. Given that selec tion can act effectively and rapidly on flowering time, the strong selection represented in these consistent seed set reductions is a force sufficient to maintain the sequential flowering of the two species at RMBL, and may have played a role in originally producing the pattern as well. The separation in flowering times of species com peting for pollination should be complete, if selection is acting only to eliminate pollen flow between them. The slight overlap in flowering times of D. nelsoni and ][. aggregata in my study meadow at RMBL may simply reflect a"' lack of proximal flowering cues' which exactly predict the flowering condition of the competitor, as a result of the great variation between years in time of snowmelt. On the other hand, it may indicate that there are forces tending to promote flowering synchrony which are at equi librium with selection to reduce competition (Section 1 of this dissertation). Such forces might include reductions 80 at low flower density in the amounts of pollen available for fertilization or in the intensity of pollinator visita tion, or simply the limited duration of the summer season in which flowering and fruiting can take place. That there are effects of flowering overlap on seed set which are independent of density, however, is indicated by the re sults of my experiments with potted transplants. In most replicates exposed to natural pollinators, competition plots contained the same number of plants as control plots; and in one replicate with D. nelsoni, the control plot contained eight plants, only half the total number in the competition plot. My counts in experimental plots in 1976 (Appendix C) indicate that the mean number of flowers produced by transplanted D„ nelsoni and I_. aggregate are very similar, so that densities of plants in competition and control plots are a reasonable indication of density of flowers. Finally, I., aggregate suffered a seed set depression when exposed to pollen mixtures in the hand pollination experiment, where density effects on polli nator visitation or amounts of pollen were not a factor. Differences between D. nelsoni and I. aggregate in characteristics related to pollination are not unique, but extend to the other major hummingbird food plants at RMBL, Castilleja miniata and. Delphinium barbeyi (Table 1). Castilleja miniata flowers over a large part of the summer 81 (Figure 11), but is confined to riparian areas which are usually separated by at least 10 m to 100 m from meadows containing the other three species» The pollen flow over such distances is likely to be negligible, given the tendency, of foraging hummingbirds to fly mostly between neighboring plants (Price and Waser 1976, see also Bradshaw 1972, Levin and Kerster 1974 and references therein). Delphinium barbeyi grows in boggy areas which are often less than 10 m from dry meadows containing D= nelsonj and I. aggregate. Pollen flow over these distances may remain slight, and flowering of D„ barbeyi also begins after that of aggregate (Figure 11), an effect which is most pro nounced where it grows closest to dry meadows, Finally, ][«, aggregate differs somewhat from both D„ nelsoni and D. barbeyi in its position of pollen placement, since its radially arranged anthers contact the upper and lower man dibles and facial plumage Of hummingbirds rather than the lower parts alone. The sequential flowering of D. nelsoni and aggregate at RMBL is not the only example of a seasonal divergence in flowering time which may be interpreted as a result of competition for pollination. In an early study, Robertson (1924) compared the mean duration of flowering and degree of flowering, synchrony of native and introduced species in Illinois. The shorter flowering 82 period. and lower synchrony: between native species led him to propose that they had been subjected fbr a longer period than introduced species to competition tor polli nators and selection for divergence, Hocking (1968) studied insect pollination in the Arctic, and his results indicate that strong divergence in flowering times occurs within two pairs of Co-occurring species which apparently share bees and other insect visitors (see Knuth 1908, 1909)« A study of insect pollination in the Canadian Rocky Mountains (Mosquin 1971) is harder to interpret. Mosquin documented a temporal subdivision of the summer flowering season among 11 species he studied, but the mechanism.of competition for pollination which he proposes to explain this is vague, and the data he presents are too sketchy to permit further analysis. Relatively clear cases of sequential flowering are also found in a number of studies of sympatric congeners or conspecifics which share pollinators and whose hybrids are sterile or maladapted to parental environments. These studies include Whitaker (1944) for Lactuca, Clausen (1951) for Madia, Lewis (1961) for Clarkia, Grant and Grant (1964) for Salvia, Macior (1970) for Pedicularis, Heinrich (1975b) for several congeneric pairs in Maine bogs, and Lack (1976) for Centaurea. Sequential flowering of co-occurring wind pollinated congeners is also reported by Stebbins (1950) 83 for three species of Pinus and my McNeilly and Antonovies (1968) for Anthoxanthum and Agrostis» The dates of flowering of many species may vary geographically not only as a function of climatic factors, but also as a response to other potential competitors which are present in each area-. Robertson (1924) found that 22 species flowered earlier in Florida than in Illinois by a margin consistent with the latitudinal progression of springtime weather„ However, he also reported several species flowering in the reverse order and others flowering in Illinois as much as six months after they do in Florida. While populations of Bouteloua curtipendula studied by Olmsted (1944) over a range of 17° of latitude usually flowered in sequence from south to north, there were several exceptions. The most striking was an asynchrony of two months in the flowering of two populations in Texas which were separated by less than 50 km. Similar results from field or greenhouse studies are those of Bernstrom (1952) for Lamium, Clausen and Hiesey (1958) for Potentilla and Mimulus, Panje and Srinivasan (1959) for Saccharum, Lewis (1961) for Clarkia, Ray and Alexander (1966) for Xanthium, and Sawamura (1967) for Polygonum. In many such studies, flowering time and photoperiodic flowering re sponse have been found to act as heritable quantitative traits (Olmsted 1944, Bernstrom 1952, Clausen and Hiesey ' • 84 1958, Hiesey and Milner 1965 and references therein, Cohn and Kucera 1969)„ These findings strongly suggest that the abiotic factors which serve as proximate cues for flowering are flexible over the range of a species, and that dif ferences in flowering times are not the result of climatic conditions alone. Reports in the literature of sequential flowering of co-occurring plant species and of- geographic variation in flowering time not attributable solely to climatic factors lead me to conclude that competition for pollina tion may have an important influence on temporal patterns of flowering in mahy systems/ Experimental manipulation under near natural conditions supplernented by field observa tion seems an especially powerful approach for testing this conclusion. I have used such an approach to document inter specific movements.of hummingbirds foraging in natural and synthetic mixtures of D= nelsoni and aggregata, to show that these movements mix pollen of the two species, and to determine that such mixing results in a reproductive loss to both species. This decrease in fitness from inter specific pollinator movements and pollen transfer represents a selective force sufficient to maintain sequential flowering. With careful hand pollination of D. nelsoni and aggregata flowers in natural populations and in transplanted individuals, and with microscopic examination of stigmatic pollen loads of flowers of known seed set, I hope to be able to elucidate the exact mechanisms by which pollen mixing results in competition between plant, species sharing a pollinatoro APPENDIX A FORTRAN PROGRAMS FOR SIMULATING THE POLLINATION OF TWO CO-OCCURRING PLANT SPECIES The programs listed here were written in FORTRAN IV for the Digital Equipment Corporation DEC-10 computer at The University of Arizona. They employ a system-specific . subroutine called SETRAN, which generates random numbers on the interval zero to one. An analogous random number generator should be available for use with most other computer systems. 86 87 The Main COMPOL Program C ♦♦THIS PHUtiRAM EXAMINES THE REPRODUCTIVE EFFECT OF C PROMISCUOUS POLLINATOR VISITATION TO A GIVEN NUMBER C OF FLOWERS OF 2 SPECIES GROWING TOGETHER. EACH C FLOWER PRODUCES AND IS SATURATED BY A LIMITED C NUMBER OF POLLEN G RAINS^ DIMENSION IDENT (10,10) ,NPOLL (10, 10) , NS1IGA (1 0 ,1 0 ), 9 NSTIGU (10, 10) COMMON NPOLL,IDENT,NSTIGA,NSTIGB, NA, NB, IASUM, IDSUN 10 FORMAT (/) 100 FORMAT(F5.2) 200 FORMAT(15) 300 FORMAT(« GIVE DIMENSION OF FLOWER ARRAY, NDIM ( l b ) ') TYPE 300 ACCEPT 2 0 0 ,NDIM 400 FORMAT (' GIVE INITIAL POLLEN/STIGMA, NSTART (15)') TYPE 400 ACCEPT 2 0 0 ,NSTART 500 FORMAT(' GIVE POLLEN PICKUP/VISIT, NLOSS (15)') TYPE 500 ACCEPT 2 0 0 ,NLOSS 600 FORMAT (' GIVE POLLEN DEPOSIT/VISIT, LOAD (15) ') TYPE 600 ACCEPT 200, LOAD 700 FORMAT (' GIVE MAX. GRAINS/STIGMA, NGRAIN (15)') TYPE 700 ACCEPT 2 0 0 ,NGRAIN BOO FORMAT(' GIVE MOVEMENTS/GENERATICN, MOVES (15) ') TYPE 800 ACCEPT 200, MOVES 900 FORMAT (' GIVE SIZE OF REFUGIA, NCOL (15)') TYPE 900 ACCEPT 2 0 0 ,NCOL 950 FORMAT(' GIVE * KEFUGI0M SEED CHOICES, NTEST (1 5 )') TYPE 950 ACCEPT 2 0 0 ,NTEST 1000 FORMAT(« GIVE SEED RANDOM NUMBER, SI (15) «) TYPE 1000 ACCEPT 2 0 0 ,SI PN=0.25 PS =0.25 P E =0.25 PW=0.25 CALL SETRAN (SI) DO 1800 NRUN= 1,20 TYPE 10 I ASUM=1000 IUSUM=1000 DO 1600 NGEN=1,25 C ♦♦CHOOSE IDENTITY OF FLOWERS, GIVE FULL POLLEN LOADS^ CALL IDEN2(I,J,NDIM,NSTART,5 I , APRIME,BPRIME,NCOL,NTEST) C ♦♦ALLOW POLLEN PICKUP, TRANSFER, 6 DEPOSIT BY VECTORS MCOUNT=0 1100 TEST2=RAN(0.0) TEST3=R AN(0.0) 1 = 1 FIX ( (TEST2) ♦ (NDIM) ) +1 J = IF IX ( (TEST3) ♦ (NDIM) ) + 1 N A = 0 N U= 0 A FR AC=0.0 DO 1200 LLL=1 ,MOVES IF (IDENT (I,J) .EQ.5) UO TO 11 50 CALL ANTHLH (I, J,tNLOSS) CALL VECTOR(1,J,NLOSS) 1150 TE3T4 = itAli (0.0) IF (TEST4. LT. PN) 1=1 + 1 IF(TEST4.GE.PM.AW0.TLST4.LT. (PN + PS)) 1=1-1 IF (TEST4. GE. (PN + PS) . AM D. T EST4. LT . (FN+PS + PE) ) J=J+ 1 IF (TEST4.GE. (PN + PS + PE)) J=J-1 IF(IDENT (1,0).EQ.5) GOTO 1175 nCOUNT=nCOUNT+ 1 iF(acouNr.Eg.aovES) go to u o o 1175 IF (I.LT. I . O l x . l.GT.HDIH) GO TO 1100 IF (J.LT. 1.0R.J.GT. NDIC5) GO TO 1100 IF (IDENT (1,0).EQ.5) GO TO 1200 CALL STIG1 (1, 0 , NG MAI N, LO A E, SI) 1200 CONTINUE C ** DETER M'INE REPRODUCTIVE EFFECT OF POLLINATOR VISITS* 1300 I ASUM = 0 I US UH=0 DO 1400 1= 1 , NDIfl DO 1400 0=1,NDIM IF(IDENT(1,0).EQ.O) IASUM=IASUM+HSTIGA(1,0) IF (IDENT (1,0) .EQ. 1) IUSU M=IBSU M+N ST IG B (1,0) 1400 CONTINUE 1500 FORMAT(5X,+APRIME=*,1X,F5.2,3X,•BPGIME=«,1X,F5.2) C TYPE 1500,APRIME,BPRIME IF(APRIME.EU.O.O.OR.BPRIME.Eg.0.0) GO TO 1700 1600 CONTINUE 1700 FORMAT(' * OF GENERATIONS = »,1X,I5) TYPE 1700,NGEN 1 BOO CONTINUE STOP END 89 IDEN1, a Subroutine of COMPQL c ♦♦CHOOSES IDENTITY OF FLOWERS, ASSIGNS FULL POLLEN c LOADS, AND ZEROS STIGilATIC LOADS + + SUBROUTINE IDBtM (I,J,NDIH,NSTART,SI,APRINE, 5PRIHE ,NCOL,NTEST) COHHON NPOLL(10,10) ,IDENT (10, 10),NSTIGA(10,10) , 9 NSTIGB(10 ,10) , N A , NB , IASU fl, IBS UN DO 100 I=1,NDIM DO 100 J=1,NDIH F ASUM=F LOAT(IASUH) FBSUM=F10AT(IBSUM) APRII1E= FASUH/ (FASUH+FBSUM) BPRIHE=F3SUH/(FASUH+FBSUK) PROP=APRIME I DENT (I,J) =5 NPOLL (I , J) = NSTART NSTIGA (I,J) =0 NSTIGB(I,J)—0 TEST1 =3AN (0.0) IF(TEST1.LS.PROP.AND.IASUN.GT.O) GO TO 50 IF (TEST1.GT.PROP.AND.IBSUtt.GT.O) GO TO 60 IF(IBSUM.LT.O) GO TO 200 IF (IASUH.LT.0) GO TO 200 50 IDENT (I, J) =?0 IASUH=IASUa-1 GO TO 100 60 IDENT(I,J)=1 IBSUa=IBSUH-1 100 CONTINUE 200 RETURN END 90 IDEN2, a Subroutine of COMPOL ♦♦CHOUSES IDENTITY OF FLOWEitS RANDOMLY, EXCEPT RETAINS COLUMNS 1 TO NCOL AMD NDIh-NCOLH TO N DIM AS "ADAPHIC REFUGIA" FOR A AND 13, NTLSI SEED CHOICES ARE MADE FOR EACH H2FUGIUM SPOT; IF ANY OF THEM IS THE PROPER SEED FOR THAT REFUGIUM, IT COLONIZES THE SPOT+^ SUBROUTINE IDEN2(I,J,NDIM,NSTAhl,SI,AVRIME,BPRIME,NCOL,NTEST) COMMON NPOLL (10, 10) , 1DENT (10 , 1 U) ,NSTIGA (10, 10) , NSTIGB( 10, 10) , NA,NB,IASUM,IHSUM FASUM = FLOAT (IASUM) FBSUM=FLOAT (II3SUM) APRIME=FASUM/(FASUM+FDSUM) BPRIME=FBSUM/(F ASUM + FBSUM) PROP=APHIME DO 100 1 = 1 ,NDIM DO 100 J= NCOL+- 1, NDIM “NCOL IDENT ( I, J) =0 TESTA=RAN (0.0) IF(TESTA.GT.PROP) IDENT (I,J )=1 CONTINUE DO 300 1 = 1 ,NDIM DO 300 J = 1 , NCOL DO 200 MMM=1,NTEST TESTB=RAN (0.0) IF(TESTD.LE.PROP) GO TO 250 IDENT (I,J ) = 1 CONTINUE GO TO 300 IDENT ( I ,J ) =0 CONTINUE DO 500 1 = 1 ,NDIM DO 500 J= (NDIM-NCOL*1) , NDIM DO 400 NNN=1,NTEST • TESTC=RAN (0.0) IF(TE5TC.GT.PROP) GO TO 450 IDENT (I,J )=0 CONTINUE GO TO 500 IDENT (I,J )=1 CONTINUE DO 600 1 = 1 ,NDIM DO 600 0 = 1 ,NDIM NPOLL ( I,J ) = NSTART NST1GA(I,J)=0 NSTIGB(1,0) =0 CONTINUE RETURN END ANTHER, a Subroutine of COMPOL ♦♦KEEPS TRACK OF POLLEN ON ANTHER OF EACH FLOWERS SUBROUTINE ANTHER(I,J,NLOSS) COMHON NPOLL (10,10) , IDENT (10,10) , HSTIGA (10, 10) , NSTIU8(10,10),NA,NB,IASUM,IBSUN IF (NPOLL(I,J). LE.0) GO TO 100 NPOLL (I , J) =NPOLL ( I , J) -NLOSS RETURN END VECTOR, a Subroutine of COMPOL ♦♦KEEPS TRACK OF POLLEN MIX CARRIED BY VECTORS SUBROUTINE VECTOR(I,J,NLOSS) COMMON NPOLL (10,10) , IDENT (10, 1 0) , NSTIGA (10, 10), NSTIG0 (10,10) , NA,NB,IASUM,IBSUM IF (NPOLL ( I ,J ) . L B . 0 ) GO TO 100 IF (IDENT (I, J) .EU.0) NA=NA+NLOSS IF (IDENT ( I , J) . EQ. 1) NB=NB+NLOSS GO TO 200 IF (IDENT (I,J) .EQ.0) NA=NA+(NLOSS+NPOLL(I,J)) IF (IUENT(I,J).EQ. 1) NB=NB> (NLOS5 + NP O L L (I,J )) RETURN END CHECK, a Subroutine of COMPOL ♦♦PRINTS INTERMEDIATE RESULTS OF I, J, IDENT (I,J ), NSTIGA, AND NSTIGB FOR EACH GENERATION; TO PERMIT CONFIRMATION OF FINAL RESULTS BY HAND^ SUBROUTINE CHECK ( I,J ) COMMON NPOLL (10,10) , IDENT(10,10) , NSTIGA (10, 10), NSTIGB(10,10),NA,NB,IASUM,IBSUM FORMAT(' 1 = ' , I 3 , 2 X , ' J = « ,IJ ) TYPE 1 0 ,I , J FORMAT (' IDENT ( I , J) =« ,13) TYPE 2 0 , IDENT ( I,J ) FORMAT( ’ N S T IG A = ',I2 ,2 X ,'N S T IG B = ',I2 ) TYPE 3 0 , NSTIGA ( I,J ) , NSTIGB ( I ,J ) RETURN END STIG1, a Subroutine of COMPOL ♦♦KEEPS TRACK OF * AND IDENTITY OF POLLEN GRAINS ON STIGMAS OF EACH FLOWERS SUBROUTINE STIG1 (I,J,NGRAIN,LOAD#SI) COMMON NPOLL ( 10, 10) , I DENT (10,10) , NSTIGA (10,1C) , N STIGB(10,10) , NA,NB,IASUM,IUSUM DO 100 KNT3=1, LOAD FNA = FLOAT (NA) FNB=FLOAT (NB) AFRAC*FNA/(FNA+FNB) TE5T5 = RAN (0.0) IF ( (NSTIGA (I,J )*N S T IG B ( I , J ) ) . EQ.NGRAIN) GO TO ^00 IF (TESTS.LT.AFLAC.AND.NA.GT.0) GO TO 50 IF (TESTS.LT.AFRAC.AND.NA.LE.O) GO TO 100 * IF (TESTS.GE.AFRAC.AND.NB.GT.O) GO TO 60 IF (TESTS.GE.AFRAC.AND.NB.LE.0) GO TO 100 NSTIGA ( I , J) = NSTIGA ( I , J) -U N A=N A - 1 GO TO 100 NSTIGB ( I , J) = NSTIGB ( I , J) +1 NB=NB-1 CONTINUE RETURN END STIG2, a Subroutine of COMPOL .♦♦KEEPS TRACK OF # AND IDENTITY OF POLLEN GRAINS ON STIGMA OF EACH FLOWER; HETEROSPECIFIC GRAINS ARE NOT COUNTED^ SUBROUTINE STIG2 (I,J,N G R A IN ,LO A D ,SI) COMMON NPOLL(10, 10) , ID E N T (10,10) , NSTIGA (10, 10) , NSTIGB(10,10),NA,NB,IASUM,IBSUM DO 100 KNTR=1 ,LOAD FNA = FLUAT (NA) FNB=FLOAT(NB) AFRAC=FNA/(FNA+FNB) TEST5= RAN(0.0) IF (NSTIGA ( I , J) .EU. NGRAIN. A NO. TESTS. LT. AFRAC) GOTO 100 IF (TESTS.LT. AFRAC.AND. NA.GT.C) NSTIGA (I, J) =NSIIGA (I,J ) +1 IF (TESI5.LT.AFRAC.AND. NA.GT.O) NA=NA-1 IF (NSTIGB ( I , J) .E g . NGRAIN. AND. TESTS. GE. AFRAC) GOTO 100 IF (TESTS. GE. AFRAC.AND. NB.GT.O) NSTIGB ( I , J) = NSTIGB (1,0) +1 IF (TESTS.GE.AFRAC.AND.NB.GT.O) NB-N8-1 CONTINUE RETURN END 93 The Main PATPOL Program C **T H IS PHOGKAM EXAMINES THE EFFECT OF POLLEN FLOW C BETWEEN ADJACENT FLOWER PATCHES ON THE OUTCOME OF C COMPETITIVE EXCLUSION INEACH PATCH; AND ON THE C GLOBAL COEXISTENCE OF TWO COMPETING FLOWERTYPES** DIMENSION IDENT( 1 0 , 1 0 , 5 , 5 ) , NPOLL (1 0 ,1 0 ,5 ,5 ) , IASUH ( 5 ,5 ) , 9 IBSUM (5,5) ,FASUM(5,5) ,FliSUrt (5,5 ) , APRIML (5,5) , 9 NSTIGA ( 1 0 ,1 0 ,5 ,5 ) ,NST1GB (10, 1 0 ,5 ,5 ) COM MON NPOLL,IDENT,NSTIGA,NSTIGb,NA,NB,IASUM, IBSUM 10 FORMAT (/) 100 FORMAT ( F 5 .2) 200 FOR MAT(15) 300 FORMAT( ’ GIVE DIMENSION OF FLOWER ARRAY, N DIM (15) ') TYPE 300 ACCEPT 2 0 0 ,NDIM 400 FORMAT (* GIVE INITIAL POLLEN/STIGMA, N START (15)') TYPE 400 ACCEPT 2 0 0 ,NSTART 500 FORMAT ( * GIVE POLLEN P IC K U P/VIS IT, NLOSS ( 1 5 ) ') TYPE 500 ACCEPT 2 0 0 ,NLOSS 600 FORMAT(' GIVE POLLEN DEPOSIT/VISIT, LOAD (15)') TYPE 600 ACCEPT 200, LOAD 700 FORMAT (' GIVE MAX. GRAINS/STIGMA, NGRAIN (15)') TYPE 700 ACCEPT 2 0 0 ,NGRAIN 750 FORMAT (' GIVE MOVEMENTS/GENERATICN, MOVES (1 5 )') TYPE 750 ACCEPT 2 0 0 ,MOVES 800 FORMAT (« GIVE DIMENSION OF PATCH ARRAY, NP (1 5 )') TYPE 800 ACCEPT 2 0 0 ,NP 850 FORMAT (' GIVE PROB. MOVE BETW. PATCHES, PATFLO (F5. 2) ') TYPE 850 . ACCEPT'100,PATFLO 900 FORMAT(' GIVE SEED RANDOM NUMBER, SI (1 5 )') TYPE 900 ACCEPT 2 0 0 ,SI 950 FORMAT (' GIVE PROB. SEED EXCHANGE, SDFLO (F5.2) ') TYPE 950 ACCEPT 1 0 0 ,SDFLO 1000 FORMAT( / , 1 7 X ,' PATCH NUMBER• , / , 2X,'1 1 * , 3X,• 12• , 3X, ' 1 3 ' , 9 3X,'21*,3X,« 22' ,3X ,'23',3X,'31»,3X,'3 2 ',3X,« 33') PN=0.25 PS =0.25 PE=0.25 PW=0.25 CALL SETRAN (SI) DO 1600 NRUN= 1, 10 TYPE 1000 DO 10 50 K= 1 , N P DO 1050 L=1, NP IASUM (K, L) = 1000 IBSUM (K,L) = 1000 1050 CONTINUE DO 1600 NGEN=1,15 C **CHOOSE IDENTITY OF FLOWERS, GIVE FULL POLLEN LOADS** CALL PIDEN2 (I,J,K,L,HP, ND1M,NSTART,SI,SDFLO) C **ALLOW POLLEN PICKUP, TRANSFER, 6 DEPOSIT BY VECTOR** DO 1225 KX= 1,NP DO 1225 L X = 1,NP 94 «COUNT=0 1100 TEST2=R AN (0.0) TEST3=RAM (0.0 ) 1 = 1 FIX ( (TEST2) * (NDIM) ) +1 J= I FIX ( (TEST3) * (NDIM) ) * 1 K = KX L=LX N A = 0 N 0=0 AFRAC=0.0 c TYPE 10 DO 1200 LLL=1, MOVES IF (IDENT ( I ,J ,K ,L ) .E U .5) GO TO 1125 c CALL PC HECK ( I , J, K, L) CALL PANTH ( I , J , K, L,NLOSS) CALL PVECT(I,J,K,L,NLOSS) 1125 TEST4=RAM (0.0) IF (TEST4.LT.PN) 1 = 1+1 IF(TEST4.GE.PN.AMD.TEST4.LT. (PN + PS)) 1 = 1-1 IF (TEST4. GE. (PN+PS) . AND. TEST4. LT. (PN+PS + PE) ) J=J+ 1 IF (TEST4.GE. (PN + PS+PE)) J=J-1 MCOUNT=MCOUNT*1 IF (MCUUNT.EQ.MOVES) GO TO. 1225 TEST5=HAK (0.0) IF(I.LT.1.AND.TEST5.LE.PATFLC) GO TO 50 IF(I.GT.NDIM.AND.TESTS.LE.PATFLC) GO TO 60 IF(J.LT.1.AND.TESTS.LE.PATFLG) GO TO 70 IF(J.GT.NDIM.AND.TESTS.LE.PATFLC) GOTO 80 IF (I.L T .1.AND.TESTS.GT.PATFLC) GO TO 1100 IF(I.GT.NDIM.AND.TESTS.GT.PATFLC) GO TO 1100 IF(J.LT.1.AND.TESTS.GT.PATFLC) GO TO 1100 IF(J.GT.NDIM.AND.TESTS.GT.PATFLC) GOTO 1100 GO TO 1150 50 I=NDIM K = K-1 GO TO 1150 60 1= 1 K = K+1 GO TO 1150 70 J = M DIM L=L- 1 GO TO 1150 HO J=1 L=L+ 1 1150 IF(K.LT.1.0R.K.GT.NP) GO TO 1 100 IF(L.LT.1.0R.L.GT.NP) GO TO 1 100 CALL PSTIG1 (I,J ,K ,L ,N G R A IN , LOAD, SI) 1200 CONTINUE 1225 CONTINUE C ♦♦DETERMINE REPRODUCTIVE EFFECT CF POLLINATOR VISITS** 1250 DO 1400 K=1,NP DO 1400 L=1,NP IASUM (K,L) =0 IBSUM(K,L)=0 DO 1300 1 = 1 ,NDIM DO 1300 J =1 , NDIM IF (IDENT ( I ,J , K , L ) . EQ.O) IASUM (K,L) = IASUH (K,L) 9 + NSTIGA (I ,J ,K ,L ) IF (IDENT ( I ,J , K , L ) .E y. 1) IDSUM (K,L) =1DSUM (K,L) 9 ♦ NSTIGti ( I,J ,K ,L ) 1300 CONTINUE 95 FASUrt(K,L) =FLOAT (IASUH (K , L) ) FDSUrt (K, L) = P LOAT (IDSUM (K , L) ) APRIMK (K,L) =FASUM (K, L) / (FASU K (K, L) +F0SUK (K,L) ) 1400 CONTINUE 1500 FORMAT( 16F5.2) TYPE 1500, ( (APHIME (K , L) , L= 1 , NP) , K= 1 , NP) 1600 CONTINUE STOP END 96 PIDEN1, a Subroutine of PATPOL c ♦♦CHOOSES IDENTITY OF FLOWERS, ASSIGNS FULL POLLEN c LOADS, AND ZEROS. ST1GHATIC LOADS^ SUBROUTINE PIDEN1(I,J,K,L,NP,NDIM,NSTART,SI, SDFLO) COMMON NPOLL(1 0 ,1 0 ,5 ,5 ),IDENT (10,10,5,5) , NSTIGA (1 0 ,1 0 ,5 ,5 ) , NSTIGB (10, 1 0 ,5 ,5 ) ,NA,NB, IASUM (5,5) , IBSUM (5,5) DO 200 K= 1 , NP DO 200 L=1 ,NP F A=0.0 FB=0.0 AFR AC=0.0 DO 100 1= 1 ,NDIM DO 100 J= 1 ,NDIM FA=FLOAT (IASUM (K,L) ) FU=FLOAT(IBSUM (K ,L )) IF (FA.EQ.C) GO TO 10 PHOP=FA/(FA+FB) GO TO 20 10 PROP=0.0 20 IDENT (I , J , K , L) =5 NPOLL (I,J,K,L)=NSTAHT NSTIGA(I,J,K,L)=0 NSTIGB ( I , J , K , L ) =0. TEST1=RAN (0.0) IF(TEST1.LE.PROP.AND.IASUM(K,L).GT.0) GO TO 50 IF(TESI1.GT.PROP.AND.IBSUM (K,L).GT.0) GO TO 60 IF (IBSUM (K,L) .LT.O) GO TO 200 ' IF (IASUM (K ,L ).L T .O ) GO TO 200 50 ID E N T ( I,J ,K ,L ) =0 IASUM (K,L) =IASUM (K,L) - 1 GO TO 100 60 IDENT(I,J,K,L) =1 IBSUM (K , L) = IBSUM (K, L) - 1 100 CONTINUE 200 CONTINUE 300 RETURN END 97 PIDEN2, a Subroutine of PATPOL C **CHOOSES IDENTITY OF FLOWERS, DRAWS ON SEED POOLS C OF GLOBAL POPULATION AS WELL AS SUBPOPULATION, C THEREBY ALLOWING SEED EXCHANGE** SUBROUTINE P ID E N 2 (I,J ,K ,L ,N P , HDIE, NSTART,SI, SDFLO) COMMON NPOLL(10,10,5,5),IDENT(10,10,5,5) , 9 NSTIGA ( 1 0 ,1 0 ,5 ,5 ) , NSTIGB (1 0 ,1 0 ,5 ,5 ) ,NA,NB, 9 IASOH(5,5),IBSUM (5,5) IAS UMG = 0 I3SUMG=0 DO 100 K=1,NP DO 100 L= 1, NP I AS UMG=IAS UMG ♦I ASU M (X, L) IBSUMG=I3SUMG+I3SUM(K,L) 100 CONTINUE DO 400 K= 1, NP DO 400 L=1,NP ?A=0.0 FB=0.0 FAS=0.0 FBS=0.0 DO 300 1 = 1 ,NDIM DO 300 J = 1 , NDIM FA=FLOAT(IASUM (X ,L)) FB=FLOAT (I3SUM (X, L) ) FAS=FLOAT(IASUMG) FBS=FLOAT (IBSUKG) IF (FA.EQ.0) GO TO 10 PROP=FA/(FA+F3) GO TO 20 10 ?ROP=0.0 20 ID E N T (I,J ,K ,L ) =5 NPOLL ( I , J,K ,L ) =NSTAtiT NSTIGA ( I , J , X , L) =0 NSTIGB(I,J,K,L)=0 TESTA=RAN(0.0) IF (TESTA.LE.SDFLO) GO TO 200 TEST3=RAN(0.0) IF(TEST3.LE.PROP.AND.IASUM(K,L).GT.0) GO TO 40 IF(TESTB.GT.PROP.AND.I BSDM (K,L) .GT.O) GO TO 50 IF (IBSUH (K,L) . LT. 0) GO TO 300 IF(IASUM(X,L).LT.O) GO TO 300 40 IDENT ( I , J , K , L ) =0 IASUM (K,L) = IASUM (K, L) -1 GO TO 300 50 IDENT ( I , J , K , L ) =1 IBSUH(K,L)=I3SUM(K,L)-1 GO TO 300 200 IF(FAS.EQ.O) GO TO 60 PROPG=FAS/(FAS+FBS) GO TO 70 60 PROPG=0.0 70 TESTC=RAN (0.0) IF(TESTC. LS. P20PG. AND.IASUMG.GT.0) GO TO 80 IF(TESTC. GT. PROPG.AND. I5SUMG. GT.0) GO TO 90 80 I D E N T ( I,J ,X ,L ) =0 IASUMG=IAS0M5-1 GO TO 300 90 IDENT(I,J,X,L)=1 iasuMG=iasuac-i 300 CONTINUE 400 CONTINUE RETURN END 98 PANTH, a Subroutine of PATPOL C **KEEPS TRACK OF POLLEN ON ANTHER OF EACH FLOWER** SUBROUTINE PANTH(I , J , K,L,NLGSS) COMMON NPOLL (10, 10, 5, 5) ,IDENT (10, 10,5,5) , y NSTIGA(10,10,5,5),NST1GB(10,10,5,5) ,NA, N B, 9 IAS UM (5,5) , IBSUM (5,5) IF(NPOLL(I,J,K,L).LE.0) GO TO 100 NPOLL(I, J,K ,L) = NPOLL (I , J, K, L) -NLCSS 100 RETURN END PVECT, a Subroutine of COMPOL ♦♦KEEPS TRACK OF POLLEN MIX CARRIED BY VECTOR** SUBROUTINE PVECT ( I , J , K,L,NLOSS) COMMON NPOLL (10,10,5,5) ,IDENT (10, 10,5,5), NSTIGA(10,10,5,5),NSTIGB(10,10,5,5),NA,NU, IASUM (5,5) , IBSUM (5,5) ' IF (NPOLL(I,J,K,L). LE.0) GO TO 100 IF (IDENT (I , J, K, L) .Eg. 0) NA=NA+NLCSS IF(IDENT(I,J,K,L).EU. 1) NB=NB+NLOSS GO TO 200 100 IF(10ENT(I,J,K,L).EQ.0) NA=NA+ (NLCSS+NPOLL(I,J,K,L) ) IF (IDENT (I,J,K ,L) .Eg. 1) NB=NB+ (NLCSS+NPOLL(I,J,K,L) ) 200 RETURN END PCHECK, a Subroutine of COMPOL C **PRINTS INTERMEDIATE RESULTS OF I ,J ,K,L,IDENT (I ,J, K,L) , C NSTIGA, AND NSTIGB FOR EACH GENERATION; TO PERMIT C CONFIRMATION OF FINAL RESULTS BY HAND** SUBROUTINE PCHECK ( I,J , K ,L ) COMMON NPOLL (10,10,5,5) , IDENT(10,10,5,5), 9 NSTIGA( 1 0 , 1 0 , 5 , 5 ) , NSTIGB (1 0 ,1 0 ,5 ,5 ) ,NA,NB 9 IASUM ( 5 , 5 ) , IBSUM (5, 5) 10 FORMAT (' I=«,I3,2X,«J=‘,I3,2X, 'K=«,I3,2X,•L=',13) TYPE 1 0 , I ,J , K , L 20 FORMAT (' IDENT ( I , J, K, L) = 1 , 13) TYPE 2 0 ,IDENT ( I,J ,K ,L ) 30 FORMAT (' NSTIGA (1, J , K, L) =' , 12 , 2X, ' NSTIG B (I , J , K , L) = ' ,12) TYPE 30, NSTIGA ( I , J , K,L),NSTIGB ( I,J ,K ,L ) RETURN END 99 PSTIG1, a Subroutine of PATPOL c ♦♦KEEPS TRACK OF » AND IDENTITY OF POLLEN GRAINS c ON STIGMAS OF EACH FLOWERS SUBROUTINE PSTIG1 (I,J,K ,L ,N G B A IN ,LO A C ,S 1) COMMON NPOLL (10, 10,5,5) , IDENT (10, 10,5,5) , NSTIGA(10,10,5,5),NSTIGB(10,10,5,5),NA,NU, IASUM (5,5) , ItiSUM (5,5) DO 100 KNTR=1 ,LOAD FNA = PLOAT (NA) FNti=FLOAT(NB) A FRAC = F NA/ (FNA+FND) TEST6=RAN(0.0) I F ( (NSTIGA ( I , J,K , L) ♦NSTIGb ( I , J , K , L) ) I EQ. NGRAIN) GO TO 200 IF (TEST6.LT.AFPAC.AND.NA.GT.O) GO TO 50 IF (TEST6.LT.AFRAC.AND.NA.LE.C) GO TO 100 IF(TEST6.GE.AFBAC.AND.NB.GT.O) GO TO 60 IF (TEST6.GE.AFRAC.AND.NB.LE.0) GO TO 100 50 NSTIGA(I,J,K,L)=NSTIGA(I,J,K,1)+1 NA=NA-1 GO TO 100 60 NSTIGB (I , J , K , L) = NSTIGB (I , J , K , L) ♦ 1 NB=NB-1 100 CONTINUE 200 RETURN END APPENDIX B TESTS OF NORMALITY AND HOMOGENEITY OF VARIANCES OF SELECTED SEED SET DATA % 100 1 0 1 Table B-lo Tests of normality of selected data on seed sets of D, nelsoni and aggregata flowers. n = size of sample of flowers; g, (p) = sample skewness and associated significance of devia tion from normality; ^ (p) = sample kurtosis and associated significance. Sample n g1 (p) g 2 (p ) (1) D. nelsoni ”humming- I 1 ro birds excluded", 1975 18 O (n.s.) O O (n.s.) (2) I. aggregata "open pollinated" 1975 37 0.06 (n.s.) -1.10 (n.s.) (3) D. nelsoni natural meadows non-overlap I. aggregata, 1976 35 0.46 (n.s.) 0.02 (n.s.) (4) I. aggregata, natural meadows non-overlap, O CTt 1976 26 I (n.s.)' -1.03 (n.s.) (5) I. aggregata "control" potted.transplants, 1 O o first replicate, 1976 42 0.23 (n.s.) CO (n. s.) (6) D. nelsoni "competi tion" potted trans plants, first Q 00 H replicate, 1976 35 -0.17 (n.s.) 1 (n.s.) (7) I. aggregata hand pollinated "control", ■ 1976 23 0.77 (n.s.) 0.72 (n.s.) (8) D. nelsoni hand pollinated "competi ro o o : tion", 1976 16 o (n.s.) -1.42 (n.s.) 102 Table B-2„ Results of Bartlett’s test of the homogeneity of variances of samples of seed set data. d.f. = degrees of freedom; p = significance level of inhomogeneity. Adjusted Sample x2 Value d.f. p All D. -nelsoni in natural meadows, 197 5-197 6 0.22 3 n. s. All I. aggregata in natural meadows, 1975-1976 0.09 1 XI o S O All D. nelsoni potted transplant replicates with controls of 16 plants 8.22 7 XI e S o All I. aggregata potted transplant replicates 8.34 5 Xlo S o D. nelsoni potted transplant replicate with control of 8 plants 0.85 1 Xlo So Hand pollinated D . nelsoni 0.14 1 XI O S O Hand pollinated I. aggregata 4.41 1 Xlo S O APPENDIX C COMPARISONS OF MEAN NUMBERS OF FLOWERS PER PLANT IN SYNTHETIC POPULATIONS, 1976 103 Table O l , The mean number of flowers per plant of D« nelson! and T« aggregata in artificial competition and control plots on different dates during 1976, Control plots for both species in the first replicate experiment con tained 16 individuals? the D, nelson! control plot in the second replicate contained eight individuals. Also shown are the differences between control and competition means, their ranks, and their signifi cance according to Willcoxon1s signed-rank test (p-values, bottom)„ Do nelson!. First Replicate I_o aggregata, First Replicate D„ nelson!, Second Replicate Date Competi- Dif- Competi- Dif- Competi- Dif- Control tion ference Rank Control tion ference Rank Control tion ference Rank 6/9 1.9 2.5 +0.6 +9 4.6 6.3 +1.7 +8 6/11 4.6 4.9 +0.3 +4 8.1 10.3 +2.2 +9 6/13 5.4 5.3 • -0.1 -1 7.4 10.0 +2.6 +10 6/15 5.6 3.4 -2.3 -13 5.3 8.9 +3.6 +13 1.5 1.6 +0.1 + 3 6/18 5.3 4.6 -0.7 -10.5 2.0 1.5 -0.5 -2 3.4 3.8 +0.4 +5 6/19 5.4 4.9 -0.5 -7 6.1 4.8 -1.3 -6 6/20 5.0 4.3 -0.7 -10.5 5.8 5.0 -0.8 -4 4.9 4.9 0.0 1.5 6/22 4.6 4.1 -0.5 -7 5.5 8.5 +3.0 +11 6.0 5. 5 -0.5 -6 6/24 3.2 3.4 +0.2 +2.5 6.0 9.8 +3.8 +14 5.8 4.8 -1.0 -9 6/26 2.7 1.5 -1.2 -12 4.4 7.9 +3 d 5 +12 " 4.9 4.0 -0.9 -8 6/28 1.3 1.1 -0.2 -2.5 5.9 5.9 0.0 1 3.8 3.8 0.0 1.5 6/30 0.6 1,0 ' +0.4 +5 6.4 5.1 -1.3 •• -6 1.3 1,9 +0.6 +7 7/4 0.0 0.5 +0.5 +7 5.9 4.6 . -1.3 -6 0.3 0.1 +0.2 +4 7/11 1.6 0.9 -0,7 -3 E Positive Ranks = 27.5 E Negative Ranks » 27 E Negative Ranks = 23 n = 13 n = 14 n = 9 p >,0.5 nes, ‘ p >,05 neSe p >»05 n,So 104 LITERATURE CITED Allard, R. 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