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Enhancing Sorghum Productivity in Acidic Soils Through Lime–
Fertilizer Synergism: Agronomic, Economic, and Composite
Performance Analysis
*Edwin Kiprono Rotich1, Peter Kisinyo Oloo2, Peter Asbon Opala3, Gudu Samwel Odundo2
1Soil Science Department, University of Eldoret.
2Department of Agronomy, Rongo University. Kenya
3Maseno University, Kenya, Department of Crops and Soil Sciences, Kenya
DOI: https://doi.org/10.51244/IJRSI.2025.1210000108
Received: 22 August 2025; Accepted: 30 October 2025; Published: 06 November 2025
ABSTRACT
Sorghum productivity in Western Kenya is severely constrained by acidic soils, particularly Ferralsols and
Acrisols prone to aluminum toxicity and phosphorus fixation. This study assessed the performance of lime-
integrated fertilizer treatments under smallholder conditions using a randomized complete block design across
three sites. Sorghum grain yield (SGY), agronomic efficiency (AE), nutrient uptake efficiency (NUE), and gross
margin (GM) were measured alongside the formulation of a composite Performance Index (PI) designed to
simulate both physiological and economic effects. We developed a composite Performance Index to integrate
agronomic and economic outcomes, enabling balanced evaluation of lime–fertilizer strategies across acid-prone
sites. The PI incorporated weighting scenarios reflecting equal and smallholder-adjusted preferences. Results
showed that lime enhanced AE (up to 55%), NUE (up to 34.6%), and SGY ≥ 1.8 t ha⁻¹ across sites, with
intermediate fertilizer rates yielding superior performance. GM exceeding $450 ha⁻¹ and benefit–cost ratios over
2.0, demonstrating strong economic viability, Lime + N37.5P13 consistently outperformed other treatments,
offering agronomic–economic balance and robust PI ranking across sensitivity models. Radar and contour plots
identified optimal combinations and revealed trade-offs between efficiency and yield. These findings support
lime as a foundational input rather than a supplemental one, and advocate for context-driven ISFM strategies
aligned with smallholder realities. The PI framework offers a flexible and empirically grounded tool for
sustainable intensification decisions in acid soil systems.
Keywords Acidic Soils Lime–Fertilizer Integration Performance Index Agronomic Efficiency Gross
Margin
INTRODUCTION AND BACKGROUND
Sorghum is a climate resilience and food security crop in sub-Saharan Africa, especially under smallholder
systems. Due to its tolerance to drought and low inputs, it is capable of performing well on marginal lands;
however, its productivity is severely limited by soil acidity that is prevalent in Western Kenya Ferralsols and
Acrisols. They are characterized by low pH levels, high aluminum saturation, and phosphorus fixation, which
together hinder root growth, nutrient acquisition, and plant performance.
Soil acidity impacts sorghum indirectly by disrupting chemical and biological processes. Root development and
nutrient uptake are inhibited by aluminum toxicity, and phosphorus is trapped by precipitation with Fe and Al
oxides. Kisinyo et al. [1] asserts that soils in which such occurrences are common include Western Kenya, where
exchangeable Al levels are typically above threshold levels to crops and hence contribute to impaired recovery
of nutrients and stunted growth. Gudu et al. [2] also illustrated that maize and sorghum yields decline
considerably under these limitations even when fertilizer is used unless liming is used.
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Liming has been broadly accepted as remedial measure. Lime alkalinizes soils which increases availability of
certain essential nutrients (such as phosphorus, calcium, and magnesium), promotes root growth and decreases
availability of exchangeable Al3+ by precipitating it. It was demonstrated by Opala [3] that application of lime
enhances quite certainly the phosphorus uptake in acid soils and the build-up of biomass, particularly in
combination with moderate rates of P fertilizers. Equally, Esilaba et al. [4] pointed out that as far as sustainable
nutrient management in highland soils in Kenya is concerned, the application of lime is a critical aspect
considering that it not only neutralizes the acid but also ensures that the fertilizer deployed is utilized effectively.
In spite of its demonstrated advantage, utilization of lime by the smallholders is not gaining a lot of headway
and this is the effect of the cost, labor intensity and lack of awareness. A pragmatic way to eliminate these
barriers is Integrated Soil Fertility Management or ISFM, which is advocated by Vanlauwe et al. [5]. ISFM
promotes site-specific blends of mineral fertilizers, organic amendments and soil conditioners such as lime and
focuses on targets of agronomic proficiency, economic feasibility and environmental sustainability.
Despite the prevalent application of single-variable metrics like grain yield or net returns to assess treatment
effectiveness, these indicators frequently obscure essential trade-offs related to nutrient uptake, soil amendment
efficiency, and farmer investment. Particularly in systems susceptible to acidity, where physiological limitations
are intertwined with economic factors, there is a pressing need for a more comprehensive evaluative framework.
In light of this, we propose a composite Performance Index (PI) that integrates agronomic and economic aspects
into a cohesive scoring system. This methodology aids in the clearer identification of treatments that provide
balanced benefits, enhances comparability across different sites, and addresses the persistent demand for
multidimensional metrics in sustainable intensification research [5–7].
The current research lays on the ISFM paradigm to assess lime and fertilizer interaction in acidic soils through
the use of sorghum as the test crop. A multiple index performance model is used where agronomic efficiency
(AE), nutrient uptake efficiency (NUE), gross margin (GM), and grain yield (SGY) are combined in determining
the best combinations of inputs. Basing the model on the multi-dimensional constructs by Congreves et al. [8]
and Weih et al. [9] premises, the model employs sensitivity-weighted scoring to simulate sustainability limits and
make decisions within the conditions of smallholder realities.
As depicted in Figure 1, the conceptual framework maps how acid soil constraints interact with nutrient
dynamics to create a productivity gap, addressed through integrated liming and fertilization. The resulting
outcomes—both physiological and economic—are captured through performance metrics feeding into a
composite recommendation index.
Fig. 1 Conceptual flow chart illustrating causal linkages from soil acidity to composite agronomic and economic
outcomes via lime–fertilizer intervention
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Footnote:
This diagram synthesizes the pathway from soil chemical limitations through physiological stress to nutrient
interventions and composite performance metrics. Arrows represent directional influence, while node groupings
reflect thematic domains of constraint, intervention, and outcome. Agronomic and economic indicators converge
toward a composite index designed to guide smallholder decision-making under acid soil stress.
MATERIALS AND METHODS
2.1 Study Sites and Experimental Design
Field trials were conducted in three sites in Western Kenya: Siaya 1 (ferralsols), Kakamega (acrisols) and Level
2 (ferralsols) over two cropping phases. The experiments were executed on smallholder farmers’ fields. The trials
involved three replications per site, and their design was the randomized complete block (RCBD). A fertilizer
dose of 0 and 4 t ha-1 of lime together with three levels of Nitrogen-Phosphorus fertilizer (N18.8P6.5, N37.5P13, and
N75P26) were set as the treatments. The crop that was tested was sorghum. Lime was applied to all the plots
before being planted and fertilizers were applied during the planting and top-dressing as recommended by the
treatments.
Soil Sampling was done randomly from the demarcated experimental plots following a zig-zag procedure. Three
composites of nine subsamples were done per replicate in each site to eliminate variability. This gave a total of
nine samples per site and a grant total of twenty-seven samples. Each sample weighed 0.5 kg each, making 4.5
kg from each study site which were Kakamega, Siaya site 1 and Siaya Site 2, all being farmers’ farms. Soils
were then extracted by using a soil auguring at soil depths of 0-30cm. The samples collected at various points
across the study sites and at the same depth were composited to make five packages per site. In total fifteen
samples were submitted to the laboratory for selected chemical (pH. P, N SOC, exchangeable acidity), and
physical (texture and bulk density) parameters as discussed in section 3.13.
2.2 Field Procedures and Agronomic Indices for Sorghum Evaluation
The experimentation of sorghum was done between 2016 and 2018 in the long rain seasons of Siaya, Koyonzo,
Homa Bay, and Migori. One month before the sowing, lime-treated plots were prepared by broadcasting lime in
the amount of 4.2 kg/10.5 m 2 and mixing it with the soil using hand hoes to provide time to reduce the acidity
before planting took place. A basal level of fertilization, including 18 kg P₂O₅ ha⁻¹ and 18.8 kg N ha⁻¹ that was
added to nutrient-amended plots was not applied on the control plots during the experiment. Harvesting was
conducted on the four middle rows of each plot in order to limit edge effects, and the effective area per treatment
shared by all the plots was 4.2 m². The total above-ground sorghum biomass, i.e., panicles, leaves, and stems,
was removed by cutting all the plants at soil level and harvesting the entire fresh biomass directly in the field
into a digital balance and weighing. Five representative samples were then taken from this bulk sample, put in
ventilated bags, labeled, and air-dried in a greenhouse for 72 hours to estimate the fraction of dry matter, which
was used to estimate dry biomass yields.
Grain and crop components were measured from the 4.2 m² harvested area and extrapolated to per-hectare output
based on the standard 10,000 m² hectare scale. The proportion of the total fresh weight to the dry weight of the
sample was determined to estimate grain yield (t ha-1) by dividing by the effective area harvested. The nutrient
uptake (kg ha⁻¹) was computed by dividing the nutrient content (kg N or P) by the crop dry mass percentage and
multiplying by 100. Leaf sampling was conducted at silking stage to determine nitrogen (N) and phosphorus (P)
uptake. In each plot, twelve randomly selected sorghum plants were used, with care taken to avoid contaminated
or dust-laden leaves. Samples were air-dried in a greenhouse and ground into fine powder before digestion using
a mixture of sulfuric acid, hydrogen peroxide, selenium powder, and lithium powder. Nutrient concentrations
from the digested samples were analyzed following Okalebo et al. [10], and the results were used to compute
total nutrient uptake by the crop.
Nitrogen and phosphorus in grain samples were determined by the same digestion procedure outlined here. The
total nitrogen content in the soil was measured using the Micro-Kjeldahl digestion method, in line with the
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AOAC International standards set in 2000. This method involves breaking down soil samples with concentrated
sulfuric acid along with a catalyst mix of potassium sulfate and copper sulfate. This process transforms the
nitrogen that is organically bound into ammonium sulfate. After the digestion, the mixture is distilled to release
ammonia, which is then measured through titration, allowing us to calculate the total nitrogen present. Grain
yield percentage over control increase was calculated as (treatment - control yield)/control yield × 100 and gave
an estimate of fertilization effect. Harvest index (HI) or the ratio of grain yield to total above-ground biomass,
was computed according to the method of Bange et al. [11] for estimating biomass partitioning efficiency towards
the grain. Agronomic efficiency (AE) was calculated as the incremental gain in grain yield due to nutrient
application over the sum of nutrients applied, as per Vanlauwe et al. [12]. Finally, the uptake of nutrients in stover
and grain was presented as kilograms per hectare and was determined by multiplying yield (kg ha⁻¹) with a fixed
percentage of nutrients and dividing by 100. This whole set of parameters facilitated a proper assessment of
treatments on sorghum growth, productivity, and nutrient uptake.
2.3 Performance Index (PI) and Sensitivity Analysis
A composite Performance Index (PI) was developed to integrate multiple agronomic endpoints into a single
scoring framework in order to facilitate assessment of treatment performance along both physiological and
economic endpoints. The PI integrated Sorghum Grain Yield (SGY), Gross Margin (GM), Agronomic Efficiency
(AE), and Nutrient Use Efficiency (NUE) and allowed for integrative interpretation of trial data. The index was
computed using the following formula:
PI=α1⋅AE+α2⋅NUE+α3⋅(GM/1000) +α4⋅SGY --------------------------------------------------- (1)
The weights of each metric are represented by the coefficients αᵢ in this formula: α₁ for AE, which indicates
responsiveness per unit input; α₂ for NUE, which indicates nutrient uptake effectiveness; α₃ for GM, which
indicates economic return and is scaled to match the magnitude of other terms; and α₄ for SGY, which captures
direct productivity. Two weighting scenarios were simulated. In the equal-weight scenario, all coefficients were
set to 1.0, assuming uniform importance. A second scenario adjusted the weights to reflect smallholder priorities
under low-input conditions: α₁ = 1.2, α₂ = 1.3, α₃ = 0.8, and α₄ = 1.0, thereby emphasizing efficiency metrics
over financial yield.
The Performance Index was calculated by taking values of each combination of fertilizer and lime treatment.
These contour plots were used to plot the surface slopes of the PI scores in order to identify the relevant areas of
intervention. The radar charts have been used to give multivariate profiles of single interventions. Replication of
context-dependent preferences and estimation by robustness included sensitivity analysis through comparison
of ranks of treatments with both weighting procedures.
2.4 Statistical Analysis and Visualization
The one-way ANOVA was used to evaluate the treatment effects, and post hoc estimates were done using the
Tukey HSD test at p < 0.001. Visualization of data in R was conducted in the ggplot2 package. The plots were
overlain with thresholds to indicate the boundaries of sustainability performance, AE 20% and GM $388 ha⁻¹.
Simulation output was validated using cross-site comparisons and sensitivity mapping in order to determine the
presence of optimal treatment zones.
RESULTS AND DISCUSSION
3.1 Sorghum Grain Yield and Biomass Response
Grain yield was boosted considerably by fertilizer application at all locations and times, with largest boost from
the application of the full NPK rate (N75P26). Micro-dose applications (N18.8P6.5) increased SGY by 27–39%, and
full-rate applications regained up to 58% gains. Lime application boosted Siaya 1 and Siaya 2 SGY consistently,
but less so in Kakamega. Composite lime × fertilizer treatments yielded additive or weakly synergistic effects,
especially with intermediate fertilizer application. Biomass yield was positively responsive to lime and fertilizer
application. Maximum SBY was obtained under N75P26 where Kakamega was superior to Siaya sites.
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Application of lime alone increased biomass significantly, notably in Kakamega and Siaya 1, suggesting
increased root growth and nutrient uptake under optimal pH.
3.2 Agronomic Efficiency and Nutrient Uptake Efficiency
Agronomic efficiency (AE) was greatest with micro-dose applications of fertilizers and reduced with the rise in
amounts of N and P. Lime enhanced AE in all locations with Siaya 2 responding highest. AE varied from 6.6%
to 11.9% with lime + N75P26, but that of lime + N37.5P13 and lime + N18.8P6.5 varied between 25–55%, reaffirming
the advantage of intermediate quantities of inputs for efficiency. Nutrient uptake efficiency (NUE) reflected
trends in AE. The greatest NUE was realized with micro-dose application, while the lowest was with N75P26.
Lime improved NUE at all sites, and Siaya 2 in the long rains of 2017 had the highest mean at 34.56%. Lime +
N37.5P13 led in all cases in nutrient recovery.
3.3 Economic Performance: Gross Margin and Benefit–Cost Ratio
Gross margin (GM) analysis showed the highest GM for lime + N75P26 ($507 ha⁻¹), followed by lime + N37.5P13
($451 ha⁻¹). Nonetheless, lime + N37.5P13 recorded better AE and NUE, making it the most sustainable treatment.
Benefit–cost ratio (BCR) values > 2.0 were realized for lime + N37.5P13 and lime + N18.8P6.5, symbolizing high
profitability at modest input investment. Lime-free treatments could not realize profitability levels, a testament
to lime's catalytic effect on economic performance.
3.4 Treatment Rankings and Sensitivity Outcomes
Composite PI values revealed that treatments combining moderate lime rates with calibrated phosphorus inputs
always ranked high in the equal-weight scenario. They offered balanced physiological response and economic
return, in line with integrated amendment strategies. Under sensitivity-adjusted weighting, some mid-ranked
treatments moved upward due to strong AE and NUE scores, while monetarily dominant but physiologically
weak treatments declined slightly. Contour mapping defined optimal performance zones at lime application (4 t
ha⁻¹) and mid-range P application. Radar plots confirmed multiple high-yielding options with low input-use
efficiency, emphasizing the value of composite ranking. Key recommendations were consistent across weighting
strategies, validating the PI as a stable and context-sensitive decision tool.
Fig. 2. Multi-metric performance profiles of selected lime–fertilizer treatments in sorghum production.
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Keynotes:
Radar plots showing scaled performance across six metrics—grain yield (SGY, t ha⁻¹), agronomic efficiency
(AE, %), nitrogen use efficiency (NUE, %), harvest index (HI), gross margin (GM, $), and benefit–cost ratio
(BCR)—for three selected treatments: 4tha-1+N37.5P13, 4tha-1+N18.8P6.5, and 0tha-1+N75P26.
3.5 Integrated Performance Profiles and Composite Scoring
Figure 2 shows radar plots of six scaled performance indicators—SGY, AE, NUE, HI, GM, and BCR—of three
selected treatments. Lime + N37.5P13 has a close-to-perfect hexagonal shape, indicating good agronomic as well
as economic performance. Lime + N18.8P6.5 is high in AE and HI, and 0tha⁻¹ + N75P26 is high in GM and BCR
but low in physiological efficiency. Figure 2 is a normalized agronomic and economic score comparison of all
eight treatments. Lime-treated sets are consistently higher than non-limed sets in both, with the highest
composite scores being 4tha⁻¹ + N75P26 and 4tha⁻¹ + N37.5P13. Table 1 provides a general performance of all the
treatments with statistical separation (LSD), coefficient of variation (CV%), and composite recommendation
ranks. The overall best ranking is lime + N75P26 (score = 0.77), followed by lime + N37.5P13 (score = 0.76) and
lime + N18.8P6.5 (score = 0.70). Non-limed treatments are categorized as "Moderately Recommended" or
"Optional" based on performance.
3.6 Interaction of Efficiency and Yield Indicators
Figure 3 shows a graph of multi-index performance, where AE (x-axis), GM (y-axis), NUE (bubble size), and
SGY (color gradient) are used. Simulated contours = composite PI values. Treatments nearest the center—most
significantly lime + N37.5P13—had great agronomic-economic performance, with yield, efficiency, and
profitability in a balance.
3.7 Economic Performance of Lime–Fertilizer Treatments
Figure 3 demonstrates the relationship between Nutrient Use Efficiency (NUE) and Gross Margin (GM_USD)
of the treatments. Treatments were normalized and ranked into AE classes (High, Moderate, Low) with different
marker shapes. A dotted threshold line at $300 ha⁻¹ indicates economic viability. Treatments below this threshold
suggest uneconomical realization of profits. Yet, treatments with medium to high NUE also surpassed the $300
ha⁻¹ threshold, indicating economically responsive nutrient processes. The most economical treatments
combined calcitic lime with moderate fertilizer rates, NUE = 2.1–2.5 and GM = $310–$420 ha⁻¹. These blends
justify lime's role in enhancing input-use efficiency under acidic conditions.
3.8 Relationship Between AE and Gross Income (GI USD ha⁻¹)
Figure 4 depicts AE vs. GI among lime–fertilizer treatment combinations. Each point is color-coded by AE class.
Generally, a moderate positive relationship exists between AE and GI.
High AE treatments had GI of $580–$750 ha⁻¹, while Moderate AE treatments ranged from $350–$610 ha⁻¹.
Some Low AE treatments posted GI over $400 ha⁻¹, suggesting factors beyond AE—like marketable yield or
rainfall—also affect returns. Lime-fertilizer treatments excelled in both AE and GI, highlighting the importance
of optimizing nutrient utilization for profitability in acidic soils.
3.9 Profitability Ratio Response to NUE Across Treatment Combinations
Figure 5 presents profitability ratio (GM ÷ TVC) versus NUE. A reference line at 1.5 marks viable smallholder
returns. Many treatments with moderate NUE (~1.8) and high AE exceeded the profitability threshold.
Treatments with high NUE (>2.0) but low profitability suggest input recovery alone does not ensure economic
success. Efficient treatments yielded at least $2 per dollar invested, affirming well-balanced input strategies.
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Fig. 3 Relationship Between NUE and GM (USD ha⁻¹) Across Lime–Fertilizer Treatments
Footnotes:
NUE is plotted along the X-axis and GM (USD ha⁻¹) along the Y-axis. Each treatment point is scaled by AE and
categorized into AE classes (High, Moderate, Low) using distinct marker shapes, ensuring accessibility for all
readers. A dotted line at $300 ha⁻¹ indicates the economic viability threshold. Treatment labels are positioned in
high-contrast, bold font for clear legibility. This visualization highlights lime–fertilizer combinations that deliver
both agronomic responsiveness and financial viability under acidic soil conditions.
Fig. 4. Relationship Between AE and GI (USD ha⁻¹) Across Lime–Fertilizer Treatments
Footnotes:
AE is plotted along the X-axis and GI (USD ha⁻¹) on the Y-axis. Treatments are categorized by AE class (High,
Moderate, Low) using shape-based markers to ensure accessibility for readers with color-vision deficiencies.
Treatment labels are rendered in bold, high-contrast font for clarity. The plot reveals treatment combinations that
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yield higher income per hectare in conjunction with elevated AE levels, enabling selection of agronomically
efficient and economically productive lime–fertilizer options.
Fig 5 Relationship Between NUE and Profitability Ratio (GM/TVC) Across Lime–Fertilizer Treatments
Footnotes:
NUE is plotted along the X-axis and Profitability Ratio (GM ÷ TVC in USD) on the Y-axis. Treatments are
categorized by AE class (High, Moderate, Low) using shape-based markers to enhance accessibility. A dotted
line at a ratio of 1.5 marks the economic viability threshold. Treatment labels are rendered in bold, high-contrast
text. This plot distinguishes lime–fertilizer treatments that optimize both nutrient use and financial efficiency.
DISCUSSION
4.1 Conceptual Alignment and Empirical Significance
These results support the theoretical depiction in Figure 1 that soil acidity is a root cause of nutrient stress. AE,
NUE, GM, and SGY are perceived as a systemic sequence incorporated into the PI model based on both farmer
and researcher interests. This aligns with recent studies in sub-Saharan Africa showing increased input recovery
and profitability under integrated nutrient management, particularly in acid soils [5,13]. Compared to traditional
yield-centric evaluations, the sensitivity analysis reorders treatments based on physiological and economic
efficiency. This reflects localized assessment models that prioritize farmer realities [7]. The PI framework
minimizes volatility among top-performing treatments and employs radar and contour visualizations to
intuitively identify multidimensional synergies.
4.2 Lime as a Substratum Modifier: Unlocking Sorghum Response in Acidic Soils
The uniform enhancement of sorghum growth on the lime-treated plots mirrors the intrinsic function of lime in
altering the soil substratum — not just for surface-acidity correction, but for redetermination of the root zone
environment. By elevating pH and precipitating exchangeable Al³⁺, lime reduces rhizotoxicity and increases root
elongation, thus increasing the volume of soil utilized for nutrient acquisition. This substratum-level adaptation
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is of special significance in Ferralsols and Acrisols, where elevated Al saturation and limited base saturation
limit root activity and mobility of nutrients [14,15].
4.3 Grain Yield and Biomass: Root-Zone Liberation and Nutrient Mobilization
The increased grain production under lime + fertilizer treatments noted are not only the result of nutrient
supplementation, but also due to release of the root zone from chemical constraint by lime. The activity of lime
increases the phosphorus availability by decreasing P fixation to Fe and Al oxides, a process with very active
reaction in weathered tropical soils [16]. This response was seen in Siaya, since, at similar levels of fertilizer,
the responses at lime + N37.5P13 and lime + N18.8P6.5 were very high. The response in biomass was also due to
this effect: lime-amended plots had increased vegetative growth, presumably due to the increased availability of
Ca²⁺ and Mg²⁺ and reduced proton toxicity, which collectively promote cell elongation and photosynthesis [17,18].
4.4 Agronomic and Nutrient Uptake Efficiency: Beyond Fertilizer Recovery
Maximum agronomic efficiency (AE) and nutrient uptake efficiency (NUE) in the lime-treated micro-dose plots
revealed that lime is doing more than optimize fertilizer recovery—it reconstitutes the plant–soil interface. By
suppressing Al-induced root pruning and root hair elongation, lime enables higher and longer-lasting nutrient
uptake [19]. The higher AE and NUE of lime + N37.5P13 and lime + N18.8P6.5 treatments validate this substratum
correction advantage. High-input non-lime treatment (e.g., 0tha⁻¹ + N75P26) was linked with low efficiency owing
to potential loss of nutrients by leaching and sorption in not corrected acidic profiles [20,21].
4.5 Economic Returns: Substratum Correction as a Profit Catalyst
The cost-effectiveness of lime + N75P26 was evident in gross margins but its efficiency indicators were behind
that of lime + N37.5P13. What it means is profitability can accompany high-input systems but reduced
physiological return. Lime's substratum correction makes intermediate-input treatment economically viable
without compromising efficiency—a good deal for smallholder sustainability. Nyokabi et al. [22] and Kula et
al. [23] research also revealed lime-integrated ISFM solutions to excel fertilizer-only conventional solutions
economically and agronomically in acid soils.
4.6 Substratum Synergy and Sustainability Thresholds
The radar plots and composite Performance Index (PI) placed the lime + N37.5P13 treatment in the sustainability-
performance consistently within beneficial range. In respect to this treatment, there was no reliance on high input
use—it achieved strong yield, efficiency, and profitability based on substratum synergy. The simulation with
weighted adjustments ensured that the action of lime to correct the root zone pH sufficiently enabling moderate
fertilizer rates, giving Pareto-efficient performance for smallholder intensification. This result is consistent with
Weih's [9] and Congreves' [8] multi-dimensional theories where nutrient recovery and robust physiology drive
sustainable agriculture.
4.7 Economic Interpretation of Lime–Fertilizer Treatment Effects
4.7.1 Nutrient Use Efficiency and Gross Margin (USD ha⁻¹)
The relationship of Nutrient Use Efficiency (NUE) and Gross Margin (GM) exhibited a stratified response to
lime–fertilizer treatment. NUE treatments in excess of 2.0 fell near or above the $300 ha⁻¹ economic break point,
indicating that physiological efficiency could be translated into profitability when inputs are managed properly.
This agrees with findings by Cheptoek et al. [24], who reported that when lime was combined with Minjingu
Rock Phosphate and NPK fertilizers, maize productivity and P use efficiency was significantly improved,
resulting in higher gross margins in acidic Kenyan soils. But the story also revealed treatments with improved
NUE but below-threshold GM, which means responsiveness to nutrients is no guarantee for profitability. Such
instances may be due to high input prices, unfavorable market price, or inefficient yield realization. This is an
omen for the warning made by Fixen et al. [20], who laid emphasis on the aspect that NUE should be interpreted
together with economic indicators to prevent false interpretation of input efficiency. The most economical
treatments in our work were those with moderate NUE (1.8–2.3) offset by high AE and low TVC, confirming
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the fundamental hypothesis that optimal nutrient use is better than maximum uptake per se. These findings justify
certain lime–fertilizer pairs as a method of maximizing both agronomic as well as economic returns under
conditions of acid soil limitations.
4.7.2 Agronomic Efficiency and Gross Income (USD ha⁻¹)
A plot of AE vs. GI showed a positive but non-linear correlation in which high-AE treatments resulted in higher
overall gross income. Plots with high-AE in most cases recorded income levels above $600 ha⁻¹, which reflected
very high predictive capacity of agronomic efficiency. This agrees with Mucheru-Muna et al. [25] study in
Tharaka-Nithi County, Kenya, where productivity and profitability of maize improved tremendously upon use
of lime and inorganic fertilizer. Some of the treatments posted high gross income (GI) but it had moderate
agronomic efficiency (AE). It implies that the increase in yield could be because of other factors which could be
better soil structure, increase in micronutrient supply or improvement in the rainfall. These results endorse
Dobermann [26] which said that AE is a temporal parameter and unable to depict an enduring or interacting state
of impacts on soil amendment. Low AE treatments garnered more than $400 ha⁻¹ even so, which promotes
situations in which an external market reward conceals internal agronomic fragilities. Nonetheless, these benefits
cannot be maintained in case of shock in input prices or yield variability. That notwithstanding, AE is an
excellent general guide to sustainable, or even intensification, in general, and of good input constraint to
smallholder especially.
4.7.3 Profitability Ratio and Nutrient Use Efficiency
The overall image of economic costs between treatments was provided by the last figure, presenting the
profitability ratio (GM/TVC) against NUE. Economically reasonable decisions were marked by the boundary
ratio of 1.5; most treatments had ratios higher than 2.0, with the implication that they produced a return on
investment of at least $2 per dollar. These efficient treatments indicated the importance of well-balanced input
strategies by having moderate NUE (1.8–2.2) augmented with greater AE and lesser TVC. The potential of
physiological efficiency at the expense of economic gain is captured through treatments with NUE > 2.0 but
profitability ratios < 1.5. This is often brought about by high fertilizer prices or diminishing marginal returns.
This observation agrees with that of Kiwia et al. [27], reported that profitability and fertilizer application
efficiency varied significantly by soils and seasons in East Africa and some of the high-NUE treatments yielded
low money return with increased production risk. On the other hand, low NUE profitability treatments with high
profitability ratios indicate that it is possible to realize low NUE profits without optimizing nutrient uptake. That
is particularly so whenever lime increases the pH of the ground and decreases the aluminum toxicity hence
making the crops vulnerable and nutrients accessible [28]. In general, the current plot brings to the fore the
necessity to assess NUE along with the measures of profitability to make input recommendations. It advocates
the use of lime as a cheap amendment that will increase the nutrient responsiveness and the returns to the
financial health of soil with acidic nature.
CONCLUSION AND RECOMMENDATIONS
This research proves that lime application, under complementation from moderate rates of nitrogen–phosphorus
fertilizer, converts soil constraints due to acidity into agronomic advantages. Lime + N37.5P13 treatment always
produced great grain yield, improved nutrient efficiency in uptake, and firm economic returns — not through
input maximization, but by maximizing the soil–plant interface. Lime-induced substratum correction increased
nutrient availability by the roots, relieved aluminum toxicity and partitioned the biomass to give rise to their
success in utilizing the resources, even at low fertilizer rates. Lime + N75P26 had shown the most significant gross
margin, but its declining agronomic and physiological efficiency shows the limitation of high-input strategies in
acidic soils. Lime + N18.8P6.5, on the other hand, recorded efficient values coupled with lower profitability and is
therefore suitable for low-resource systems where input recovery is a greater concern than high yield. The
combined Performance Index (PI) validated Lime + N37.5P13 as the most balanced and sustainable treatment that
held the position within the convergence zone where agronomic performance, economic profitability, and
physiological stability meet. This result is consistent with the overall ISFM paradigm favoring context-oriented,
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)
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efficiency-maximizing nutrient management. Sorghum intensification on Western Kenya's acidic soils is not
input maximization but balance—and lime is the fulcrum on which this synergism turns.
Funding
This work was supported by the University of Eldoret by providing laboratory facilities used during soil and
plant tissue analyses. Fieldwork was partially supported by the McKnight International Collaborative Crop
Research Program.
Author Contributions
Material preparation, data collection and analysis were performed by Edwin Kiprono Rotich. Conceptualization:
The first draft of the manuscript was written by Edwin Kiprono Rotich while Prof. Peter Kisinyo and Prof. Peter
Opala both refined to the current versions of the manuscript. All authors read and approved the final manuscript.
Prof. Peter Kisinyo and, whose guidance was instrumental in shaping the experimental design while Prof. Peter
Opala weighed in on refining the thesis from which this manuscript was developed.
Data Availability
The corresponding author will make the data available upon request.
Competing Interests
The authors have no relevant financial or non-financial interests to disclose.
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