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Management flexibility of a grassland agroecosystem: A modeling approach based on viability theory
Agricultural Systems 139 (2015) 76–81
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Agricultural Systems journal homepage: www.elsevier.com/locate/agsy
Management flexibility of a grassland agroecosystem: A modeling approach based on viability theory R. Sabatier a,⁎, L.G. Oates b, R.D. Jackson b a b
INRA UMR 1048 SADAPT, AgroparisTech, 16 rue Claude Bernard, 75005 Paris, France Department of Agronomy, University of Wisconsin–Madison, 1575 Linden Drive, Madison, WI 53706, USA
a r t i c l e
i n f o
Article history: Received 26 November 2014 Received in revised form 26 June 2015 Accepted 29 June 2015 Available online xxxx Keywords: Grazing Resistance Flexibility Adaptive management Dynamic modeling
a b s t r a c t A growing awareness of the negative consequences induced by post-WWII conventional agriculture has led to renewed interest for grazing-based livestock farming systems. A major characteristic of grassland based farming systems is the high unpredictability of forage resource in grassland ecosystems due to weather uncertainty. Two main management strategies can be followed by farmers to cope with this uncertainty: rely on ecosystem resistance — the ability of the system to remain viable for a wide range of environmental conditions or work with ecosystem flexibility by monitoring and adapting management strategies in response to perturbations. With a strategy based on resistance the farmer defines a priori the grazing sequence and does not modify it with time, while a strategy based on flexibility (also called adaptive management) requires defining grazing sequences that can be modified (adapted) in response to the environmental conditions observed. In this study we developed a simple model of a grassland agroecosystem dynamics under the mathematical framework of viability theory so as to quantify the resistance and flexibility of a set of grazing sequences. Our results show (1) for a given grazing sequence, applying a flexibility strategy leads to higher levels of production than a resistance strategy (+100 LU days ha−1 on average), (2) the number of adaptations needed to maintain system viability increases with the level of production and decreases with the resistance of the system, and (3) grazing sequences requiring the most adaptations to stay viable are also the ones with the lowest potential of adaptation (flexibility). We conclude that grazing sequences are located along a gradient ranging from low production with high resistance and high flexibility, to high production with low resistance and low flexibility and requiring constant adaptations to remain viable. Adaptive management makes it possible to benefit from environmental variability and increase the level of production, while management strategies based on resistance are coherent when managers do not target maximal production and can maintain a margin to cope with unexpected events. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction Negative environmental, economic, and social consequences of the post-WWII conventional model of agriculture (Wilkins, 2008; Steinfeld et al., 2006; Brock and Barham, 2009) have led to renewed interest for grazing-based livestock farming systems (Franzluebbers et al., 2012). Knowledge of the principles required to conduct productive grazing has been available for many decades (Voisin, 1957), and complex knowledge of local pasture plant communities, soils, climate and weather, types of livestock, and marketing opportunities have improved (Franzluebbers et al., 2012), but graziers still face the issue of high unpredictability in resource availability and weather uncertainty (Lyon et al., 2011). Farmers should therefore not only design grazing sequences aimed at high levels of production, but also adopt management strategies that make it possible to cope with environmental uncertainty
⁎ Corresponding author. E-mail address: [email protected] (R. Sabatier).
http://dx.doi.org/10.1016/j.agsy.2015.06.008 0308-521X/© 2015 Elsevier Ltd. All rights reserved.
(sensu Westoby et al., 1989). Two contrasted archetypes of management strategies can be followed to this aim: resistance or flexibility (sensu Ten Napel et al., 2011).1 Resistance (or passive robustness) is the ability of a grazing sequence to remain viable for a wide range of environmental conditions. A farmer using a strategy based on resistance will choose a grazing sequence that makes it possible to feed livestock irrespective of those conditions. Flexibility (or active robustness) is the ability of a grazing sequence to be modified (adapted) in response to the environmental conditions observed. A farmer using a flexible strategy will choose a grazing sequence that can be adapted throughout the year as time
1 Many terms have been used with different meanings to characterize different properties related to system behavior in the face of uncertainty. Here, we follow the terminology used by Ten Napel et al. (2011), although flexibility (sensu Ten Napel et al., 2011) also refers to adaptive management (Holling, 1973) and would often be called adaptability, and resistance (sensu Ten Napel et al., 2011) corresponds to the definition of robustness given by Stelling et al. (2004).
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passes and weather conditions become known. With this strategy, the farmer follows the model of Sebillotte and Soler (1990) in which a management strategy made at the beginning of the year is followed by tactical adjustments throughout the year when weather conditions become known. These two properties (resistance and flexibility) are difficult to quantify in real time as this would require numerous replicates of the same system being submitted to a wide range of environmental conditions. Modeling approaches have therefore been used to estimate the resistance of a grassland agroecosystem to environmental uncertainty (Sabatier et al., 2015). Quantifying resistance did not imply any major methodological issues, but the question of flexibility is more complex. Some papers have addressed the flexibility of farming systems, but it is generally to compare the production performance (mean and variability) of systems a priori designed to be flexible (e.g. Rodriguez et al., 2011). But systematically quantifying the flexibility of a set of management strategies on which we make no assumption goes one step further. It requires exploring grazing sequences as well as a set of alternative options in a stochastic context, and this may quickly require vast computing time. To overcome this issue, we conducted our study in the mathematical framework of the viability theory (Aubin, 1991) applied to stochastic systems (Doyen and de Lara, 2010). Viability theory makes it possible to look for the whole set of management sequences that ensures the maintenance of a dynamic system within a defined set of constraints through time. In this study, the system was a temperate grassland agroecosystem calibrated on cool-season grasslands of southcentral Wisconsin, USA. Management options were grazing sequences, and constraints were defined to ensure that the level of production remained above a minimum threshold and that overgrazing did not occur. Based on a set of representative grazing sequences, we quantified six indicators: Resistant production, resistance, flexible production, adaptations, flexibility, and production variability. The first two indicators refer to properties of the system managed with a resistance strategy. Resistant production is the total harvested biomass divided by the daily feeding requirement of one animal unit and averaged over n = 500 random weather scenarios. Resistance is the proportion of weather scenarios (within n = 500 random weather scenarios) for which the grazing strategy does not lead to overgrazing. The next two indicators refer to properties of the system managed with a flexibility strategy. Similar to resistant production, flexible production is the total harvested biomass divided by the daily feeding requirement of one animal unit and averaged over n = 500 random weather scenarios. Adaptation is the average number (within n = 500 random weather scenarios) of modifications that farmers would have to do to maintain a viable system. The fifth indicator, flexibility, aims to quantify the potential of the system to adapt. It does not refer specifically to any strategy as it reflects a general property of the system. It quantifies the number of alternative decisions available to the farmer throughout the year. Finally, production variability corresponds to the coefficient of variation of production (standard deviation divided by average production) of each grazing sequence over the 500 replications. Based on these indicators, we (1) quantified production differences between the resistance strategy and the flexibility strategy, (2) quantified the number of adaptations needed to cope with environmental uncertainty, (3) quantified grazing strategy flexibility, and (4) depicted the relationships between production, adaptations, flexibility, and resistance of the grazing strategies. 2. Methods 2.1. Model description Our study was based on a simple model simulating grass growth during the grazing season (1 April to 1 November) with a daily time step that was developed by Sabatier et al. (2015). In this model, grass
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growth follows a logistic curve (Voisin, 1957) in which the key parameters depend on time to reflect the seasonality of grass dynamics and the effects of biomass intake by livestock. The structure of the model was: 8 <
X ðt Þ X ðt Þ − min qU ðt Þ; rðt; ωÞX ðt Þ 1− −X min X ðt þ 1Þ ¼ rðt; ωÞX ðt Þ 1− K ðt Þ K ðt Þ : P ðt þ 1Þ ¼ P ðt Þ þ U ðt Þ
ð1Þ where X(t) is the grass biomass at time t, U(t) the stocking rate at time t expressed in LU ha−1 (Livestock Unit per hectare), K a saturation coefficient, q the daily intake of cattle, Xmin the level of grass biomass below which livestock cannot graze (corresponding to 5 cm residual stubble height), and r(t,ω) the growth coefficient that depends on time t and ω ∈ Ω (where Ω = [0.95, 1.0, 1.05]), a random multiplying coefficient that reflects the daily environmental variation (e.g. weather). P(t) is a second state variable corresponding to the production of the system. The model was calibrated to reflect the behavior of a cool-season grassland of southcentral Wisconsin, USA, based on datasets from Brink et al. (2013) and Oates et al. (2011). For full details on model calibration, see Sabatier et al. (2015). 2.2. Viability analysis Two viability constraints were defined — one that ensured that the stocking rate does not exceed the density that can be fed by the available resource, qU ðt Þ ≤ X ðt Þ−X min
ð2Þ
and a second that ensured that the level of production was greater than a given threshold P ðT Þ ≥ P min :
ð3Þ
Finding the set of states [X, P] that respect the viability constraints through time corresponds to the computation of the viability corridor, Viab(t). More precisely at t = t *, Viab(t *) was defined as the set of states, [X(t *),P(t *)], such as that there exist combinations of controls, U and states, [X(t),P(t)], starting from [X(t *),P(t *)], satisfying constraint (Eq. (2)) for any time t = t *,…T and satisfying constraint (Eq. (4)) for t = T. After the viability corridor was determined, we computed the set of viable grazing sequences (or controls), Uv, which match the viability constraints. A viable control existed as long as the corresponding state, [X(t + 1),P(t + 1)], was within the viability corridor, Viab(t + 1) for any value of ω. The set of viable controls at time, t, for a given viable grass state, [X(t),P(t)], was: U V ðt; X ðt Þ; P ðt ÞÞ constraints are satisfied ¼ ðU ðt ÞÞ; ∀ω ∈ Ω : ½X ðt þ 1; U ðt Þ; ωÞ; P ðt þ 1; U ðt Þ; ωÞ ∈ Viabðt þ 1Þ
ð4Þ Following the approach of Doyen and de Lara (2010), dynamic programming was applied for numerical approximation of Viab(t) and Uv. Eq. (5) corresponds to a robust approach in the sense of Doyen and de Lara (2010). For the applied point of view, this approach considers that the farmer has no knowledge of environmental conditions for the next time step and that s/he looks for a stocking rate (control) that would be viable whatever the conditions. Considering the farmer has knowledge of the conditions for the next time step (i.e. access to a
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reliable weather forecast; Eq. (5)) did not significantly affect our results (Appendix S1). U V ðt; X ðt Þ; P ðt ÞÞ ¼ fUg; ∀ω∈Ω∃U ðt Þ ∈ fU g constraints are satisfied ½X ðt þ 1; U ðt Þ; ωÞ; P ðt þ 1; U ðt Þ; ωÞ ∈ Viabðt þ 1Þ ð5Þ To limit computing time, we considered that controls could only vary on a 8-day time step and focused on a single initial condition (25 cm grass height; 0 LU days ha− 1). Pmin represents the minimal level of production that a grazing sequence shall ensure whatever the weather conditions (i.e. even in the worst case where the lowest value of ω is chosen at each time step). This constraint was arbitrarily set to 200 LU days ha−1, which corresponds to a quite high value of the constraint. Indeed, above Pmin = 250 LU days ha−1 the viability kernel becomes empty which means that it is not possible to find a grazing strategy that ensures a production above 250 LU days ha− 1 even in the worst environmental scenario. Bellow 250 LU days ha−1, the value of this viability threshold had little effect on the general shape of the curves found in the results (Appendix S2). 2.3. Scenarios The set of viable grazing sequences Uv was too large to be systematically explored. We therefore focused the analysis on a smaller subset of trajectories that were relevant from the farming point of view and were built based on our expertise of the area. This set S (n = 21,057) was composed of a series of random scenarios plus two series of grazing sequences corresponding to two types of management commonly found in the North Central Region of the United States: continuous grazing (CONT) and management-intensive rotational grazing (MIRG). Continuous grazing is where livestock are left on the grassland for a long period of time at a low stocking rate, whereas rotational grazing entails livestock grazing at high stocking rates but frequently rotated between paddocks. Parameters of CONT and MIRG scenarios were picked up to cover a wide array of situations. CONT scenarios included in S were the set of grazing sequences for which livestock densities ∈ [0, 2, 4, 6, 8] only varies from one month to the next between 1 May and 1 November. MIRG scenarios included in S were the set of scenarios defined by a starting date ∈ [105, 120, 135], a livestock density during grazing events ∈ [2, 4, 6, 8, 10, 12, 14, 16], a resting time between two grazing events ∈ [8, 16, 24, 32, 40, 48], and a grazing end date ∈ [210, 240, 270]. In line with results found in Sabatier et al. (2015), results obtained with the MIRG scenarios did not fundamentally differ from the ones found with the CONT scenarios, therefore we will not distinguish them in the rest of the article. In order to explore a range of scenarios as wide as possible and not to exclude possibly interesting options, we added a third option composed of 5000 random scenarios. From this set S, we only considered the grazing sequences that were viable in the particular case where Ω = [1] (n′ = 5613). In other words, we only considered the grazing sequences that respected the constraints in a deterministic environment with average weather. We considered this subset of S so as to limit the drivers of adaptations to environmental uncertainty only.
With a flexibility strategy, the farmer defines a grazing sequence at the beginning of the year but may modify it in order to maintain system viability. The farmer only modifies the grazing strategy when compelled (i.e. if constraints are not going to be respected in the future) and chooses the closest stocking rate possible. The decision is formulated as follows: if [X,P](t + 1,ω,U) ∈Viab(t + 1), control U is applied; if not, the algorithm selects an alternative control U′ such as [X,P](t + 1,ω,U′) ∈Viab(t + 1). U′ is chosen to minimize the distance between U and U′. 3. Results 3.1. Production performance was greater under a flexibility strategy Resistance and flexibility strategies differed in performance. Resistant production ranged from 150 to 550 LU days ha−1 year−1, and flexible production ranged from 200 to 650 (Fig. 1). For all grazing sequences, the flexibility strategy increased production and this increase averaged almost 100 LU days ha−1 year−1. This increase in production was a positive side-effect since adaptations were not aimed at increasing production but only at respecting the constraints. At the lowest levels of production, the farmer would have to adapt their management to ensure the respect of the production constraint; at the highest levels of production, s/he had to adapt their management to avoid overgrazing, which explains why production is increased for all levels. It shows that farmers can capitalize on environmental variability as a resource once they adopt an adaptive approach (flexibility strategy). 3.2. Increased production required frequent management adaptations Following a flexibility strategy implied adaptations were necessary for most scenarios tested (Fig. 2). The number of adaptations needed to remain viable increased with level of production. Attaining high levels of production, which pushed the system closer to its limits (i.e., viability constraints), required frequent management adjustments in order to maintain grassland viability. Eight adjustments were needed for the most productive scenarios, which corresponded to almost one-third of the management decisions (28 in total given the 8-day time step). The number of adaptations required decreased when resistance increased, showing that resistant scenarios did not require many adjustments to remain viable (Fig. 3). This result was not surprising since resistant grazing sequences are ones that do not lead to overgrazing and therefore respect viability constraints.
2.4. Management strategies We modeled two types of management strategies: resistance and flexibility. With a resistance strategy, the farmer selects a grazing sequence at the beginning of the year and does not modify it through time, whatever the environmental conditions. This may lead to overgrazing: situations where the forage resource is not sufficient to feed the livestock or situations where production is below Pmin (i.e., nonviable situations).
Fig. 1. Relationship between flexible and resistant production for modeled scenarios. The dashed line corresponds to scenarios where production would be identical (y = x), and the continuous line corresponds to a situation where the flexible strategy would increase production by 100 LU days ha−1 year−1.
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Fig. 2. Number of adaptations required for the different grazing sequences managed with a flexibility strategy as a function of flexible production.
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Fig. 4. Relationship between the number of adaptations and the flexibility of the modeled grazing sequences.
3.3. Adaptations are the most needed in the situations with the lowest flexibility Adaptations differed from flexibility and the two dimensions showed a strong negative relationship (Fig. 4). This indicated that strategies needing the highest number of adaptations to stay viable were also the ones with the lowest potential for adaptation (flexibility). Following from this result, it is logical that flexibility showed a negative relationship with production (Fig. 5a) and a positive one with resistance (Fig. 5b). We observed that the Pareto-frontiers of Fig. 5a (the set of states from which it is not possible to increase production without decreasing flexibility) is not linear. After a first phase where increase of production results in a minor reduction in flexibility (200–350 LU ha− 1) we see a second phase with an almost linear decrease in flexibility (350–600) followed by a sudden drop in flexibility. This last phase corresponds to the situation where the number of adaptations needed increases exponentially (Fig. 2) and where the system has reached its limit. Flexibility shows a positive relationship with resistance which shows that the two properties characterizing the ability of the system to cope with uncertainty evolve in the same way (Fig. 5b). However,
Fig. 3. Relationship between adaptation and resistance for modeled grazing sequences.
Fig. 5. Relationship between flexibility and production (a) or resistance (b) of the modeled grazing sequences.
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here also, the relationship is not linear showing that flexibility increases faster than resistance. 3.4. Variability of production increases with the level of production Our results on production variability show similar patterns with the resistance or the flexibility strategy. For both strategies, production variability increases with the level of production. At low levels of production, risk of overgrazing is low and production shows little variability. At high levels of production, the system is very sensitive to overgrazing and variability in production is high (Fig. 6). These results interpreted in relation with the ones of Fig. 1 show that the flexibility strategy does not control and limit variability but benefit from it. 4. Discussion 4.1. Limits and perspectives Our study made it possible to study how fine tuning of management at the plot level balanced production objectives with resistance and flexibility of management. The main limitation of this study is that the model is defined at the level of organization of the plot. Such an approach is pertinent to study the fine scale cattle-grass dynamics but does not consider interactions between plots. A main perspective of this work would be to move to the farm level. It would make it possible
Fig. 6. Relationship between production variability (coefficient of variation of production) and resistant production (a) or flexible production (b).
to account for other dimensions of the system such as working time (a strong limiting factor in rotational grazing) and therefore evaluate the overall profitability of the farming system. A difficulty with such an upscaling is the exponential increase of computing time if upscaling is simply done by juxtaposing a dozen of plot-level models and therefore running dozens of viability algorithms in parallel. Alternative options such as the use of a multi-scale viability algorithm (Sabatier et al., 2015) would make it possible to bypass this problem. Upscaling to the farm level would also imply a simplification of the plot level model to limit the space of possible management options like in Jakoby et al. (2014). Moving to an upper level of organization would make it relevant to move the focus to a larger temporal scale. This would imply an adjustment of the agro-ecological dynamics considered toward longer term ones such as the grass legume balance like in Kaine and Tozer (2005), the bush encroachment like in Accatino et al. (2014) or the underground biomass dynamics like in Joly et al. (2014). Widening the temporal scale of the study would make it possible to apply the viability theory to the quantification of the resilience of the system toward extreme events (see Martin, 2004; Deffuant and Gilbert, 2011 for details). 4.2. A gradient of situations The use of the viability theory made it possible to explore management of the system based on the flexibility strategy (or adaptive management). Doing so, we could go beyond the assessment of the trade-off between production and resistance done in Sabatier et al. (2015) and quantify the flexibility of the agroecosystem as well as the number of adaptations needed to overcome uncertainty. The aim of this study was not to provide recipes to be implemented in the field (which would be counterproductive; Lyon et al., 2011) but rather to take a wider point of view on the system so as to provide more general results on the behavior of the system in face of uncertainty. Our results showed that grazing sequences ranged from resistant and flexible with corresponding low production, to more productive sequences associated with low flexibility and resistance that required constant adaptations to cope with, and possibly benefit from, environmental variability. The two management strategies studied here (resistance and flexibility) are suited to the two extremes of this gradient. The resistant strategy embodies approaches to grazing that lead to low production but rarely result in overgrazing (resistant sequences), and for which adaptations are not needed. Conversely, the flexible strategy is an approach aimed at high levels of production where overgrazing is very likely to occur (low resistance) and constant adaptations are necessary to maintain system viability. These findings correspond to two of three principles described by Nozières et al. (2011) on which a farmer builds the adaptive capacity of their system: overcapacity (pushing the system in sub-optimal situations) and adaptive management (in the sense of Holling, 1973). Their review however leaves largely unanswered the question of how to choose between adaptive management and overcapacity. We show that this choice is highly dependent on the production objectives of the farmer and how their strategy performs at the paddock level as well as their overall strategy at the farm level. If the objective is high production, adaptations are necessary to maintain system viability but if the objective is to retain system viability in most weather conditions with few management interventions, the farmer would choose resistant grazing sequences and the attendant lower production. In this second case, the farmer may determine the higher management cost associated with adaptive management may not be compensated by productivity gains. The third principle by which the farmer builds adaptive capacity according to Nozières et al. (2011) is the buffering capacity of the system and its components. At the animal level, a simple example of this is the ability to use its body reserves to compensate for a short-term lack of feed. This source of flexibility is often used in extensive livestock farming systems based on uncertain forage resources. Our results
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showed that increasing production pushes the system toward unviable situations, limiting its flexibility and requiring constant adaptations to maintain the system. Eventually, the system reaches a stage where it is no longer possible to increase production while respecting the constraints. At this stage, the system is no longer resistant and adaptations become more and more difficult. The buffering capacity of systems could be an interesting way to cope with uncertainty. Considering buffering capacity in our model would imply adding a third state variable representing the dynamics of animal body reserves and their capacities to use them in the short-term and would strongly increase computing time. The use of a minimum time of crisis algorithm (Doyen and SaintPierre, 1997) could be an efficient alternative to consider situations where constraints may not be respected for a short period of time. 4.3. Dealing with uncertainty or benefiting from variability? From an applied point of view, our results illustrate strong differences in the relation to uncertainty in grass-based livestock farming systems or in controlled confinement system. The aim of confinement feeding is to control environmental unpredictability as much as possible, i.e., minimize environmental variation and minimize uncertainty of forage availability (although economic unpredictability remains a major issue). By confining the system, farming indoors transform uncertainty into known variability. Once variability is known, it can be used to the farmer's advantage with adaptation of farming practices (review in Puillet, 2010). Variability is also a characteristic of pasturebased systems from which farmers often benefit (e.g. Andrieu et al., 2007; Martin et al., 2009a, 2009b). However uncertainty is generally high in these systems and it is generally not possible to adapt a priori a management strategy to environmental conditions. To maximize the number of days possible to feed livestock, adaptations need to be made when environmental conditions become known (i.e. when uncertainty has been transformed into variability). Such adaptive management (Holling, 1973) makes it possible to benefit from the “productivity of variability” (Bell et al., 2008) of unpredictable variables, which increases the level of production as shown by our results. Maintaining flexibility of a farming system is therefore crucial to be able to adapt it to (and therefore benefit from) environmental variability. 5. Conclusions In this study, we illustrated how management strategies based on resistance or flexibility made it possible to cope with environmental uncertainty in a grassland agroecosystem. Our results illustrate the central role played by uncertainty in these systems and are in line with most findings regarding sustainable agriculture. The transformation of agriculture into more sustainable forms like agroecology will require accepting and integrating environmental uncertainty into management. This changes the research questions asked and highlights the need for agronomic research to not only focus on optimum production in controlled conditions, but also on new dimensions for enhancing the performance of farming such as flexibility and resistance. Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.agsy.2015.06.008. References Accatino, F., Sabatier, R., De Michele, C., Ward, D., Wiegand, K., Meyer, K.M., 2014. Robustness and management adaptability in tropical rangelands: a viability-based assessment under the non-equilibrium paradigm. Animal 8, 1272–1281. http://dx. doi.org/10.1017/S1751731114000913.
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Management flexibility of a grassland agroecosystem: A modeling approach based on viability theory R. Sabatier a,⁎, L.G. Oates b, R.D. Jackson b a b
INRA UMR 1048 SADAPT, AgroparisTech, 16 rue Claude Bernard, 75005 Paris, France Department of Agronomy, University of Wisconsin–Madison, 1575 Linden Drive, Madison, WI 53706, USA
a r t i c l e
i n f o
Article history: Received 26 November 2014 Received in revised form 26 June 2015 Accepted 29 June 2015 Available online xxxx Keywords: Grazing Resistance Flexibility Adaptive management Dynamic modeling
a b s t r a c t A growing awareness of the negative consequences induced by post-WWII conventional agriculture has led to renewed interest for grazing-based livestock farming systems. A major characteristic of grassland based farming systems is the high unpredictability of forage resource in grassland ecosystems due to weather uncertainty. Two main management strategies can be followed by farmers to cope with this uncertainty: rely on ecosystem resistance — the ability of the system to remain viable for a wide range of environmental conditions or work with ecosystem flexibility by monitoring and adapting management strategies in response to perturbations. With a strategy based on resistance the farmer defines a priori the grazing sequence and does not modify it with time, while a strategy based on flexibility (also called adaptive management) requires defining grazing sequences that can be modified (adapted) in response to the environmental conditions observed. In this study we developed a simple model of a grassland agroecosystem dynamics under the mathematical framework of viability theory so as to quantify the resistance and flexibility of a set of grazing sequences. Our results show (1) for a given grazing sequence, applying a flexibility strategy leads to higher levels of production than a resistance strategy (+100 LU days ha−1 on average), (2) the number of adaptations needed to maintain system viability increases with the level of production and decreases with the resistance of the system, and (3) grazing sequences requiring the most adaptations to stay viable are also the ones with the lowest potential of adaptation (flexibility). We conclude that grazing sequences are located along a gradient ranging from low production with high resistance and high flexibility, to high production with low resistance and low flexibility and requiring constant adaptations to remain viable. Adaptive management makes it possible to benefit from environmental variability and increase the level of production, while management strategies based on resistance are coherent when managers do not target maximal production and can maintain a margin to cope with unexpected events. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction Negative environmental, economic, and social consequences of the post-WWII conventional model of agriculture (Wilkins, 2008; Steinfeld et al., 2006; Brock and Barham, 2009) have led to renewed interest for grazing-based livestock farming systems (Franzluebbers et al., 2012). Knowledge of the principles required to conduct productive grazing has been available for many decades (Voisin, 1957), and complex knowledge of local pasture plant communities, soils, climate and weather, types of livestock, and marketing opportunities have improved (Franzluebbers et al., 2012), but graziers still face the issue of high unpredictability in resource availability and weather uncertainty (Lyon et al., 2011). Farmers should therefore not only design grazing sequences aimed at high levels of production, but also adopt management strategies that make it possible to cope with environmental uncertainty
⁎ Corresponding author. E-mail address: [email protected] (R. Sabatier).
http://dx.doi.org/10.1016/j.agsy.2015.06.008 0308-521X/© 2015 Elsevier Ltd. All rights reserved.
(sensu Westoby et al., 1989). Two contrasted archetypes of management strategies can be followed to this aim: resistance or flexibility (sensu Ten Napel et al., 2011).1 Resistance (or passive robustness) is the ability of a grazing sequence to remain viable for a wide range of environmental conditions. A farmer using a strategy based on resistance will choose a grazing sequence that makes it possible to feed livestock irrespective of those conditions. Flexibility (or active robustness) is the ability of a grazing sequence to be modified (adapted) in response to the environmental conditions observed. A farmer using a flexible strategy will choose a grazing sequence that can be adapted throughout the year as time
1 Many terms have been used with different meanings to characterize different properties related to system behavior in the face of uncertainty. Here, we follow the terminology used by Ten Napel et al. (2011), although flexibility (sensu Ten Napel et al., 2011) also refers to adaptive management (Holling, 1973) and would often be called adaptability, and resistance (sensu Ten Napel et al., 2011) corresponds to the definition of robustness given by Stelling et al. (2004).
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passes and weather conditions become known. With this strategy, the farmer follows the model of Sebillotte and Soler (1990) in which a management strategy made at the beginning of the year is followed by tactical adjustments throughout the year when weather conditions become known. These two properties (resistance and flexibility) are difficult to quantify in real time as this would require numerous replicates of the same system being submitted to a wide range of environmental conditions. Modeling approaches have therefore been used to estimate the resistance of a grassland agroecosystem to environmental uncertainty (Sabatier et al., 2015). Quantifying resistance did not imply any major methodological issues, but the question of flexibility is more complex. Some papers have addressed the flexibility of farming systems, but it is generally to compare the production performance (mean and variability) of systems a priori designed to be flexible (e.g. Rodriguez et al., 2011). But systematically quantifying the flexibility of a set of management strategies on which we make no assumption goes one step further. It requires exploring grazing sequences as well as a set of alternative options in a stochastic context, and this may quickly require vast computing time. To overcome this issue, we conducted our study in the mathematical framework of the viability theory (Aubin, 1991) applied to stochastic systems (Doyen and de Lara, 2010). Viability theory makes it possible to look for the whole set of management sequences that ensures the maintenance of a dynamic system within a defined set of constraints through time. In this study, the system was a temperate grassland agroecosystem calibrated on cool-season grasslands of southcentral Wisconsin, USA. Management options were grazing sequences, and constraints were defined to ensure that the level of production remained above a minimum threshold and that overgrazing did not occur. Based on a set of representative grazing sequences, we quantified six indicators: Resistant production, resistance, flexible production, adaptations, flexibility, and production variability. The first two indicators refer to properties of the system managed with a resistance strategy. Resistant production is the total harvested biomass divided by the daily feeding requirement of one animal unit and averaged over n = 500 random weather scenarios. Resistance is the proportion of weather scenarios (within n = 500 random weather scenarios) for which the grazing strategy does not lead to overgrazing. The next two indicators refer to properties of the system managed with a flexibility strategy. Similar to resistant production, flexible production is the total harvested biomass divided by the daily feeding requirement of one animal unit and averaged over n = 500 random weather scenarios. Adaptation is the average number (within n = 500 random weather scenarios) of modifications that farmers would have to do to maintain a viable system. The fifth indicator, flexibility, aims to quantify the potential of the system to adapt. It does not refer specifically to any strategy as it reflects a general property of the system. It quantifies the number of alternative decisions available to the farmer throughout the year. Finally, production variability corresponds to the coefficient of variation of production (standard deviation divided by average production) of each grazing sequence over the 500 replications. Based on these indicators, we (1) quantified production differences between the resistance strategy and the flexibility strategy, (2) quantified the number of adaptations needed to cope with environmental uncertainty, (3) quantified grazing strategy flexibility, and (4) depicted the relationships between production, adaptations, flexibility, and resistance of the grazing strategies. 2. Methods 2.1. Model description Our study was based on a simple model simulating grass growth during the grazing season (1 April to 1 November) with a daily time step that was developed by Sabatier et al. (2015). In this model, grass
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growth follows a logistic curve (Voisin, 1957) in which the key parameters depend on time to reflect the seasonality of grass dynamics and the effects of biomass intake by livestock. The structure of the model was: 8 <
X ðt Þ X ðt Þ − min qU ðt Þ; rðt; ωÞX ðt Þ 1− −X min X ðt þ 1Þ ¼ rðt; ωÞX ðt Þ 1− K ðt Þ K ðt Þ : P ðt þ 1Þ ¼ P ðt Þ þ U ðt Þ
ð1Þ where X(t) is the grass biomass at time t, U(t) the stocking rate at time t expressed in LU ha−1 (Livestock Unit per hectare), K a saturation coefficient, q the daily intake of cattle, Xmin the level of grass biomass below which livestock cannot graze (corresponding to 5 cm residual stubble height), and r(t,ω) the growth coefficient that depends on time t and ω ∈ Ω (where Ω = [0.95, 1.0, 1.05]), a random multiplying coefficient that reflects the daily environmental variation (e.g. weather). P(t) is a second state variable corresponding to the production of the system. The model was calibrated to reflect the behavior of a cool-season grassland of southcentral Wisconsin, USA, based on datasets from Brink et al. (2013) and Oates et al. (2011). For full details on model calibration, see Sabatier et al. (2015). 2.2. Viability analysis Two viability constraints were defined — one that ensured that the stocking rate does not exceed the density that can be fed by the available resource, qU ðt Þ ≤ X ðt Þ−X min
ð2Þ
and a second that ensured that the level of production was greater than a given threshold P ðT Þ ≥ P min :
ð3Þ
Finding the set of states [X, P] that respect the viability constraints through time corresponds to the computation of the viability corridor, Viab(t). More precisely at t = t *, Viab(t *) was defined as the set of states, [X(t *),P(t *)], such as that there exist combinations of controls, U and states, [X(t),P(t)], starting from [X(t *),P(t *)], satisfying constraint (Eq. (2)) for any time t = t *,…T and satisfying constraint (Eq. (4)) for t = T. After the viability corridor was determined, we computed the set of viable grazing sequences (or controls), Uv, which match the viability constraints. A viable control existed as long as the corresponding state, [X(t + 1),P(t + 1)], was within the viability corridor, Viab(t + 1) for any value of ω. The set of viable controls at time, t, for a given viable grass state, [X(t),P(t)], was: U V ðt; X ðt Þ; P ðt ÞÞ constraints are satisfied ¼ ðU ðt ÞÞ; ∀ω ∈ Ω : ½X ðt þ 1; U ðt Þ; ωÞ; P ðt þ 1; U ðt Þ; ωÞ ∈ Viabðt þ 1Þ
ð4Þ Following the approach of Doyen and de Lara (2010), dynamic programming was applied for numerical approximation of Viab(t) and Uv. Eq. (5) corresponds to a robust approach in the sense of Doyen and de Lara (2010). For the applied point of view, this approach considers that the farmer has no knowledge of environmental conditions for the next time step and that s/he looks for a stocking rate (control) that would be viable whatever the conditions. Considering the farmer has knowledge of the conditions for the next time step (i.e. access to a
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reliable weather forecast; Eq. (5)) did not significantly affect our results (Appendix S1). U V ðt; X ðt Þ; P ðt ÞÞ ¼ fUg; ∀ω∈Ω∃U ðt Þ ∈ fU g constraints are satisfied ½X ðt þ 1; U ðt Þ; ωÞ; P ðt þ 1; U ðt Þ; ωÞ ∈ Viabðt þ 1Þ ð5Þ To limit computing time, we considered that controls could only vary on a 8-day time step and focused on a single initial condition (25 cm grass height; 0 LU days ha− 1). Pmin represents the minimal level of production that a grazing sequence shall ensure whatever the weather conditions (i.e. even in the worst case where the lowest value of ω is chosen at each time step). This constraint was arbitrarily set to 200 LU days ha−1, which corresponds to a quite high value of the constraint. Indeed, above Pmin = 250 LU days ha−1 the viability kernel becomes empty which means that it is not possible to find a grazing strategy that ensures a production above 250 LU days ha− 1 even in the worst environmental scenario. Bellow 250 LU days ha−1, the value of this viability threshold had little effect on the general shape of the curves found in the results (Appendix S2). 2.3. Scenarios The set of viable grazing sequences Uv was too large to be systematically explored. We therefore focused the analysis on a smaller subset of trajectories that were relevant from the farming point of view and were built based on our expertise of the area. This set S (n = 21,057) was composed of a series of random scenarios plus two series of grazing sequences corresponding to two types of management commonly found in the North Central Region of the United States: continuous grazing (CONT) and management-intensive rotational grazing (MIRG). Continuous grazing is where livestock are left on the grassland for a long period of time at a low stocking rate, whereas rotational grazing entails livestock grazing at high stocking rates but frequently rotated between paddocks. Parameters of CONT and MIRG scenarios were picked up to cover a wide array of situations. CONT scenarios included in S were the set of grazing sequences for which livestock densities ∈ [0, 2, 4, 6, 8] only varies from one month to the next between 1 May and 1 November. MIRG scenarios included in S were the set of scenarios defined by a starting date ∈ [105, 120, 135], a livestock density during grazing events ∈ [2, 4, 6, 8, 10, 12, 14, 16], a resting time between two grazing events ∈ [8, 16, 24, 32, 40, 48], and a grazing end date ∈ [210, 240, 270]. In line with results found in Sabatier et al. (2015), results obtained with the MIRG scenarios did not fundamentally differ from the ones found with the CONT scenarios, therefore we will not distinguish them in the rest of the article. In order to explore a range of scenarios as wide as possible and not to exclude possibly interesting options, we added a third option composed of 5000 random scenarios. From this set S, we only considered the grazing sequences that were viable in the particular case where Ω = [1] (n′ = 5613). In other words, we only considered the grazing sequences that respected the constraints in a deterministic environment with average weather. We considered this subset of S so as to limit the drivers of adaptations to environmental uncertainty only.
With a flexibility strategy, the farmer defines a grazing sequence at the beginning of the year but may modify it in order to maintain system viability. The farmer only modifies the grazing strategy when compelled (i.e. if constraints are not going to be respected in the future) and chooses the closest stocking rate possible. The decision is formulated as follows: if [X,P](t + 1,ω,U) ∈Viab(t + 1), control U is applied; if not, the algorithm selects an alternative control U′ such as [X,P](t + 1,ω,U′) ∈Viab(t + 1). U′ is chosen to minimize the distance between U and U′. 3. Results 3.1. Production performance was greater under a flexibility strategy Resistance and flexibility strategies differed in performance. Resistant production ranged from 150 to 550 LU days ha−1 year−1, and flexible production ranged from 200 to 650 (Fig. 1). For all grazing sequences, the flexibility strategy increased production and this increase averaged almost 100 LU days ha−1 year−1. This increase in production was a positive side-effect since adaptations were not aimed at increasing production but only at respecting the constraints. At the lowest levels of production, the farmer would have to adapt their management to ensure the respect of the production constraint; at the highest levels of production, s/he had to adapt their management to avoid overgrazing, which explains why production is increased for all levels. It shows that farmers can capitalize on environmental variability as a resource once they adopt an adaptive approach (flexibility strategy). 3.2. Increased production required frequent management adaptations Following a flexibility strategy implied adaptations were necessary for most scenarios tested (Fig. 2). The number of adaptations needed to remain viable increased with level of production. Attaining high levels of production, which pushed the system closer to its limits (i.e., viability constraints), required frequent management adjustments in order to maintain grassland viability. Eight adjustments were needed for the most productive scenarios, which corresponded to almost one-third of the management decisions (28 in total given the 8-day time step). The number of adaptations required decreased when resistance increased, showing that resistant scenarios did not require many adjustments to remain viable (Fig. 3). This result was not surprising since resistant grazing sequences are ones that do not lead to overgrazing and therefore respect viability constraints.
2.4. Management strategies We modeled two types of management strategies: resistance and flexibility. With a resistance strategy, the farmer selects a grazing sequence at the beginning of the year and does not modify it through time, whatever the environmental conditions. This may lead to overgrazing: situations where the forage resource is not sufficient to feed the livestock or situations where production is below Pmin (i.e., nonviable situations).
Fig. 1. Relationship between flexible and resistant production for modeled scenarios. The dashed line corresponds to scenarios where production would be identical (y = x), and the continuous line corresponds to a situation where the flexible strategy would increase production by 100 LU days ha−1 year−1.
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Fig. 2. Number of adaptations required for the different grazing sequences managed with a flexibility strategy as a function of flexible production.
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Fig. 4. Relationship between the number of adaptations and the flexibility of the modeled grazing sequences.
3.3. Adaptations are the most needed in the situations with the lowest flexibility Adaptations differed from flexibility and the two dimensions showed a strong negative relationship (Fig. 4). This indicated that strategies needing the highest number of adaptations to stay viable were also the ones with the lowest potential for adaptation (flexibility). Following from this result, it is logical that flexibility showed a negative relationship with production (Fig. 5a) and a positive one with resistance (Fig. 5b). We observed that the Pareto-frontiers of Fig. 5a (the set of states from which it is not possible to increase production without decreasing flexibility) is not linear. After a first phase where increase of production results in a minor reduction in flexibility (200–350 LU ha− 1) we see a second phase with an almost linear decrease in flexibility (350–600) followed by a sudden drop in flexibility. This last phase corresponds to the situation where the number of adaptations needed increases exponentially (Fig. 2) and where the system has reached its limit. Flexibility shows a positive relationship with resistance which shows that the two properties characterizing the ability of the system to cope with uncertainty evolve in the same way (Fig. 5b). However,
Fig. 3. Relationship between adaptation and resistance for modeled grazing sequences.
Fig. 5. Relationship between flexibility and production (a) or resistance (b) of the modeled grazing sequences.
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here also, the relationship is not linear showing that flexibility increases faster than resistance. 3.4. Variability of production increases with the level of production Our results on production variability show similar patterns with the resistance or the flexibility strategy. For both strategies, production variability increases with the level of production. At low levels of production, risk of overgrazing is low and production shows little variability. At high levels of production, the system is very sensitive to overgrazing and variability in production is high (Fig. 6). These results interpreted in relation with the ones of Fig. 1 show that the flexibility strategy does not control and limit variability but benefit from it. 4. Discussion 4.1. Limits and perspectives Our study made it possible to study how fine tuning of management at the plot level balanced production objectives with resistance and flexibility of management. The main limitation of this study is that the model is defined at the level of organization of the plot. Such an approach is pertinent to study the fine scale cattle-grass dynamics but does not consider interactions between plots. A main perspective of this work would be to move to the farm level. It would make it possible
Fig. 6. Relationship between production variability (coefficient of variation of production) and resistant production (a) or flexible production (b).
to account for other dimensions of the system such as working time (a strong limiting factor in rotational grazing) and therefore evaluate the overall profitability of the farming system. A difficulty with such an upscaling is the exponential increase of computing time if upscaling is simply done by juxtaposing a dozen of plot-level models and therefore running dozens of viability algorithms in parallel. Alternative options such as the use of a multi-scale viability algorithm (Sabatier et al., 2015) would make it possible to bypass this problem. Upscaling to the farm level would also imply a simplification of the plot level model to limit the space of possible management options like in Jakoby et al. (2014). Moving to an upper level of organization would make it relevant to move the focus to a larger temporal scale. This would imply an adjustment of the agro-ecological dynamics considered toward longer term ones such as the grass legume balance like in Kaine and Tozer (2005), the bush encroachment like in Accatino et al. (2014) or the underground biomass dynamics like in Joly et al. (2014). Widening the temporal scale of the study would make it possible to apply the viability theory to the quantification of the resilience of the system toward extreme events (see Martin, 2004; Deffuant and Gilbert, 2011 for details). 4.2. A gradient of situations The use of the viability theory made it possible to explore management of the system based on the flexibility strategy (or adaptive management). Doing so, we could go beyond the assessment of the trade-off between production and resistance done in Sabatier et al. (2015) and quantify the flexibility of the agroecosystem as well as the number of adaptations needed to overcome uncertainty. The aim of this study was not to provide recipes to be implemented in the field (which would be counterproductive; Lyon et al., 2011) but rather to take a wider point of view on the system so as to provide more general results on the behavior of the system in face of uncertainty. Our results showed that grazing sequences ranged from resistant and flexible with corresponding low production, to more productive sequences associated with low flexibility and resistance that required constant adaptations to cope with, and possibly benefit from, environmental variability. The two management strategies studied here (resistance and flexibility) are suited to the two extremes of this gradient. The resistant strategy embodies approaches to grazing that lead to low production but rarely result in overgrazing (resistant sequences), and for which adaptations are not needed. Conversely, the flexible strategy is an approach aimed at high levels of production where overgrazing is very likely to occur (low resistance) and constant adaptations are necessary to maintain system viability. These findings correspond to two of three principles described by Nozières et al. (2011) on which a farmer builds the adaptive capacity of their system: overcapacity (pushing the system in sub-optimal situations) and adaptive management (in the sense of Holling, 1973). Their review however leaves largely unanswered the question of how to choose between adaptive management and overcapacity. We show that this choice is highly dependent on the production objectives of the farmer and how their strategy performs at the paddock level as well as their overall strategy at the farm level. If the objective is high production, adaptations are necessary to maintain system viability but if the objective is to retain system viability in most weather conditions with few management interventions, the farmer would choose resistant grazing sequences and the attendant lower production. In this second case, the farmer may determine the higher management cost associated with adaptive management may not be compensated by productivity gains. The third principle by which the farmer builds adaptive capacity according to Nozières et al. (2011) is the buffering capacity of the system and its components. At the animal level, a simple example of this is the ability to use its body reserves to compensate for a short-term lack of feed. This source of flexibility is often used in extensive livestock farming systems based on uncertain forage resources. Our results
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showed that increasing production pushes the system toward unviable situations, limiting its flexibility and requiring constant adaptations to maintain the system. Eventually, the system reaches a stage where it is no longer possible to increase production while respecting the constraints. At this stage, the system is no longer resistant and adaptations become more and more difficult. The buffering capacity of systems could be an interesting way to cope with uncertainty. Considering buffering capacity in our model would imply adding a third state variable representing the dynamics of animal body reserves and their capacities to use them in the short-term and would strongly increase computing time. The use of a minimum time of crisis algorithm (Doyen and SaintPierre, 1997) could be an efficient alternative to consider situations where constraints may not be respected for a short period of time. 4.3. Dealing with uncertainty or benefiting from variability? From an applied point of view, our results illustrate strong differences in the relation to uncertainty in grass-based livestock farming systems or in controlled confinement system. The aim of confinement feeding is to control environmental unpredictability as much as possible, i.e., minimize environmental variation and minimize uncertainty of forage availability (although economic unpredictability remains a major issue). By confining the system, farming indoors transform uncertainty into known variability. Once variability is known, it can be used to the farmer's advantage with adaptation of farming practices (review in Puillet, 2010). Variability is also a characteristic of pasturebased systems from which farmers often benefit (e.g. Andrieu et al., 2007; Martin et al., 2009a, 2009b). However uncertainty is generally high in these systems and it is generally not possible to adapt a priori a management strategy to environmental conditions. To maximize the number of days possible to feed livestock, adaptations need to be made when environmental conditions become known (i.e. when uncertainty has been transformed into variability). Such adaptive management (Holling, 1973) makes it possible to benefit from the “productivity of variability” (Bell et al., 2008) of unpredictable variables, which increases the level of production as shown by our results. Maintaining flexibility of a farming system is therefore crucial to be able to adapt it to (and therefore benefit from) environmental variability. 5. Conclusions In this study, we illustrated how management strategies based on resistance or flexibility made it possible to cope with environmental uncertainty in a grassland agroecosystem. Our results illustrate the central role played by uncertainty in these systems and are in line with most findings regarding sustainable agriculture. The transformation of agriculture into more sustainable forms like agroecology will require accepting and integrating environmental uncertainty into management. This changes the research questions asked and highlights the need for agronomic research to not only focus on optimum production in controlled conditions, but also on new dimensions for enhancing the performance of farming such as flexibility and resistance. Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.agsy.2015.06.008. References Accatino, F., Sabatier, R., De Michele, C., Ward, D., Wiegand, K., Meyer, K.M., 2014. Robustness and management adaptability in tropical rangelands: a viability-based assessment under the non-equilibrium paradigm. Animal 8, 1272–1281. http://dx. doi.org/10.1017/S1751731114000913.
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