Reproductive responses of cowpea (Vigna unguiculata (L.) Walp.) to heat stress. I. Responses to soil and day air temperatures

Field Crops Research, 8 (1984) 3--16 Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands

3

REPRODUCTIVE RESPONSES OF COWPEA (VIGNA UNGUICULATA (L.) Walp.) TO HEAT STRESS. I. RESPONSES TO SOIL AND DAY AIR TEMPATURES

M.O.A. WARRAG and A.E. HALL

Department of Botany and Plant Sciences, University of California, Riverside, CA 92521 (U.S.A.) (Accepted 29 September 1983)

ABSTRACT Warrag, M.O.A. and Hall, A.E., 1984. Reproductive responses of cowpea (Vigna unguiculata (L.) Walp.) to heat stress. I. Responses to soil and day air temperatures. Field Crops Res., 8: 3--16. Cowpea (Vigna unguiculata (L.) Walp.) plants are characterized by occasional excessive abscission of reproductive organs which result in low numbers of pods per unit area and consequently low seed yields. The possibility that heat stress may cause this excessive abscission was examined. Interactive effects of different soil and two day air temperatures on growth and reproductive performance of cowpea cultivar 'California Blackeye No. 5' were determined in controlled environments. Emergence was slow, and the seedlings were stunted at constant soil temperatures equal to or lower than 23°C. Seedlings at 19°C soil temperature exhibited nitrogen deficiency, and they developed bigger and more numerous nodules on their roots. The different soil and air temperatures did not influence the duration from emergence to appearance of the first floral bud or to anthesis. The duration from anthesis to maturity of individual pods was six days longer with the cooler day air temperature, but it was not influenced by the different soil temperatures. Plants produced more pods at 27/19°C than at 33/19°C day/night air temperature; however, the variation in number of pods was associated with variation in the number of reproductive nodes per plant. Levels of flower abscission were not excessive in any of the environments, and plants at 33/19°C air temperature exhibited less percent flower abscission than plants at 27/19°C air temperature. The seeds produced at 33/~9°C air temperature were misshapen. Normal and misshapen seeds exhibited high percent emergence when sown at a depth of 2.5 cm at all soil temperatures studied, whereas 5-cm sowing depth resulted in poor emergence at high soil temperatures with misshapen seeds exhibiting less percent emergence than normal seeds. INTRODUCTION

Cowpea (Vigna unguiculata (L.) Walp.) occasionally exhibits excessive abscission of reproductive organs such as peduncles, flowers, and pods (Ojehomon, 1968; Sene, 1974; Sinha, 1977). While searching for explanations for the occurrence of low seed yields in cowpea, Turk et al. (1980) observed that under frequently irrigated field conditions in a subtropical climatic

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zone, seed yields and numbers of pods per unit area were negatively correlated with hot weather during the month of flowering. Based upon controlled environment studies, it has been proposed that high day air temperatures (Stewart et al., 1980) and high soil temperatures (Minchin et al., 1976) may be major factors limiting seed yields of cowpea in tropical climatic zones. In the studies of the effects of air temperature on cowpea, day/night temperatures of 33/19°C resulted in lower seed yields, fewer pods, fewer reproductive nodes, enhanced peduncle abortion, and earlier senescence compared with the effects of day/night temperatures of 27/19°C. However, in these studies pot temperatures were not separately controlled, and the roots may have been subjected to temperatures similar to those experienced by the shoots. In contrast, under natural conditions the dense canopy covering the soil, as the cowpea plants begin flowering, acts to insulate the soil, resulting in only small variations in temperature in the root zone. Minchin et al. (1976) conducted an experiment to determine the effects on cowpea of the diurnal variations in pot temperature that occur in greenhouses. The combination of higher soil temperatures and larger day/night variations in soil temperature resulted in lower seed yields, fewer peduncles, and reduced vegetative growth. In another greenhouse study, soils were subjected to different ranges of day/night temperatures before and after the beginning of flowering, and it was observed that the combination of high soil temperatures and large day/night variation in soil temperature during flowering inhibited reproduction (Stewart and Summerfield, 1978). Under these conditions, they observed a high level of peduncle abscission and a very high proportion of abnormal, male-sterile flowers which also exhibited a high level of abscission. Consequently, it is not known whether the detrimental effects of high temperatures on seed production reported by Stewart et al. (1980) were caused by high day air temperature or by large diurnal variation in pot temperature. In addition, interactions may occur as observed in the effects of high soil and high air temperatures on photosynthsis and stomatal conductance of cowpea by Ki]ppers et al. (1982). Controlled environment studies of the separate and interactive effects of air and soil temperatures on cowpea could improve our understanding of the effects of hot weather on seed yield under natural conditions. Cowpea plants were subjected to different day air temperatures at different constant levels of soil temperature in growth chambers to determine their effects on reprodutive performance. MATERIALS AND METHODS

Seeds of cowpea cultivar 'California Blackeye No. 5' were inoculated with rhizobia (EL type, Nitragin Co., Milwaukee, Wisconsin) and sown 2.5 cm deep in 19-1 plastic pots filled with UC Mix C (Univ. Calif. Agric. Ext. Serv. Man. 23, 1957). The rooting medium had been inoculayed with the vesicular-arbuscular endomycorrhizal fungus Glomus fasciculatus (Thaxter) Gerd.

and Trappe. A layer of perlite, 3 cm deep, was placed on the surface of the soil for insulation. Soil temperatures were maintained at different constant levels within +1°C by pumping controlled-temperature water through plastic hoses coiled around the inner surface of the pots. Three replicate pots were used for each treatment. Seedlings were thinned to two per pot after the expansion of the first trifoliate leaf. One plant was removed for analysis at the end of the vegetative stage (5 weeks after sowing), whereas the other plant was harvested when most of the pods had become dry. The space provided for each pot, and available to each plant from flowering to harvest, was 0.15 m 2. Plants were subjected to two day/night air temperatures of 27/19°C and 33/19°C using two reach-in growth chambers. Day-night relative humidities were 40--50%/70--80%, and the average wind speed was 0.2 m s -1 in both chambers. The photoperiod was 13 h, 20 min. Light was supplied by twelve clear 400-W metal-halide vapor and ten frosted 150-W tungsten lamps. The photon flux density at the top of the canopy was 800--900 pmol m -2 s-1 (for wavelengths between 400 and 700 nm). During the first experiment, treatments were subjected to the following soil temperatures from sowing: 19, 23, and 27°C in the 27/19°C day/night air temperature chamber, and 19, 27, and 33°C in the 33/19°C day/night air temperature chamber. The plants subjected to a constant soil temperature of 19°C were stunted and chlorotic up to the end of the third week after sowing, after which they recovered and the foliage appeared green and healthy. This chlorosis was avoided during the second experiment by maintaining soil temperatures of all treatments at 27°C until the seedlings had emerged and the first trifoliate leaf had begun to expand. After this time, the soil temperatures were changed to provide treatments of 21, 27, and 33°C in both growth chambers, which had the same air temperatures and general environmental conditions as in the first experiment. In both experiments, plants were watered on alternate occasions with half-strength Hoagland's solution and then tap water until flowering, after which only tap water was used. Plants were watered whenever tensiometers placed in the pots indicated approximately 20 centibars. Soil temperatures were continuously monitored using copper/constantan thermocouples inserted 20 cm deep in the soil. Five weeks after sowing, a plant was taken from each pot for vegetative analysis. In addition, in the first experiment, the mineral contents of leaves were analyzed at this time. Total nitrogen was determined by the micro-Kjeldahl method. Phosphorus was determined by the Molybdivanadate colorimetric method (Kitson and Mellon, 1944). K, Ca, Mg, Na, Zn, Cu, Mn, and Fe were determined by atomic absorption spectrophotometry (Model 303, Perkin Elmer). Every flower was tagged at anthesis, and the total number of flowers per plant, the percent set (number of pods per plant × 100 per number of flowers per plant), and the period from anthesis to maturity of individual pods were recorded.

When most of the pods had become dry, the plants were harvested. Seeds were removed from the pods, dried in a bell jar containing silica gel, and weighed separately for each inflorescence. Mineral analysis was conducted on seed samples during the first experiment using the methods described earlier. The roots were cleaned and nodules were separated. The shoots, roots, and nodules were dried at 60°C for 48 h and weighed. Seeds collected from plants grown at the two air temperatures were sown in the same type of potting medium. Sowing depths of 2.5 and 5.0 cm were used. Seeds in each sowing depth treatment were subjected to temperatures of 25, 30, and 35°C. Percent emergence was calculated after emergence had ceased. RESULTS AND DISCUSSION In the first experiment, the earliest seedlings were observed 2, 3, 5, and 6 days after sowing at soil temperatures of 33, 27, 23, and 19°C, respectively; and 100% emergence was attained 4, 5, 9, and 10 days after sowing at these same temperatures (Fig. 1). Under field conditions, emergence within 5 days is considered desirable since it results in less damage to germinating seeds and seedlings due to disease and pests.

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~_ 40 0

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2

4 6 DAYS AFTER SOWING

8

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Fig. 1. Effect of soil temperature on cowpea seedling emergence (from 2.5-cm sowing depth).

Seedlings growing in soil at a temperature of 19°C had very low growth rates, and the first trifoliate leaves were small in size, curled, and chlorotic. Three weeks after sowing, the leaves turned green, but growth was still slow and the plants produced mature seeds without producing branches. Plants

s u b j e c t e d t o 23°C soil t e m p e r a t u r e also e x h i b i t e d s o m e chlorosis and stunting b u t m u c h less t h a n t h o s e at 19°C. Similar seedling chlorosis a n d stunting was o b s e r v e d in several c o w p e a fields in California during the early p a r t o f t h e growing season in 1 9 8 2 . I t was an u n u s u a l l y c o o l spring w i t h average air t e m p e r a t u r e s o f a p p r o x i m a t e l y 19°C. Mineral analysis o f leaves 5 weeks a f t e r sowing s h o w e d t h a t plants at 19°C r o o t t e m p e r a t u r e had o n l y 1.7% n i t r o g e n o n a d r y w e i g h t basis, w h i c h is c o n s i d e r e d to be d e f i c i e n t c o m p a r e d w i t h values o f 3--5% w h i c h w e r e o b s e r v e d at w a r m e r soil t e m p e r a t u r e s ( T a b l e I), and w h i c h are c o m m o n l y f o u n d w i t h h e a l t h y c o w p e a plants u n d e r field conditions (Ziska and Hall, 1 9 8 3 ) . S o m e plants were r e m o v e d f r o m t h e p o t s at final harvest and, c o n t r a r y to o u r e x p e c t a t i o n s , the plants growing in soil at t e m p e r a t u r e s o f 19°C h a d t h e biggest and m o s t n u m e r o u s n o d u l e s o n t h e i r r o o t s t h a t we have ever o b s e r v e d o n c o w p e a plants. This p o i n t will be discussed f u r t h e r w h e n t h e results o f t h e s e c o n d e x p e r i m e n t are considered.

TABLE I Mineral content of cowpea leaves 5 weeks after sowing in experiment 1 Day/night temperature

(oc)

Soil temperature

Macronutrients (%)

Micronutrients (ppm)

(oc)

N

P

K

Ca

Mg

Na

Fe

Mn

27/19

19 23 27

1.6 3.4 4.2

0.5 0.7 0.6

2.0 2.4 2.8

2.4 2.1 1.8

0.6 0.5 0.4

0.02 0.02 0.01

80 112 121

84 7.0 162 8.3 184 8.7

96 102 93

33/19

19 27 33

1.8 4.5 4.2

0.5 0.6 0.7

1.9 2.7 2.8

2.5 1.7 1.9

0.6 0.4 0.4

-0.04 0.03

79 128 157

108 5.3 173 7.7 129 7.3

142 101 75

LSD (0.05)

0.4

0.2

0.4

0.4

0.1

--

34

NS ** NS

NS ** NS

NS ** NS

----

56

Cu

Zn

2.6

48

NS NS ** NS NS NS

NS NS NS

Significance of F a

Air

**

NS

Soil

**

*

Interaction

**

NS

* ** NS

aNS indicates not significant at 5% level; *significant at 5% level; **significant at 1% level. In t h e s e c o n d e x p e r i m e n t , w h e r e soil t e m p e r a t u r e s were o n l y changed w h e n t h e seedlings h a d e m e r g e d , all o f the seedlings a p p e a r e d t o be h e a l t h y . This e x p e r i m e n t is n o w discussed in detail because it is c o n s i d e r e d t h a t the e f f e c t s o f d a y air t e m p e r a t u r e and soil t e m p e r a t u r e w h i c h w e r e o b s e r v e d are m o r e t y p i c a l o f c o m m e r c i a l field c o n d i t i o n s t h a n t h e responses in the first e x p e r i m e n t , w h e r e s o m e t r e a t m e n t s w e r e adversely i n f l u e n c e d b y cool soil during e m e r g e n c e .

Vegetative growth Five weeks after sowing experiment 2, plant height was not influenced by air temperature (Table II). However, plants at intermediate soft temperatures were taller and had longer internodes than plants at soil temperatures of 21 or 33°C. Plants at 27/19°C air temperature had fewer but longer internodes than plants at 33/19°C air temperature. Low soil temperatures of 21°C resulted in plants with less leaf area at both day-air temperatures, compared with the intermediate soil temperature, due to smaller and fewer leaves. The dry weight of the shoots at 5 weeks was less at 27[19°C air temperature than at the higher day air temperature, and the lowest soil temperature resulted in the least production of shoot dry matter at both air temperatures (Table II). However, at final harvest, there were no significant differences in shoot dry weight, due to either the soil temperature or the air temperature treatments (Table IV). At the lowest soil temperature, in both experiments, the diameters of fresh nodules were as large as 6 mm, and most of the nodules were aggregated at the root crown. At higher soil temperatures, the nodules were less than 3 mm in diameter and distributed throughout the root system. The dry weight of nodules per plant at 21°C soil temperature was four times greater than at higher soil temperatures (Table IV). Air temperature had no obvious effect on nodulation. Greater nodulation has been reported for Glycine max (soybean) grown at lower soil temperatures (Gibson, 1976). In our studies, it is possible that the greater nodulation may have been indirectly induced by nitroge~ deficiency in the plants caused by low root temperatures. In addition, differences in root morphology were observed. At low soil temperature, the root system consisted of many lateral roots and an extremely small tap root, whereas at higher soil temperatures there were fewer lateral roots and a conspicuous tap root.

Phenology and reproductive development The number of days from emergence to appearance of the first macroscopic floral buds in experiment 2 was not affected by root or air temperatures (Table III). Plants grown at 27/19°C air temperature and moderate to high soil temperatures reached anthesis 2 to 3 days earlier than plants at 33/19°C air temperature, but the differences were not significant. Floral buds were first observed on the second and third nodes, but in most cases, these floral buds did not produce pods. The lowest node to produce pods at harvest was usually one node higher for plants at 33/19°C air temperature than for plants at 27/19°C (Table III). The average number of days from anthesis to maturity for individual pods was 6 days longer at the lower day air temperature than at 33°C with no influence of soil temperature. This effect of day air temperature on the duration of pod filling is consistent with the findings of Roberts et al. (1978).

0.8

10

LSD (0.05)

NS ** NS

** ** NS

6.3 7.7 7.0

** ** NS

1.1

2.6 4.9 2.7

2.7 5.8 4.4

(cm)

Length of internode

** NS NS

1.1

1.7 2.7 2.7

1.3 2.0 1.3

No. o f branches

** ** NS

89

774 1132 1023

659 958 1016

(cm 2)

Total leaf area

b N S i n d i c a t e s n o t significant a t 5% level; * s i g n i f i c a n t a t 5% level; * * s i g n i f i c a n t at 1% level.

Air Soil Interaction

Significance o f F b

8.0 8.7 8.3

21 43 23

21 27 33

33/19

17 44 31

21 27 33

27/19

nodes

(°C)

No. o f inter-

(°C)

Height (cm)

Soil temperature

Day/night temperature

V e g e t a t i v e g r o w t h o f c o w p e a 5 w e e k s a f t e r s o w i n g in e x p e r i m e n t 2

TABLE H

27 32 26

29 35 39

** NS NS

** * **

6

27 34 40

25 29 25

7

Area per leaflet (cm=):

No. of leaflets

* * NS

1.7

4.6 6.5 5.9

3.2 5.0 5.0

(g)

Shoot dry weight

CD

10 TABLE III Phenology and reproductive development of cowpea in experiment 2 Day/night temperature (°C)

Soil temperature (°C)

Days from emergence to first floral bud

Days from emergence to first flower

Average number of days from anthesis to maturity

Node of first floral bud

Node of lowest peduncle with pods

27/19

21 27 33

21 21 21

42 41 40

23 23 22

2 3 2

2.7 3.7 3.0

33/19

21 27 33

22 21 21

41 43 43

17 17 17

2 3 3

4.0 4.0 4.7

1

4

1

1

1.4

NS NS NS

NS NS NS

** NS NS

NS * NS

* NS NS

LSD (0.05) Significance of F c Air Soil Interaction

cNS indicates not significant at 5% level; *significant at 5% level; **significant at 1% level.

Yield components In experiment 2, more pods were produced per plant at the lower day air temperature and intermediate soil temperatures although the differences were not significant at the 5% level (Table IV). Average seed weight and the number of seeds per pod were not influenced by day air temperature. In contrast, Wein and Ackah (1978) had observed that when the temperature of the pods was increased by covering them with black cloth, the period from anthesis to maturity and the average seed size were both decreased. However, the decrease in seed size which they observed may have been due to reductions in photosynthetic rates of pods caused by the shading because covering with white cloth also reduced seed size, even though it decreased pod temperature and increased the period from anthesis to maturity. In the present studies, the number of pods, number of seeds per pod, and average seed weight were the same at identical nodes on the main stem at both air temperatures, whereas Roberts et al. (1978) reported a decrease in number of seeds per pod and average seed weight at 33/19°C air temperature compared with 27/19°C. However, Roberts et al. (1978) used a different cultivar (K2809) and diurnally fluctuating root temperatures. There was a similar pattern in the effects of soil temperature on the number of pods per plant and the number of reproductive nodes per plant (Fig. 2). In addition, low numbers of pods per plant were not caused by high

17 19 17 10

21 27 33

LSD (0.05)

33/19

NS

Interaction

NS

NS NS

8

11 13 11

13 16 10

NS

NS NS

0.3

1.7 1.6 1.6

1.7 1.7 1.8

NS

NS NS

2.3

6.8 6.9 6.2

6.4 6.8 7.4

No. of No. of No. of peduncles pods per seeds with pods peduncle per pod

NS * NS

* NS

0.4

2.0 3.0 2.7

1.7 3.3 1.3

NS

1.4

21.5 21.7 20.4

22.6 21.4 20.8

17 0.4

NS

NS NS

45 46 56 1.2 0.2 0.3

NS

5O 68 44

(g)

Shoot dry weight (excluding seeds)

1.1 0.3 0.3

Nodule 100-seed No. of weight branches dry weight (g) wt (g)

dNS indicates not significant at 5% level; *significant at 5% level; **significant at 1% level.

NS NS

Significance of F d Air Soil

22 27 18

21 27 33

27/19

No. of pods

Soil temperature (°C)

Day/night temperature (°C)

Yield components and biological yield per plant of cowpea at harvest in experiment 2

TABLE IV

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SOIL TEMPERATURE °C Fig. 2. Effects of 27/19°C (o) and 33/19°C (-) day/night air temperatures, and soil temperatures on: (a) number of pods per plant; (b) number of reproductive nodes per plant; and (c) percentage of flowers which produced pods.

levels of abscission. Plants in the hotter chamber had fewer pods but a higher percent set. The higher percent abscission at the lower air temperature was associated with the production o f more flowers per peduncle. The number of peduncles and pods on the main stem was relatively constant for the different temperature regimes (five to six peduncles and ten to twelve pods per plant). The greater number of peduncles and pods per plant at the lower air temperature (Table IV) was due to a greater number of nodes (mostly reproductive) per branch. Percent peduncle abortion at 33/19°C was more than double that at the lower air temperature (Fig. 3). However, the level of peduncle abortion was

13

DAY/NIGHT AIR TEMPERATURE 27/19

(°C) 33/19

I00 N u m b e r of produc(

80 w

< IZ hi 0

Ovule oborl

60

rr

,,, 4 0 (1.

Flower obsc

20 Peduncle ob 21

27

33 21 27 SOIl TEMPERATURE (°C)

33

Fig. 3. Contributions of peduncle abortion, flower abscission, and ovule (and/or developing seed) abortion to reductions in seed numbers as percentages of potential seed production in cowpea.

small (6--24%) compared to the findings of Stewart et al. {1980). Flower abscission resulted in a 40% loss in potential seed yield at 27/19°C and only 30% loss at the higher air temperature. Ovule and developing seed abortion constituted about 30% loss in potential yield for all treatments. The actual seed yield that was obtained was about one-fourth of the potential yield. Actual seed yields are strongly influenced by interactions among reproductive events, such as the tendency for substantial early pod set to be associated with reduced flower production during later stages. The leaves on the main stem at 27/19°C air temperature remained green until harvest, or senesced later than those on identical nodes at the higher air temperature, which usually senesced and abscised before the maturation of the subtended pods. The higher rate of seed development in plants at higher air temperatures may have resulted in a more rapid withdrawal of nitrogen and carbon from the leaves which accelerated their senescence (Sinclair and De Wit, 1976).

Seed shape The seeds produced by plants at 27/19°C air temperature appeared normal with symmetrical cotyledons, while seeds from 33/19°C air temperature had

14

asymmetrical cotyledons and wrinkled seed coats, irrespective of the soil temperature regimes (Fig. 4). Assymetric seeds have also been obtained from plants subjected to h o t weather in the field. Both kinds of seeds had similar average weight (Table IV) and similar mineral content (Table V). The misshapen seeds exhibited a lower percent germination than normal seeds when

Fig. 4. Appearance of the seeds produced by cowpea plants grown at 27/19°C (A) and 33/19°C (B) day/night air temperature.

15

sown at 5-cm depth but not when sown at a shallower depth (2.5 cm) (Table VI). Both types of seeds exhibited a lower percent germination when sown deeper and with soil at higher temperatures (Table VI). These results suggest that it may not be advisable to use seed with asymmetric cotyledons as sources of seed for subsequent sowing. It has been reported that the decrease in percent emergence with higher soil temperatures may be due to the retardation of hypocotyl elongation (Wein, 1973; Onwueme and Adegoroye, 1975), and this effect would be aggravated by deep sowing. This problem could be overcome by shallower sowing providing there is sufficient moisture in the seed and root zones. TABLE

V

Mineral content of cowpea seeds in experiment 1 Day/night temperature

Soil temperature

Macronutrients (%)

Micronutrients (ppm)

(°c)

(°c)

N

P

K

Ca

Mg

Na

Mn

Cu Fe

Zn

27/19

19 23 27

3.6 4.9 4.7

0.4 0.4 0.4

1.4 1.4 1.3

0.11 0.09 0.08

0.17 0.18 0.17

0.03 0.03 0.03

16 16 16

9 9 8

116 92 84

56 53 59

33119

19 27 33

4.1 4.9 4.1

0.5 0.5 0.5

1.3 1.3 1.3

0.13 0.08 0.10

0.18 0.19 0.18

0.03 0.03 0.03

18 16 16

5 7 5

113 101 97

56 53 49

LSD (0.05)

0.3

0.1

0.1

0.02

0.01

0.01

3

2

26

8

NS NS NS

** NS NS

NS NS NS

** ** *

NS * NS

NS NS NS

Significance of F e Air Soil Interaction

NS NS NS

** NS NS * NS NS

NS NS NS

eNS indicates not significant at 5% level; *significant at 5% level; **significant at 1% level. TABLE VI Effect o f soil temperature and sowing depth on the percent emergence of normal and misshapen seeds of cowpea

Soil temperature (°C)

25 30 35

Normal seeds'

Misshapen seeds 2

2.5 cm

5.0 cm

2.5 cm

5.0 cm

100 100 100

100 80 46

100 100 100

88 73 36

' Seeds produced by plants at 27/19°C day/night air temperatures. 2 Seeds produced by plants at 33/19°C day/night air temperatures.

16 CONCLUSION High d a y air t e m p e r a t u r e a n d high soil t e m p e r a t u r e did n o t cause excessive p e d u n c l e a b o r t i o n , f l o w e r abscission, or ovule a b o r t i o n w i t h c o w p e a in c o n t r o l l e d e n v i r o n m e n t s . This indicates t h a t the negative c o r r e l a t i o n s bet w e e n seed yields and h o t w e a t h e r d u r i n g flowering, t h a t have been observed u n d e r field c o n d i t i o n s , m a y have been d u e t o d e t r i m e n t a l effects o n r e p r o d u c t i o n o f o t h e r associated factors, such as high night t e m p e r a t u r e s . This possibility is e x a m i n e d in a s u b s e q u e n t paper.

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