Treatments consisted of factorial arrangement of five rates each of N (0, 30, 60, 90 and 120 kg∙ha⁻¹) and P (0, 40, 80, 120 and 160 kg∙ha⁻¹) in randomized complete block design with four replications. Determination of the N and P rates were based on previous reports from similar studies and the location soil mean N and P contents as contents as well as sweetpotato N and P nutrient requirements. Field grown planting materials (slips) with about four nodes were planted into four row plots (4 × 6 m) at a spacing of 100 by 30 cm to obtain a plant population density of about 33,333 plants∙ha⁻¹. Apomuden, an orange-fleshed sweetpotato variety was used as the test crop. Each slip was planted with two nodes underground and the other two nodes above the soil surface. The N was split applied as recommended by Barber et al. [42] . At two weeks after planting (WAP), one half of the N rates, as sulphate of ammonia [(NH₄)₂SO₄] with full rate of P as triple super phosphate [Ca(H₂PO₄)₂∙H₂O] were applied by banding along the row and covered with soil and the other half of the N rates were applied at 6 WAP. Weeds were controlled at 2 and 6 WAP to ensure a clean field within the first 6 WAP as recommended by Seem et al. [43] .

Composite soil samples were taken from depths of 0 - 15 cm and 15 - 30 cm prior to planting at both locations. These samples were air dried, ground, sieved with 2 mm mesh and analyzed at CSIR-SARI’s Soil Chemistry laboratory. Soil total N was determined by Kjeldhal method [44] , available P by Bray I procedure [45] , exchangeable K and magnesium by ammonium acetate extraction determined by Atomic Absorption Spectrophotometry (AAS) [46] , soil pH was determined in 0.01 M CaCl₂ solution in 1:2.5 soil:solution ratio and soil organic carbon determined by wet combustion method [47] . The soil analysis result and the location weather data during the growing period are presented in Table 1 and Table 2 , respectively. The Nyankpala experiment was harvested after 96 days after planting (DAP) while the Bawku study was harvested 85 DAP.

Lengths of vines were measured and numbers of leaves on vines were counted from four randomly tagged plants in each plot for the first four weeks after treatment application. Shoot and SR yield as well as total biomass were taken at harvest. Leaves, stems (vines with petioles) and roots were oven-dried at 80 over 72 h and then weighed to determine individual component dry weights before summing up to obtain total biomass.

The experimental data were subjected to analysis of variance using the General Linear Model procedure of the Statistical Analysis System [48] to determine main factor effects and treatment interactions. Means were separated by Fisher’s protected LSD test at the 0.05 level of probability. Best-fit equations were determined using coefficient of variation and root mean square error. Graphical analyses were carried out using SigmaPlot 11.0 [49] .

*Analysis made by soil chemistry laboratory, CSIR-SARI, Nyankpala, Ghana.

Partial budget analysis was used to assess the net benefit due to N or P based fertilizer applications at the two locations. The economic viability of the N and P treatments was assessed based on the investments made with comparison to the untreated checks/control plots. Prices for the analysis were based on the market rate of the N and P based fertilizers. Also, value of production was based on the output prices of sweetpotatoes at the market prices. The assumption underlying this analysis was that, all other costs were constant and the costs that vary were used to calculate the input cost. Hence, value of increased yields due to N and P fertilizers was calculated using the following:

$V_{yield}=p_{mkt}\times \left(q_{t1}-q_{t0}\right)$

where $p_{market}$ is the market price of sweetpotato (GHS) and $q_{t1}$ is the output of treated plot (kg∙ha⁻¹) and $q_{t0}$ is the output of untreated check/control plot (kg∙ha⁻¹).

The total variable cost of N or P based fertilizer application was calculated as:

$TV{C}_{t1}=\left(P_{t1}\times q_t{}_n\right)+La{b}_{t1}$

where $TV{C}_{t1}$ is the total variable cost (GHS), $P_{t1}$ is the market price of N or P fertilizers used, $q_t{}_n$ is the quantity of N or P fertilizers per hectare (kg∙ha⁻¹) and the labour cost for applications (GHS ha⁻¹).

The net benefit was calculated using the following:

$\text{Net benefit due to fertilizer application}=V_{yield}-TV{C}_{t1}$

where $V_{yield}$the value of increased yield due to N or P based fertilizers and $TV{C}_{t1}$ is total variable cost of fertilizer and its application.

The returns to fertilizer application were then calculated using the following:

$\text{Returns to N or P fertilizer}=\frac{V_{yield}\left(GHS/ha\right)}{TV{C}_{t1}\left(GHS/ha\right)}$

There was no significant interaction between N and P on vine growth (p = 0.7243) and leaf addition (p = 0.0644) within the first four weeks after treatment

*Significant at the 0.05 probability level, **Significant at the 0.01 probability level. ***Significant at the 0.001 probability level, ns, not significant at the 0.05 probability level.

application at Nyankpala and Bawku ( Table 3 ). But, while the main effect of P was not significant on vine growth (p = 0.0681) and leaf addition (p = 0.1105), the main effect of N was however, significant on vine growth (p < 0.0001) and leaf addition (p < 0.0001) ( Figures 1(A) - 1(D) ). The trends of the responses of sweetpotato vine length and number of leaves within the first four weeks after treatment application to increasing rates of N are linear at both locations ( Figures 1(A) - 1(D) ). No significant difference was recorded with number of leaves∙plant⁻¹ at Nyankpala, but significant differences existed at Bawku. All N treated plots were significantly different from the untreated checks over the first four weeks after treatment application.

At Bawku, the application of N at 30, 60, 90 and 120 kg∙ha⁻¹ resulted in a significantly higher vine growth over the first four week period after treatment application, when compared to the untreated check ( Figure 1(A) ). Vine growth was less when no N was applied; it grew at 11.1 cm∙plant⁻¹ kg N∙ha⁻¹, but when 30, 60, 90 and 120 kg N∙ha⁻¹ were applied; it grew at 13.9, 15.4, 17.32 and 15.4 cm∙plant⁻¹ kg N∙ha⁻¹, respectively ( Figure 1(A) ). The application of 90 kg N∙ha⁻¹ produced the highest rate of vine growth in this study at Bawku. At Nyankpala, vines grew at the rate of 6.1, 6.4, 47, 39 and 52 cm∙plant⁻¹ when N was applied at 0, 30, 60, 90 and 120 kg∙ha⁻¹, respectively ( Figure 1(C) ). The highest rate of vine growth in Nyankpala was obtained when 120 kg N was applied. Like vine length, leaf addition plant⁻¹ displayed a linear response for all levels of N within the first four weeks after treatment application at both Bawku and Nyankpala. At Bawku, number of leaves increased at a rate of 4, 5, 6, 7 and 5 leaves plant⁻¹ kg N∙ha⁻¹. Like vine growth in Bawku, the applications of 30, 60, 90 and 120 kg N∙ha⁻¹ produced significantly higher number of leaves within the first four weeks after treatment application in comparison to the untreated check ( Figure 1(B) ). At Nyankpala and within four weeks after treatment application, number of leaves increased at a rate of 6, 7, 8, 7 and 7 leaves plant⁻¹ week⁻¹ at 0, 30, 60, 90 and 120 kg N∙ha⁻¹ applied, respectively ( Figure 1(D) ). At this location, the highest rate of leaf development occurred at 60 kg N∙ha⁻¹.

Like vine growth and number of leaves per plant, there was no interaction between N and P for shoot yield at both locations ( Table 3 ). However, the main effect of N was significant for shoot yield (p < 0.0001). Similar to vine growth and leaf development plant⁻¹ during the first month after treatment application, shoot yield increased linearly in both locations when N increased from 30 to 120 kg∙ha⁻¹ at 20 and 100 kg N∙ha⁻¹ kg⁻¹ N applied in Bawku and Nyankpala, respectively ( Figure 2(A) ). Shoot yield increased by 31, 63, 94 and 125% in Bawku and 49, 98, 148 and 197% in Nyankpala, when N was applied at 30, 60, 90 and 120 kg∙ha⁻¹, related to the untreated check. Our results are similar to earlier studies where N application was observed to promote shoot growth [12] [51] [52] and excess N application beyond optimal levels tends to promote shoot growth at the expense of storage root formation and development. The optimum N required to maximize shoot yield in both locations were not reached in this study.

There was no N by P interaction (p = 0.7488) for SR yield at both locations. However, significant N (p < 0.0001) and P (p = 0.0001) main effects were observed for SR yield ( Table 1 ). When N rate increased from 20 to 120 kg∙ha⁻¹, there was a quadratic increase in SR yield at both locations ( Figure 2(B) ). In comparison with the untreated check, when N was applied at 30, 60, 90 and 120 kg∙ha⁻¹, SR yield increased by 30%, 46%, 48%, and 37% in Bawku and by 13%, 17%, 14% and 3% in Nyankpala. Judicious N fertilization results in high SR yield while excessive fertilization leads to a reduction in yield. Moderate N application promotes the formation of anomalous cambium resulting in initiation of SRs and suppression of root lignification subsequently causing maximization of SR number per plant and development [10] [15] [53] , and excessive N supply inhibits root thickening or SR formation by reducing the formation of regular vascular cambium, anomalous cambium and promoting lignification of adventitious roots thereby causing a decrease in SR yield [15] [20] [54] . It has been reported from similar studies that, sweetpotato SR yield increased with increasing rates of N up to a point after which it starts to decline [47] [51] [55] - [60] .

In this study, the optimum N required to maximized SR yield are 80 and 62.5 kg∙ha⁻¹ for Bawku and Nyankpala, respectively, in a split application at 2 and 6 weeks after transplanting. This is similar to N recommendation in other jurisdictions. Recommended N for sweetpotato production in Virginia for instance is 28 kg∙ha⁻¹ at transplanting and 28 to 56 kg∙ha⁻¹ at 4 to 5 weeks after transplanting [61] [62] , though, this was updated in a later study to about 35 kg∙ha⁻¹ 2 to 3 weeks after transplanting for ‘Beauregard’ sweetpotato [63] . It must however, be noted that sweetpotato response to N application is cultivar dependent [23] [24] .

P and location significant interaction (p < 0.0001) occurred for SR yield. The trend of the response of sweetpotato SR yield to increasing rates of P at both locations are quadratic with coefficient of determination values of 0.82 and 0.99 for Nyankpala and Bawku, respectively ( Figure 3 ). When compared to the untreated check, SR yield increased by 4%, 5%, 2% and −4% in Nyankpala and by 54%, 81%, 82%, 56% in Bawku, when 40, 80, 120 and 160 kg P were applied. In related studies, P has been found to increase sweetpotato SR yield [64] [65] . Optimum P required to produce the highest SR yield in this study are 67.5 and 101.25 t∙ha⁻¹ for Nyankpala and Bawku, respectively. Our finding is similar to the report by Dumbuya et al. [66] that found 60 kg∙ha⁻¹ as the optimum P rate to maximize growth and SR yield of sweetpotato in the semi-deciduous forest agroecological zone of Ghana.

Like N effects on shoot yield, the mean storage root yield was significantly greater at Nyankpala than at Bawku with or without N or P application ( Figure 2(A) and Figure 3 ). Differences in soil, climatic characteristics and field management history could affect N uptake and utilization efficiencies in these two locations. The Nyankpala site has a sandy clay loam soil which is relatively fertile than that of Bawku (sandy loam soil) as well as better distribution and greater amount of rainfall during the crop growing period ( Table 1 and Table 2 ). Bawku is noted for high rainfall variability and frequent droughts [67] as well as poor soil fertility [68] [69] .

The results of a partial budget for Nitrogen based fertilizer, as shown in Table 4 below, gave a positive value of increased yield for all treatments (30, 60, 90 and 120 kg∙ha⁻¹) compared to the untreated check/control. This translates to positive net returns on investing in Nitrogen fertilizer application on sweetpotatoes at both locations. The net returns to N fertilizer is more than one (1) for all the N-rates at both locations. Among the N-rates, 30 kg∙ha⁻¹ N gave the highest net returns to the N-application at both locations. The results show diminishing net returns as the N-rate increases with the increasing cost per hectare.

The results of the partial budget analysis on P-fertilizer rates effects is shown in Table 5 below. The results gave positive net returns to all the P-rates at both locations except that of 120 kg∙ha⁻¹ of P at Nyankpala. The results of the net returns at Nyankpala defied economic logic to some extent. This is because, the expected diminishing returns observed in the N-rates above is not shown but rather a decreasing returns as the P-rate increases. However, at Nyankpala, the net returns to P-fertilizer, is higher for rates 40 kg∙ha⁻¹, 80 kg∙ha⁻¹ and 120 kg∙ha⁻¹ but was less than one for 160 kg∙ha⁻¹.

At Bawku, all the net returns on the different rates of P were positive. The implication is that, increasing P-fertilizers increases the value of sweetpotato due to increased yield over the untreated check/control. The net returns in Bawku

followed the decreasing returns to P-fertilizers as increasing rates increases cost but the net returns reduces as the rates continue to increase. The net returns to different rates of P-fertilizers is more than unity and very high. The implication is that, at each of the rates of P-fertilizer application, the production of sweetpotato is profitable but the profitability reduces as you increase the rate from 40 - 80 kg∙ha⁻¹ etc.