REGENA: Growth Function for Regenerative Farming

Abstract

Our work develops the structural mathematical framework of the REGENerative Agriculture (REGENA) Production Function, contributing to the limited global literature of regenerative farming production functions with consistency to the 2nd Law of Thermodynamics and the underlying biophysical processes for ecosystem services’ generation. The accurate structural economic modeling of regenerative farming practices comprises a first vital step for the shift of global agriculture from conventional farming—utilizing petrochemical fertilizers, pesticides and intensive tillage—to regenerative farming—utilizing local agro-ecological capital forms, such as micro-organisms, organic biomasses, no-tillage and resistant varieties. In this context, we empirically test the REGENA structural change patterns with data from eight experimental plots in six Mediterranean countries in Southern Europe and Northern Africa for three crop compositions: (a) with exclusively conventional practices, (b) with exclusively regenerative practices and (c) with mixed conventional and regenerative practices. Finally, we discuss in detail the scientific, institutional, economic and financial engineering challenges for the market uptake of regenerative farming and the contribution of REGENA for the achievement of this goal. In addition, as regenerative farming is knowledge-intensive, we review the vital aspect of Open Innovation (OI) and protected Intellectual Property (IP) business models as essential parts of regenerative farming knowledge-sharing clusters and trading alliances.

1. Introduction

The large-scale enactment of Regenerative Agriculture (RA) practices comprises an element of vital importance for the economic transformation of the agricultural sector of the European Union (EU) towards the classification [1] and monetization [2] of its natural capital via conservation practices. Such an endeavor is accompanied by several scientific, institutional, economic and financial engineering challenges for establishing self-sustained markets. The cornerstone of addressing these challenges consists in the design of unified national and corporate accounting frameworks [3] for incorporating the environmental costs and benefits to an agricultural product’s final price within a consistent scientific and economic rationale. In turn, such a framework would provide a signal to both the market and investors on the economic potential of regenerating farming practices. At the core of this discussion is the monetization of derived ecosystem services from regenerative farming and their various interconnections. Although several research and business cases on regenerative farming have shown promising results [4], a major obstacle for its large-scale market uptake is lack of knowledge on the underlying biophysical processes in the soil, as well as the generated values from synergistic land management (e.g., crop rotation). These two pillars comprise the main advantage of regenerative farming practices in relation to conventional practices [5] that rely on intensive tillage practices and the use of synthetic fertilizers and pesticides. This inertia preventing a large-scale adoption of regenerative farming practices is further enhanced by the significant lack of literature on a consistent system of RA structural equations that depict the underlying processes in the soil that are utilized by RA, within a wide range of pedoclimatic conditions (e.g., Koppen–Geiger classification), and further interpret them into economic variables and within an integrated modeling framework.

Conventional and Regenerative Farming Modeling

The value of modern regenerative farming practices can be highlighted via a historical overview of agricultural practices. From a historical perspective, we may outline three sequential types of socio-ecological organization with their dominant energy harvesting pattern as the criterion: the hunters-gatherers, the agrarian societies, and the fossil-fueled industrial societies [6]. The agrarian phase of human civilizations took place across the period 10,000 BC–1800 AC, where humans first achieved the large-scale and systematic accumulation of net food surpluses by harnessing secondary solar energy inputs in the form of plant biochemical energy [6,7]. In this phase, the adaptation to ecosystem functions can be identified as a universal feature across various civilizations [8], affecting both the allocation of land between cropland and grazing land [7] for the optimized flow of energy in societies [6] and the socio-economic structure and complexity [9,10]. The transition to industrial agriculture essentially distorted this socio-ecological equilibrium via the large-scale use of petrochemical fertilizers and pesticides [11] that allowed the rapid increase in food production and population growth at the cost of disrupting the biophysical soil processes that sustain its quality. The very definition “regenerative” essentially comprises the direct acknowledgment that the modern inventory of regenerative farming practices aims at restoring soil quality to its pre-industrial levels, maintaining at the same time the high level of crop output to sustain the global population. Such an approach requires a fundamental change in agricultural systems modeling [12], which is the main contribution of this work.

The foundation of economic modeling is production functions [13]; essentially mathematical models that depict in an abstract but accurate way how production factors, such as manual labor, Research and Development (R&D), mechanical capital and a variety of natural resources, combine for a product’s output. In turn, agricultural production functions that we examine in this work as background [14] comprise a subset, where production factors include special inputs, such as irrigation water, fertilizers as nutrients, climate conditions, etc. RA production functions constitute a special subset with even more production factors within the inner workings of the soil [15] that still remain widely uncharted.

The literature of RA production functions is still limited, lacking a sufficient number of works developing an integrated mathematical framework, consistent to the biophysical principles of soil science and the 2nd Thermodynamic Law [16,17,18,19]. However, a trend towards development and synthesis of elaborate biophysical models [12] is definitely clear. In this context, we develop the structural mathematical framework of the REGENerative Agriculture (REGENA) Production Function to contribute to the stock of academic literature, business practice and policy. REGENA introduces several originalities that depict the biophysical and business realities of RA, such as the following: (a) the incorporation of endogenous growth elements that, besides conventional production factors (e.g., manual labor, mechanical capital, petrochemical fertilizers), account for knowledge accumulation; (b) the synergistic or competitive metabolic topology between micro-organisms, biomasses and petrochemical fertilizers; (c) the identification of structural change patterns across the shift from conventional to regenerative practices; (d) the flexibility to mathematically formulate REGENA as a Computable General Equilibrium Model (CGEM) and a Machine Learning (ML) algorithm to achieve multi-variate global optimizations and (e) the monetization of derived environmental values and ecosystem services, as well as lower lifecycle impacts.

In our Materials and Methods, we provide a view of the EU’s agricultural policy framework to highlight the importance of introducing the REGENA function and the motivation to structure it for addressing the challenges of regenerative practices adopted at an increasing rate [20]. Specifically, we present the six pillars of the EU Sustainability Finance Taxonomy (SFT) [21] as the financial vehicle of the EU Green Deal (GD) [22] and the Mediterranean as an area of special pedoclimatic challenges [23]. In turn, we present the regenerative farming pillars [Appendix A.1] of the examined Case Studies (CSs) and the process for classifying them by their similarity [Appendix A.2] and availability of socio-economic data [Appendix A.3]. Finally, we present the REGENA structural equations as an original model that can depict the shift from Conventional Agriculture (CA) to RA or a CA-RA mix. In regard to this task, we present the mathematical forms of selected agricultural production functions [14,24,25,26,27,28] that are widely used [see Appendix B]. On this ground, we substantiate the differentiation of REGENA as a generalized endogenous growth function [29,30,31] with consistency to regenerative economics’ epistemology [11,32,33,34,35,36,37,38], with knowledge creation and accumulation at the macroscopic and the microscopic level.

In our Results, we present the REGENA structural change simulations with data from eight CSs in the Mediterranean, combining regenerative farming pillars, such as beneficial micro-organisms (pillar M), organic biomasses (pillar B), resistant varieties (pillar R) and agronomical practices (pillar A), pedoclimatic data (e.g., temperature and precipitation) and economic data (e.g., energy, water and fertilizers’ use). The interconnections between the variables are presented with parameters and nested functions. For instance, the effect of tillage as an agronomic practice is depicted as a function of mechanical capital use (e.g., tractors), affecting irrigation water use intensity and soil Evapotranspiration (ET). In overall, as each CS uses only some of the regenerative pillars [see Appendix A.1] from the complete ABMR range, we present the simulations for the three REGENA basic states; with exclusively CA, with exclusively RA and a CA-RA mix as the most indicative case of short-term transition. Not all CSs implement field experiments; hence, reference values on crop outputs were based on external references, assumptions and simulations. Finally, in our Discussion, we examine selected REGENA versions and their endogenous growth aspects in relation to the business models of Intellectual Property (IP) as part of a farm’s private competitive assets [10]—historically observed in industrial transitions [39]—and Open Innovation (OI) [40,41,42] as part of the business inventory of regenerative farming clusters for accelerating their market penetration within an environment of agricultural supply chains’ localization and global trade competition.

2. Materials and Methods

In this section, our core task is to set the theoretical background and data of RA into a concise and consistent economic framework for structuring the REGENA mathematical model on a farm’s crop output by each of the ABMR regenerative farming pillars. In the first part we examine the compatibility of REGENA v2.0 to EU Taxonomy framework and in the second part we develop analytically the set of structural equations.

2.1. Regenerative Farming, REGENA and the EU Taxonomy

The EU SFT constitutes the main financial vehicle of the EU GD. REGENA addresses the specific EU SFT objectives and pillars, aiming at the substantiation of the environmental value of RA solutions. The monetization of regenerative practices’ costs [43] and values [44,45], whether they concern the value of agro-ecosystems’ state improvement from reducing the use of petrochemical fertilizers at lifecycle [46], the generation of new ecosystem services [44,47] or land tenure optimization [48], constitutes a prerequisite for financial institutions to direct capital towards RA investments with measurable impact on their credit rating profiles and monetary yields. Experimental crops have demonstrated significant profitability potential in EU countries [49,50,51], as well as in other continents [52,53,54] within integrated economic–environmental accounting frameworks [3].

In such a context, the EU GD and SFT address the scientific challenges of RA and the conditions for its market upscale future commercial utilization. Specifically, we may identify four priority objectives of REGENA in relation to the six EU SFT pillars: (a) the depiction of tailored approaches to address climate change, desertification, pollution and low-income challenges into a concise and coherent microeconomic production function, applicable to small farms in the EU with focus on areas under significant pedoclimatic stress, such as the Mediterranean [23]; (b) the production function’s capacity to depict adequately the positive effect of chemicals’ use reduction via their substitution by organic fertilizers, biostimulants and organic waste biomasses; (c) the deriving restoration and regeneration of soil health via consortia of beneficial micro-organisms [55,56,57], the use of resistant local varieties and their synergies with the soil’s microbiome [58,59] and adoption of agronomical practices, such as no-tillage and cover crops; and (d) the production function’s capacity to depict the farm’s potential for restructuring its production factors [60,61] and grow its income from the knowledge of local natural capital.

Table 1. REGENA ABMR (A = Agronomical Practices; B = Biomasses; M = Micro-organisms; R = Resistant Varieties) relevance to the EU SFT pillars with a 1 (least relevant) to 5 (most relevant) scale.

EU SFT Pillar	REGENA ABMR Relevance	REGENA ABMR Relevance Substantiation
Climate Change Mitigation	5	Pillars B, M contribute synergistically to the removal of atmospheric CO2 and its transformation to SOC and plant biomass.
Climate Change Adaptation	4	Pillar R contributes to higher resilience via the varieties of higher resistance to abiotic (e.g., weather) and biotic (e.g., pests) stresses.
Sustainable Water and Marine Resources	3	Pillar A contributes to freshwater and marine resources conservation via lower water use intensity and coastal eutrophication risk.
Transition to a Circular Economy	4	Pillar B contributes to the Circular Economy via reducing agricultural wastes, petrochemical fertilizers and enhancing pillar M.
Pollution Prevention and Control	5	Pillars A, B, M reduce water use intensity and eutrophication (A); recycle and reuse biomasses (B) that enhance nitrogen fixation (M).
Biodiversity and Ecosystems	5	Pillars A, M, R increase biodiversity via crop rotation (A); increase soil and root biodiversity (M); improve ecosystems’ resilience (R).

below presents the relation of the REGENA function to the six pillars of the EU SFT.

By the above criteria, REGENA is directly related to the EU Taxonomy pillar 1 (Climate Change Mitigation), accounting for CO₂ removal from the atmosphere and its transformation into Soil Organic Carbon (SOC). SOC is a fundamental indicator for regenerative farming [62,63,64] and forest conservation [64,65], where both are part of Nature-based Solutions (NBS). A respective strong relevance is found for pillar 2 (Climate Change Adaptation) via the use of resistant varieties for coping with extreme weather phenomena, as well as pillar 6 (Biodiversity and Ecosystems) via micro-organisms that enhance soil biodiversity and generated ecosystem services. Pillar 4 (Transition to a Circular Economy) follows, as REGENA includes the effect of organic biomasses for micro-organisms’ growth along with pillar 5 (Pollution Prevention and Control), as N-fixation bacteria can reduce the use of petrochemical fertilizers. Respectively, resistant varieties can reduce the use of chemical pesticides, while agronomical practices, such as no-tillage and cover crops, can increase soil water retention capacity, reduce ET and minimize excessive water use that combined with excessive use of fertilizers causes eutrophication and aquifer pollution. Finally, pillar 3 (Sustainable Water and Marine Resources) is mainly related to Blue Economy; hence, it is the least relevant to REGENA, with its main direct connection being the variables of water resource depletion and marine eutrophication (for discharges in coastal areas) in the Product Environmental Footprint (PEF) [66] method, as a benchmark EU lifecycle analysis standard.

As regenerative farming utilizes soil micro-biodiversity and organic biomasses, this work primarily examines the farm’s production factors’ composition change. Of vital importance is the farm’s knowledge stock on the soil’s natural capital features and its utilization for endogenous growth and income increase. Empirical studies [9,67,68,69] show that the driving force for the transition from subsistence (as the lower poverty bound) to surplus agriculture across various historical periods was the knowledge accumulation on the features of local agro-ecosystems and its sharing between neighboring farms. Modern cases of subsistence farming in Africa [29] demonstrated that the knowledge of the features of local ecosystems, combined with crop diversification, yielded promising results for small farms in terms of income growth and emancipation of women. This aspect is simulated by REGENA v2.0, expressing the endogenous growth potential from the equal participation of women in the research process in the examined plots.

Finally, a frequent confusion is observed when regenerative practices are interpreted as primitive methods that were prevalent in the agrarian phase of human civilizations [6] and currently an option exclusively for developing countries that lack access to mechanical capital. This confusion is enhanced when regenerative farming is considered to incorporate many hydroclimatic risks due to its high dependence on rain-fed agriculture [70]. However, although regenerative farming shares with rain-fed agricultural practices the low environmental footprint at lifecycle as a common feature, it should be distinguished from it. For instance, regenerative farming adopts irrigation technologies; however, those of high water efficiency (such as drip irrigation) are a feature also incorporated in pillar A of the REGENA v2.0 function.

2.2. Structuring the REGENA Function

The foundation of REGENA is the mathematical formulation of the ABMR pillars to depict their synergistic or competitive activity. From an economic perspective, this is translated as substitutability or complementarity. The modeling of the ABMR pillars is enriched with environmental, economic and social data from each examined CS, which are classified into 5 categories: (a) Energy use; (b) Water use; (c) Fertilizer use; (d) Climate; and (e) Social. The list of the metadata is presented in Appendix A.3. The limitations concerned (i) the low availability of data; (ii) the type of the experiments, as some CSs performed pot experiments—incorporating significant uncertainty on how an upscaled open field experiment would behave—and (iii) scale, as even the CSs performing field plot experiments were too small in size to be considered representative of a real-world farm. To cope with these constraints, it was necessary to resort to external data, combined with rational assumptions. These inputs were then transformed into the variables of REGENA to perform structural change simulations. The simulations compare the output of a standardized conventional farm to a hypothesized regenerative farm of the same size for each CS.

REGENA v2.0 combines elements from the Cobb–Douglas [25], the Halter Transcendental [27] and the de Janvry Generalized Power [26] production functions (for a thorough mathematical formulation see Appendix B.1, Appendix B.2, Appendix B.3 and Appendix B.4). REGENA consists of a system of nested relationships and output elasticities that signify the productivity of each production factor separately. These two features endogenize the physical properties of agro-ecosystems that affect the number of other inputs. For instance, the high supply of residual organic biomasses that enhance the growth of the populations of micro-organisms signifies that lower amounts of chemical fertilizers will be required. The general form of the REGENA function is:

$$Q=Q_0\cdot {\displaystyle \prod _{i=1}^n\left[X_i{\left(X_j,X_k\dots ,X_{n-1}\right)}^{{\left(1-a_i\right)}^{-1}}|i\ne j,\dots ,n\right],i,j,\dots ,n\in {\mathrm{N}}^{+}};Q_0,X_i\in R^{+};a_i\in \left(-\infty ,1\right)$$

(1)

Equation (1) combines features from Equations (A1)–(A3), as it adopts the multiplicative formulation on the relation between production factors. The necessary condition of multiplicative forms is the positive quantity of all production factors. If the quantity of even one production factor is zero (=0), the total output will collapse. This condition is consistent to physical properties of agricultural systems as it suggests the validity of Liebig’s Law of the Minimum [71], determining total output (further analyzed in Equation (9)). In contrast to the Cobb–Douglas function, this formulation does not require the assumption of constant returns to scale. Any input X_i is expressed endogenously as a function of 0 → n − 1 inputs, which stands for the input is either an independent variable or it is a function combining up to n − 1 nested variables, raised in the exponent a_i that depicts output elasticity. In addition, the constant Q₀ depicts the minimum (reference) agricultural output level that grows by how effectively the production factors combine. Hence, for a_i ∈ (0, 1), production factors combine ineffectively, as Q₀ divisor; for a_i = 1, production factors combine with neutral effectiveness; while for a_i ∈ (1, +∞), production factors combine effectively as Q₀ multiplier. Equation (1) can express both the Halter [27] and de Janvry [26] forms, as presented in Equations (A2) and (A3). By simply assuming that each variable X_i follows the General Power form of Equation (A3), where for f_i(X) > 0 and e^g(x) = 1 → g(X) = 0, the variable reduces to the Cobb–Douglas-type [25] monotonic form, as in Equation (A1).

The first REGENA element is the stock of scientific and technological knowledge (A) that regenerative farms accumulate across their shift from conventional practices. Even if conventional production functions—including Equations (A1)–(A4)—depict (A) as exogenous coefficient that multiplies linearly total output across technical level upgrades, we depict it as an endogenous variable depending on the knowledge accumulation on beneficial micro-organism (pillar M) and biomass (pillar B) species (S) as complementary inputs:

$$A=A_0\cdot e^{{\left(1-m\right)}^{-1}\cdot M_S+{\left(1-b\right)}^{-1}\cdot B_S},{A_0,M_S,B_S\in R}^{+};m,b\in \left(-\infty ,1\right)$$

(2)

Equation (2) basically suggests that as the species of populations of micro-organisms (M_S) grow, statistically new and more available samples can be identified so that the total knowledge on the micro-ecosystem becomes increasingly representative of the full regenerative potential of the farm, at rate (m). Respectively, organic biomass species (B_S) have a similar effect; as their quantity increases, farmers can classify, separate and utilize them with higher precision for the soil’s fertilization, at a rate (b). Equation (2) also constitutes a multiplier of manual Labor (L_M), as every additional hour dedicated in the farm is increasingly efficient due to the (exponential) accumulation of knowledge [30,31,36]. Hence, the total labor (mental and manual) in the farm is:

$$L_T=A^{{\left(1-\alpha \right)}^{-1}}\cdot L_M^{{\left(1-\lambda \right)}^{-1}}={\left(A_0\cdot e^{{\left(1-m\right)}^{-1}\cdot M_S+{\left(1-b\right)}^{-1}\cdot B_S}\right)}^{{\left(1-\alpha \right)}^{-1}}\cdot L_M^{{\left(1-\lambda \right)}^{-1}},A_0,L_T,L_M,M_S,B_S,\alpha ,\lambda ,m,b\in \left(-\infty ,1\right)$$

(3)

Equation (3) depicts the manual labor L_M variable as independent, as it only concerns standard works that any unskilled worker can perform. Any special skill, knowledge and technique that is beneficial for the better care of the soil is a part of variable A₀, depicting mental labor that is further augmented by the knowledge stock on micro-organisms and biomasses. The output elasticities (λ) of manual labor, as well as (α) of knowledge, are the typical exponents found in all multiplicative production functions. Equation (3) suggests an exponential growth of knowledge even when the diversity of micro-organisms M_S and biomasses B_S reaches its maximum value. The background rationale for this assumption is that even when a farm fully adopts regenerative practices, its knowledge continues to grow, becoming more elaborate via the study of M_S, B_S combinations in variable pedoclimatic conditions. In contrast, the use of conventional Fertilizers (F) is competitive with the use of biomasses and the growth of micro-organism populations, as follows:

$$M_F=M_0\cdot e^{-{\left(1-\varphi \right)}^{-1}\cdot F},{M_0,F\in R}^{+};\varphi \in \left(-\infty ,1\right)$$

(4)

Equation (4) depicts the competitive relationship between micro-organisms and conventional fertilizers (F) by a rate (φ). This rate expresses the intensity of micro-organisms crowding-out by the use of each unit of conventional fertilizer. Biochemically, coefficient (φ) derives from the modeling of kinetic responses and essentially expresses macroscopically the kinetic response of micro-organisms to the toxicity of petrochemical fertilizers in terms of population decay. It is anticipated that different micro-organisms have different response towards conventional fertilizers; hence, this coefficient is essentially a weighted average of a “basket” of selected (tested) micro-organisms. In addition, the total amount of fertilizers (F_T) is the sum of all species of petrochemicals and organic biomasses, as:

$$F_T={\displaystyle \sum _{i\in \left[C,B\right]}{\displaystyle \sum _{j=1}^n{F}_{ij}}},{F\in R}^{+};n\in {\mathrm{N}}^{+}$$

(5)

Equation (5) essentially depicts that the composition of fertilizers is categorized into two major classes that are competitive with each other in the plot. An issue of major importance is to model the effectiveness equivalence between conventional and organic fertilizers to identify two major dimensions: (a) the conditions where the two fertilizer types can achieve the same crop output—irrespective of long-term sustainability dimensions—and (b) the real potential of substituting petrochemicals with (waste) organic biomasses in the field. The equivalent quantity of each unit of organic biomass (B) that is competitive with a unit of chemical fertilizer (F) is:

$$B_{\to F}={\left(1-h\right)}^{-1}\cdot B_0,B_0,F,h\in \left(-\infty ,1\right)$$

(6)

Equation (6) suggests that the petrochemical fertilizer equivalent of a total quantity of biomass (B_→F) as organic fertilizer consists of a base amount (B₀), normalized (multiplied or divided) by the equivalence coefficient (h). The underlying assumption is that petrochemical fertilizers are manufactured and processed to maximize the concentration of nutrients per unit mass [72]; hence, unprocessed (recycled) organic biomasses produced naturally contain these nutrients in lower concentrations. The value domain of coefficient (h) practically expresses the biomass quantity required to substitute one unit of fertilizer for an equivalent result. Hence, for h < 0, the conventional fertilizer is more efficient than the biomass, for h = 0, both are qualitatively equivalent, while for h ∈ (0, 1), the biomass is less efficient due to lower concentration of necessary nutrients. Respectively, the base amount B₀ is considered to be a fraction of total output (Q) at the previous time step t − 1 in Equation (1), as:

$$B_0=q\cdot Q_{t-1},{B_0,Q\in R}^{+};q\in \left(0,1\right)$$

(7)

Equation (7) suggests that the (thermodynamic) losses abstracted from total output are assessed as inadequate for consumption along with any other material losses across cropping and harvesting. These residuals can be reused as biomasses for organic fertilization. The notation in Equation (7) also suggests a closed self-sustained circular system, in compliance with EU Taxonomy pillar 4 (Table 1). Organic biomasses can be supplied by a wide range of sources [73], such as symbiotic livestock and agricultural systems [74], or food wastes from consumer centers that are processing, and distributed back to the farm [29]. For simplicity we will assume the form of Equation (7) on a closed-loop local supply system and discuss selected REGENA extensions in relation to local, national and global trade facets.

The effect of organic biomasses and petrochemical fertilizers on the growth of micro-organisms’ populations constitute an essential part of the REGENA function. Specifically, 99.6% of global biomass is composed of plants (82.4%) and micro-biota (bacterial biomass with 12.8% share, fungi biomass with 2.2% and single-cell microbes’ biomass with 1.5%) [72]. Closing the loop that governsthe relationships between micro-organisms, biomasses and petrochemical fertilizers, we model the population growth of micro-organisms as:

$$M=\left(M_0\cdot e^{-{\left(1-\varphi \right)}^{-1}\cdot F}\right)\cdot {\left(1+M_0\cdot e^{-{\left(1-\gamma \right)}^{-1}\cdot B_{\to F}}\right)}^{-1},M_0,F,B_{\to F}\in R^{+};\gamma ,\varphi \in \left(-\infty ,1\right)$$

(8)

Equation (8) suggests that micro-biota diversity and population sizes grow proportionally to the quantity of organic biomasses fertilizing the soil. The coefficient (γ) depicts the metabolic ability of micro-organisms, which depends on their ensembles’ composition (i.e., how well their composed consortia work synergistically or competitively); maximizing energy and nutrient inputs’ efficiency [75,76]. Higher values of (γ) signify higher metabolism and population growth, reaching the maximum population level more quickly. The maximum population (M₀) is constrained by the Sprengel–Liebig Law of the Minimum [71], suggesting that biomass growth is constrained by the growth factor (e.g., nutrient C, N, P, S) in minimum relative availability. Relative availability is defined as the exact ratio of the minimum quantity of a nutrient n, combined with the respective minimum quantities of n − 1 complementary nutrients to form one unit of biomass, in relation to their environmental availability. Hence, M₀ is modeled to depend on the system’s limiting factor, as:

$$M_0=Max\left\{M\left[\left(C_1\cdot R_1^{-1}\right);\left(C_2\cdot R_2^{-1}\right);\dots ;\left(C_n\cdot R_n^{-1}\right)\right]\right\},{C\le R,C,R_{1\to m}\in R}^{+}$$

(9)

Equation (9) depicts the law of the minimum as a Consumption to Reserves (C/R) ratio, which is widely used in natural resource economics and is equivalent to the standard formulation [72]. In regard to this relation’s physical meaning, a typical necessary ratio of carbon, nitrogen and phosphorus nutrients C/N/P = 41/7/1, with a natural availability of phosphorus at only 0.5 units, will allow the system to utilize only 20.5 units of carbon and 3.5 units of nitrogen to preserve this ratio. Any excess amounts will remain unutilized by the system at the risk of flowing to wetlands and groundwater aquifers; causing eutrophication and pollution. This is an additional value-added of regenerative practices, as nitrogen-fixing bacteria optimize the above ratio [61] and substitute the use of petrochemical fertilizers, along with the attached risks of water overuse and eutrophication. Results for the use of soil and plant growth-promoting micro-organisms to cope with biotic stresses in economically important crops [55,56,57,58] demonstrate a respective value for the reduction in chemical pesticides, highlighting the pivotal role of micro-biota for regenerative practices and knowledge accumulation. Completing the modeling of population size of micro-organisms, we postulate the general condition of total output (Q) in relation to the state of fully adopting regenerative practices or deviating from them (via CA or CA-RA mixes), as follows:

$$Max\left(Q\right):\left\{\left[M_0^{{\left(1-a_n\right)}^{-1}}\cdot {\displaystyle \prod _{i=1}^{n-1}{X}_{i|M_0}^{{\left(1-a_i\right)}^{-1}}}|M=M_0\right];\left[Q_0\cdot {\displaystyle \prod _{i=1}^n\left[X_i{\left(X_{i0,}{X}_j,\dots ,X_{n-1}\right)}^{{\left(1-a_i\right)}^{-1}}\right]|M<M_0}\right]\right\}$$

(10)

Equation (10) essentially suggests that with full adoption of regenerative practices, the system’s growth will be determined by the micro-organisms’ maximum population (M₀), which in turn depends on the regenerative input (such as organic biomasses) as the limiting factor. Any additional conventional input (such as chemical fertilizers) will either reduce M₀ or will not have any further effect on total output growth. Hence, three deriving conditions are the following: (a) the fully regenerative plot follows a logistic growth pattern that is frequently observed in continental natural ecosystems [75,76], with the form of the Chapman–Richards (CR) logistic model (see Appendix B.4) that is widely used for modeling biomass growth in forest ecosystems. This concept is physically backed by the fact that fully regenerative farms utilize the natural capital of local agro-ecosystems; (b) micro-organisms constitute the pivotal factor, serving multiple purposes in fully regenerative plots; (c) total output of mixed conventional–regenerative or fully conventional practices is not necessarily lower than the full regenerative farm’s output. However, conventional practices are long-term unsustainable, as they require extensive fallow periods after the intensive use of chemical fertilizers and pesticides, while regenerative farming are able to produce perpetually, via cover crops and crop rotation. This is an issue that this work discusses later in more detail.

Modeling crop resistance against weather and climate stresses, such as heat shocks and droughts, is an additional vital element of the REGENA structural equations. A range of favorable statistical temperature properties (such variability) for plant growth constitutes by itself a production factor for crop output. Stability of plant biomass growth across a wider range of temperatures signifies higher resistance and crop output predictability. Economically, that translates into lower risk of crop failure, ecosystem services’ provision [72], as well as lower insurance costs, either as compensations or weather derivatives [77]. Although with technological progress the dependence of agriculture from hydrometeorological phenomena is highly mitigated [70], optimal combinations of weather conditions maximize crop output and reduce costs. The underlying variable is temperature (T), modeled as a stochastic process following the Normal Distribution T(μ,σ), with μ as the mean value and σ depicting standard deviation [48]. Irrespective of the real distribution of temperature, we may depict the map of a crop variety’s internal productivity (H) across a range of temperatures with the following general mathematical form:

$$H^{{\left(1-\delta \right)}^{-1}}={\left[\epsilon \cdot T\cdot \left(1-\eta \cdot T\cdot {\epsilon }^{-1}\right)-c\right]}^{{\left(1-\delta \right)}^{-1}},{H,T,\epsilon ,\eta ,c\in R}^{+};\delta \in \left(-\infty ,1\right)$$

(11)

Equation (11) is essentially the continuous and symmetrical quadratic map [65,72], where the parameter values determine the range of the map’s positive values, as well as its global maximum value. For simplicity, we may assume c = 0, so that the initial value of the map is T = 0. Its physical meaning is that for any deviation from an optimal temperature, the system will perform less than maximum. In our case, this concerns crop output that is highest at a specific temperature, while it will be reduced for any deviation from it; higher or lower. The significance of temperature-output quadratic map is to indicate crop intrinsic productivity. For instance, as the maximum point of the quadratic map is for T = ε/2∙η [6,72], setting a reference optimal temperature at 25 °C and beginning from a reference value of a crop with neutral resistance ability at ε = 1, the quadratic map yields by default a value of η = 0.02 for a ε/η ratio equal to 50 °C. Hence, the physical meaning of the quadratic map is that the crop will be able to survive within a range of 0–50 °C, with its maximum productivity at 25 °C.

This ε/η ratio can be preserved for infinite combinations of parameters ε and η values. For example, even if both combinations ε₁/η₁ = 1/0.02, ε₂/η₂ = 2.5/0.05 preserve this ratio, the second combination suggests higher crop intrinsic productivity, as for any temperature T it is capable of higher yield. Respectively, exponent (δ) is a smoothing resistance or homeostasis coefficient. This approach is quite representative of the arid and semi-arid conditions in the Mediterranean [23] and related to the use of Weather Derivatives (WDs) [77] as financial instruments for managing operational risks deriving from weather variability. From a financial standpoint, planting resistant varieties in heat-stressed areas constitutes a form of future cost savings, from the avoidance of paying the premiums of such instruments. These aspects are part of regenerative financial engineering schemes discussed in the results, as simulations show that regenerative practices outperform conventional or mixed practices with significant time lag.

The next category of variables concerns environmental footprint intensity of natural resource inputs. These inputs are further grouped into energy-intensive and water-intensive. The group of energy-intensive resources is modeled as follows:

$$E=\left(k\cdot E_K\right)\cdot K\cdot \left[F^{{\left(1-s\right)}^{-1}}\cdot \left({\left(1-\pi \right)}^{-1}\cdot P^{{\left(1-p\right)}^{-1}}\right)\cdot W^{{\left(1-w\right)}^{-1}}\right],{E,E_K,K,F,P,W,k\in R}^{+};s,p,\pi ,w\in (-\infty ,1)$$

(12)

Equation (12) expresses the farm’s energy use (E) as a function of mechanical capital (K), petrochemical fertilizers (F) and conventional pesticides (P). The coefficients concern the energy use by each unit of mechanical capital (E_K) as the weighted average of the vehicles’ energy mix, multiplied by parameter (k), depicting CO₂ emissions intensity (such as kg of CO₂ emissions per liter of liquid fuel type) [78]. Here, the pivotal variable is the base quantity of mechanical capital K. In the literature of production functions [14,24,25,26,27,28,29], mechanical capital refers to all kinds of material tools and machinery used to leverage the output of manual labor. In this context, K is the minimum quantity of machinery (such as vehicles, sensors, data centers, monitoring tools) in a fully regenerative farm. The energy use of this base machinery stock increases along with the increase in fertilizers and pesticides that are assumed to be utilized by the multi-functional machinery (such as a tractor with multiple compounds’ spraying capacity). Exponents (s) and (p) depict the environmental efficiency of fertilizers and pesticides use. Practically, s and p function as resource input elasticities, where contrarily to the output elasticities of Equations (1)–(3), their desired value is as low as possible for higher environmental efficiency. Respectively to coefficient (h) in Equation (6), exponents s and p operate as multipliers or dividers; specifically, for s, p < 0, fertilizers and pesticides are used efficiently, for s, p = 0, they are used with standard (baseline) efficiency, while for s, p ∈ (0, 1), they are used inefficiently.

Such a formulation provides the flexibility to utilize Equation (12) both as nested REGENA module for measuring the contribution of resources’ thermodynamic depletion at each output level (also compatible with the PEF), as well as an independent environmental footprint production function. The physical meaning of Equation (12) concerns how well mechanical capital operates as a multi-purpose production factor. For instance, a tractor may have attached systems for spraying both fertilizers and pesticides instead of using different vehicles. The combined increase in fertilizers and pesticides will increase monotonically the energy use of the farm, but at a diminishing rate. Finally, coefficient (π) expresses the planted variety’s pest resistance. The coefficient (π) is complementary to its heat stress resistance counterpart coefficient (δ) shown in Equation (11); here addressing biotic stresses. Specifically, π < 0 suggests that the crop requires fewer chemical pesticides than the standard level (π = 0) to cope with biotic stress, while π ∈ (0, 1) signifies that the crop is very sensitive to biotic stress, requiring pesticide inputs above the standard.

In a respective context, the extraction of freshwater resources is modeled in Equation (12) as an energy-intensive input for processing and groundwater pumping. Exponent (w) essentially expresses the energy use intensity per unit of water, functioning as a multiplier or divider following extraction efficiency. Specifically, a value w < 0 suggests that to make each unit of water available to the plot is energy efficient above the standard (w = 0), while for w ∈ (0, 1), it is highly inefficient. Such a case could concern the pumping of water from increasing depths in nearly depleted groundwater aquifers. As the formulation of energy-intensive production factors in Equation (12) provides flexibility to model their combinations in terms of their overall energetic efficiency (e.g., how productive each fuel and CO₂ emission unit is) or their Global Warming Potential (GWP), a respective rationale is adopted for the category of water-intensive inputs that are directly related to the soil’s water retention capacity from applied agronomical practices, as follows:

$$W={\left(1-\omega \right)}^{-1}\cdot W_0\cdot {\left(K^{{\left(1-z\right)}^{-1}}\right)}^{{\left(1-\xi \right)}^{-1}},W,W_0,K,B_{\to F},\omega ,z,\xi \in \left(-\infty ,1\right)$$

(13)

Equation (13) suggests that water use (W) inputs are a function of mechanical capital inputs (K). Coefficient (ω) expresses the reference state of the soil’s water retention capacity and stress from the currently applied treatment [79]. Specifically, a value of ω < 0 can indicate high soil water retention capacity, where tillage has either not been a main treatment type or tillage practices were not intensive or the soil demonstrates high water retention capacity recovery, after tillage. For ω = 0, soil water retention capacity is at reference level [79], while for ω ∈ (0, 1), water retention capacity is below standard, requiring frequent inputs of water to compensate for increased evapotranspiration (ET) and maintain the crop. Coefficient (ω) is multiplied to the minimum required water amount W₀ needed to sustain a completely regenerative plot. Mechanical capital used for tillage, such as tractors, decreases soil water retention capacity by a coefficient (z). Coefficient z is mitigated by exponent (ξ), depicting organic biomass inputs that stabilize soil aggregates and increase Soil Organic Matter (SOM). SOM reduces ET and minimizes new surface or groundwater inputs, thus conserving the soil’s water capital [80,81,82].

After structuring the REGENA equations, three crop compositions are simulated in the 8 examined CSs: (a) exclusively conventional practices, with a global reference plot to which all CSs are compared; (b) mixed conventional and regenerative practices, focusing on the share of regenerative pillars to total crop output across the increase in conventional inputs and (c) exclusively regenerative practices, as part of the EU GD and EU SFT.

3. Results

After the classification of CSs by similarity of their regenerative pillars (see Appendix A.2), we simulate their growth output patterns in the three basic states of REGENA (conventional, regenerative and mixed practices). The major simulation challenge was to treat the regenerative pillars that CSs left out of their experiments as neutral (for the case of full regenerative practices) or as substituted with conventional practices (for the case of mixed conventional–regenerative practices; for instance, substitution of organic biomasses with fertilizers). In addition, the endogenous growth potential due to the equal allocation of R&D works between genders is simulated via the Normal Distribution with parameters μ and σ. Results show that the increased participation of women in R&D brings an overall increase in total productivity due to synergies between male and female coworkers.

3.1. Simulation of Structural Change Patterns

We simulate with REGENA the differential and cumulative output patterns of each CS, based on the available data from laboratory, pot and field experiments, literature sources regarding metabolic coefficients, soil health states [79] and rational assumptions on benchmark values for critical variables that were unavailable. To achieve comparability, we assume a universal reference conventional farm of 1000 m² with potato crop that has the same composition in all CSs and consider it unaffected by the differences in pedoclimatic conditions (by Koppen–Geiger classifications). This assumption establishes an average benchmark for a wide area in the Mediterranean, including countries from South Europe and North Africa like Italy, Spain, Portugal, Morocco, Tunisia and Egypt that have significant differences in their soil states, temperature, ET and precipitation patterns. Such a reference farm achieves uniformity and comparability—even if it incorporates partial uncertainty—for assessing structural change patterns and performances, in relation to the globally dominant production practice. Such a comparison provides a basic assessment of the potential to substitute imports with local production and supply chains, as well as of the time lags required for shifting from conventional to mixed and regenerative farming. An additional important assumption is the upscaling of laboratory and pot experiments to hypothetical plots of 1000 m² size. It should be denoted that it is highly uncertain if the crop composition in pot experiments would behave in the exact same way as if exposed to open environmental conditions. In any case, these assumptions are necessarily adopted in the context of this work’s methodological value for the scientific literature and business practice, as a starting point for modeling the structure of regenerative practices.

For the reference conventional farm, we assume that the values of regenerative pillars are negligible. In addition, the reference conventional farm is assumed to achieve the maximum and fastest (due to intensive farming and chemical fertilizers) crop output, irrespective of its long-term environmental sustainability. To simulate the conventional farm dynamics, we increase each input of Equations (1)–(13) except for the ABMR pillars that are considered to remain at a minimum value. We then normalize the conventional farm outputs to a unit maximum value (=1), to compare the differential and cumulative outputs of mixed and regenerative practices in the CSs, as well as their time lag for converging to the output of the conventional farm. In mixed practices, the examined ABMR pillars in each CS grow as inputs along with the other production factors. Finally, the fully regenerative farm is simulated by allowing the examined ABMR pillars in each CS to grow at the expense of their competitive production factors. For instance, biomasses grow at the expense of petrochemical fertilizers, with the system growing up to its carrying capacity, as determined by its limiting factor in Equation (9) [6,71,72]. The production factors are also normalized as a weighted average Inputs Basket Index (IBI), with range IBI ∈ [0, 300]. Figure 1 presents the REGENA simulation results for each of the eight CSs for each state (conventional, regenerative, mixed) for both differential and cumulative output patterns.

The simulations show that the cumulative output of all CSs manages to surpass the cumulative output of the reference conventional farm, with both mixed and fully regenerative practices. Some CSs, such as CS1, CS4, CS6 and CS7, manage to achieve a significantly higher cumulative output, while others, such as CS2, CS3, CS5 and CS8, achieve a marginally higher cumulative output than the reference conventional farm. An interesting additional pattern is that for the latter category of CSs, regenerative practices eventually yield a higher output even in comparison to mixed practices. The common feature of these CSs is that only two regenerative pillars are examined. Another clear pattern, common for all CSs, is the significant time lag of cumulative outputs in both mixed and fully regenerative practices for converging to the maximum cumulative output of the reference conventional farm. The cumulative output of mixed practices was anticipated to converge to the maximum conventional output faster, due to the eventual prevalence of the conventional elements in the IBI mix that stimulate the soil for more intensive yield. This is evident in the gradual decay of differential patterns, with the output of mixed practices eventually becoming zero. This pattern is similar to the conventional differential pattern across the IBI increase, but with a positive marginal output across a wider IBI range due to the existence of regenerative elements in the mix. Such a behavior is an expression of the law of diminishing returns, embodied in all production functions [13,14,24,25,26,27,28,29], suggesting that for a plot of fixed surface, the addition of inputs at a constant rate will gradually grow the output at a diminishing rate, until the contribution of new inputs becomes zero. In contrast, the differential output patterns of fully regenerative practices stabilize at the carrying capacity level (determined by the crop’s limiting factor) that continues to grow in the long-term. The IBI levels at which mixed and fully regenerative cumulative outputs reach the conventional cumulative output are presented in Figure 2 below.

With an assumed strong synergistic relation between organic biomasses and micro-organisms, as in Equation (8), we may attribute the marginally better cumulative output performance of mixed practices in CS2, CS3, CS5, CS8 and—partially—CS6 to the lack of one or both B and M pillars. From the assumptions, when an ABMR pillar is not examined by a CS, it is substituted with a respective conventional input; for instance, biomasses are substituted with chemical fertilizers that according to Equation (8) impact negatively the growth of micro-organisms. Another common pattern of the differential outputs of CSs is the dominance succession of conventional practices, then of mixed practices and eventually of fully regenerative ones across the IBI. This succession pattern is common in all CSs with only different (wider or shorter) ranges of dominance. At initial stages of the IBI increase, conventional differential outputs prevail. At the mid-stages of the IBI, mixed practices will become prevalent, while at very high IBI values, fully regenerative practices prevail.

Finally, a major issue concerns the significant time lag of fully regenerative practices that surpass cumulative conventional and mixed outputs at very high IBI levels, suggesting that regenerative practices prevail only after the soil has been excessively stressed by the long-term use of conventional inputs (if we consider that the IBI increase by one unit corresponds to a respective time step), with naturally occurring nutrients and microbiota becoming extremely scarce. Regenerative practices rely on ecosystem functions, metabolizing primary solar energy into secondary plant biochemical energy [6]; hence requiring more time to generate symbiotic effects without requiring periodical disruptions for putting the soil into fallow. As discussed, this is an aspect of vital importance that will require new financial engineering approaches as part of the EU SFT to increase respective investments and market uptake [83,84,85].

3.2. R&D Participation and Endogenous Growth

In this section, we simulate the productivity increase from the equal participation of men and women in R&D, based on Equations (2) and (3). The initial per gender allocation of R&D working hours in each CS, as well as the increase of productivity for each gender after the equal allocation of working hours are presented in

Table 2. Simulated productivity growth benefits from the equal participation of genders in R&D for each CS.

Productivity Growth	CS 1	CS 2	CS 3	CS 4	CS 5	CS 6	CS 7	CS 8
Annual work hours Men	1728.0	1536.0	1968.0	1783.0	1968.0	1920.0	192.0	1020.0
Annual work hours Women	0.0	0.0	0.0	200.0	0.0	640.0	180.0	1020.0
Productivity ↑ (%) Men	0.23	0.12	0.19	0.26	0.19	0.21	0.25	0.50
Productivity ↑ (%) Women	1.00	1.00	1.00	0.87	1.00	0.63	0.31	0.50

below.

Equations (2) and (3) were applied in each CS, assuming that men keep their existing level of working hours, but share their current knowledge equally with their female colleagues. As knowledge within the same farm is treated as a public good, women receive all accumulated knowledge benefits as a “copy” (which is, without respective loss from men), while synergies (as economies of scale) increase gender and total productivity. The simulation results are presented in Figure 3 below.

According to Table 2, as the initial allocation of female working hours in the majority of CSs were zero (=0.0), their productivity increase was assumed to be 100% (=1.0) by default. For CSs with a positive number of working hours by female colleagues, simulations demonstrated an increase between 31% and 87%. For CS8 specifically, productivity increases were equally shared, as the initial conditions of equal allocation of working hours remained unchanged. Figure 3 demonstrates a higher percent (%) productivity increase in women, as men were already utilizing a higher fraction of their maximum potential.

4. Discussion

A pivotal aspect addressed in this section is the integration between the crop output and crop value paths, considering that the REGENA simulations demonstrated significant time hysteresis for mixed and regenerative practices to outperform the cumulative output of conventional practices. Both options incorporate benefits and costs; however, the monetization of conventional farming is favored at the expense of regenerative farming. Below, the three major pillars of proper regenerative farming monetization are discussed.

4.1. Long-Term Farming Sustainability

Regenerative farming incorporates several direct and indirect values that are left out of conventional corporate and national accounting standards. Such oversights underestimate its financial investment potential. Indicative cases include the cost of CO₂ emissions and the depletion of fuel and water resources, where regenerative practices have an indisputable advantage, in terms of pollution avoidance and ES generation. In respect of this, a large fraction of the full environmental cost of conventional practices still remains unaccounted for. However, conventional practices are long-term unsustainable, requiring scheduled repeated disruptions of the crop output to put the soil into a fallow state, due to its accumulated stress from petrochemical fertilizers, pesticides and tillage, as depicted in REGENA Equations (12) and (13). During fallow periods, regenerative practices (and in part, mixed practices) rejuvenate soil health and recompose its microbiota and nutrients’ structure, so that it can support even higher long-term output with minimal use of chemicals. Essentially, the choice between conventional and regenerative practices is a type of (an accelerating but with constrained long-term stability) rabbit and (slowly and steadily moving for long distances) turtle dilemma. Schematically, the dilemma is presented in Figure 4 below.

Figure 4 shows schematically how regenerative farming is compatible with the EU GD and EU SFT, for both long-term environmental and economic sustainability. From a modeling perspective, revenue reductions in conventional farming due to increasing environmental costs are explained by the exponential decay part of the Halter transcendental and de Janvry production functions (see Appendix B.2 and Appendix B.3), where fallow periods will follow for the replenishment of soil nutrients, thus putting a temporary cap on cumulative output, until the next conventional farming cycle can begin. In contrast, regenerative farming can be adopted perpetually, utilizing ecosystems’ functions without intermediate fallow periods. As regenerative practices maximize output at carrying capacity, this output level accrues at every time step, so that eventually regenerative output surpasses conventional. Although it is beyond this work’s scope, it is necessary to point out the importance of tailored financial instruments that adapt to the biophysical realities of regenerative practices, such as risk-adjusted payoffs and credits by the expected value of ecosystem services [72,83]. Finally, although in a simplified manner, Figure 4 may also highlight the long-term factors from conventional practices affecting soil health, where the fallow periods could be considered an economic opportunity of “reset” and regime shift to regenerative practices.

4.2. Regenerative Farning Business Models

A core issue in the literature of endogenous growth theories [30,31] concerns the type of accumulated knowledge. In agro-ecosystems, knowledge derives from increased diversity of soil microbiota and diversification of crops [29]. REGENA addresses such issues in Equations (2) and (3). In this section, this dimension is discussed in relation to the available business models for valorizing and capitalizing the accumulated knowledge of a regenerative farm. Indicative questions are the following: (a) Which factors activate the process of producing knowledge on the soil, the rhizosphere, micro-organisms and the biomasses, optimizing their combinations and population sizes? (b) Why can the optimal use of conventional fertilizers not be classified as knowledge and a factor of endogenous growth?

Historically, knowledge accumulation deriving from the observation and classification of agro-ecosystems’ natural capital is observed across the agricultural phase of human civilizations, where it defines the population equilibriums in relation to local carrying capacities [8] and the concept of private property itself [10]. In addition, knowledge sharing between communal farms for enhancing crop output and protection against various natural and social risks was a common practice in several remote communities, as well as the Western European Middle Ages [6]. Furthermore, in relation to Equations (2) and (3) and Section 3.2 on the allocation of R&D works between genders, evidence shows that the overall shaping of small independent farms in agrarian societies (~10 ka BC–1800 AC) and the achievement of food surpluses via crop optimization techniques that further enhanced demographic growth were determined by the allocation of works between genders in the farm household [8]. In such allocations, men performed muscle-demanding works, while women contributed with the identification and classification of local natural capital species and the selection of optimal varieties [6,8,10,86]. Besides this historical evidence, this pattern is observed even in contemporary subsistence agriculture [9,29,68,69,70], increasing productivity and free time in the households, that is in turn dedicated to research, learning and knowledge accumulation of the properties of local ecosystems for further output diversification and growth [29].

Today, the model for knowledge accumulation and diffusion that embodies the features of endogenous growth in regenerative farming is Open Innovation (OI) [40,41]. OI is a form of free-access and outsourced knowledge that is incorporated into a firm’s (here a farm’s) internal works. This model establishes the conditions for a positive sum game for both the external innovator and the farmer. As the accumulation of knowledge occurs in the form of OI, it essentially comprises a public good, where the R&D results are reproducible via a repetitive learning by doing process [42]. A public good is defined as a good, the use of which by one individual does not exclude its use by any other individual. In contrast, conventional fertilizers based on industrial patents are directly related to Intellectual Property (IP). Farmers using IP-protected fertilizers are limited to the role of users, even when receiving special training on their optimal use, with no flexibility to modify the fertilizer’s specifications without permission from its proprietor. This allows the farmer only to use an exogenously developed product (here, the fertilizer). Essentially, the farmer makes use of a final product from the perspective of the industry and an intermediate product from his perspective, to grow his own final product (here, the crop). This detachment imposes an upper limit to the farm’s knowledge potential of the environmental impacts of the exogenously developed product, over which the farm holds no direct control.

To resolve the above issue and find a golden section for mixed and regenerative practices, business models such as Chemical Leasing (ChL) have been developed to include the Extended Producer’s Responsibility (EPR) principle. With ChL, the fertilizer’s manufacturer is obliged by law to offer the farmer know-how on its optimal use [85] in specific pedoclimatic conditions, while also obligated to manage the generated wastes. ChL creates checks and balances between counterparties, as it motivates users to certify the use of the product in the designated way and manufacturers to design more ecologically friendly products, focusing more on the knowledge of pedoclimatic conditions in various geographies, thus inevitably investing in regenerative R&D. The combination of endogenous R&D in regenerative farms and ChL practices by fertilizer manufacturers, with the adoption of an OI or shared IP model, paves the way for regenerative farming and agri-trade conglomerates.

4.3. Global Agri-Trade Extensions

With the prospect of market uptake of regenerative farming via the suitable business models to manage accumulated knowledge and the adoption of tailored financial instruments for monetizing ecosystem services, several considerations on the future global, regional and national agri-trade networks emerge. Specifically, as regenerative agriculture primarily concerns a micro-economic structural change via the utilization of local biodiversity, an emerging issue is its effect on the farm’s meso-economic organization and synergistic clustering. A possible future trend could be the convergence of OI to protected IP across the formation of farming alliances and conglomerates for economies of scale. In turn, the replication of such a clustering pattern poses the question of its macro-economic impact on the global agri-trade web [87], via imports’ substitution and the enhancement of national food autarky. Indicative—but not exhausting—special issues are the following: (a) the national, regional and global demand for regenerative farming products, considering that local supply and value chains would be favored; (b) the potential of regenerative farming for biodiversity-rich nations [88], in terms of output and value; (c) the potential of regenerative farming for substituting soy-based cattle feed with legumes, to maintain the high protein content for livestock [74], as a priority issue for the EU and its new Common Agricultural Policy (CAP) [89]; (d) the impact of the EU GD and EU SFT on private investment standards, favoring accounting and valuation of ecosystem services [72,83,88] and (e) the paradox of increasing geopolitical uncertainty and risks from enhancing national supply and value chains—that would, respectively, increase national food autarky and security—at the expense of current global agri-trade relations.

5. Conclusions

This work contributes to the academic literature and business practice of regenerative farming economics with the postulation of the REGENA Production Function and its structural equations. REGENA is the first function with an integrated system of equations, covering the full range of regenerative farming ABMR pillars. This constitutes a significant enrichment of agricultural production functions that focus on conventional farming practices, based on petrochemical fertilizers, pesticides and tillage. In contrast, REGENA accounts for soil micro-organisms, organic biomasses, resistant varieties and no-tillage agronomical practices as the main inputs for the output of a regenerative farm.

After conducting a literature review of regenerative economics from global and EU pilots, it is argued that there is need for postulating a generalized quantitative framework that depicts consistently the soil’s ecosystem properties as a source of economic value and investment attraction for its conservation [15]. Essentially, the fundamental hypothesis of this work is condensed in the phrase to manage it, we have to be able to measure it. With this starting point, we build the structural equations of REGENA, as an endogenous growth regenerative farming function, including the inputs of each ABMR pillar, their synergistic dynamics and the knowledge accumulation from their R&D. As regenerative farming is based on the biophysical properties of the soil, a vital aspect of REGENA is its consistency with the Second Thermodynamic Law, in terms of both metabolic processes [6,18,19,29,65,71,72,73,75,76] and natural resource depletion [16,78,79,80,81,82,83,84]. Additional production factors incorporated in REGENA are pedoclimatic conditions and resources, such as mechanical capital, fuels and water. Another vital aspect is the compatibility of REGENA with the EU GD [22,23] and EU SFT [21] policy directions of EU member-states. This concerns the compliance with the EU’s institutional framework, as well as a fundamental recognition of the necessity of a unified corporate and national accounting framework for the derived environmental values of regenerative farming [3,5,6], such as ecosystem services [1,2,32,34,45,46,47,48,49,52,53,54,60,61,62,63,64,65,66,72]. Furthermore, REGENA v2.0 contributes to the establishment and enrichment of a Regenerative Agriculture Economics (RAE) database with valuable information for building tailored instruments for financial institutions that seek accurate metrics to upscale their investments towards regenerative farmers.

After building the REGENA v2.0 structural equations, a number of simulations were performed for 8 CSs in the Mediterranean (see Figure A1), where the experimental sites were selected for maximum representation of pedoclimatic conditions in Southern Europe and Northern Africa through a limited sample. The simulations were performed for three crop composition scenarios: (1) fully conventional practices, as the benchmark and comparison state, (2) fully regenerative practices and (3) mixed conventional and regenerative practices. The simulations incorporate significant uncertainty due to the normalization of highly heterogenous data from laboratory, pot and field experiments. In any case though, the results confirm already observed patterns, such as a significant time lag for the cumulative output of mixed and fully regenerative practices to surpass the cumulative output of conventional practices. Economically, this indicates the need for inventing new credit and financial instruments that reflect the biophysics of soil regeneration [77,83,85]. Each simulated CS examines different combinations of ABMR pillars, respectively addressing different regeneration challenges, such as soil carbon and nitrogen increase (CS1); increase in farm income, water efficiency and substitution of conventional fertilizers with organic biomasses (CS2); planting and testing the abiotic and biotic resistance of selected varieties (CS3); increase the share of organic biomasses and enhance biological pest control in soils coping with lack of nutrients (CS4, CS5); mitigate soil nitrate pollution via the increase in water use efficiency and carbon sequestration for enhancing soil health (C6, CS7) and enhance biological pest control along with resistant varieties (CS8).

Finally, a part of the REGENA equations simulates the endogenous growth potential of each CS, via the equal participation of genders in R&D. The simulations indicate that the equal participation in R&D leads to higher productivity and knowledge accumulation via synergies. In addition, as research-derived knowledge from the study of local ecosystems constitutes a core income source for regenerative farmers, selected aspects of regenerative farming are discussed, such as the financial discounting of long-term sustainability, the business models of Open Innovation and Intellectual Property across the formation of regenerative farming conglomerates and trading alliances, as well as the disruption of the global agri-trade web from the localization of supply and value chains. Irrespective of its current limitations from its application only in the Mediterranean, REGENA is an original synthesis of several widely used production functions (see Appendix B) to promote academic discussion and business practices. Updated and more elaborate versions of REGENA with the introduction of Machine Learning (ML) elements for its universal application to any pedoclimatic condition and geography, are under development and will comprise the subject of a future work.