Delineating investment opportunities for stakeholders in sorghum seed systems: a logit model perspective

Background: Seed systems are considered as a vehicle through which the sustainable agricultural intensification can be achieved. However, most sub-Saharan African countries have been ineffective to provide sufficient incentives for stakeholders to consistently invest in the seed systems specifically for crops like sorghum. This study was therefore conducted to uncover investment opportunities for stakeholders in the sorghum seed systems to attain an impactoriented seed production and delivery systems. Results: The study applied descriptive statistics, Logit regression model, and Gross margin to analyze possible areas for investments. Descriptive statistics analyzed the percentage of farmers using sorghum improved varieties and sources used to obtained improved variety seeds. Logit regression model was applied to analyze factors correlating with planting of improved seeds. Gross margin was applied to show profitability of growing improved sorghum seeds and grain. Findings revealed that 39.2% of the sampled farmers were growing improved sorghum variety seeds. Farmers obtained improved variety seeds from both informal (57.8%) and formal (42.2%) sources. Logit estimates indicate that variety preference, unavailability of seeds, resistance to diseases, and drought had significant correlation with planting of improved variety seeds. Seed companies and quality declared seed (QDS) producers earned high margin of 53,08,900 Tanzanian Shillings per hectare (TZS/ha, 1 USD = 2315 TZS during the period of data collection) and 33,94,709 TZS/ha, respectively. Farmers using improved variety seed earned higher margin (8,19,805 TZS/ha) than farmers who did not use improved variety seeds (3,17,373 TZS/ha) Conclusions: The identified investment opportunities were increasing number of farmers using improved variety seeds that would drive increased production, distribution, and marketing of quality seed. The large number of farmers still sourcing seed from the informal channel provides avenue to reach out to these farmers through demand creation and wide variety popularization meeting farmer preferences. The huge margin seed producers make provides good incentive to drive private seed companies and individual seed entrepreneurs to make sustainable business out of sorghum seed. The policy implications for reviving sorghum production and productivity are further discussed.

more food available to households [2]. Food security exists when all people, at all times have physical, socio, and economic access to sufficient, safe, and nutritious food that meets their dietary needs and food preferences for an active and healthy life [3]. For decades' food and nutrition security and poverty reduction have been among the top areas of interventions in SSA countries through various public policies and investments for agricultural development. Yet, tackling these issues in the developing countries continues to be a major challenge [4]. In most SSA countries, agricultural productivity challenges are still persistent, and the region has the lowest productivity in the world [5]. As a result, food insecurity and extreme poverty are still rampart, especially in rural areas. In addition, the challenges of rapidly increasing population, natural resource depletion, increased negative impacts of climate change further exacerbate the problems. The aforementioned factors are therefore compelling for an increased sustainable agriculture productivity [6]. Increased agricultural productivity can improve the welfare of households by enhancing their income and food security [7]. In that regard, sustainable agricultural intensification measures to raise yields and production in the currently available arable land without destroying the environment become a requisite. This is also one of the requirements for attaining the Malabo Declaration goal of eradicating hunger, halving poverty in Africa by 2025, as well as achieving the sustainable development goals by 2030, which particularly aims to achieve food security, improve nutrition, and promote sustainable agriculture [8].
Seed systems are considered as a vehicle through which the sustainable agricultural intensification can be achieved. By seed systems, we understand the different ways farmers can access seeds including the different actors involved in the seed value chain [9]. The seed sector plays an important role in combating food insecurity by availing quality seeds to farmers. Seed is the single most important input for agricultural systems [10]. It possesses a unique feature of being both an agricultural input and output at different periods to different users. Seed is a key determinant of agricultural productivity as it determines both the quantity and quality of the outputs [11]. It is a vehicle for delivering a range of advances such as promoting productivity, nutrition, and resilience, all of which benefit smallholder farmers [12]. In every country, the seed systems are composed of different components, broadly categorized into two and known as formal and informal seed systems [13]. The formal seed system is made up of strict quality-controlled seed. It is usually governed by strict policies and regulations. It is market-oriented and managed by public and private sectors [14]. The informal seed system is a farmer-and community-based, local or traditional seed sector. Activities in the informal seed system are mostly decentralized and depend on the farmers' knowledge [12]. It includes continuous use of home-saved seed [15]. It does not conform to any rule prescribed in the seed regulations at national, regional, and international levels [16].
Between the formal and informal seed systems, there is an intermediate system that integrates the formal and informal systems [17]. The intermediate seed system also called semi-formal seed system aims at empowering registered farmer groups to produce seeds from known source and make them accessible to their peer farmers [18]. These farmer groups are registered either at village or ward level by the local authority, programs or projects. Intermediate seed system looks for opportunities and options to improve both formal and informal systems by recognizing and supporting integration through combining methods from both systems [19]. The three principal components of the intermediate system include cultivars developed and used, seed produced, and stored by famers under local conditions and seed exchange mechanism [20]. Research and development organizations are the pioneers of the intermediate systems as a strategy to fast track quality seed supply to smallholder farmers.
Investments to improve the delivery of seed systems have long been an important component of agricultural development strategies. This can yield high returns in terms of seed production security, food and nutritional security, agricultural productivity, as well as poverty reduction [21]. Diverse and often opposing philosophies shapes seed sector development and much depends on what actors see as the entry point [12]. Levels of investment in many national seed systems tend to be low, varieties produced are not being multiplied, and if they are multiplied, then they do not reach most of the small-scale farmers [22]. However, over the years, gaps within the seed systems have led to different types of interventions, supported by various narratives that foresee different pathways into the future, and it has attracted substantial investments. For instance, from 2007 to 2012, the World Bank has funded 87 seed sector projects worth $US 513 million with strong focus on marginal crops such as sorghum [12]. Although these projects vary in shape and scale, the majority strive to make quality seeds and traits more available and accessible to farmers. There is however still a notion that despite the tremendous investments, the outcomes are yet to meet expectations and interest of farmers are left unattended [23].
This justifies the need for further research to delineate investment opportunities for enhanced and sustainable quality seed production and delivery to marginalized farming communities in the dryland areas. Therefore, this study aims at delineating the investment opportunities in seed systems, with a case study on sorghum.

Study context
In Tanzania, agriculture accounts for 25.8% of the GDP and provides 80% of the total employment [24]. Like most SSA countries, Tanzanian seed industry consists of formal, informal, and intermediate seed systems [25]. With the formal system accounting for around 25% of required seeds [26], the informal system remains a highly important seed supply source for farmers who continue expanding it [27]. To meet seed demand, Government and development organizations, through public and private seed companies and farmer organizations [28] have been investing in seed delivery systems to facilitate quality seed access. Quality seed which in this study refers to improved variety seed can briefly be defined as seeds that have been produced using formal plant breeding methods with the aim of increasing productivity and production of crops to farmers. Food security and nutrition of people depends on the amount and stability of their farm outputs and income [29] which can be achieved through a good choice of seeds to grow and a strong seed system that supports delivery of quality seeds to farmers.
Development organizations including CGIAR, ASARECA, and AGRA have undertaken many seed system initiatives through various projects and programs to ensure reliable supply of affordable quality seeds to the farmers [30], so that they can increase agricultural productivity, nutrition and rural well-being [31], as well as food security.
Despite these public and private investments and assistance of development organizations, the seed sector is still underdeveloped with mixed performance in most SSA countries [32]. In the context of Tanzania, only a few crops such as maize and rice have a much-advanced seed production and delivery systems as compared to dryland crops like sorghum [33]. Insufficient policy initiatives, including poor public investments to support sorghum seed systems, undermine the reliable availability of quality sorghum seeds. It is still unclear whether the current sorghum seed system will generate enough motivations for the private sector to deliver quality seeds at affordable prices and at scale.
The study aims to define the investment opportunities for stakeholders in the sorghum seed systems. It focuses on the following four research questions (i) to what extent farmers are growing improved variety seeds? (ii) What are the source farmers use to obtain improved varieties? (iii) What are the main factors positively associated with planting of improved variety seeds by farmers? (iv) Is there profitability of producing certified seed and quality declared seeds (QDS)?
This paper is organized into seven sections. "Background" section provides information on relevant literature related to seed systems, their categorization and functions; also efforts to invest in the existing seed systems are discussed. "Study context" section presents seed systems in Tanzania and initiatives that have been taken to improve it. "Conceptual framework" section discusses different approaches employed to uncover the investment opportunities in the sorghum seed systems. "Data and Methodology" section delivers the methodological approach to achieving the objectives of the study. "Results" section presents the findings and some analyses. "Discussion" section discusses results of the study and place them into the wider context. "Conclusion" section summarizes the paper and presents recommendations arising from this study.

Conceptual framework
Circumventing investment areas in seed systems to enhance seed production and delivery to farmers can be approached from various angles. In this study, we approach the subject from the perspective of existing gaps in the seed production and delivery systems. According to McGuire [34], gaps in seed system permit a holistic analysis of possible areas for investment. This involves analysis of the number of potential users, understanding seed sources farmers use, understanding factors correlated with farmer choices of improved variety, and profitability of producing seed and grain.
On one hand, the low number of farmers using seed of improved varieties might indicate difficulties in new variety seed uptake. On the other hand, the low number of potential users is concerned with the assumption that there is a large market opportunity to conquer. Supplying seed to those farmers who have not been using improved varieties through collaboration with various stakeholders could then be explored. The sources farmers use to obtain seed of improved varieties provide option to identify the most predominant seed source and subsequent steps needed to boost quality seed demand. The different seed sources that farmers use shows the path that the public and private sectors can leverage on to disseminate improved variety seeds that reach more farmers. The channels farmers use to assess improved variety seeds are important especially in determining the degree and nature of investment within the seed systems [35]. In this study, the formal and intermediate seed systems are put together and termed as formal seed systems, while the informal seed system is taken as stand-alone system.
The factors with positive correlation with improved variety seed planting by farmers indicate the areas to work on by various stakeholders. Understanding these factors and how they influence the use of improved variety seeds is important to develop strategies to sustain sorghum variety seed delivery. Farmer's decision to whether and how to use improved variety seeds are conditioned by a number of factors and circumstances [36]. Logit model can be used to analyze underlining factors of farmer's decision to use improved seeds. Several studies (e.g., [29], [37], [38]) have used logit model to analyze different factors influencing farmers' choice to use seed of improved varieties.
The profitability of producing certified and QDS seeds and grain also provides investment incentive for seed producers and farmers. Profit is a main indicator of viability of an enterprise, and ideally, it can be measured using gross margin. This is supported by Mvungi et al. [39] that gross margin is used as a measure of enterprise profitability. Moreover, Fani et al. [40] asserted that gross margin has been used for many years in various literatures to analyze the profitability of farm production practices. Gross margin is the difference between total revenue and total variable cost associated with the enterprise [41]. In that regard, for this study, gross margin can be used to measure profitability of sorghum seed producers and farmers, since it analyzes the performance of an enterprise. Good margin would be an incentive to seed companies to invest in sorghum seed production and farmers to look for quality seed.

Data and methodology
The study was conducted in nine districts of which seven had undergone seed system interventions through project activities to facilitate seed access to communities. The project "harnessing opportunities for productivity enhancement (HOPE)" was implemented in the intervention areas between 2009-2020. The project facilitated seed production and delivery to farmers using public and private partnerships and community seed production scheme. These districts were Mkalama, Singida DC, Iramba, Ikungi, Serengeti, Rombo, and Momba, whereas the districts that had no intervention were Kongwa and Tarime.
Cross-sectional research design was employed, and data were collected across the surveyed districts. To obtain detailed information, household survey was conducted as well as key informant interviews, with the household survey conducted using semi-structured interviews. To gather information from the respondents, face to face interviews were employed per person using a questionnaire. The sample frame was composed of farmers and seed producers. Some of the information collected from the households included type of varieties used by farmers, sources farmers use to obtain improved seeds, socio-economic characteristics, and cost of grain production. Seed producers' information included cost of seed production, price of seed sold/kg, and amount of sorghum seed sold.
Two types of sampling were used namely purposive sampling and simple random sampling. The purposive sampling was used to select nine main sorghum growing districts and the main sorghum growing villages per selected district. The simple random sampling was used to select 212 farmers and five seed producers.
Data were analyzed in Stata version 13 software using descriptive statistics, gross margin, and logit regression model. Descriptive statistics included percentage of growers of improved variety seeds vs. non-growers and sources used by farmers to obtain improved variety seeds. Gross margin was used to evaluate the profitability for seed enterprise and farmers but also one of the ways to identify investment opportunities in sorghum seed systems. Values computed for gross margin of seed production and grain production are individual data obtained from the interviews on a hectare basis.
It was computed by where GM = Gross Margin; Q y = Total output of crop (kg); P y = Unit of price of output (TZS); X i = Quantity of the input used (kg); P x i = Price per unit of the input (TZS); Q y P y = Total revenue associated with the output (TZS); ∑ X i P x i = Summation (overall inputs to give the Total Variable Costs). Thus GM = Gross total revenue − Total variable costs. Here, GM = Gross Margin (TZS/ha); GTR = Gross total revenue (TZS/ha); TVC = Total variable costs (TZS/ha). Logit regression model was used to identify factors positively correlated with planting of improved variety seeds by sorghum farmers. The model was fit to estimate the relationship to planting of improved variety seeds, since it analyzes the association between a categorical dependent variable and a set of independent variables [42]. In this study, the dependent variable is the use or not of seed of improved sorghum varieties by farmers, taking the values of 1 or 0. The value 1 indicates farmers who planted improved sorghum seeds and value 0 indicates farmers who did not. The independent variables linked to the binary dependent variables were variety preference, group membership, availability of improved variety seeds, seed price, resistance to drought, resistance to disease, farm size, and education level.
Past studies have suggested that farmer's decision to plant improved variety seeds is associated with different factors such as socio-economic, institutional, production characteristics, and preference. Socio-economic factors like education, whereby education level is associated with the ability to acquire and use improved seeds [43]. Hence, farmers who are educated may use improved seeds than farmers with no education. Farm size is a key indicator of the capacity to earn agriculture income [44], and often, it represents wealth status of the family. Therefore, farmers with large farm size may have more proceeds to purchase improved seeds than farmers with small farm size. Group membership of a farmer may increase access to information on improved seeds [45]. Thus, membership of a farmer's group may increase the likelihood of planting improved seeds. Variety preference has been incorporated in the model, because it captures the effect of farmer's variety preference which may affect farmers' choice of variety for planting. Availability of seed enhances the farmers' decision to plant improved seeds [44]. Availability of improved seeds ensures food security and prosperity of the farmer. Thus, when improved seeds are available to the farmers at the right time, then it may improve farmers' access to seed and ultimately influence the farmers to plant improved seeds. Production characteristics like resistance to drought and resistance to disease are important for explaining choice of planting improved seeds [46,47]. This is because varieties that can resist drought and disease have more potential of producing more yield than variety without these characteristics, therefore increasing the likelihood of farmers to plant improved seeds. Seed price is a valuable factor in shaping farmer's choice to plant improved seeds [48]. Although improved seeds might give high yield, but if it is not affordable, then it can cause farmers to be reluctant to plant it. The probability (P i ) that a farmer plants improved sorghum seeds is as follows: where β 0 is constant and Y i is equal to one (1) when a choice is made to plant improved seed and zero (0) otherwise; this means: the equation represents a binary choice involving the estimation of the probability of planning improved sorghum seeds (Y) as a function of independent variables (X).
The logit model uses a logistic cumulative distributive function to estimate, P given by where k represents number of independent variables to be analyzed.
The model is specified as indicated by Eq. (6): where Y = growing of improved variety seeds; Ln ( P 1−P ) = the ratio of probability of planting improved variety seeds (p) to not planting improved variety seeds (1 − p); β = Slope of coefficient; X k = vector of the explanatory variables (variety preference, group membership, seed availability, seed price, resistance to diseases, resistance to drought, farm size, and education level); ε = error term.
The model was expanded to include the variables in Table 1.

Farmers growing improved variety seeds among intervention districts and non-intervention districts
Out of the 212 farmers sampled, 39.2% were growing improved variety seeds. Table 2 shows that Singida DC in the intervention districts had the highest rate of farmers growing improved variety seeds of about 23%, followed by Momba with 20.7%. The results also show that within the intervention areas, there were districts that have below 5% of farmers producing improved varieties. Kongwa, a non-intervention district hosting the largest grain market in Tanzania, showed 20.4% of growers of improved variety seeds. The lowest percentage (1.3%) was recorded in Tarime which is a non-intervention district.

Sources used by farmers to obtain seed of improved varieties
Farmers using improved varieties obtained their seeds from both formal and informal sources. However, it was observed that 57.8% of the farmers used informal sources to acquire improved variety seeds (own-saved seeds, neighbor), while 42.2% of them obtained seeds from formal sources (NGOs, QDS producers, Government, agro-dealers). Specifically, the survey identified six different sources of seed supply used by farmers to access the improved variety seeds (Table 3). It was noted that 48.2% of the farmers obtained seeds from their own stock, indicating that this source was the most important of the six sources. The Government as well as NGOs were also important sources of seed supply to the farmers with 25.3% and 13.3%, respectively. The use of other sources than the ones mentioned above was modest with 9.6% farmers accessing seeds from neighbors and 2.4% farmers accessing seed from QDS producers. Seed access through agro-dealers was almost non-existent, representing only 1.2% of farmer's seed source.

Factors correlated with planting of improved variety seed by farmers
The results of the Chi-square test were statistically significant at 1% level, suggesting that the explanatory variables jointly account for planting of improved sorghum seeds. Variety preference, seed availability, diseases resistance, and drought resistance significantly influenced planting of improved sorghum seed. Variety preference had a positive influence on planting of improved variety seeds at 10% significance level (p < 0.1). It is estimated that farmer preference for improved variety leads to the increase of probability of growing the seed by 3.6% (Table 4). Seed availability was also positive and had a significant effect on planting of improved variety seeds (p < 0.01). This indicates that an increase in availability of improved variety seed enhances the probability of farmers growing improved seeds by 10.6% holding other factors constant.
The estimated coefficients of resistance to diseases were positive and significant at 1% significance level (p < 0.01). Implying that ability of the improved variety seed to tolerate diseases increases the probability to grow improved variety seeds by 6.1%. Tolerance to drought was positively correlated with the planting of improved variety seeds and significant at 1% significance level (p < 0.01). The estimates show that the farmer planting of improved variety seeds increases by 7.2% if the improved variety is drought-tolerant (Table 4).

Gross margin analysis of sorghum seed production by seed companies and QDS producers
It was important to show the margins that different seed producers obtained from sorghum seed production per ha to understand the viability of the seed business. Seed producers interviewed included seed companies and farmers who produced quality declared seed. The quality declared seed was produced by either individual farmer or a farmer group. Results from the interview show that (Table 5) the expenses on materials and operations incurred by seed producers in the production of sorghum seed. The total variable costs of producing sorghum seed was 59,41,100 TZS for seed companies and 4,85,291 TZS for QDS producers. Among the components of the total variable costs, the expenditure on operational costs accounted for the largest cost item and amounted about 60% for both seed companies and QDS producers. For the seed companies, certification costs had the major operational costs accounting for about 15%, while for the QDS producers, weeding and land preparation were the major operational activities that contributed to the cost of sorghum seed production accounting for around 21% and 13%, respectively ( Table 5). Cost of chemicals was highest for seed companies, accounting for about 34%, while for QDS producers, fertilizer and rented land were the major inputs on which material expenditure was substantial accounting for about 14% each. Cost of seeds, bags and fertilizer application accounted for smaller share of the variable cost for seed  companies (about 0.5% each), while for QDS producers, the lowest cost was for chemical application accounting for about 0.2%.
The revenue per hectare of the seed companies and QDS farmers is presented in Table 6. Results from the interviews show that sorghum seed production is highly variable. Both categories of seed producers obtained a positive return. Seed companies producing certified seeds make larger revenue from sorghum seed production than QDS producers.

Gross margin for growers and non-growers of seeds of improved varieties
Results from the interview show that the total variable cost for growers of improved variety seeds was 5,30,980 TZS/ha, while for the non-growers, it was 4,73,886 TZS/ ha (Table 7). Among the components of the total variable costs, land rental, weeding labor, and land preparation were high for farmers. For growers of improved variety seeds land rental, weeding labor and land preparation were about 37%, 17%, and 14%, respectively, whereas non-growers of improved variety were about 34%, 13%, and 15%, respectively. However, planting material added more cost for non-growers of improved variety accounting for about 11.5%, since broadcasting method involves more amount to plant as compared to growers of improved variety seeds. The cost of insecticide accounted for a small share especially for non-growers of improved variety (0.4%) of the total variable cost against about 2% for growers of improved variety seeds. Table 8 shows that the average gross margin earned by farmer for sorghum production was 5,18,346 TZS/ ha. For farmers growing improved varieties, the average gross margin was significantly higher (8,19,805 TZS) than their counterpart producing old varieties (3,17,373 TZS) (p < 1%).
When data are disaggregated by intervention and nonintervention areas (Table 9), the average gross margin was 5,34,517 TZS/ha for farmers in district that underwent project intervention, while for farmers in nonintervention districts, it was 4,51,738 TZS/ha. This shows   that farmers in the intervention districts were obtaining higher profit than those in non-intervention districts.

Discussion
Effective seed systems have the potential to increase productivity and production by delivering quality seeds of new varieties to farmers. The development of an impactoriented seed system is a strategic choice which can be done through appropriate handling of investments areas in the seed sector.

Filling the gaps of improved variety seed use by farmers
Quality seed is vital to raising agricultural production and it is one of the basic inputs needed for breakthrough in crop production. Unfortunately, the results of this study demonstrate that most of the farmers were not growing improved variety seeds. Only about 39% of farmers planted improved variety seed among sampled farmers. This conquers with Aloyce et al. [49] who observed that improved variety seed planting by most sorghum farmers is low. The low proportion of farmer growing improved varieties indicates that most farmers were not experiencing maximum benefits from sorghum production. The high number of non-growers of improved variety seed constitutes an investment opportunity for seed companies, QDS producers, and farmer organizations involved in seed business. It is believed that an effective way to increase productivity and enhance peoples' livelihood is broad-based use of new farming technologies such as improved quality seeds. Unfortunately, farmer demand for quality seed remains inconsistent in SSA. Seed companies in Southern Africa failed to invest in developing rural retail networks for open pollinated varieties (OPV) seeds because of the uncertainty in seed demand [50]. Similarly, McGuire et al. [12] added that over the years, seed producers have been producing and supplying seeds, but they have been hindered by lack of demand. Nevertheless, if there is still score number of farmers that are still using landraces, it pertains that there is a huge market gap for the improved variety seeds that needs to be filled. There have been efforts by development organizations to fund the research, production, and supply of improved variety seed and awareness creation through projects, but a few areas have been covered [12]. For instance, organizations such as the International Crops Research Institute for the Semi-Arid Tropics (ICRISAT) have been developing and evaluating sorghum varieties targeting the dry lands in collaboration with Tanzania Ministry of Agriculture and other partner organizations [49]. The survey showed that in the intervention areas, there were higher proportions of farmers growing improved variety seeds against the non-intervention districts. This is a clear indication of the milestones that can be achieved through awareness creation activities to increase use of improved varieties. Only about 2% of total demands of certified seeds of sorghum were made available to the farmers in Tanzania in 2019 [51]. This emphasize that more investment is needed in production, marketing, promotion, and distribution of improved variety seeds to reach the majority of farmers who are not growing improved varieties. ESAFF [14] acknowledges that the lack of awareness negatively impacts the wide use of improved variety seeds. There is a need to accelerate the use of improved variety seeds to enhance the seed systems through synergized interventions from public and private sectors [14]. The private sector also bears responsibilities to increase farmer's awareness to grow the seed market.

Sources used by farmers to acquire improved variety and avenue for growing seed market
The study shows that farmers used both the informal and formal seed systems to obtain improved variety seeds for planting, with 57.8% of the farmers obtaining planting material from the informal sources during planting season. Similar findings were reported by Louwaars et al. [19] that most of the improved variety seeds were accessed through the informal seed system. Kusena et al. [52] add that informal seed system supports more than 80% of farmers in sub-Saharan Africa and feeding more than 70% of its population. This system is dominated mostly by own-saved seeds and seeds from neighbors. This corroborates the findings by Alemu et al. [53] that most farmers still depend on the use of saved seed or locally purchased seed. Farmers asserted using their own-saved seeds, because it is usually available during planting season compared to other sources of seed [54]. The dominance of the informal seed system shows that it will continue to play a major role in supplying sorghum seeds to farmers for the coming years. NGOs and government officers were facilitating more in seed delivery than agro-dealers and QDS producers. According to ESAFF [14], the coverage from agro-dealers is minimal in rural areas resulting in limited use of agri-inputs. Agro-dealers have a major role in seed supply systems. For proximity seed supply, agro-dealers network needs to be expanded through close collaboration with public and private seed companies. In the same vain, win-win linkages between QDS producers and seed companies will introduce more farmers to improved varieties and significantly increase the seed market. Croft et al. [55] noted that formal systems contribute very little amount of seeds accessed by farmers, even though they are responsible for developing new improved varieties. The gap in formal seed system opens up an opportunity for investors both in public and private sectors to develop strategic business partnerships to make seed available and accessible to smallholder farmers. This would meet the criteria of strong seed systems as reported by Etten et al. [21] who posited that a strong seed system relies on the interconnected performance of three key functions namely seed production and distribution, innovation, and regulations. The observation showing farmers purchasing a modest part of their seed from various sources implies that farmers would be willing to buy seeds. Similar results were observed in the study conducted on seed systems smallholder farmers use [12]. Farmers are usually reluctant to invest in quality seeds [56]. Thus, the presence of farmers purchasing improved variety seeds shows that farmers are already making such investments and this presents an opportunity to define strategies to improve seed supply to farmers. Understanding the commercial behavior of farmers concerning seed in terms of purchasing practices or use of own-saved seeds helps to gauge the seed market and target promotion to create demand and ensure supply [53]. The integration of both formal and informal seed systems is a major avenue to enhance effectiveness and expansion of seed market. This integration strengthens breeder-led and farmer-led linkages [57]. Through this, more farmers who are experienced with proper technical support and capacity building can invest in producing and diffusing enough quantity and quality improved variety seeds to other peer farmers.

Opening seed market though factors correlated with farmers' planting of improved variety
It is vital to know the underlying factors that correlate positively with planting of improved variety seeds by farmers. Finding solutions to such factors may in turn improve the use of seeds and ultimately improve sorghum seed system.
The results indicated that variety preference, availability of seeds, resistance to diseases, and drought as the most significant factors motivating farmers to grow improved variety. Similar findings were reported by Timu et al. [58] and Tambo et al. [59]. These factors are perceived to improve crop yield. Akwango et al. [60] asserted that poor harvest threatens food security and livelihoods of household who depends on agriculture for food and income. Moreover, the above-mentioned significant factors are also perceived to develop resource use efficiency, and show consumer preference and acceptability in grain market [58,61,62]. The aforementioned factors indicate opportunity for investment to all stakeholders such as research institutes, seed companies, NGOs, and international institutions to develop the improved variety that meet the consumer expectations. Furthermore, the findings show that farmers' preference for variety traits affects their choice, implying that if the variety that does not have the desired traits is produced and supplied, then very few farmers will be attracted to purchase. Improved assessment of farmers' desire and preference contributes to improved seed system interventions [63]. In the light of this, Fadillah et al. [48] opined that the knowledge of ecological, genetic diversity, and traditional varieties in the crops provides much needed resource to build priority breeding programs for varieties preferred by farmers and markets. This implies that through understanding different factors hindering the use of improved variety seed, there is an opportunity for public and private sectors to invest in advanced research, breeding, and development of varieties that meet the market demand. Once seed enters the market, it should be considered part of the farmers' asset to nurture and grow, with support from public and private sector institutions as well as expertise to maintain and improve those varieties [64]. It is crucial that more scientific technologies are developed such as mutation genes of sorghum varieties for improved resistance to biotic and abiotic stresses as well as informing the production environment of farmers [65].

Profitability of producing certified seed, QDS, and grain of improved variety as investment incentive
The results showed a positive gross margin for both seed companies and QDS producers. The difference in the margins obtained was mostly due to the price difference between the seed company and QDS producers with the QDS farmers gaining lower margin than the seed companies. Similar findings were reported by Katungi et al. [66] on common bean, Akpo et al. [67] on groundnut. Moreover, QDS producers did not bear certification fee and are able to sell their seeds at a lower price. Pal et al. [5] reported that certification costs were additional cost that increased seed production cost. Even though QDS is availed at affordable prices, it only sells within their local areas (ward) [68]. As a result, farmers outside these areas could not access seed; thus, they either access seed through researchers or extension officers. The potential of QDS lies in the ability to produce and supply quality seeds addressing the issue of affordability and proximity availability. This is supported by Coomes et al. [31] that farmer's seed and networks can be advantageous in terms of crop choice, accessibility, and cost. The potential to invest in seed systems lies in the positive gross margin obtained by seed companies and QDS producers. Private companies are profit motivated and usually deal in only small volumes for the less profitable crops [50]. Therefore, only profitable crops and varieties will drive investments in the seed systems. Thus, this becomes a motivation for private seed companies and QDS producers to sustainably invest in sorghum seed business.
The gross margin for grain producers showed that using improved variety significantly incurs higher gross margin compared to old varieties. This result is in conformity with the findings of Maroud et al. [69] that farmers who used improved varieties showed higher marginal returns as opposed to those that used local varieties. Seed system also involves farmers [23] and this implies that they are major stakeholders in the seed system to be critically considered. A positive gross margin for farmers growing improved variety becomes an incentive to their peer invest in improved varieties that meet market demand. An increase in seed demand will also encourage seed companies and other player to expand their activities to areas that have not been reached. According to Rohrbach et al. [22], seed enterprise will only thrive in an appropriate environment and the primary characteristic of such environment is the incentive for farmers to purchase seeds. Finally, project interventions showed positive effects on the realized gross margin by farmers. In the districts that underwent project interventions, the farmers made higher margin, indicating that investments through projects by public sector as well as private sector are critical for boosting the use of improved variety seed and enhancing the seed system performance.

Conclusion
In this study, we used survey data from farmers and seed producers to examine the investment opportunities for various stakeholders in the seed systems. The findings show that only 39.2% of the surveyed farmers used improved variety seeds, indicating that there is an investment opportunity in producing and supplying quality seeds for farmers who are currently growing old varieties. Researchers, extension agents, seed companies, agro-dealers, as well as NGOs will have a major role to play through awareness creation to enhance farmer knowledge of new varieties and increase demand. Variety demonstrations and field days are good mechanisms to upscale the new and improved varieties. The findings showing that farmers obtained improved variety seeds from both informal and formal seed systems indicate the need to support the farmer to shift from the informal sector through demand creation. There is an opportunity to invest in formal system, whereby seed companies and QDS farmers, agro-dealers can deliver more seeds and expand their business in areas that farmers have not yet accessed seeds. The proper use of informal seed systems through linkage with formal seeds is very important to promote integrated seed supply systems.
Factors such as variety preference, availability of improved variety seeds, resistance to diseases, and drought had significantly correlated with planting of improved variety seeds by farmers. This shows that there is a need to invest in refining varieties that have desirable traits of farmer and consumers in the grain market. This calls for joint and coordinated collaboration between breeders, private sector, and the end-pull. Certified seed and QDS can be produced and availed to farmers' profitability. And this represents an incentive for investment by seed companies, individual seed entrepreneurs, as well as farmer groups or organizations. The higher earning of farmers using improved variety seeds is also an incentive for farmers to invest in the improved variety seeds. From the findings, we can argue that the investment potentials in sorghum seed system are still high and yet to be taped in by various stakeholders so has to develop the seed sector.

Limitations to this study
This study was conducted in nine districts of sorghum production in Tanzania. Even if few districts were sampled, the coverage of the main sorghum producing areas in the country allowed to capture the relevant information to uncover investment opportunities in sorghum seed systems. The findings are sound for the readily use by a wider audience and stakeholders interested in investing in sorghum seed systems.