Ecology, Economy and Society–the INSEE Journal 6(1): 81-108, January 2023 RESEARCH PAPER Investigating the Health of a Rice Field Ecosystem Using Thermodynamic Extremal Principles Ayan Mondal, Nilanjan Das,** Rituparna Banerjee,*** Sunanda Batabyal,**** Sohini Gangopadhyay,***** Harisankar Ray,# Nivedita Biswasd,  Sudipto Mandal### Abstract: This study investigates the dynamic behaviour of a rice field ecosystem and aims to define its integral features using the stability concept of an ecological goal function. This function is based on the extremal principles of  Ecology and Environmental Modelling Laboratory, Department of Environmental Science, University of Burdwan, Golapbag-713104, Purba Bardhaman, West Bengal, India. mondalayan.zoo@gmail.com ** Ecology and Environmental Modelling Laboratory, Department of Environmental Science, University of Burdwan, Golapbag-713104, Purba Bardhaman, West Bengal, Indianilanjandas1995@gmail.com *** Ecology and Environmental Modelling Laboratory, Department of Environmental Science, University of Burdwan, Golapbag-713104, Purba Bardhaman, West Bengal, India. rituparna93banerjee@gmail.com **** Ecology and Environmental Modelling Laboratory, Department of Environmental Science, University of Burdwan, Golapbag-713104, Purba Bardhaman, West Bengal, India. sunanda.envs@gmail.com ***** Ecology and Environmental Modelling Laboratory, Department of Environmental Science, University of Burdwan, Golapbag-713104, Purba Bardhaman, West Bengal, India. aslgsohini@gmail.com # Ecology and Environmental Modelling Laboratory, Department of Environmental Science, University of Burdwan, Golapbag-713104, Purba Bardhaman, West Bengal, India. rayharisankar1996@gmail.com  Ecology and Environmental Modelling Laboratory, Department of Environmental Science, University of Burdwan, Golapbag-713104, Purba Bardhaman, West Bengal, India. niveditabiswas.1143@gmail.com ### Ecology and Environmental Modelling Laboratory, Department of Environmental Science, University of Burdwan, Golapbag-713104, Purba Bardhaman, West Bengal, India. sudipto11@gmail.com Copyright © Mondal, Das, Banerjee, Batabyal, Gangopadhyay, Ray, Biswas and Mandal 2023. Released under Creative Commons Attribution © NonCommercial 4.0 International licence (CC BY-NC 4.0) by the author. Published by Indian Society for Ecological Economics (INSEE), c/o Institute of Economic Growth, University Enclave, North Campus, Delhi 110007. ISSN: 2581–6152 (print); 2581–6101 (web). DOI: https://doi.org/10.37773/ees.v6i1.925 mailto:mondalayan.zoo@gmail.com mailto:nilanjandas1995@gmail.com mailto:rituparna93banerjee@gmail.com mailto:sunanda.envs@gmail.com mailto:aslgsohini@gmail.com mailto:rayharisankar1996@gmail.com mailto:niveditabiswas.1143@gmail.com mailto:sudipto11@gmail.com https://doi.org/10.37773/ees.v6i1.925 Ecology, Economy and Society–the INSEE Journal [82] thermodynamics, which assume that certain energetic processes of ecosystems— such as the rate of exergy destruction—are directed by the self-organizing informatics of the systems towards maxima or minima. In our study, we exploit the availability of substantially long time-series data relating to a rice field ecosystem to gain an evocative understanding of its growth trajectory in light of the thermodynamic principles. We accomplished this by constructing a model based on the STELLA 9.0 software and calculating the extremal values of growth rates (storage) and those of exergy destruction and entropy creation. The results showed that the values of both maximum dissipation and maximum exergy progressed apace with that of maximum storage till the maturation of rice and became stable thereafter, whereas maximum residence time and maximum specific dissipation values initially decreased before their asymptotic rise. A similar pattern was also observed for the maximum specific exergy. However, the maximum power dissipation curve followed a highly fluctuated course before becoming stable on the maturation of rice. Keywords: Far-from-equilibrium system; goal-function; rice field ecosystem; thermodynamic ecology 1. INTRODUCTION Ecosystems are complex, hierarchic, adaptive, and organized, as they are comprised of many components. These biotic and abiotic components interact to produce new emergent states that are impossible to predict accurately (Nielsen and Ulanowicz 2011). However, ecosystems exhibit certain common structural and functional characteristics that suggest they are driven by some directive principles that determine their future trajectories, such as the extremal principle of least action. Modern research in ecology aims to test the application of various goal functions in characterizing ecosystems’ structure and evolution (Mauersberger and Straškraba 1987; Jørgensen et al. 2007). Using goal functions in ecology simplifies ecological modelling and stability concepts by introducing extremal principles from which the “integral features” of the ecosystem can be derived (Mauersberger and Straškraba 1987; Jørgensen et al. 2007). According to Nielsen and Jørgensen (2013), there are three goal functions: biotic, network, and thermodynamic. Biotic goal functions are related to biodiversity, biomass, species number, richness, and evenness while network goal functions involve flow matrix, respiration, and import–export analysis (Ulanowicz 1986; Baird and Ulanowicz 1989; Christensen and Pauly 1992; Fath and Patten 1999). Thermodynamic goal functions, summarized by Yen et al. (2014), essentially seek to maximize or minimize a thermodynamic property of the macroscopic state of the system. These include a large set: “maximum exergy storage” (Jørgensen and Svirezhev 2004), “maximum energy storage” (Odum 1988), “maximum residence [83] Mondal, Das, Banerjee, Batabyal, Gangopadhyay, Ray, Biswas and Mandal time” (Fath, Patten, and Choi 2001), “maximum entropy production” (Dewar 2010; Kleidon 2010), “minimum entropy production” (Prigogine 1995; Martyushev and Seleznev 2006), “min-max principle of entropy production” (Aoki 2006), “maximum rate of gradient degradation” (Schneider and Kay 1994), “maximum power” (Lotka 1922; Brown, Marquet, and Taper 1993; DeLong 2008), “maximum empower” (Odum and Pinkerton 1955), “maximum ascendency” (Ulanowicz 1980, 2003), “minimum specific energy dissipation” (Margalef 1963), “constructal law of evolution” (Bejan and Lorente 2010), and “maximum rate of cycling” (Morowitz 1968). Several of these different quantities are, in fact, equivalent or complementary, as explained by several researchers (Jørgensen 1992, 1994; Patten 1995; Jørgensen and Nielsen 1998; Fath, Patten, and Choi 2001; Ray 2006; Yen et al. 2014). Limits and extremal principles are found to order many natural phenomena, such as animal sizes and the heights of mountain chains, and provide a rationale to order masses of data in an analytical framework. Indeed, the first such principle to explain ecological processes was formulated in 1859 by Darwin as the “survival of the fittest”—those ablest to harvest the available resources. The recognition of ecological systems as open systems powered by the sun and maintaining a dynamically stable state by exchanging energy and materials from their surroundings—like a thermodynamic engine—led Lotka to propose in the 1920s that ecosystems flourished by maximizing the rate of entropy production. Several related extremal principles have been formulated (Figure 1) towards developing the ecology theory since then. However, the examples of testing these in the field are still too few to warrant a clear direction. In this study, we present an application of four of these formulations to data from rice fields to test their relative or collective fruitfulness in explaining the growth trajectory of rice plants. These are based on the concepts of energy, exergy, total systems throughflow, and ascendency. 2. DATA AND APPLICATION OF THE EXTREMAL PRINCIPLE The experiment was carried out at two sites: The Crop Research and Seed Multiplication Farm (CRSMF) (Lat: 23°15'4.09"N, Lon: 87°50'41.05"E) for the ecosystem of domesticated rice fields and Bamchandaipur village (Lat: 23°13'35.95"N, Lon: 87°54'34.34"E) for the ecosystem of wild rice fields in Purba Bardhaman district, West Bengal, India (Figure 2). Ecology, Economy and Society–the INSEE Journal [84] Figure 1: A Chronological Snapshot of Different Propositions and Events Depicting the Evolution in the Concept of Goal Functions Through Time Source: Authors Figure 2: Study Sites of Domesticated (Left) and Wild Rice Field (Right) Ecosystems Source: Authors 2.1. Data Collection Field sampling was carried out for three consecutive years, from March 2016 to June 2019. The sampling was carried out at weekly intervals during the morning (7:00–10:00 IST) and evening (15:00–18:00 IST) hours throughout the study period. Accordingly, there were 170 sampling days during the entire study. There are four zones in the rice field ecosystem: benthic or littoral, limnetic, transitional, and terrestrial. Various forms of [85] Mondal, Das, Banerjee, Batabyal, Gangopadhyay, Ray, Biswas and Mandal sampling were used for the multiple taxa occupying each zone to record total biodiversity. Water and soil collection and sweeping were done through a randomized complete block design method to reduce sampling bias. The eight functional compartmental guilds were assigned based on trophic levels—green plants as producers, phytophagous as herbivores, predators as carnivores, omnivores, detritivores, and parasitoids. In some cases, where direct observation of food habits was not possible, a coffee- table experiment was performed to determine the food preferences, and the guild was assigned accordingly. All the collected and calculated data are provided in Appendix 1. Water-level data for wild rice fields were recorded at weekly intervals throughout the year and averaged to identify the monthly values (Figure 5). 2.2 The Extremal Principles Tested in this Study Four thermodynamic extremal principles were tested on the rice field data described in the previous section. These are emergy, exergy, total system throughflow, and ascendency; and are outlined here: 2.2.1. Energy Energy and exergy, the two target functions, are based on thermodynamics. Emergy, or embodied energy (Odum 1983), is a concept that assesses how much solar radiation is required to create a particular organism (biomass). The biomass, or its free energy, is multiplied by a factor determined by the amount of solar energy required to generate one unit of energy in the organism. The number of transfer and transformation stages a system has taken away from its input source is assumed to increase the quality of energy brought into it and its energy content. Because they are farther away from solar-energy inputs than photosynthesizing primary producers, upper trophic-level animals in ecosystems are thought to have a higher energy quality. 2.2.2. Exergy The amount of work a system can do when it is brought into equilibrium with its surroundings is thermodynamically characterized as exergy. Exergy attempts to account for both the free energy stored in biomass and the free energy stored in information. Exergy represents the quality of the ecosystem’s energy. The expression for exergy calculation proposed by Mejer and Jørgensen (1979) is (1) Ecology, Economy and Society–the INSEE Journal [86] Where R = gas constant, T = absolute temperature, ci = concentration in the ecosystem of the component, i. Index 0 = inorganic components of the considered chemical element and cieq = corresponding concentration of ith component at the thermodynamic equilibrium. Boltzmann’s constant (1.3803 × 10-23 J molecules-1 deg-1) equals kT lnI, where I is the pieces of information we have about the state of the system and k is Boltzmann’s constant (1.3803 × 10-23 J molecules-1 deg-1). This means that the exergy of one bit of information is equal to kT ln2. Information transfer from one system to another is frequently a nearly entropy-free energy transfer. As an ecosystem grows, it becomes increasingly successful in capturing and dissipating the exergy of incoming solar radiation (Schneider and Kay 1994). Schneider and Kay (1994) propose the dissipation of exergy as a target function. This exergy is employed to create and maintain organization and structure. Exergy accounts for the biomass and information stored in it; therefore, increased nutrient concentrations will likely result in more exergy. The ability to account for the system’s ability to use available resources would be beneficial. The concept of specific exergy is used to describe this ability, which is defined as (Equation 2): (2) Where β = quality factor, calculated based on the amount of information embedded in the genes, and X = biomass concentration of the ith species relative to the total biomass concentration. When the temperatures of the two systems vary, the entropy lost by one system does not equal the entropy acquired by the other. Still, the exergy lost by one system equals the exergy transferred and obtained by the other. In this case, exergy is more convenient than entropy. Exergy can be used to express the second rule of thermodynamics as follows (Equation 3): (3) This implies that exergy is always lost, that is, work is lost as heat that cannot be used to perform work. The entropy and exergy formulations of the second law of thermodynamics are, of course, interchangeable. 2.2.3 Total System Throughflow (TST) The first quantitative attempt to quantify ecosystem growth was Lotka’s “maximum power idea” (Lotka 1932, which defined power as work per unit of time. The concept evolved into a theory by Odum and Pinkerton (1955), [87] Mondal, Das, Banerjee, Batabyal, Gangopadhyay, Ray, Biswas and Mandal who stated that ecosystems act to maximize their power output. TST refers to the energy flow throughout the entire system (Equations 4 and 5). (4) (5) Where j=1, 2,…,n Although this concept was not explicitly related to energy quality or system organizational traits, it was indicated that systems that generated more power were better suited and favoured in evolutionary selection. 2.2.4 Ascendency Ulanowicz (1986) created the concept of ascendency to account for the throughflow of energy in an ecosystem (T) and network (A). Ascendency refers to the part of a system’s intercompartmental articulation that is dictated by the entire complexity of the collection of processes that corresponds to organized flows and is weighted by the TST (Equation 6). (6) Maximizing this aim function should describe the autocatalytic tendencies inherent in structuring emerging ecological networks. Ascendency takes into account the network’s size (T) and the information contained inside it. A is a massive variable; the size term T is the most important in most calculations (Equation 7). (7) As a result, the structural exergy should be firmly linked to A-T, whereas the exergy should be more strongly linked to the size term T but perhaps also to A because T is the most dominating term. Average mutual information is dimensionless and has a limited range of values—generally between 2.0 and 6.0. In non-negative real values, TST— which scales this information quantity—can be highly variable. As a result, the ascendency metric is dominated by throughflow, resulting in highly correlated findings for power and ascendency (Jorgenson 1992). 2.3. Model Development Ecology, Economy and Society–the INSEE Journal [88] An eight-compartment model was constructed (Table 1 and Figure 3) to evaluate the interrelationship among extremal principles and subsequent stability analysis. The components of the model are presented in Table 1. The model used these components as state variables to calculate the extremal principles. Table 1: The Eight Major Components (Producer, Herbivore, Carnivore, Detritus, Detritivore, Omnivore, and Parasitoid) with Examples Components Examples Components Examples Producer Detritivore Herbivore Omnivore Carnivore Parasitoid Detritus Nutrient Source: Authors The description of equations (Eq) and symbols are given in Appendices 1 and 2. Equation 8 describes the carnivore dynamics, with inflows primarily based on pred, detcarn, and pred1 and outflows primarily based on mortfish, refi, omni3, and para3. Herbivores and carnivores both had an impact on predation (Eq 8.1). Carnivores and detritivores both had an impact on the detcarn (Eq 8.2). Carnivores and omnivores both had an impact on pred1 (Eq 8.3). Only carnivores had an impact on both the mortfish (Eq 8.4) and refi (Eq 8.5). Carnivores and omnivores influenced the omni3 (Eq 8.6). Carnivores and para were both affected by para3 (Eq 8.7). Eq 9 describes the detritus dynamics, with inflows primarily based on mortfish, mz, mort, mortomni, and mortpara and outflows primarily based on outdet, detfed, and omni5. Carnivores had an impact on the mortfish (Eq 9.1). Carnivores and herbivores both had an impact on the mz (Eq 9.2). Herbivores and producers had a consequence on the mort (Eq 9.3). The [89] Mondal, Das, Banerjee, Batabyal, Gangopadhyay, Ray, Biswas and Mandal omnivores influenced the mortomni (Eq 9.4). Para had an impact on the mortpara (Eq 9.5). Detr and qv influenced the outlet (Eq 9.6). Detr and water level had an impact on the detfed (Eq 9.7). Omnivore and detr were both influences on the omni5 (Eq 9.8). Eq 10 can be used to define the detritivore dynamics. Detfed is the most common inflow, whereas detexcr, detcarn, omni4, para5, and rdetri are the most common outflows. Detr and water level had an impact on the detfed (Eq 10.1). Detritivore and water level both influenced the detexcr (Eq 10.2). Carnivores and detritivores both had an impact on the detcarn (Eq 10.3). There were detritivore and omnivore influences on the omni4 (Eq 10.4). Detritivore and para5 both had an impact on para5 (Eq 10.5). Detritivores affected the rdetri (Eq 10.6) Eq 11 describes the herbivore dynamics, with inflows mostly based on gr and outflows depending on pred, mz, rz, omni2, and para5. Herbivores and producers had an impact on the gr (Eq 11.1). Herbivores and carnivores both had an impact on predation (Eq 11.2). Herbivores and carnivores had an impact on the mz (Eq 11.3). Herbivores had an impact on the rz (Eq 11.4). Herbivore and omnivore interactions altered the omni2 (Eq 11.5). Herbivore and para were both impacted by para5 (Eq 11.6). Eq 12 can be used to define nutrient dynamics. Outflows are primarily based on up and outn while inflows are primarily based on input and detexcr. Nutin, qv, and the water level all had an impact on the input (Eq 12.1). Detritivores and the water level both influenced the detexcr (Eq 12.2). Nutr, producers, and the water level all had an impact on the upt (Eq 12.3). Nutr and qv had an impact on the outn (Eq 12.4). Eq 13 can be used to define the omnivore dynamics; outflows are primarily based on mortomni, pred1, para4, and romni. In contrast, inflows are primarily based on omni1, omni2, omni3, omni4, and omni5. Producers and omnivores had an impact on the omni1 (Eq 13.1). Herbivore and omnivore interactions altered the omni2 (Eq 13.2). Carnivores and omnivores influenced the omni3 (Eq 13.3). There were detritivore and omnivore influences on the omni4 (Eq 13.4). Detr and omnivore had an impact on the omni5 (Eq 13.5). The omnivore had an impact on the mortomni (Eq 13.6). Carnivores and omnivores both had an impact on pred1 (Eq 13.7). Para and omnivores had an influence on para4 (Eq 13.8). The omnivorous had an impact on the romni (Eq 13.9). Eq 14 can be used to define parasite dynamics. Outflows depend primarily on mortpara and rpara while inflows are primarily based on para1, para2, para3, para4, and para5. Para and producer had an impact on para1 (Eq 14.1). Ecology, Economy and Society–the INSEE Journal [90] Para and herbivore had an effect on para2 (Eq 14.2). Para and carnivore had an impact on para3 (Eq 14.3). Para and omnivore had an impact on para4 (Eq 14.4). Para and detritivore affected para5 (Eq 14.5). Para impacted the mortpara and rpara (Eq 14.6, 14.7). Figure 3: The Calculation Framework of Extremal Principles Values in STELLA 9.0 Source: Authors Eq 15 can be used to define the producer dynamics. Upt and uptc are the most common inflows whereas gr, mort, out ph, omni1, para1, and rpro are the most common outflows. Nutr, producers, and the water level all had an impact on the upt (Eq 15.1). Up had an impact on the uptc (Eq 15.2). Producers and herbivores both had an impact on the gr (Eq 15.3). Producers and herbivores both had an impact on the mort (Eq 15.4). qv and producers influenced the out ph (Eq 15.5). Omnivores and producers had an impact on the omni1 (Eq 15.6). Para and producers had an impact on para1 (Eq 15.7). Producers had an impact on the rpro (Eq 15.8). [91] Mondal, Das, Banerjee, Batabyal, Gangopadhyay, Ray, Biswas and Mandal The sums of rdetri, refi, romni, rpara, rpro, and rz was utilized to determine dissipation in Eq 16. The exergy dynamics can be defined using Eq 17, which is the sum of all the producers, herbivores, omnivores, carnivores, deter and detritivores, and para. Where the values of and . When the TST was divided by TSS, Eq 18 was used to calculate the residence time. When the dissipation was divided by throughflow-derived storage (TSS), Eq 19 was utilized to define the specific dissipation. When the exergy was divided by TSS, Eq 20 was utilized to define the specific exergy. Eq 21 can be used to calculate the TSS, which is the sum of all of the carnivore, detritivore, herbivore, omnivore, para, and producer populations. The TST is defined by Eq 22 as the sum of detcarn, detexcr, detfed, gr, mort, mortfish, mortomni, mortpara, mz, omni1, omni2, omni3, omni4, omni5, para1, para2, para3, para4, para5, pred, pred1, and upt (Refer Appendix 1). 3. RESULT AND DISCUSSION 3.1. Integration of Goal Function Theoretical approaches have dominated the investigation of the thermodynamic extremization principle. Consistencies between energy storage and dissipation showed that existing thermodynamic extremization principles might be unified. Hence, interaction between the two categories (energy storage and dissipation) is possible. Based on the aforementioned theories, the extremal principles could be integrated as shown in Figure 5. Maximal energy storage implies maximum energy dissipation (metabolic rate). Because living species always dissipate energy, an ecological system can improve energy dissipation by increasing energy storage (biomass) until the energy storage reaches a maximum (that is, the system becomes resource-limited). By combining maximum energy dissipation and maximum energy storage, all thermodynamic extremization concepts are compatible. Numerous thermodynamic extremization principles have been proposed and applied to ecological issues. Many of the energy quantities have been linked (Figure 4) to ecological quantities including biomass, food-web complexity (e.g., link density), growth rates, life-cycle duration, and community stability, all of which have been shown to follow predictable trajectories during ecosystem evolution (Odum 1969; Loreau 1998). The relevant literature is scattered and distinguishing between possible extremization principles has received much attention. Despite their apparent differences, multiple thermodynamic extremization principles may Ecology, Economy and Society–the INSEE Journal [92] be boiled down to two main themes: energy storage and dissipation (Fath, Patten, and Choi 2001). Various energy storage and energy dissipation principles are discussed in their paper. Figure 4: Mathematical Integration of Extremal Principles Source: Authors Note: All acronyms have been elaborated in paragraph 2.2 According to energy-dissipation principles, natural systems utilize energy at extreme rates. Maximum energy dissipation indicates high throughput whereas minimum energy dissipation indicates efficient energy utilization (that is, organisms using energy as fast as possible). Maximum energy dissipation does not always imply poor use of other resources—such as water or nutrients—as efficient use of these resources is sometimes required for high energy dissipation. In this study, two scenarios are considered: maximum entropy creation and maximum power. According to the principle of maximal entropy production (MEP), all non-equilibrium thermodynamic systems produce entropy as quickly as feasible, returning the system to a state of maximum entropy as soon as possible (Martyushev and Seleznev 2006). Several attempts have been made to derive generic proof for far-from-equilibrium systems (Dewar 2003, 2005), but none have been successful (Grinstein and Linsker 2007). The rate of “useful” energy usage (e.g., conversion to biomass or reproduction) (Jorgensen and Svirezhev 2004), the rate of “emergy” use (Odum 1996, Hall 2004, Tilley 2004), and “fitness” or rate of reproduction have all been linked to power (Brown, Marquet, and Taper 1993). Loreau (1998) proposes that adequate definitions of power should be based on ecological processes because each of these definitions of power only covers one component of energy consumption (e.g., demography, resource use). The exergy principle has been provided as a tentative thermodynamic law that might be used as a hypothesis in the present research. Ecosystems have [93] Mondal, Das, Banerjee, Batabyal, Gangopadhyay, Ray, Biswas and Mandal a lot of different paths and much exergy flowing through them. Increases in system features such as distance from thermodynamic ground, structure, heterogeneity, organization, gradients, and energy quality result from incremental exergy increases that accompany rising path lengths. As throughflows increase with the increase of path length, this feature becomes more aligned with exergy and emergy. ASC (ascendency) in ecosystem networks leads to the maximum of these values because TST corresponds to power output, which is often a substantial component of ascendency. As a result, the four extreme principles of exergy maximization, emergy, power, and ascendency are linked by a single process: exergy propagation in ecological networks. According to our findings, exergy, emergy, power, and ascendency are all found in the structure and microscopic dynamics of energy, matter flows, and storages in ecosystems. 3.2. Health of Rice Field Ecosystem in Relation to the Extremal Principles The present study showed that nutrition and water level are the most important and main regulatory parameters for wild and domesticated rice field ecosystems. The nutrient content and water level in domesticated and wild rice fields were different. The nutrient content of a domesticated rice field was 40 mgCg-1 but only 18 mgCg-1 in a wild rice field environment. Water concentration in domesticated rice field systems varies between 2.8–12 cm, but in wild rice field systems, it varies between 10–70 cm due to higher rainfall during monsoon seasons. Figure 5 depicts the water level in the domesticated and wild rice field ecosystems. Figures 6 and 7 describe the conditions of extremal principles in the domesticated and wild rice field ecosystems, respectively. Zehe et al. (2010) studied the maximum energy dissipation and the connection between water flow and soil structure. They concluded that biological soil structures are crucial for infiltration and soil water flow. Hence, the burrows created by the worms allow for a more efficient redistribution of water within the soil, which implies a more efficient dissipation of free energy. In the present comparison, the maximum dissipation values for the domesticated rice field ecosystem touch 175 KJ near around 100 days of rice cultivation and then decrease with time, whereas, in the wild rice ecosystem, the value is nearly 16 KJ around 120 days of cultivation and remain stable throughout the study period. Hence, it could be said that the water flow of the domesticated rice fields was controlled and infiltration of the water-forming network within the soil Ecology, Economy and Society–the INSEE Journal [94] structure is temporary with high dissipative energy—implying higher entropy production. However, no such mechanism occurred in the wild rice ecosystem. The field was a natural wetland system and was always inundated by water flow depending upon rainfall. Although the values of maximum dissipation were lower than domesticated fields, the value (17.5 KJ) reached an asymptote beyond the shattering of rice seeds, implying lower entropy in the system. Sheng et al. (2020) add that the shattering of rice seeds is an evolutionarily beneficial phenomenon for wild rice varieties. This trait is beneficial for dispersal, preventing the seeds from drying and losing seed dormancy. Figure 5: Temporal Variation of Water Levels in Domesticated (Annual Plant) and Wild Rice (Perennial Plant) Field Ecosystems Source: Authors In the present study, the minimum specific dissipation of the domesticated rice field ecosystem was constant (0.020) during rice cultivation. However, the values are a bit higher for wild rice fields (0.020–0.040), meaning the values were greater till the panicle initiation stage of rice and behaved the same as domesticated fields after the development of reproductive structures. Ludovisi, Pandolfi, and Taticchi (2005) propound that specific dissipation is a good indicator of ecosystem health. Moreover, the higher the specific dissipation of a system, the lower the capacity of a system to convert the incoming entropy energy into internal organization. The nutrient input of the wild rice fields was non-controlled, resulting in differential resource utilization by the rice plants until the crop reached its sexual maturity. After the panicle initiation period to shattering, the system behaved quite self-organized. However, in the domesticated fields, the nutrient input was controlled throughout the study. Hence, all the rice plants showed high productivity and greater self-organization compared [95] Mondal, Das, Banerjee, Batabyal, Gangopadhyay, Ray, Biswas and Mandal with wild rice throughout the period, from germination to harvest. Despite having higher entropy in the system, the rice plants managed the nutrients efficiently in the domesticated rice fields. Hovelius (1997) compared the exergy and energy values for salix, winter wheat, and winter rape cultivation in Sweden. She reports that the exergy values were always greater than the energy values depicting the quality of energy utilized by the crops. In the domesticated rice fields, the values ranged between 350,000–400,000 KJ, which was 10 times higher than the wild rice fields throughout the study, confirming the better energy quality in the system. It also showed better resource utilization and nutrient accumulation in the biomass of rice seeds in the domesticated rice fields. The values in the wild rice fields increased like a growth curve and reached an asymptote after shattering, implying the gradual accumulation of nutrients throughout the growth period. However, the values increased till crop maturity in the domesticated rice field and then decreased after harvest, that is, the post-harvest situation of rice straws in the field. The present findings are in agreement with Hoang and Alauddin (2011). Jekayinfa et al. (2022) observed that the use of machinery in the processing and production of soybean crops fetches higher exergy values. In the domesticated rice fields, the labour cost, tractors for irrigation, use of fertilizers and pesticides, and weeding resulted in higher cumulative exergy values than in the wild rice fields. Similar results were obtained by Yıldızhan (2017) during his study on wheat production in Turkey. The minimum specific exergy was almost identical for wild and domesticated rice field ecosystems (40 KJ kg-1 oC), showing no change in the specific exergy at each phenological stage from germination to shattering in the wild rice fields. However, variation was observed for domesticated rice fields. Hence, minimal useful work was observed for domesticated rice fields. The wild rice field ecosystem possesses more faunal biodiversity than the domesticated rice fields, resulting in a complex food web and more ecological interactions among the organisms. Hence, the specific exergy change between the two trophic levels is minimum and uniform. However, the man-made or domesticated system is destroyed after a certain time or harvest. Also, irrigation destroys the soil structure, altering the existing biodiversity and specific exergy. The average maximum residence time in the domesticated rice fields was (0.6), while in the wild rice fields, it was (0.35)—showing higher throughput-derived storage in the previous field than the latter with the same TST values. Schramski et al. (2015) advocate that the average Ecology, Economy and Society–the INSEE Journal [96] residence time of an ecological system is dependent upon the body size, temperature, and structural organization of the system. With the increase of species number in the wild rice fields, the TST, maximum power, or cycling of the nutrients and energy transfer was low compared to domesticated rice fields. The maximum storage (TSS) was almost 10 times higher in the domesticated fields. Hence, the ratio between TSS and TST appeared to be small for the wild rice system. Figure 6: Temporal Variation of Seven Different Extremal Principles (Dissipation, Exergy, Residence Time, Specific Dissipation, Specific Exergy, TSS-storage, TST- power) in the Domesticated Rice Field Ecosystem Source: Authors [97] Mondal, Das, Banerjee, Batabyal, Gangopadhyay, Ray, Biswas and Mandal Figure 7: Temporal Variation of Seven Different Extremal Principles (Dissipation, Exergy, Residence Time, Specific Dissipation, Specific Exergy, TSS-storage, TST- power) in the Wild Rice Field Ecosystem Source: Authors 4. CONCLUSIONS The present research shows that current extremization theories could be merged to exhibit a pattern of significant correlation. This integration of extremization ideas ought to make using them easier and enable a change in emphasis toward empirical investigations. It could be concluded that maximum dissipation and maximum exergy progressed apace with that of maximum storage till the maturation of rice and became stable thereafter. In contrast, maximum residence time and maximum specific dissipation values initially decreased before their asymptotic rise. A similar pattern was also observed for maximum specific exergy. However, the maximum power dissipation curve followed a highly fluctuated course before becoming stable on the maturation of rice. Although they are uncommon, empirical investigations of thermodynamic extremization principles are crucial to our comprehension and use of these strategies. We used a dynamic ecosystem modelling technique in wild and domesticated rice fields to see how they reacted to various environmental conditions. This result indicates that wild rice fields are healthier and more stable than domesticated ones. Our approach might be modified to forecast a wider variety of ecological patterns that could help determine how applicable thermodynamic concepts are to ecology. Exciting areas of study Ecology, Economy and Society–the INSEE Journal [98] include the development of quantitative theories and the empirical verification of these hypotheses, which should make it easier to apply thermodynamic concepts to common ecological issues. ACKNOWLEDGEMENTS The authors would like to thank the funding agency, SERB, DST, Government of India, New Delhi, (Project No. EMR/2016/002618) for conducting the research work. The authors also acknowledge the agricultural scientists of the Department of Agriculture, Government of West Bengal, and the officials of the Crop Research and Seed Multiplication Farm, The University of Burdwan, for extending their help and valuable suggestions for the research. The authors declare no conflict of interest. REFERENCES Aoki, Ichiro. 2006. “Min-Max Principle of Entropy Production with Time in Aquatic Communities.” Ecological Complexity 3 (1): 56–63. https://doi.org/10.1016/j.ecocom.2005.05.006 Baird, Daniel, and Robert E. Ulanowicz. 1989. “The Seasonal Dynamics of the Chesapeake Bay Ecosystem.” Ecological Monographs 59 (4): 329–364. https://doi.org/10.2307/1943071 Bejan, Adrian, and Sylvie Lorente. 2010. “The Constructal Law of Design and Evolution in Nature.” Philosophical Transactions of the Royal Society B: Biological Sciences 365 (1545): 1335–1347. https://doi.org/10.1098/rstb.2009.0302 Brown, James H, Pablo A Marquet, and Mark L Taper. 1993. “Evolution of Body Size: Consequences of an Energetic Definition of Fitness.” The American Naturalist 142 (4): 573–584. https://doi.org/10.1086/285558 DeLong, John P. 2008. “The Maximum Power Principle Predicts the Outcomes of Two‐species Competition Experiments.” Oikos 117 (9): 1329–1336. https://doi.org/10.1111/j.0030-1299.2008.16832.x Dewar, Roderick C. 2003. “Information Theory Explanation of the Fluctuation Theorem, Maximum Entropy Production and Self-Organized Criticality in Non- Equilibrium Stationary States.” Journal of Physics A: Mathematical and General 36 (3): 631. https://doi.org/10.1088/0305-4470/36/3/303 ———2005. “Maximum Entropy Production and the Fluctuation Theorem.” Journal of Physics A: Mathematical and General 38: 371–381. https://doi.org/10.1088/0305-4470/38/21/L01 ———2010. “Maximum Entropy Production and Plant Optimization Theories.” Philosophical Transactions of the Royal Society B: Biological Sciences 365 (1545): 1429–1435. https://doi.org/10.1098/rstb.2009.0293 https://doi.org/10.1016/j.ecocom.2005.05.006 https://doi.org/10.2307/1943071 https://doi.org/10.1098/rstb.2009.0302 https://doi.org/10.1086/285558 https://doi.org/10.1111/j.0030-1299.2008.16832.x https://doi.org/10.1088/0305-4470/36/3/303 https://doi.org/10.1088/0305-4470/38/21/L01 https://doi.org/10.1098/rstb.2009.0293 [99] Mondal, Das, Banerjee, Batabyal, Gangopadhyay, Ray, Biswas and Mandal Fath, Brian D, and Bernard C Patten. 1999. “Review of the Foundations of Network Environ Analysis.” Ecosystems 2 (2): 167–179. https://doi.org/10.1007/s100219900067 Fath, Brian D, Bernard C Patten, and Jae S Choi. 2001. “Complementarity of Ecological Goal Functions.” Journal of Theoretical Biology 208 (4): 493–506. https://doi.org/10.1006/jtbi.2000.2234 Grinstein, G, and R Linsker. 2007. “Comments on a Derivation and Application of the ‘Maximum Entropy Production’ Principle.” Journal of Physics A: Mathematical and Theoretical 40 (31): 9717. https://doi.org/10.1088/1751-8113/40/31/N01 Hall, Charles AS. 2004. “The Continuing Importance of Maximum Power.” Ecological Modelling 178 (1–2): 107–113. https://doi.org/10.1016/j.ecolmodel.2004.03.003 Hoang, Viet‐Ngu, and Mohammad Alauddin. 2011. “Analysis of Agricultural Sustainability: A Review of Exergy Methodologies and their Application in OECD Countries.” International Journal of Energy Research 35 (6): 459–476. https://doi.org/10.1002/er.1713. Hovelius, Karolina. 1997. Energy-, Exergy- and Emergy Analysis of Biomass Production. Uppsala: Swedish University of Agricultural Engineering. Jekayinfa, Simeon O, Kehinde M Adeleke, Clement A Ogunlade, BF Sasanya, and Nurudeen A Azeez. 2022. “Energy and Exergy Analysis of Soybean Production and Processing System.” Cleaner Engineering and Technology 10: 100540. https://doi.org/10.1016/j.clet.2022.100540. Jørgensen, Christian, Katja Enberg, Erin S Dunlop, Robert Arlinghaus, David S Boukal, Keith Brander, Bruno Ernande et al. 2007. “Ecology: Managing Evolving Fish Stocks.” Science 318 (5854): 1247–1248. https://doi.org/10.1126/science.1148089 Jørgensen, Sven Eric, and Søren N Nielsen. 1998. “Thermodynamic Orientors: Exergy as a Goal Function in Ecological Modeling and as an Ecological Indicator for the Description of Ecosystem Development.” In Eco Targets, Goal Functions, and Orientors, 63–86. Berlin, Heidelberg: Springer. https://doi.org/10.1007/978-3-642- 58769-6_5 Jørgensen, Sven Eric, and Yuri M Svirezhev. 2004. “Teleology and Extreme Principles: A Tentative Fourth Law of Thermodynamics.” Towards a Thermodynamic Theory for Ecological Systems. Oxford, UK: Elsevier Ltd: 301–322. https://doi.org/10.1016/B978-008044166-5/50012-4 Jørgensen, Sven Eric. 1992. Integration of Ecosystem Theories: A Pattern. Netherlands: Springer. https://doi.org/10.1007/978-94-011-2682-3 ———1994. “Review and Comparison of Goal Functions in System Ecology.” Vie et Milieu 44 (1): 11–20. ———2010. “Non-equilibrium Thermodynamics, Maximum Entropy Production and Earth-System Evolution.” Philosophical Transactions of the Royal Society A: https://doi.org/10.1007/s100219900067 https://doi.org/10.1006/jtbi.2000.2234 https://doi.org/10.1088/1751-8113/40/31/N01 https://doi.org/10.1016/j.ecolmodel.2004.03.003 https://doi.org/10.1016/j.clet.2022.100540 https://doi.org/10.1126/science.1148089 https://doi.org/10.1007/978-3-642-58769-6_5 https://doi.org/10.1007/978-3-642-58769-6_5 https://doi.org/10.1016/B978-008044166-5/50012-4 https://doi.org/10.1007/978-94-011-2682-3 Ecology, Economy and Society–the INSEE Journal [100] Mathematical, Physical and Engineering Sciences 368 (1910): 181–196. https://doi.org/10.1098/rsta.2009.0188 Loreau, Michel. 1998. “Ecosystem Development Explained by Competition Within and Between Material Cycles.” Proceedings of the Royal Society of London. Series B: Biological Sciences 265 (1390): 33–38. https://doi.org/10.1098/rspb.1998.0260 Lotka, Alfred James. 1922. “Contribution to the Energetics of Evolution.” Proceedings of the National Academy of Sciences 8 (6): 147–151. ———1925. Elements of Physical Biology. Williams & Wilkins. https://doi.org/10.1073/pnas.8.6.147 Ludovisi, Alessandro, Piera Pandolfi, and Maria Illuminata Taticchi. 2005. “The Strategy of Ecosystem Development: Specific Dissipation as an Indicator of Ecosystem Maturity.” Journal of Theoretical Biology 235 (1): 33–43. https://doi.org/10.1016/j.jtbi.2004.12.017 Margalef, Ramon. 1963. “On Certain Unifying Principles in Ecology.” The American Naturalist 97 (897): 357–374. https://doi.org/10.1086/282286 Martyushev, Leonid M, and Vladimir D Seleznev. 2006. “Maximum Entropy Production Principle in Physics, Chemistry and Biology.” Physics Reports 426 (1): 1– 45. https://doi.org/10.1016/j.physrep.2005.12.001 Mauersberger, Peter, and Milan Straškraba. 1987. “Two Approaches to Generalized Ecosystem Modelling: Thermodynamic and Cybernetic.” Ecological Modelling 39 (1– 2): 161–169. https://doi.org/10.1016/0304-3800(87)90018-4 Mejer, Henning, and Sven Erik Jørgensen. 1979. “Exergy and Ecological Buffer Capacity.” In Proceedings of the Conference on Ecological Modelling, Copenhagen, Denmark, 28 August–2 September 1978, 829–846. https://doi.org/10.1016/B978-0-08-023443- 4.50042-7. Morowitz, Harold J. 1968. Energy Flow in Biology; Biological Organization as a Problem in Thermal Physics. New York: Academic Press. Nielsen, Søren Nors, and Robert E Ulanowicz. 2011. “Ontic Openness: An Absolute Necessity For All Developmental Processes.” Ecological Modelling 222 (16): 2908–2912. https://doi.org/10.1016/j.ecolmodel.2011.05.012 Nielsen, Søren Nors, and Sven Eric Jørgensen. 2013. “Goal Functions, Orientors and Indicators (GoFOrIt’s) in Ecology. Application and Functional Aspects – Strengths and Weaknesses.” Ecological Indicators 28: 31–47. https://doi.org/10.1016/j.ecolind.2012.12.015 Odum, Eugene P. 1969. “The Strategy of Ecosystem Development: An Understanding of Ecological Succession Provides a Basis for Resolving Man’s Conflict with Nature.” Science 164 (3877): 262–270. https://doi.org/10.1126/science.164.3877.262 Odum, Howard T. 1983. Systems Ecology: An Introduction. Wiley. ———1988. “Self-organization, Transformity, and Information.” Science 242 (4882): 1132–1139. https://doi.org/10.1126/science.242.4882.1132 https://doi.org/10.1098/rsta.2009.0188 https://doi.org/10.1098/rspb.1998.0260 https://doi.org/10.1073/pnas.8.6.147 https://doi.org/10.1016/j.jtbi.2004.12.017 https://doi.org/10.1086/282286 https://doi.org/10.1016/j.physrep.2005.12.001 https://doi.org/10.1016/0304-3800(87)90018-4 https://doi.org/10.1016/j.ecolmodel.2011.05.012 https://doi.org/10.1016/j.ecolind.2012.12.015 https://doi.org/10.1126/science.164.3877.262 https://doi.org/10.1126/science.242.4882.1132 [101] Mondal, Das, Banerjee, Batabyal, Gangopadhyay, Ray, Biswas and Mandal ———1996. Environmental Accounting: Emergy and Environmental Decision Making. Wiley. ———2002. “Explanations of Ecological Relationships with Energy Systems Concepts.” Ecological Modelling 158 (3): 201–211. https://doi.org/10.1016/S0304- 3800(02)00232-6 Odum, Howard T, and Richard C Pinkerton. 1955. “Time’s Speed Regulator: The Optimum Efficiency for Maximum Power Output in Physical and Biological Systems.” American Scientist 43 (2): 331–343. Patten, Bernard C. 1995. “Network Integration of Ecological Extremal Principles: Exergy, Emergy, Power, Ascendency, and Indirect Effects.” Ecological modelling 79 (1–3): 75–84. https://doi.org/10.1016/0304-3800(94)00037-I. Prigogine, Ilya. 1995. Thermodynamics of Irreversible Processes. New York: Wiley. Ray, Santanu. 2006. “Extremal Principles with Special Emphasis on Exergy and Ascendency – The Modern Approach in Theoretical Ecology.” Journal of Biological Systems 14 (02): 255–273. https://doi.org/10.1142/S0218339006001817 Schneider, Eric D, and James J Kay. 1994. “Life as a Manifestation of the Second Law of Thermodynamics.” Mathematical and Computer Modelling 19 (6–8): 25–48. https://doi.org/10.1016/0895-7177(94)90188-0 Schramski, John R, Anthony I Dell, John M Grady, Richard M Sibly, and James H Brown. 2015. “Metabolic Theory Predicts Whole-ecosystem Properties.” Proceedings of the National Academy of Sciences 112 (8): 2617–2622. https://doi.org/10.1073/pnas.1423502112 Sheng, Xiabing, Zhizhong Sun, Xuefeng Wang, Yanning Tan, Dong Yu, Guilong Yuan, Dingyang Yuan, and Meijuan Duan. 2020. “Improvement of the Rice “Easy- to-Shatter” Trait via CRISPR/Cas9-mediated Mutagenesis of the qSH1 Gene.” Frontiers in Plant Science 11: 619. https://doi.org/10.3389/fpls.2020.00619 Tilley, David Rogers. 2004. “Howard T Odum’s Contribution to the Laws of Energy.” Ecological Modelling 178 (1–2): 121–125. https://doi.org/10.1016/j.ecolmodel.2003.12.032 Ulanowicz, Robert E. 1980. “An Hypothesis on the Development of Natural Communities.” Journal of Theoretical Biology 85 (2): 223–245. https://doi.org/10.1016/0022-5193(80)90019-3 ——— 1986. Growth and Development: Ecosystems Phenomenology. New York: Springer- Verlag, NY. ———1995. “Ecosystem Integrity: A Causal Necessity.” In Perspectives on Ecological Integrity, 77–87. Dordrecht: Springer. ———1999. “Life after Newton: An Ecological Metaphysic.” BioSystems 50 (2): 127–142. https://doi.org/10.1016/S0303-2647(98)00097-5 ———2003. “Some Steps Toward a Central Theory of Ecosystem Dynamics.” Computational Biology and Chemistry 27 (6): 523–530. https://doi.org/10.1016/S1476-9271(03)00050-1 https://doi.org/10.1016/S0304-3800(02)00232-6 https://doi.org/10.1016/S0304-3800(02)00232-6 https://doi.org/10.1142/S0218339006001817 https://doi.org/10.1016/0895-7177(94)90188-0 https://doi.org/10.1073/pnas.1423502112 https://doi.org/10.3389/fpls.2020.00619 https://doi.org/10.1016/j.ecolmodel.2003.12.032 https://doi.org/10.1016/0022-5193(80)90019-3 https://doi.org/10.1016/S0303-2647(98)00097-5 https://doi.org/10.1016/S1476-9271(03)00050-1 Ecology, Economy and Society–the INSEE Journal [102] ———2012. Growth and Development: Ecosystems Phenomenology. New York: Springer Science & Business Media. Ulanowicz, Robert E, and James J Kay. 1991. “A Package for the Analysis of Ecosystem Flow Networks.” Environmental Software 6 (3): 131–142. https://doi.org/10.1016/0266-9838(91)90024-K Volvenko, IV. 2012. “Extremal Principles and Goal Functions of Biocenotic Systems.” Biophysics 57 (3): 350–362. https://doi.org/10.1134/S0006350912030219 Yen, Jian DL, David M Paganin, James R Thomson, and Ralph Mac Nally. 2014. “Thermodynamic Extremization Principles and their Relevance to Ecology.” Austral Ecology 39 (6): 619–632. https://doi.org/10.1111/aec.12130 Yıldızhan, Hasan. 2019. “Energy and Exergy Utilization of Some Agricultural Crops in Turkey.” Thermal Science 23 (2) Part A: 813–822. Zehe, Blume and Bloschl. 2010. “The principle of ‘maximum energy dissipation’: a novel thermodynamic perspective on rapid water flow in connected soil structures”. Philosophical Transactions of the Royal Society B: Biological Sciences 365(1545): 1377-1386. https://royalsocietypublishing.org/doi/epdf/10.1098/rstb.2009.0308 Zhou, Jizhong, Shijun Ma, and George W Hinman. 1996. “Ecological Exergy Analysis: A New Method for Ecological Energetics Research.” Ecological Modelling 84 (1–3): 291–303. https://doi.org/10.1016/0304-3800(94)00135-9 https://doi.org/10.1016/0266-9838(91)90024-K https://doi.org/10.1134/S0006350912030219 https://doi.org/10.1111/aec.12130 https://royalsocietypublishing.org/doi/epdf/10.1098/rstb.2009.0308 https://doi.org/10.1016/0304-3800(94)00135-9 [103] Mondal, Das, Banerjee, Batabyal, Gangopadhyay, Ray, Biswas and Mandal APPENDIX 1: Symbols and Initial Inputs Used in the Construction of the Model 1 Symbol Explanation Values and Equations pred Predation rate of carnivore upon herbivore IF (herbivore>3) THEN (0.1*carnivore*(herbivore-0.1)/(1+herbivore)) ELSE (0) detcarn Predation rate of carnivore upon detritivore 0.33*carnivore*0.17*detritivore/(detritivore+1) pred1 Predation rate of carnivore upon omnivore 0.1*carnivore*(omnivore-0.1)/(0.5+omnivore) mortfish Mortality rate of carnivore 0.02*carnivore refi Respiratory rate of carnivore 0.06*carnivore omni3 Predation rate of omnivore upon carnivore 0.04*(carnivore-0.1)*(0.2*omnivore)/(carnivore+2) para3 Parasitization rate of parasite/parasitoid upon carnivore carnivore*para*0.00001 mz Mortality rate of herbivore 0.2*herbivore+0.04*carnivore*(herbivore-0.1)/(1+herbivore) mort Mortality rate of producer 0.25*producer+0.17*(producer-0.1)*herbivore/(producer+2) mortomni Mortality rate of omnivore 0.034245*omnivore mortpara Mortality rate of parasite/parasitoid para*0.03 outdet Outflow rate of detritus detr*(qv+0.9) detfed Feeding rate of detritivore upon detritus (0.1*detr)++((IF (waterlevel<10) THEN (waterlevel*detr/3) ELSE (detr/3))) omni5 Feeding rate of omnivore upon detritus omnivore*detr*0.0176 detexcr Excretion rate of detritivore (0.1*detritivore)++((IF (waterlevel<10) THEN (waterlevel*detritivore/3) ELSE (detritivore/3))) omni4 Feeding rate of omnivore upon detritivore 0.04*(detritivore-0.1)*(0.1*omnivore)/(detritivore+1) para5 Parasitization rate of parasite/Parasitoid upon detritivore detritivore*para*0.00001 rdetri Respiratory rate of detritivore 0.09*detritivore gr Grazing rate of herbivore upon producer IF (producer>30) THEN (0.4*herbivore*(producer-1)/(2+producer)) ELSE (1) rz Respiratory rate of herbivore 0.125*herbivore Ecology, Economy and Society–the INSEE Journal [104] omni2 Predation rate of omnivore upon herbivore 0.04*(herbivore-0.1)*(0.2*omnivore)/(herbivore+1) para2 Parasitization rate of parasite/parasitoid upon herbivore herbivore*para*0.00001 input Nutrient input into system from out- source (nutin*qv)++((IF (waterlevel<10) THEN (waterlevel*nutin/3) ELSE (nutin/3))) upt Nutrient uptake rate by producer (IF (nutr>0.2) THEN (1.0*producer*(nutr-1)/(5+nutr)) ELSE (0))+((IF (waterlevel<10) THEN (waterlevel*nutr/3) ELSE (nutr/3))) outn Nutrient outflow rate from system qv*nutr omni1 Grazing rate of omnivore upon producer 0.04*(producer-0.1)*(0.2*omnivore)/(producer+2) para4 Parasitization rate of parasite/parasitoid upon omnivore para*omnivore*0.00001 romni Respiratory rate of omnivore 0.02*omnivore para1 Parasitization rate of parasite/parasitoid upon producer para*producer*0.00001 rpara Respiratory rate of parasite/parasitoid 0.001*para out_ph Outflow of producer from system producer+qv+0.1*producer rpro Respiratory rate of producer 0.02*producer qv Outflow constant 0.05 nutin Nutrient input into the system from out-source 40 producer Autotrops in the system 35 para Parasite/parasitoid in the system 1 omnivore Omnivore in the system 1.5 nutr Nutrient in the system 1.6 herbivore Herbivore in the system 10 detritivore Detritivore in the system 0.6 detr Detritus in the system 16 carnivore Carnivore in the system 1 [105] Mondal, Das, Banerjee, Batabyal, Gangopadhyay, Ray, Biswas and Mandal APPENDIX 2: Equations Used in the Construction of the Model 2 Equations No 8 Inflows 8.1 8.2 8.3 Outflows 8.4 8.5 8.6 8.7 9 Inflows 9.1 9.2 9.3 9.4 9.5 Outflows 9.6 9.7 9.8 10 Inflows 10.1 Ecology, Economy and Society–the INSEE Journal [106] Equations No 10.2 Outflows 10.3 10.4 10.5 10.6 10.7 (11) 11 Inflows 11.1 Outflows 11.2 11.3 11.4 11.5 11.6 12 Inflows 12.1 12.2 Outflows [107] Mondal, Das, Banerjee, Batabyal, Gangopadhyay, Ray, Biswas and Mandal Equations No 12.3 12.4 13 Inflows 13.1 13.2 13.3 13.4 13.5 Outflows 13.6 13.7 13.8 13.9 14 Inflows 14.1 14.2 14.3 14.4 14.5 Outflows 14.6 14.7 Ecology, Economy and Society–the INSEE Journal [108] Equations No 15 Inflows 15.1 15.2 Outflows 15.3 15.4 15.5 15.6 15.7 15.8 16 17 18 19 20 21 22 3