Identifying elite rhizobia for soybean ( Glycine max ) in Kenya

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African Journal of Crop Science Vol. 2 (2), pp. 060-066, June, 2014. Available online at
www.internationalscholarsjournals.org © International Scholars Journals
Full Length Research Paper
Identifying elite rhizobia for soybean (Glycine max) in
Kenya
1Maureen Nekoye Waswa, 2Nancy K. Karanja, 3Paul L. Woomer and 4George M. Mwenda
1,2Department of Land Resource Management and Agricultural Technology, University of Nairobi P.O. Box 29053-
00100, Nairobi.
3N2Africa Program, International Centre for Tropical Agriculture (CIAT), P.O Box 823 – 00621, Nairobi, Kenya.
4Centre for Rhizobium Studies, School of Veterinary and Life Sciences, Murdoch University, South St., Murdoch, WA
6150, Australia.
Accepted 05, May 2014
Bio-prospecting was conducted in Kenya to identify elite isolates of rhizobia capable of effectively
nodulating promising soybean varieties. One hundred isolates were recovered from nodules of wild and
cultivated legume hosts. These isolates were authenticated and tested for effectiveness on soybean
(Glycine max) var. SB 19 in sterile vermiculite, and the twenty-four most promising isolates screened in
potted soil to assess their competitive abilities on two varieties ("promiscuously nodulating" SB 19 and
specific SC Safari). The six best performing isolates were then evaluated under field conditions, comparing
them to strain USDA110. Test isolates were classified into; non-infective, ineffective, partly effective,
effective and highly effective based on their performance relative to controls and industry standards. In
potted soil, native rhizobia isolates nodulated promiscuous soybean (SB19) but only 46% of them
nodulated specific soybean (Safari). In the field experiment, isolate NAK 128 performed best on both
promiscuous and specific soybean varieties, significantly (p<0.05) outperforming USDA110 by 29% and
24%, respectively. Partial economic return to inoculation with NAK 128 was about 21:1, justifying
inoculation as a field practice and producing up to 2.5 million nodules (334 kg) ha-1, significantly (p<0.05)
more than USDA 110. The best isolates from this investigation have commercial potential.
Key words: African biodiversity, bio-prospecting, promiscuous soybean, rhizobia isolate selection, USDA 110.
INTRODUCTION
Rhizobia are soil-inhabiting bacteria that form root
nodules where symbiotic biological nitrogen fixation
occurs (Howieson and Brockwell, 2005; Weir, 2006). This
process, where atmospheric N is captured for
assimilation by plants is under-utilized by small-scale
African farmers, in part because they do not understand
its mechanism and management. Ninety-five per cent of
farmers in East and Southern Africa are familiar with
legume root nodules but only 26% considered them
beneficial (Woomer et al., 1997). In Kenya, only one per
cent of farmers use inoculants (Karanja et al., 2000).
Competitiveness of native rhizobia also poses a barrier
to the benefits of inoculation (Shamseldin and Werner,
2004). Tropical soils are often rich in less-effective, native
*Corresponding author. maureewaswa@yahoo.com
rhizobia and a key to overcoming their competitive
advantage is through the composition and delivery of
legume inoculants (Theis et al., 1991), especially for
soybeans, a more specifically nodulating host legume
(Sanginga et al., 2000). One pathway to improvement is to
identify native rhizobia with superior symbiotic and
competitive abilities and to use them in large doses within
inoculants, building upon the biodiversity of indigenous
rhizobial populations. The adaptability of indigenous rhizobia
to their environment results in high levels of saprophytic
competence. Therefore, continual identification of new, elite
isolates offers the opportunity to improve BNF within fine-
tuned geographical targets (Zengeni et al., 2006; Appunu
and Dhar, 2006). In this way, a wide diversity of rhizobia
isolates ensures a sustainable source of strains for
commercial application into the future (Musiyiwa et al.,
2005).
One empirical approach to rhizobia strain selection
focuses upon the stepwise collection, isolation and authen-

Waswa et al. 060
tication of native rhizobia, the screening of the isolates
against reference strains for symbiotic effectiveness, the
assessment of their competitive abilities and the
evaluation of their performance under a range of field
conditions (Howieson et al., 2000). Each step eliminates
the worst performing isolates from further consideration.
In this way, the identified elite rhizobial strains are likely
to colonize the soil, tolerate environmental stresses, and
compete with background populations (Slattery and
Pearce, 2002).
Ideally, this empirical approach identifies the elite
strains of rhizobia across a range of agro-ecologies,
mass produces them as inoculant and makes them
available to legume farmers so that they benefit from
native microbial biodiversity. Kenya is an excellent
location to test this approach. It has a wide range of
ecosystems, legume communities (White, 1983) and soils
(Sombroek et al., 1982), and a large population of
farmers cultivating legumes, including soybean as an
increasingly important cash crop. Moreover, these
farmers are in the process of advancing from subsistence
to market-based agriculture and seeking to improve their
field practices and yields (Woomer et al., 1998). This
study evaluates the effectiveness of Kenya's native
rhizobia on farmer accepted varieties of soybean and is
ultimately intended to result in improved legume
inoculants by identifying elite indigenous rhizobia.
MATERIALS AND METHODS
Three sets of experiments were performed to identify elite
rhizobia from our collection: authentication and
effectiveness screening of rhizobial isolates in potted
sterile media under greenhouse conditions, subsequent
evaluation of the better strains in a representative potted
soil also in the greenhouse, and finally on-farm testing of
the best strains in an area where soybean enterprise is
being rapidly adopted by small-scale farmers.
Greenhouse studies were conducted at University of
Nairobi field station, Kabete Campus, situated about 15
km to the west of Nairobi at 1015’S and 360 44’ E, in the
Central Kenyan Highlands (Sombroek et al., 1982.). The
field experiment was conducted at Nyabeda in a
smallholder farming community in west Kenya, located at
000 08’N and 0340 24’ E, 1331 m above sea level.
A Complete Randomized Design with three replicates
consisting of 104 treatments was established in a
greenhouse, 100 indigenous test isolates, two reference
strains (SEMIA5019 and USDA110), and non-inoculated
plants with and without mineral N. Promiscuous soybean
(SB19) was used as the test crop. Clean three liter
plastic pots containing heat-treated gravel for drainage
were filled with 750 g rhizobia-free vermiculite and
covered with a clean plastic plate with two access holes
to accommodate the test crop sprouts and a watering
tube.
Soybean seeds were surface sterilized (Somasegaran
and Hoben, 1994), pre-germinated in vermiculite and
three uniform sprouts transplanted per pot, later thinned
to two. Test isolates were cultured in Yeast Extract
Mannitol broth (YMB) after Vincent (1970), incubated at
28 0C until turbid and 1 ml of broth was applied to the
roots of each plant. For the mineral nitrogen control,
KNO3 (0.05%) was applied following (Broughton and
Dillworth, 1971). After eight weeks, nodulation was
observed by careful recovery of roots and shoots were
harvested, oven dried and weighed. An Effectiveness
Index was calculated by dividing shoot biomass of test
isolates by that of USDA 110. With this index and isolate
performance relative to experimental controls, isolates
were categorized as non-infective, ineffective (less than -
N control), partly effective (<75% of USDA 110), effective
(75% or equal to USDA 110) or highly effective (>USDA
110) and ranked in ascending order.
A red clayey loam collected from a farm in Butula, west
Kenya was used as media for competitive screening in
the greenhouse. The soil was characterized for its
chemical characteristics as follows. Nitrogen was
determined using a steam distillation method (Bremner
and Keeney, 1965) and organic carbon (C) by wet
oxidation using a modified Walkley-Black procedure as
described by Nelson and Sommers (1982). Phosphorus
(P) and potassium (K) were extracted by Mehlich-3
procedure (Mehlich, 1984) and then measured by
automated colorimetry using an Inductively Coupled
Plasma Atomic Emission Spectrophotometer (Kalra and
Maynard, 1991).
A second experiment was established in the
greenhouse at the Kabete Campus using this soil with the
24 best performing isolates from the first screening. This
experiment utilized a similar approach, three liter plant
containers, sprout transplants, YMB isolate preparation
and non-inoculated and industry standard controls, but
included two soybean varieties, a promiscuous (SB19)
and specific soybean (SB97) variety. Indigenous rhizobia
populations in the test soil were determined using the
plant infection technique (Somasegaran and Hoben,
1994). Experimental units were arranged as a Split-Plot
by varieties with four replicates. The soil was fertilized
with Sympal, a commercially-available blend for legumes
(0-23-15 + Ca, Mg and S) at a rate of 500 kg ha-1 mixed
with two kg of soil pot-1. Pots were regularly irrigated with
rhizobia-free water. After eight weeks, plants were
carefully uprooted, nodules observed, shoots, roots and
nodules recovered, oven dried at 70°C for 48 hours, plant
biomass recorded, summary statistics calculated and
two-way ANOVA (variety x N source) performed. The
best performing isolates were selected for field testing.
In addition to USDA110, six indigenous rhizobia
isolates (6%) were selected from the potted soil
experiment to test their effectiveness in field under farmer
conditions. A field experiment was established in west
Kenya at Nyabeda during 2012-2013 short rains (Septem-

061 Afr. J. Crop Sci.
0
0.2
0.4
0.6
0.8
1,0
1.2
1.4
-N USDA
110 +N
ineffective
partly
effective
effective
SM
5019
highly
effective
rhizobia isolates and controls
Effectiveness Index (USDA 110 = 1.0)
0
0.2
0.4
0.6
0.8
1,0
1.2
1.4
-N USDA
110 +N
ineffective
partly
effective
effective
SM
5019
highly
effective
rhizobia isolates and controls
Effectiveness Index (USDA 110 = 1.0)
Figure 1. Effectiveness Index of 80 Kenya isolates on soybean variety SB 19 grown in
rhizobia-free vermiculite for 56 days.
Figure 1. Effectiveness Index of 80 Kenya isolates on soybean variety SB 19 grown in rhizobia-free vermiculite for 56 days.
ber to January). The red clayey loam at Nyabeda has the
following characteristics: pH=5.7, organic C=2.32%, total
N=0.21%, extractable P=5.0 ppm and exchangeable
K=398 ppm. Six indigenous isolates and USDA110 were
compared on promiscuous (SB19) and specific (SB97)
soybeans. Non-fertilized maize was grown the previous
season to reduce soil N. Indigenous rhizobia populations
were determined using the plant infection technique
(Woomer et al., 1994). Sympal fertilizer was applied at
the rate of 200 kg ha-1. Sugarcane bagasse was also
applied at a rate of 2 t ha-1 to immobilize soil N. Calcium
ammonium nitrate (CAN) fertilizer was applied at the rate
of 78 kg N ha-1 to one treatment (+N). Plots were
arranged as a Randomized Complete Block with each
consisting of 6 rows 45 cm apart and seed planted at 5
cm intervals. Each plot was separated by three non-
inoculated rows to reduce cross-contamination. The test
isolates were NAK 84, 89, 115, 117, 128 and 135 with
USDA110 included as a reference strain. Legume
inoculants were prepared from these isolates using
sterilized sugar mill filter mud as a carrier, cured for 14
days and applied at 10 g kg seed-1 with 16% gum arabic
adhesive using the two-step inoculation method of
Woomer (2010). Soybeans were managed according to
usual farmer practice, weeding twice by hoe prior to
canopy closure. Plants were sampled for nodulation eight
weeks after emergence coinciding with 50% flowering in
0.225 m2. Plants were carefully uprooted, root systems
recovered, washed, nodules recovered, counted, oven-
dried for 24 hours at 700C and dry weight recorded. At
grain maturity, soybean grain was harvested from 5.4 m2,
dried and weighed. Data was compiled on a
spreadsheet, inspected and then summary statistics
calculated and ANOVA performed.
RESULTS
One hundred isolates obtained from diverse agro-
ecologies were tested for effectiveness on SB 19 in the
greenhouse using rhizobia-free sterile vermiculite as a
rooting media. Negative (-N) and positive (+N) controls
were not nodulated. Of the test isolates, 20% did not form
nodules and were eliminated from further consideration.
The remaining isolates were classified as ineffective
(26%), partly effective (26%), effective (17%) or highly
effective (11%) based upon their performance compared
to the non-inoculated control and USDA 110, the local
industry standard (Figure 1). Total plant biomass ranged
from 0.5 to 13.5 g per pot and nodule number from zero
to 151 per pot (data not presented), suggesting that the
growth system allowed for large differences between
treatments.
The best performing 24 isolates were then compared to
USDA110 using the same greenhouse growth system,
but substituting a red clayey loam soil from western
Kenya for of vermiculite. MPN using SB 19 as host
estimated that the soil contained 2.7 x 103 native rhizobia
g-1 soil. In this way the non-inoculated treatment serves
as a useful control allowing the most competitive and
effective isolates to distinguish themselves (Figure 2).
Plant biomass and nodulation were greater for SB 19
than cv. Safari (p < 0.001 and 0.001, respectively). Only
25% of the isolates outperformed the native population in
terms of plant biomass on SB 19 and 16% did so on cv.
Safari. In contrast, many isolates formed more nodules
than the native population, 67% and 38% on SB 19 and
cv. Safari, respectively (data not presented). The native
population and many of the test isolates failed to nodulate
Safari, while all formed nodules on SB 19, reaffirming the

Waswa et al. 062
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
NAK12
NAK160
NAK83
NAK144
NAK161
NAK89
NAK30
NAK122
NAK179
NAK176
NAK146
NAK127
NAK84
NAK9
NAK182
NAK10
NAK139
NAK117
NAK152
SEMIA5019
natives
NAK96
NAK149
USDA110
NAK128
NAK135
NAK115
less
competitive more
competitive
plant biomass (g pot-1)
rhizobia isolate
a) variety SB 19
LSD 0.05
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
NAK12
NAK160
NAK83
NAK144
NAK161
NAK89
NAK30
NAK122
NAK179
NAK176
NAK146
NAK127
NAK84
NAK9
NAK182
NAK10
NAK139
NAK117
NAK152
SEMIA5019
natives
NAK96
NAK149
USDA110
NAK128
NAK135
NAK115
less
competitive more
competitive
plant biomass (g pot-1)
rhizobia isolate
a) variety SB 19
LSD 0.05
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
NAK146
NAK115
NAK122
USDA110
NAK30
NAK127
NAK117
NAK152
NAK161
NAK96
SEMIA5019
NAK149
NAK179
NAK139
NAK84
NAK135
NAK9
NAK182
NAK128
NAK176
NAK10
NAK83
natives
NAK12
NAK144
NAK89
NAK160
less
competitive more
competitive
LSD 0.05
plant biomass (g pot-1)
rhizobia isolate
b) cv. Safari
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
NAK146
NAK115
NAK122
USDA110
NAK30
NAK127
NAK117
NAK152
NAK161
NAK96
SEMIA5019
NAK149
NAK179
NAK139
NAK84
NAK135
NAK9
NAK182
NAK128
NAK176
NAK10
NAK83
natives
NAK12
NAK144
NAK89
NAK160
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
NAK146
NAK115
NAK122
USDA110
NAK30
NAK127
NAK117
NAK152
NAK161
NAK96
SEMIA5019
NAK149
NAK179
NAK139
NAK84
NAK135
NAK9
NAK182
NAK128
NAK176
NAK10
NAK83
natives
NAK12
NAK144
NAK89
NAK160
less
competitive more
competitive
LSD 0.05
plant biomass (g pot-1)
rhizobia isolate
b) cv. Safari
Figure 2. Plant biomass of two soybean varieties, SB 19 (a) and SC Safari (b) in potted soil
receiving different N sources including 24 test isolates of Kenyan indigenous rhizobia.
Figure 2. Plant biomass of two soybean varieties, SB 19 (a) and SC Safari (b) in potted soil receiving different N
sources including 24 test isolates of Kenyan indigenous rhizobia.
latter's "promiscuous" pedigree. The best six isolates
were then evaluated under field conditions at Nyabeda
farm for comparison to USDA 110 and non-inoculated
and N-fertilized managements, again with promiscuously
nodulating (SB 19) and specific (SB 97) varieties of
soybean. With both varieties, NAK 128 emerged as the
most promising isolate, producing an average 1439 kg
grain ha-1 and outperforming both the non-inoculated
control and USDA 110 by 22% and 27%, respectively
(Table 1). Nodule number and biomass from the field
experiment are presented in Table 2.
DISCUSSION
The empirical, stepwise approach to strain selection
employed was largely successful in that it started with a
large number of test isolates and systematically reduced

063 Afr. J. Crop Sci.
Table 1. Grain yield by two soybean varieties under different nitrogen management at the Nyabeda field
experiment in west Kenya.
N source
------ SB 19 ------
------ SB 97 ------
grain yield
partial returna
grain yield
partial returna
kg ha-1
$ per $
kg ha-1
$ per $
Non-inoculated
1057
n.a.
1301
n.a.
USDA 110
1129
3.9
1139
-
NAK 115
1153
5.2
1140
-
NAK 117
1210
8.2
1086
-
NAK 135
1212
8.3
1230
-
N-fertilizer applied
1299
0.2
1304
0.0
NAK 89
1317
13.9
1230
-
NAK 84
1339
15.1
1182
-
NAK 128
1462
21.7
1416
6.2
LSD0.05
364
294
a Partial return calculated as increased soybean value/cost of N source with soybean valued at $0.613 kg-1, inoculant at $11.40
ha-1 and CAN-N at $2.38 kg-1. Not calculated when non-inoculated management outperformed inoculants (-).
Table 2. Nodule number (x102) and biomass per ha by soybean after 58 days at the
Nyabeda field experiment in west Kenya.
N source
Nodule number
Nodule biomass
---- no ha-1 (x102) ----
---kg ha-1 (10-1)-----
SB 19a
SB 97a
SB 19
SB 97
N applied
37.0
0.0
7.0
0.0
Native rhizobia
181.2
82.9
21.0
60.0
NAK 135
344.1
509.5
20.0
79.0
USDA 110
600.4
372.8
67.0
29.0
NAK 117
924.1
793.8
99.0
80.0
NAK 115
1222.2
1124.1
126.0
78.0
NAK 128
2469.9
1446.0
334.0
207.0
NAK 84
3999.7
6908.0
291.0
538.0
NAK 89
4227.0
3323.1
326.0
306.0
LSD0.05
--------- 2779.7 --------
---------- 200 ---------
a SB 19 is promiscuously nodulating and SB 97 is more specific.
them to a few, highly effective and competitive strains.
Part of this success is due to reliance upon large pots
used in our greenhouse experiments, and the
greenhouse design and sanitation that permits these
units not to become contaminated. Another component
is the comprehensive strategy to bio-prospecting
throughout Kenya's diverse wild and cultivated legume
communities, but this aspect will be covered in a later
paper. Part of this success is perhaps due to luck,
because bio-prospecting for rhizobia intended for a
moderately specific legume host away from its Center of
Origin is risky, but Africa is an ancient land mass and
Kenya embraces considerable biodiversity. One indicator
of our success is the performance of the best isolates
compared to long-time industry standard USDA 110.
There was considerable variation in nodulation and
plant biomass among the test isolates in sterile media,
indicative of varying ability as symbiotic partners of
soybean. Other investigations (Terpolilli et al., 2008;
Karaca and Uyanöz, 2012) noted that efficiency of nitrogen

Waswa et al. 064
fixing symbioses can vary from those that fix little or no
nitrogen to those that fix at levels equivalent to even
greater than plants provided mineral N (Figure 1). It is
essential that both negative (-N) and positive (+N)
controls were not nodulated as the former indicates that
contamination was minimized and the latter suggests that
sufficient mineral N was applied to meet soybean
demand for nitrogen.
In later experiments, differences between soybean
varieties were observed. Saeki et al. (2005) also
reported differences in nodulation of different soybean
varieties grown in soil with some rhizobia better able to
overcome native background populations. Dhami and
Nandan (2009) reported better nodulation where
inoculants were applied in higher concentrations because
they overwhelmed native rhizobia. Theis et al. (1991)
identified a critical threshold of native rhizobia beyond
which inoculation proved no longer effective. These
mechanisms are presumable operative within our
experimental conditions as well. Nonetheless, several of
our isolates from a range of legume hosts and ecologies
outperformed industry standard strains (Table 3) even in
soils with relatively large native populations of rhizobia.
Several native isolates failed to nodulate soybean SC
Safari, a non-promiscuously nodulating variety while all
formed nodules on SB19, a promiscuous variety arising
from the decades-long breeding program at IITA, leading
to the TGx series (Sanginga et al., 2000). Based on
recovery of isolates by TGx lines from 65 African soils,
Abaidoo et al. (2000) concluded that bradyrhizobia
nodulating promiscuous soybean are diverse and
genetically distinct from those nodulating North Americam
soybeans. Several isolates performing well on the TGx
lines were obtained from a range of hosts not usually
considered to cross-infect soybean (e.g. Eriosema sp.)
reaffirming that TGx is more promiscuously nodulating.
This conclusion is reinforced by a report by Maingi et al.
(2006) on most-probable number obtained from cowpea,
and TGx and Clark soybean using two soils where TGx
recovers a greater proportion of native bradyrhizobia
nodulating cowpea. Similarly, Salvucci et al. (2012)
reported different response to rhizobial inoculation across
soybean genotypes in Argentina. Certainly, a similar
phenomenon operated within our rhizobia selection
process, suggesting that our best isolates warrant
effectiveness testing across a wider range of soybean
germplasm. For example, one test isolate, NAK 179,
performed very well with SB 19 in potted soil and poorly
with Safari, and was dropped from further testing, an
exclusion that may have been premature. From a more
practical standpoint, however, we have empirically
established which rhizobia perform best on soybean
varieties that have achieved farmer and market
acceptance.
Even promiscuous SB 19 responds to inoculation under
field conditions. This response to inoculation by TGx
soybean was also observed in Nigeria (Muhammad, 2010)
and Ghana (Kumaga and Etu-Bonde, 2000), although in
the latter case USDA 110 (=TAL 102) proved the best
inoculant rhizobia. Promiscuous Asian soybeans are
often nodulated by ineffective rhizobia (Eaglesham, 1985)
and the same may be true in Africa, possibly explaining
this response. Indeed, response to inoculation was not
considered in the breeding program that developed the
TGx promiscuous lines (Dashiell et al., 1985). Non-
promiscuity in soybean is a dominant trait (Gwata et al.,
2004), perhaps explaining why the development of the
promiscuous TGx lines required so many years and is
incomplete.
Despite differences in symbiotic relations by
promiscuous and specifically nodulating soybean, isolate
NAK 128 emerged as the most productive effective
isolate on both SB 19 and SB 97 (Table 1) but without
producing the most nodules or nodule mass (Table 2).
The latter observation further reinforces our conclusion
that this is a highly effective strain, certainly more so than
USDA 110 under our field conditions, offering greater
economic partial return to inoculation as a field practice
(Table 1). Presumably, NAK128 outperformed both native
rhizobia and USDA 110 because it was more effective
and competitive. Appunu and Dhar (2006) and Appunu et
al. (2008) also concluded that native rhizobia can be
symbiotically more effective than reference strains of
foreign origin. In addition to NAK 128, five other isolates
have favorable abilities to fix nitrogen compared to USDA
110, NAK 84, 89, 115, 117 and 135. While rhizobia
isolated from many legume species in Kenya were
evaluated, all six of these superior strains were isolated
from non-inoculated soybean growing in farmers' fields,
and not from natural habitats. While the strategy that
recovered, tested and identified these candidate elite
strains was otherwise expedient, it was not particularly
comprehensive. Our laboratory facilities did not allow us
to characterize isolates using molecular tools, and these
isolates may comprise identical strains or different
species. The genetic stability of nodulation and nitrogen
fixation under laboratory culture is not yet established,
nor is the ability of the isolates to utilize lower cost carbon
sources. Characterization and testing of these isolates
continues, and we invite other laboratories and
commercial inoculant producers to join us in exploring the
potential of these elite rhizobia from Kenya.
ACKNOWLEDGEMENT
The Legume Agronomy Team at the CIAT Maseno
Station assisted in the installation and maintenance of the
field experiment. This research is carried out in the
context of, and financial support from, the N2Africa
project “Putting Nitrogen fixation to work for small holder
farmers in Africa”. N2Africa project is funded by the Bill
and Melinda Gates Foundation and implemented by the
Tropical Soil Biology and Fertility Institute of CIAT in Kenya.
The University of Nairobi provided scientific supervision
and logistical support. Coordinator of N2 Africa project in

065 Afr. J. Crop Sci.
Kenya, Jeroen Huising provided useful comments on this
paper. Each of these contributions is truly appreciated.
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