Survey

The analysis of the financing networks of the major players of the national agricultural research system considered the application of 164 surveys to research institutions established in Mexico. The survey was conducted nationwide between September and October 2014. The mechanics to obtain the surveys was to use the infrastructure from INIFAP, INIFAP has national coverage so that in each of the states of the country there is infrastructure and human capital. Thus, the steps followed to implement the survey were:

The main question that shaped and network structure of funding of actors was: ¿Did I mention the name of the sources of research funding that was in 2013?

Social network indicators

Data to identify knowledge networks of institutions were captured in Excel and then exported to Microsoft Notepad version 6.1 using the DL protocol and nodelist 1 format as this format allows to capture as a list of nodes to respondent and their respective relational links (^{Rendon et al., 2007}). The file generated in notebook was exported directly to NetDraw 2.097 software. For the calculation of the indicator social network the Ucinet 6.288 software was used with ^{Borgatti et al., (2002)} procedures. The graphics and coverage indicators were made using the Key Player 2 software (^{Borgatti and Dreyfus, 2003}), which focuses on the identification and selection of relevant actors, characterized by receiving or sending information to most network actors. The indicators used for the analysis of social networks were: density, network size, degree centrality of entry and degree centrality of output, in addition to identify the level of coverage that a node may have within the network was used the diffuser node indicator. The mathematical formulation to obtain this indicator is as follows:

Network density: Number of relationships between those possible. Where L = number of relationships. n (n-1) = number of possible relationships (^{Borgatti et al., 2002}).

Size: Where Τn is the size of the individual network from node n, and An are the actors directly related with actor n. A larger network suggests that actors or nodes are mostly connected (^{Borgatti et al., 2002}).

For the analysis of this study, the degree centrality indicator was used: the degree is the number of points to which the node is adjacent, that is, with which has direct links. From this perspective, centrality would be defined by the potential capability of communication that nodes have. Degree centrality is calculated by recording the amount of links that address to an actor or leaving from the same actor. Calculated as follows:

Degree centrality is defined as the number of links from actor i. Worth noting that this may be a centrality entry (InDegree), referred to the links that reach the actor or the centrality of output (OutDegree), counting only the links that leave the actor. If an actor receives many links can be interpreted that has a greater "prestige" as the others want to relate with him. If an actor has a high degree centrality of output, it can be interpreted that this actor tends to have a greater "influence" as it is capable of bargaining with others or make other to agree with his interests (^{Freeman, 2000}; ^{Williner et al., 2012}).

The identification and selection of stakeholders was performed with keyplayer 2 software (^{Borgatti and Dreyfus, 2003}), same that focuses on the identification of a group of nodes characterized by the ability to receive all kinds of information from most nodes of the network. The diffuse are the group of nodes in the actual position of sending information to most nodes. Other key player are the arrangers of the -disrupt- network; i.e. those nodes that in case of disappearing fragment the network (^{Borgatti, 2003}). Diffuser actor: is calculated using the following algorithm. The letter R as abbreviation of reach used in the literature of networks. Considering that distance dij from the last node to any other node is 1, and N is total nodes (^{Rendon et al., 2007}).

Financing network of higher education institutions (IES)

The approaches on innovation systems emphasize that "organizations and institutions do not innovate in isolation but in the context of a system. Thus, the central idea is that the essence of a SNI that works well is the existence of a dense network of systemic interactions among agents"(^{Casas et al., 2014}). In this sense, the analysis performed to the financing network of actors from the agricultural research system in Mexico shows a low density of interactions between the different agents that make up this system. The network density was 0.38% which means that there are few sources of funding at national level and therefore low SNIA articulation; i.e. few actors keep united the system.

Centrality entry and output quantifies the power exercised by an actor or actors within the network either as referrals or information seekers, the value of centrality entry 18.09% suggests that there is an actor or referred actors whose coverage relation is 18.09%, this centrality entry indicates that there are referred actors in the network with a certain concentration of power. Moreover, centrality output is low (2.15%) which refers to information seekers, this value suggests low prevalence of some actors and under the leadership of institutions, i.e., a large part or all institutions seek various funding sources separately and in a very low proportion together (Table 1).

The key actors identified (collector and diffusor) are important from the point of view of coverage, the first with a value of 20.65% indicates that three sources of funding CONACYT, Own resources, SAGARPA, are actors who have referred the institutions as main funders, these three have the ability to concentrate about 20% of the relationships between network nodes (Figure 1). The diffusers value of 5.07% suggests that through the links generated through project financing, the ECOSUR Chiapas and Biological Sciences from IPN actors are best suited to play a role as disseminators of information; however, their coverage is low, this is explained because many of the institutions go to funding sources individually and a very low percentage does it together in addition to few existing funding sources in Mexico.

Figure 1. Financing Network from IES in Mexico. 

Network structure is defined as those actors or institutions that when disappear can fragment the network relations shown, as the network is very weak if any of the funding sources CONACYT, own resources and SAGARPA, stop financing research projects the network would fragment almost completely. The funding sources that act as arrangers correspond to the same actors identified as collectors, if these actors disappear from the network there would be no funding sources and also the network would fragment at 99.8%; i.e., there would not be links or network of actors who had relation for the development of research and innovation in the agricultural sector of our country.

This network without being a network with a high concentration of power is too weak because only three actors or institutions (funding) are supporting the lattice structure from SNIA. Recent studies on SNIA indicate that efforts to articulate and detonate innovation in the agricultural sector have not been consistent with the objectives and goals set, it also presents a variety of actors that includes both those linked to the productive chain as government actors, and policy frameworks (^{Solleiro et al., 2015}).

Financing Network from public research centers (CPI)

The financing network from public research centers analyzed shows a more extensive network compared to the network of higher education institutions in research, has more actors involved because each of the centers seek funding partners locally and at regional level. Network indicators indicate a density of 1.24% which is very low; however, considering that each research center has regional coverage and funders, it is not possible that all centers relate to all funders. Centrality entry and output is very low, this suggests a regional concentration of some actors which is not perceived with the national analysis (Table 2).

Research centers that for the amount of projects funded are presented as possible diffusers and in this case could have a coverage of 45.6% between research network actors are the regional research center CIR-CENTRO and Northwest CIR -NOROESTE, both from INIFAP. Research centers that act as support structure for research in higher amount of funds raised corresponds CIR-CENTRO and CIR-NOROESTE, if at some point these research centers ceased to receive funds the financing network would fragment 99.5% this percentage of fragmentation is a weakness for public centers analyzed as it shows the vulnerability (and in the same sense the importance of INIFAP) of the financing system from agricultural and forestry research in Mexico (Figure 2).

Figure 2. Financing network from CPI in Mexico. 

It is important to note that unlike IES, CPI whose primary mandate is research, originating to obtain a network with a large number of funding sources SAGARPA through Fundacion Produce in each of the states, (SEP-CONACYT, SAGARPA-CONACYT, CIMMYT, PRONATURA, and CONAFOR, among others) at national level, with regions that have greater linkages and therefore major projects for the generation of innovations.

Financing network from private sector institutions (SP) conducting research in the agricultural sector in Mexico

The private sector represents a potential in generating research, however is recurrent that project funders of this actor are practically the same as public research funding. In the agrifood industry of Mexico, research results from private sector are virtually unknown to various users, or at least are not public the research products they get, which causes possibly to be private research funded with public funds. The density of private institutions that conduct research is only 4.40%, but also the number of institutions analyzed was low. Centrality both entry and output is low which means that there is no preponderance of private institutions in access to public financing (Table 3).

The actors that can act as information collectors and which are who fund the private sector are CONACYT and own resources, these concentrated 33.30% of the relations on this network. Diffusers that can reach 50% of the actors in the network are two private companies, which take in the same way the role of arrangers (Figure 3).

Figure 3. Financing network of SP in Mexico. 

In accordance with ^{Dutrénit et al. (2010)}, the funding from private sector in SNIA is virtually absent. The results obtained in the analysis of the funding network to private research institutions in the agricultural sector show a low level of articulation and linkage of the actors in Mexico. Studies conducted at national level indicate that the Mexican Innovation System (SMI) has two main characteristics as interactions refers (^{Dutrénit et al., 2010} cited in ^{Casas et al., 2014}), on one hand, the private sector acts as a isolated agent within the system, maintaining relationships almost exclusively with other companies in the business sector, with the Government through macroeconomic policy and access to incentives and to various funds. And secondly, most interactions occur between public institutions, particularly between CONACYT and Public IES, between CONACYT and CPI, and between public research centers-public research institutes. This study confirms what some authors (^{Casas et al., 2014}; ^{Solleiro et al., 2015}) said: "the national innovation system in Mexico disarticulated".

SNIA has a low density of links between its actors, this may contribute to what happens in reality: the existence of a low use of innovations by agricultural, livestock and forestry producers. So it requires greater efforts to increase density, but even more, to ensure that final beneficiaries use innovations that impact their production systems. One possible way is to support through SNIA greater validation processes and technology transfer, as ^{Busse et al. (2015)} says the validation process of innovation is a key to increase the use of these, as producers will only use those that are practical, simple and useful for their production processes.

On the other hand, it is important to identify what some authors call innovation intermediaries (^{Howells, 2006}) to generate links that favor the development and increased research and development projects that generate useful innovations for the primary sector in Mexico. An innovation system with weak links between actors that integrate them demand strengthening of intermediary organizations in creating an institutional environment that promotes links and interactions required in order to build dynamic networks within and between research projects and innovation (^{Klerkx et al., 2009a}); in this regard, cooperation between different types of actors is seen as key to success in the generation and adoption of innovation (^{Howells, 2006}; ^{World Bank 2007}; ^{Klerx et al., 2009b}).

The analysis conducted in this study show that the density of the funding network from the National Agricultural Research System in Mexico is low; 0.38% (IES), 1.24% (CPI) and 4.4% (SP), which implies that there is little relationship and linkages between actors, and also, and perhaps most importantly: the financing network of agricultural research in Mexico is mainly supported by the governmental sector: CONACYT and SAGARPA, with very little participation from private companies.