Evaluating long-term economic and ecological consequences of continuous and multi-paddock grazing -

Agricultural Systems 165 (2018) 197–207

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Agricultural Systems journal homepage: www.elsevier.com/locate/agsy

Evaluating long-term economic and ecological consequences of continuous and multi-paddock grazing - a modeling approach

T

⁎

Tong Wanga, , W. Richard Teagueb, Seong C. Parkb, Stan Beversc a

Department of Economics, South Dakota State University, Brookings, SD 57007, United States Texas A&M AgriLife Research, Vernon, TX 76384, United States c Professor and Extension Specialist Emeritus, Texas A&M AgriLife Extension, Vernon, TX 76384, United States b

A R T I C LE I N FO

A B S T R A C T

Keywords: Continuous grazing Multi-paddock grazing Economic returns Grass composition Rangeland health

Aside from overstocking, inappropriate grazing management strategies may cause rangeland degradation in commercial scale ranches. In this paper we construct a dynamic model to study the economic and ecological consequences of continuous and multi-paddock (MP) grazing. Simulations on long-term economic profitability and ecological indices were carried out for continuous vs. MP grazing management strategies under different grass growth rates, grass dormant periods, initial ecological conditions and various installation costs for MP grazing. Results show that compared to continuous grazing, MP grazing on large commercial ranches greatly increases the optimal 30-year net present value (NPV) by sustaining much higher stocking rates. At realistic stocking rates, MP grazing both increases long-term economic profit and improves ecological conditions. The advantage of MP grazing is more pronounced under xeric conditions, longer grass dormancy period, and initial prevalence of less palatable grasses and weeds. However, ranch managers for smaller ranches and/or ranches under short-term leases are less likely to adopt MP grazing due to its diminished economic advantages on those ranches.

1. Introduction Arid and semi-arid rangeland make up about one third of the earth's land use area (Sayre et al., 2012) and the primary use of these ecosystems is livestock grazing. Global livestock production has been increasing steadily since the 1960s (FAO, 2010) in response to increasing demand for animal protein and other products by a growing world population (Rosegrant et al., 2009). Unless resources are managed sustainably, the pressure on these ecosystems will cause degradation that will adversely impact the continued delivery of ecosystem goods and services upon which human well-being depends (Teague et al., 2013). With at least one billion people relying on rangelands for their livelihoods (Ragab and Prudhomme, 2002), it is vital for land managers to maintain resilient rangeland ecosystems while optimizing long-term economic returns.

In this regard, stocking rate decisions have been widely considered as the most important in terms of vegetation, livestock, wildlife and economic returns (Holechek et al., 1989; Briske et al., 2008) and thus have received intensive examination under various circumstances.

Among these, Huffaker and Wilen (1991) investigated optimal stocking rate under conditions of declining forage and pointed out that

⁎

Corresponding author.

E-mail address: tong.wang@sdstate.edu (T. Wang).

https://doi.org/10.1016/j.agsy.2018.06.012 Received 20 July 2017; Received in revised form 13 April 2018; Accepted 18 June 2018 0308-521X/ © 2018 Elsevier Ltd. All rights reserved.

intensive-early-stocking can outperform the season-long-stocking strategy in a variety of circumstances; Huffaker and Cooper (1995) studied optimal annual stocking decisions and the long-term impacts of the composition of rangeland vegetation; Kobayashi et al. (2007) examined the stocking decision for herders with restricted access to capital and found that increased capital cost will lower optimal stocking rates; Ritten et al. (2010) studied the impact of stochastic precipitation on optimal stocking density and suggests optimal stocking rates and profitability decrease in the face of increased precipitation variability; Teague et al. (2009) demonstrated that stocking for maximum longterm profit decreased ecological condition while managing stocking rates to improve ecological condition over the long term resulted in reduced profit; while Torell et al. (1991) compared the stocking decisions under short- and long-terms and found that stocking rate to maximize profit in the long term was well below that which caused severe deterioration of the rangeland.

While proper stocking rate ensures forage production and individual livestock performance in the short-term, inappropriate grazing management strategies can still cause rangeland degradation in commercial scale operations (Quaas et al., 2007; Wang et al., 2016). Despite the intensive scrutiny on the economic significance of stocking rates,

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previous economic literature has rarely analyzed the importance of grazing management strategies as a means of achieving economic and ecological goals. An exception is Jakoby et al. (2014), who found that MP grazing using a high number of paddocks per herd resulted in higher net returns, lower income variability when grazing using short periods of grazing with long periods of recovery. In this paper we study the long-term economic profitability for continuous vs. various multipaddock (MP) grazing management strategies under different grass growth rates, initial ecological conditions and feeder market prices.

Ecological conditions, including grass biomass and composition dynamics, are also determined for each grazing strategy.

Native grasslands comprise a mixture of many plant species and provide greater and more stable primary production as a consequence of this high diversity. Most modeling studies, however, have assumed the presence of only one species of grass, when comparing different grazing strategies (e.g., Noy-Meir, 1976; Woodward et al., 1993, 1995; Martin et al., 2014; Jakoby et al., 2014, 2015). By incorporating spatial heterogeneity, multispecies and grass selectivity, as well as intra-annual processes into the model, Wang et al. (2016) overcame short-comings inherent in most small-scaled experimental research as well as some limitations of modeling studies due to the monoculture assumption.

However, it includes no economic component to reflect the significant short- and long-term costs from installing the infrastructures necessary for MP grazing. Therefore, for producers who mainly focus on monetary incentives, either in the short or long-term, Wang et al. (2016) provides little guidance.

In this paper we will extend the modeling framework of Wang et al.

(2016), in which a dynamic mathematical model was developed that includes two interacting components: 1) an ecological component that describes the essential features of plant responses under livestock grazing and 2) a livestock grazing component that characterizes livestock grass consumption as a function of livestock body mass, forage availability and stocking rates. In this paper, an economic component has been added to the Wang et al. (2016) model to assess livestock production and economic implications of using MP grazing relative to continuous grazing management. To simplify the modeling and interpretation of results, our study only considers a stocker operation simulating the growth of feeder animals on native rangeland from weaning to sale off the ranch for finishing in a feedlot or on forages.

The stocker phase of the beef supply chain followed the cow-calf phase as featured by Wang et al. (2016), which assumed a fixed cow weight during the grazing period. Under the stocker phase, management aims at providing daily livestock weight gain. Therefore, for the livestock-grazing component, we incorporate an interaction between forage grazing and the livestock weight on a daily basis. The long-term economic profitability for continuous vs. MP grazing management strategies are simulated under different grass growth rates, grass dormant periods, initial ecological conditions and various levels of infrastructure costs required to implement MP grazing management.

Through different simulation scenarios, comparisons of using MP grazing vs. continuous grazing will be made in terms of livestock, grass and economic performance.

G1 (V 1, V 2) = g1V 1 ⎛1 − ⎝

V 1 + ρV 2 ⎞ Vm ⎠

G 2 (V 1, V 2) = g 2V 2 ⎛1 − ⎝

ρV 1 + V 2 ⎞ Vm ⎠

⎜

⎜

⎟

(1)

⎟

(2) 1

Similar to Noy-Meir (1976), g stands for the maximum relative growth rate of the palatable grass, while g2 denotes that of the less palatable grass. On a natural rangeland, as palatable grass of the same stature always grows faster than less palatable grass (Crawley, 1983; Oksanen, 1990; Teague and Dowhower, 2001). Consequently, we assume g1 > g2. Here V1 and V2 stand for biomass densities of the palatable and less palatable grass, respectively, and Vm is the maximum plant biomass on a per unit of land basis. Variable ρ ∈ (0, 1] is used to capture the competition between these two grass functional groups. It indicates the growth rate of each grass species is negatively related to the biomass density of the other. An abundance of the less palatable grass will result in less growth of the palatable grass over the management unit and vice versa.

Given that the initial biomass density is V0, with sp percent of palatable grass and su percent of less palatable grass, wheresp + su = 1, the initial biomass density is thus V01 = V0sp for palatable grass and V02 = V0su for less palatable grass. For the paddock currently under grazing, the defoliation rate for palatable grass is dp and that for the less palatable grass is du. The overall percentage of grass that is defoliated is therefore d = spdp + sudu. As livestock tend to defoliate a higher percentage of the palatable grass in both management practices, we have dp ≥ du .

Similar to Wang et al. (2016), denote the biomass densities of the defoliated and non-defoliated palatable grass as Vd1 and Vnd1 and those of the defoliated and non-defoliated less palatable grass as Vd2 and Vnd2.

Note that Vd1dp + Vnd1(1 − dp) = V1 and Vd2du + Vnd2(1 − du) = V2.

Assume the initial biomass density for the defoliated and non-defoliated portions are the same and we have Vd1 = Vnd1 = V0sp for palatable grass and Vd2 = Vnd2 = V0su for less palatable grass. The defoliated palatable grass will change over time as:

δVd1 = G1 (Vd1 , V 2) − C1 (w, Vd1) − ϕ⋅Vd1 δt

(3)

Note that different from Wang et al. (2016), the consumption of defoliated palatable grass, C1(w, Vd1) is a function of steer weight, w, which is changing daily and will be explained further in the grazing component section. Here we assume the existing biomass will die at a rate of ϕ, which has the same value regardless of the grass species. In a similar way, the defoliated portion of less palatable grass will change over time according to:

δVd2 = G 2 (V 1, Vd2) − C 2 (w, Vd1 , Vd2) − ϕ⋅Vd2 δt

(4)

The consumption of defoliated less palatable grass is denoted as C2(w, Vd1, Vd2), with more details provided in the grazing component section. Accordingly, the palatable grass and less palatable grass will change over time based on (5) and (6) respectively:

δV 1 1 = dp [G1 (Vd1 , V 2) − C1 (w, Vd1) − ϕ⋅Vd1] + (1 − dp )[G1 (Vnd , V 2) − ϕ δt

2. Model

1 ⋅Vnd ]

2.1. Ecological component

(5)

δV 2 = du [G 2 (V 1, Vd2) − C 2 (w, Vd1 , Vd2) − ϕ⋅Vd2] δt

Here we consider two functional groups of grasses: perennial palatable grass and perennial less palatable grass. Each group may contain different grass species. To simplify, we will refer to the perennial palatable grass as palatable grass, and the perennial less palatable grass as less palatable grass. Following Wang et al. (2016), grass growth-competition functions can be described in the form of the Lotka-Volterra equation:

2 2 + (1 − du )[G 2 (V 1, Vnd ) − ϕ⋅Vnd]

(6)

To provide a measurement of ecological condition on the rangeland, we define two ecological indices, namely the grass biomass index and the grass composition index. The grass biomass index (BI) is defined as the total available biomass divided by the maximum plant biomass, BI = (V1 + V2)/Vm, while the grass composition index (CI) is defined as 198

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the palatable grass biomass divided by the total biomass, CI = V1/ (V1 + V2).

of reduced consumption rate per steer. The total cost incurred on the farm on a per steer basis is denoted as TC(b).

As only one cohort is produced annually, the net present value (NPV) on a per hectare basis over a span of B years is calculated as:

2.2. Livestock grazing component

B

As mentioned in the ecological component, the livestock consumption function for the two grass species is C1(w, Vd1) for defoliated palatable grass and C2(w, Vd1, Vd2)for defoliated less palatable grass.

Similarly, Noy-Meir (1976) assumed that the consumption function takes the form of the Michaelis function if the biomass density of both species is greater than the residual biomass density, i.e., Vd1 > Vr1, Vd2 > Vr2. Therefore:

C1 (w, Vd1) = cm1 (w )

Vd1 − Vr1 H (Vd1 − Vr1) + (Vk1 − Vr1 )

C 2 (w, Vd1 , Vd2) = cm2 (w, Vd1 )

(Vd2 −

Vd2 Vr2)

− +

Vr2 (Vk2

− Vr2 )

NPV (B, H ) =

b=1

2.4. Description of MP grazing scheme Following Noy-Meir (1976) and Wang et al. (2016), we assume the MP grazing scheme is determined by two parameters, the number of paddocks, n, and the length of the MP grazing cycle, tr. Only the strict cyclic MP grazing scheme as defined by Woodward et al. (1995) is considered, where the grazing periods on each paddock are equal and livestock are introduced to successive paddocks in strict sequence. This means for the first tr/n days out of a typical MP grazing cycle, the first paddock is being grazed, while the other n − 1 are in recovery; for the second tr/n days the second paddock is being grazed and so on. Under the continuous grazing scheme, the whole ranch can be considered as one paddock that is continuously grazed as long as the stocker steers are retained on the farm. In this special case, n = 1.

Denote H as the average stocking density on the entire pasture. We assume that if the grass is 100% defoliated, the stocking density for the paddock under grazing will be nH (Noy-Meir, 1976). In our paper the overall grass defoliation rate is d, as explained in Section 2.1. Therefore, the stocking density on the defoliated grass is nH / d , while that on nondefoliated grass is 0. During a typical MP grazing cycle, each paddock has a recovery period of tr(n − 1)/n days, under which the stocking density is 0.

(8)

The satiation consumption increases as the steer weight w increases, as expressed by cm(w) = κ ⋅ w, where κ is denoted as the satiated forage consumption rate. Following Huffaker and Cooper (1995), assume that the satiated consumption rate of the palatable grass is cm1(w) = cm(w), while that of the less palatable grass is cm2(w, Vd1) = cm(w) − C1(Vd1). It indicates the livestock will graze the palatable grass first and will graze little or none of the less palatable grass if they get a sufficient supply of the palatable grass. Similar to Wang et al. (2016), Vki(i = 1, 2) denotes the Michaelis constant, at which the animal consumption is half of the satiated consumption rate.

Suppose the consumption of the palatable grass reaches the point such that the existing palatable grass biomass is less than the residual biomass, then the animal will consume the less palatable grass only.

That is, if Vd1 ≤ Vr1 and Vd2 > Vr2 then we have:

C1 (w, Vd1) = 0 C 2 (w, Vd1 , Vd2) = cm2

(9)

(Vd2

Vd2 − Vr2 H − Vr2) + (Vk2 − Vr2 )

2.5. Simulation experiments

(10)

Finally, if Vd1 ≤ Vr1 and Vd2 ≤ Vr2, then the consumption of both grass species is zero, i.e.:

C1 (w, Vd1) = 0 and C 2 (w, Vd1 , Vd2) = 0

As no simple analytic solution is readily obtainable regarding the optimal stocking rate for the MP grazing (Noy-Meir, 1976), we conduct simulation experiments using a set of parameters to compare long-term economic and ecological consequences under the different grazing scenarios.

Table 1 provides a summary of baseline parameter values that capture the characteristics of a stocker operation. A peak biomass value (Vm) of 4000 kg ha−1 is chosen (Wright and Baars, 1976; Teague et al., 2011; Wang et al., 2016). Similar peak biomass values had been reported by Salo et al. (2004) in South Central North Dakota, with an average of 4068 kg ha−1 on overflow range sites. The initial total plant biomass V0 is assumed to be 80% of the peak biomass value, which is composed of sp = 50% palatable grass and su = 50% less palatable grass.

We assume that higher quality grass is associated with a lower Michaelis constant, i.e., Vk1 = 15%⋅Vm and Vk 2 = 25%⋅Vm (Wang et al., 2016). The maximum grass growth rate is assumed as g1=0.03 per day on average during the grass growth season for palatable grass, which is 30% of the maximum growth rate for highly productive grassland assumed by Noy-Meir (1976). We assume the average growth rates of the two grass functional groups are correlated in the way that g2 = 0.8g1 (Wang et al., 2016). This is based on publications indicating that, compared with less palatable grass, palatable grass has evolved to grow quickly rather than invest resources in defense (Crawley, 1983; Oksanen, 1990; Teague and Dowhower, 2001). Following Noy-Meir (1981), assume the interaction between these two grass groups is ρ = 0.8.

The ungrazeable residual plant biomass Vr for both grass functional groups are assumed as 200 kg ha−1 (Noy-Meir, 1976; Wang et al.,

(11)

Clearly this case is non-sustainable. The stocker steer weight, starting from the purchase weight of wp, will change over time according to:

δw = θ⋅[C1 (w, Vd1) + ℓ⋅C 2 (w, Vd1 , Vd2)] δt

(12)

The consumption to weight gain conversion ratio is denoted as θ, which means 1 kg of daily grass consumption will generate θ kilogram of daily weight gain. We use parameter ℓ to stand for the relative conversion rate of less palatable grass to that of the palatable grass. In other words, 1 kg of less palatable grass is equivalent to ℓ kilogram of palatable grass for weight gain purpose. Given that less palatable grass could sometimes be of higher nutritious value than palatable grass, parameter ℓ is not necessarily less than 1.

2.3. Economic component Given that the average stocking rate is H per hectare, economic profit for cohort b on a per hectare basis can be defined as:

π (b, H ) = [ws (b, H ) Ps (b) − wp (b) Pp (b) − TC (b)]⋅H

(14)

where r denotes the real discount rate, meaning that the $1 economic return earned in year b is equivalent to $(1 − r)b earned in the current period.

(7)

H

∑ (1 − r )bπ (b, H )

(13)

The purchase weight and purchase price of the weaning steer for cohort b are denoted as wp(b) and Pp(b), while the selling price and selling weight of the steer are Ps(b) and ws(b, H). Note that the selling weight per steer usually declines as stocking rate increases, as the result 199

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weaned calves are stocked each year on November 15 with an average weight of 216 kg (475 lbs). The steers spend a total of 270 days on the farm. For the first 120 days after the purchase, the grass is in dormant period. We assume the steers graze on the standing grass or the initial plant biomass during this period. For the next 150 days, the steers graze on the growing grass until the August 15th when all the steers are sold.

The grass remains actively growing for the next 90 days without any grazing.

Based on the Cattle Fax data of the most recent 5 years (2012–2016), feeder price at 204 kg (450 lbs) in the month of November averaged at $4.77 kg−1. Based on a sliding price scale, the purchase price for a 216-kg feeder cattle can be calculated as $4.73 kg−1. Assume the stockers will be sold in mid-August of the following year, with selling prices contingent on the cattle ending weight. Selling prices can be calculated using the sliding scale based on the August average prices of 295-kg (650-lbs) and 341-kg (750-lbs) feeders of the recent 5 years, which were $4.11 kg−1 and $3.90 kg−1 respectively.

During each production period, we assume both continuous grazing and MP grazing incur a common production cost of $162 steer−1, which includes labor cost, herbicide cost, veterinarian costs, supplemental feed cost, interest cost, repair cost and property tax (Bevers, pers. comm.).2 However, as the focus is on the relative performance of the two grazing strategies, this common production cost incurred by both grazing strategies is immaterial for our comparison purpose. An important factor to consider is the additional cost incurred by MP grazing, which is discussed below.

For MP grazing, some initial investment on infrastructure is necessary, which includes new fencing and water systems.3 Different investment costs were estimated in previous studies. Therefore, we present a range of cost scenarios that will later be used for sensitivity analysis. A major source of cost difference is the size of grazing unit (Probert, 2013). While it cost more than $173 ha−1 ($70 acre−1) for a small pasture of less than 41 ha (100 acres), such cost was reduced to less than $25 ha−1 ($10 acre−1) for a pasture with more than 162 ha (400 acres) (Probert, 2013). Similar costs were estimated by Undersander et al. (2002), which ranges from $74 to $173 ha−1 ($30 to $70 acre−1), with the higher price range including costs of livestock lanes construction. Compared with these two studies, a much lower initial investment was estimated by Walt Davis, Grazing Management Consultant in Oklahoma. Using a commercial-scale ranch of 2072-ha (5120-acre), Davis estimated the total investment cost as $15,341 with average investment costs of $7.40 ha−1 (Details of calculation are shown Appendix).4 To evaluate the long-term grazing management impact on economic return and ecological condition, we chose a study period of 30 years.

We assume constant real prices and costs throughout the study period, meaning that if they were converted to nominal terms prices and costs would increase at the same rate as inflation. For the initial MP grazing investment, except for the cost of items needed to establish additional

Table 1 Parameters of the Baseline Simulation Model.

Symbol Vm V0 Vr sp su Vk1 Vk2 ρ dpc duc dpr dur g1 g2 ϕ n tr θ l B r TC Pp wp κ

Meaning maximum plant biomass initial plant biomass ungrazeable residual plant biomass percentage of palatable grass percentage of less palatable grass Michaelis constant for palatable grass Michaelis constant for less palatable grass interaction between two grasses palatable grass defoliation rate- continuous grazing less palatable grass defoliation rate- continuous grazing palatable grass defoliation rate- MP grazing less palatable grass defoliation rate- MP grazing maximum relative growth rate of palatable grass maximum relative growth rate of less palatable grass average daily death rate number of paddocks length of MP grazing cycle Forage conversion coefficient Relative conversion rate of less palatable grass Length of study period Real discount rate Total cost incurred per steer Steer purchase price Steer purchase weight Satiated forage consumption rate

Units

Values −1

kg ha kg ha−1 kg ha−1 % % kg ha−1 kg ha−1 – %

4000 0.8 ⋅ Vm 200 50 50 0.15 ⋅ Vm 0.25 ⋅ Vm 0.8 80

%

10

% % day−1 day−1

90 50 0.03 0.024

day−1

0.01 30 90 0.096 0.75 30 0.05 162 4.73 216 2.5%

days – – years – $ steer−1 $ kg−1 kg –

2016). In addition, assume a grass dormancy period of 120 days for both grass functional groups, from mid-November to mid-March, for which the growth rate of the grass is assumed as zero. The average daily death rate of the grass is assumed as 0.01 per day when not consumed.

The same grass death rate is assumed in the dormant period, as even though the microbial breakdown of the grass is slower, the wind breakdown rate is higher (Foy et al., 1999).

For MP grazing, assume the number of paddocks is n = 30, and the length of the MP grazing cycle is Tr = 90 (Wang et al., 2016). This indicates that the cows spend 3 days grazing on each paddock per cycle, with a recovery period of 87 days before the next grazing occurs on the same paddock. According to Teague et al. (2013), utilization of the less palatable grass is much higher for a short period under MP grazing due to increased stock density in the smaller paddocks while they are grazed. With MP management, livestock change the way they select the plants they consume once acclimated to the new high-density grazing management. This acclimation takes 2–3 years, after which, they use a broader spectrum of species (Provenza, 2003; Provenza, 2008). Under MP grazing, assume a defoliation rate of 50% for less palatable grass (dur) and 90% for palatable grass (dpr).

For continuous grazing, the entire ranch is considered as one paddock and grazing continues without any recovery period. Under continuous grazing, as livestock prefer areas close to water and shade (Stuth, 1991; Wallisdevries et al., 1999), livestock-preferred patches are heavily grazed and less-preferred patches are lightly used and only a relatively small portion of the landscape carries the grazing pressure. In addition, little or no grazing of the less palatable grass occurs under light continuous grazing in commercial scale paddocks (Teague et al., 2013). Defoliation rates of 10% for less palatable grass (duc) and 80% for palatable grass (dpc) are assumed for continuous grazing (Wang et al., 2016).

The satiated forage consumption rate is assumed as 2.5% of current body weight while they are grazing (Wang et al., 2016). Following Huffaker and Wilen (1991), assume the forage conversion coefficient as θ = 0.096 and the relative conversion rate as l = 0.75.

Fig. 1 demonstrates the timeline of the stocker operation of grassfed beef production1 to be modeled in the baseline scenario. Assume

1 Note that the stocker operation for feedlot beef production usually has a much shorter period on the grass, which is not considered separately in this paper.

2 Professor Stan Bevers, Professor and Extension Specialist Emeritus, Texas A&M AgriLife Extension, Vernon, Texas. According to Bevers, currently there are two methods to fatten the steers, either on owned grass, or on leased grass. It is generally assumed the costs incurred on owned grass are the same as those incurred on leased grass, when taking opportunity cost into account. The cost on owned grass can be roughly estimated by using a calculation formula for the cost incurred on leased grass. Given that the steers gain 0.45 kg (1 pound) per day on average on the rangeland at a fattening cost of $1.32 kg−1 ($0.60 pound−1), on leased grass it will cost about $162 steer−1 over the 270-day grazing period.

3 Note that no extra annual labor cost is assumed for MP grazing, since even though more labor is involved in moving the cattle, averaging 15 min per day, it saves labor to make hay and to haul manure (Undersander et al., 2002).

4 Note that no separate labor costs is included in the investment cost calculated by Walt Davis. It is assumed that as most ranchers complete installation in increments with existing ranch labor, which has already been covered in the production costs.

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Fig. 1. Timeline of a stocker operation with grass growing condition.

6) The forage conversion rate for less palatable grass. Many less-palatable forage species have reasonably high nutritive value even though they are consumed less. We considered the case where less palatable grass has a higher forage conversion coefficient, which is l = 1.25, against the baseline case where l = 0.75.

7) Plant selection rules. We consider less selective behavior for continuous grazing. That is, for continuous grazing a defoliation rate of 40% for less palatable grass and 80% for palatable grass are assumed, compared with the baseline case of 10% defoliation rate for less palatable grass and 80% for palatable grass.

8) Extra cost incurred by MP grazing strategy. MP grazing requires an investment in infrastructure to be adequately managed. We present 1) the baseline cost scenario estimated by an academic (Probert, 2013) of $25 ha−1; 2) the lower cost scenario of $7.40 ha−1estimated by Walt Davis, a successful grazing consultant on commercial operations; and 3) the high cost scenario estimated

by Undersander et al. (2002) of $74 ha−1, and the extreme high cost scenario, estimated by Undersander et al. (2002) and Probert (2013) as $173 ha−1.

9) Short-term vs. long-term decision. As some ranchers may emphasize more on quick returns we compared 5-year NPV vs. the 30-year NPV scenarios to determine if MP grazing management was economically feasible in both the short and long-term.

electric fences and additional water points, such as fence chargers with remote charge sensors etc. ($320), which requires replacement every 5 years, and the float valves (2 @ $30 each), which lasts around 10 years, everything else will last for 30 years with minor maintenance.5 2.6. Analysis of key elements To evaluate the economic and ecological consequences of differing grazing strategies under various stocking rates, several additional scenarios are analyzed and compared with the baseline scenario described in Section 2.5. For each studied scenario, we simulated a range of stocking rates and examined the impact of grazing strategies on 30-year total NPV. As noted in Gillespie et al. (2008), even though a precise profit maximizing stocking level cannot be determined, they can be approximated after studying several discrete stocking levels. We also checked the ending steer weight, average daily grass biomass index, and average daily composition index for the 30th year, the last year of our studied period.6 The alternative scenarios studied in this paper include: 1) Length of grass dormant period. We considered an alternative situation where grass dormant period is 90 days vs. the baseline of 120 days.

2) Absolute grass growth rate. We checked how the key variables change under a relatively high grass growth rate simulating a higher rainfall scenario relative to the baseline scenario of g1 = 0.03 and g2 = 0.8 g1 = 0.024. Specifically, we chose g1 = 0.04 (fast growth rate period) and g2 = 0.8 g1 = 0.032.

3) Relative grass growth rate. We tested how the key variables change when the growth rates of the palatable grass and less palatable grass are assumed as the same, i.e., g2 = g1 = 0.03 compared to the baseline scenario of g1 = 0.03 and g2 = 0.8 g1 = 0.024.

4) Initial forage biomass index. We compared the lower initial biomass index scenario that would be found with poor ecological condition and productivity BI = 0.6 compared with the baseline scenario BI = 0.8.

5) Initial grass composition index. Under a lower initial grass composition index CI = 0.3 vs. baseline of CI = 0.5 we investigate how a scenario with a high proportion of less-palatable species compare to the baseline scenario.

3. Results and discussion 3.1. Baseline model result Table 2 shows the steer ending weight, 30-year NPV per hectare, forage biomass index and composition index for different stocking rates under continuous and MP grazing. For a given grazing strategy, it is not surprising that a higher stocking rate, associated with more competitive grazing behavior and lower grass consumption per steer, always results in lower ending weight. The forage biomass indices for both grazing strategies decline gradually as stocking rates increase beyond the level resulting in maximum biomass. However, the biomass index for MP grazing is consistently higher, as more grass is produced with appropriately managed MP grazing resulting in more grass available for cattle to consume under each stocking scenario as has been previously reported (DeRamus et al., 2003; Gerrish, 2004; Teague et al., 2011; Teague et al., 2013).

With increasing stocking rate, composition index under continuous grazing decreases more precipitously, lagging far behind its MP grazing counterpart under moderate stocking rates. It shows that due to severe patch grazing under continuous grazing, the favorable grass species are rapidly depleted and the invasion of less palatable grasses and weeds, as

5 This cost information is provided by Walt Davis, Grazing Management Consultant in Oklahoma.

6 Note that each of these variables tend to reach the equilibria after around 20 years, therefore our reported values are also the equilibrium values.

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was stocked at nearly twice the level of continuous grazing, individual animal performance between two grazing strategies were no different.

In other words, animal production per hectare has significantly increased. Similarly, Heitschmidt et al. (1990) found MP grazing with 16 paddocks increased production per acre compared to heavy stocked continuous grazing.

The 30-year NPV per hectare, which is related to ending weight, also indicates a consistent advantage of MP grazing over continuous grazing. For example, when the stocking rate increases from 30 to 50 steers per 100 ha, 30-year NPV decreases sharply for continuous grazing, but it still increases considerably for MP grazing. Therefore, it can be inferred that, by sustaining a much higher stocking density compared to continuous grazing, MP grazing greatly increases maximum 30-year NPV. Heitschmidt et al. (1990) found that compared to heavy stocked continuous grazing, MP grazing increased average profit per acre during 1982 to 1987 study period. Several other modeling studies simulated multi-decadal responses and also reached similar conclusions (Jakoby et al., 2014; Jakoby et al., 2015; Teague et al., 2015).

In this paper, we do not consider the difference in forage quality between the two grazing strategies. It is noteworthy that patch grazing with continuous grazing management also has a strong negative impact on the preferred areas, causing resource deterioration in those preferred areas of the landscape (Thurow, 1991; Fuls, 1992; O'Connor, 1992; Teague et al., 2004; Teague et al., 2010). This impacts animal nutrition later as the avoided areas quickly move from the vegetative growth phase to reproductive phase resulting in very low-quality forage.

Eventually the livestock are confronted with most of the forage in this low quality state, resulting in poorer animal performance.

In contrast, ranches under appropriately managed MP grazing on commercial ranches are managed primarily to have sufficient forage for the livestock by timeously adjusting animal numbers. Overgrazing is strongly reduced or eliminated by grazing for very short periods followed by adequate time for recovery before re-grazing (Teague et al., 2011; Teague et al., 2013; Teague and Barnes, 2017). This keeps the plants vegetative over a much larger portion of the ranch facilitating higher quality diets for longer through the year, which results in a higher diet quality with MP grazing compared to continuous grazing (Heitschmidt et al., 1987).

Table 2 Effect of grazing practice on 30-year steer selling weight, Net Present Value (NPV) per hectare, biomass index and composition index (Growth rate g1 = 0.03; g2 = 0.024; initial plant biomass index is 0.8 and initial plant composition index is 0.5; grass dormant period is 120 days.

Stocking rate (# of steers per 100 ha) Ending Weight (kg steer−1) Continuous MP 30-year NPV ha−1 ($ × 102) Continuous MP Biomass Index Continuous MP Composition Index Continuous MP

15

20

25

30

35

40

50

55

340 353

337 352

331 351

323 349

311 348

300 345

285 337

279 330

3.22 4.03

3.91 5.35

4.20 6.59

4.04 7.70

4.00 8.65

2.64 9.39

−0.29 9.78

−1.86 9.12

0.43 0.52

0.42 0.51

0.42 0.51

0.40 0.50

0.39 0.50

0.39 0.49

0.38 0.47

0.37 0.46

0.93 0.89

0.87 0.87

0.78 0.84

0.68 0.80

0.57 0.77

0.51 0.73

0.44 0.62

0.42 0.55

Relative conversion rate of less palatable grass is 0.75. Under continuous grazing defoliation rate is 80% for palatable grass and 10% for less palatable grass; Under MP grazing there are 30 paddocks and the grazing period on each paddock is 3 days per MP grazing cycle; defoliation rate is 90% for palatable grass and 50% for less palatable grass; the purchase price for a 216 kg (475 pound) steer is 4.05 per kg. Real discount rate = 0.05.

well as bare ground, persist and expand, progressively degrading the landscape (Fuls, 1992, O'Connor, 1992, Bullock et al. 1994, Bailey et al., 1998, Teague et al., 2004).

Sustainable rangeland management can be achieved if overstocking and overgrazing are avoided. Overstocking is avoided by ensuring that livestock numbers do not exceed the amount of forage available to them and to leave sufficient herbaceous material to ensure maintenance of essential ecosystem functions. Overgrazing is avoided by having short grazing periods followed by adequate recovery after grazing (Teague and Barnes, 2017).

Results in Table 2 indicate that MP grazing, characterized by using short periods of grazing and adequate recovery periods, have a consistent advantage over continuous grazing. As shown in Table 2, when comparing the stocking rate of 30 under continuous grazing with 40 under MP grazing, the latter is noticeably superior in each of the categories. Similar conclusions have been reached in field experiments by Heitschmidt et al. (1987), who report rotational grazing with 16 paddocks can support higher levels of stocking with no detriment to the land resource. Compared to continuous grazing, the alternative MP grazing strategy can achieve the goal of increasing stocking rates and economic returns without deteriorating ecological conditions (Teague et al., 2011; Teague et al., 2013).

Under extremely high stocking rates, for both grazing management strategies there will be an increase in bare ground and replacement of productive, desirable herbaceous plants with low seral grasses and forbs lowering plant productivity, precipitation infiltration and provision of other ecosystem functions. This is consistent with the literature where many studies have demonstrated that the higher stocking rates combined with no recovery period after grazing, inevitably result in poorer range condition (Milchunas and Lauenroth, 1993; Vetter et al., 2006; Briske et al., 2008; Moreno García et al., 2014; Müller et al., 2015).

Table 2 in our simulation study indicated that there is an increase in ending weights per steer under MP grazing when compared with continuous grazing, especially under high stocking rates. Note that this comparison was done under the same stocking rate, which means MP grazing will increase animal production per hectare. Most field studies used heavier stocking rate under MP grazing and found individual animal performance were similar between continuous and MP grazing.

For example, Heitschmidt et al. (1982) showed even though MP grazing

3.2. Grass dormant period In Table 3, a shorter grass dormant period is considered - 90 days versus the baseline scenario of 120 days in Table 2. We can see that the shorter dormant period increases animal performance, economic profit and biomass index considerably under continuous grazing.

Table 3 Effect of grazing practice on steer selling weight, Net Present Value (NPV), biomass index and composition index when the dormant period is 90 days, otherwise as for Table 2.

Stocking rate (# of steers per 100 ha)

15

20

25

30

35

40

50

55

355 356

354 355

351 354

347 353

340 351

326 349

304 340

297 333

30-year NPV ha−1 ($ × 102) Continuous 4.42 MP 4.25

5.71 5.66

6.79 6.99

7.52 8.20

7.54 9.27

6.40 10.1

4.78 10.7

3.29 10.1

Biomass Index Continuous MP

0.51 0.52

0.51 0.51

0.50 0.51

0.49 0.50

0.48 0.50

0.46 0.49

0.45 0.47

0.45 0.46

Composition Index Continuous MP

0.87 0.89

0.82 0.86

0.76 0.84

0.68 0.80

0.58 0.77

0.46 0.72

0.36 0.61

0.34 0.54

Ending Weight (kg steer−1) Continuous MP

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The corresponding indicators increase for MP grazing too, but to a lesser extent. Therefore, the advantage of MP grazing over continuous grazing diminishes under the shorter grass dormant period, especially with the lower stocking rates. This implies that when the grass is dormant for a longer period, continuous grazing has more detrimental effect on grass biomass, which reduces animal performance more noticeably. Thus more supplement hay needs to be purchased to meet the animal nutrition requirement. For MP grazing, the negative influence of a longer dormant period can be partly counteracted by more even grazing of the available grass, which reduces the need for supplement hay.

The results of Tables 2 and 3 reveal that the benefit of MP grazing is more explicit under both longer grass dormant period and higher stocking rate. For example, at the stocking rate of 20, compared to continuous grazing, MP grazing increases 30-year NPV by 36.8% under 120-day dormant period scenario (Table 2), but decreases it by 0.88% under 90-day dormant period scenario (Table 3). At the stocking rate of 40, MP grazing increases 30-year NPV by 256% under 120-day dormant period scenario (Table 2), and by 57.8% under 90-day dormant period scenario (Table 3).

Table 5 Effect of grazing practice on 30-year steer selling weight, Net Present Value (NPV), biomass index and composition index at growth rate g1 = 0.03; g2 = 0.03. Otherwise as for Table 2.

Stocking rate (# of steers per 100 ha) Ending Weight (kg steer−1) Continuous MP 30-year NPV ha−1 ($ × 102) Continuous MP Biomass Index Continuous MP Composition Index Continuous MP

Table 4 illustrates the response of key variables under higher average season-long grass growth rate. Note that this sensitivity analysis aims to study the consequences of MP vs. continuous grazing in regions with more favorable rainfall conditions compared to that presented in the baseline case, rather than studying the effect of a rainfall increase in one single year. Higher grass growth rates result in a considerable increase in biomass index for both grazing strategies, which can in return sustain more grazing steers without overgrazing.

A comparison between Tables 2 and 4 clearly demonstrates the importance of rainfall in determining the productivity and optimal stocking rate. An element that our model does not capture though, is that with excessive rainfall, much of the forage will grow beyond the vegetative phase and decline markedly in quality, which would cause a negative influence on animal performance.

Although the amount of grass increases under more mesic conditions, the composition index has generally decreased when compared with the baseline case. This is due largely to the livestock's more selective consumption of abundant palatable grass. When the stocking rate increases, the selective grazing behavior decreases and the composition index under more mesic conditions gets closer to that under xeric conditions.

While MP grazing still excels for each of the indicators studied, this relative advantage diminishes for all stocking rates in the mesic

20

25

30

35

40

50

55

356 366

354 365

351 364

347 363

342 362

336 360

321 356

315 353

30-year NPV ha−1 ($ × 102) Continuous 4.42 MP 4.90

5.67 6.52

6.75 8.09

7.57 9.59

8.04 11.0

8.03 12.3

6.69 14.5

7.56 15.2

Biomass Index Continuous MP

0.57 0.64

0.56 0.64

0.55 0.64

0.55 0.63

0.54 0.63

0.53 0.62

0.52 0.61

0.52 0.61

Composition Index Continuous MP

0.76 0.75

0.72 0.73

0.67 0.71

0.62 0.69

0.56 0.67

0.50 0.65

0.40 0.59

0.37 0.56

Ending Weight (kg steer−1) Continuous MP

25

30

35

40

50

55

315 344

306 337

300 329

296 323

292 317

289 313

283 306

281 304

2.19 3.50

2.24 4.18

2.06 4.48

1.73 4.50

1.30 5.17

0.76 5.38

−0.52 5.19

−1.38 4.97

0.49 0.56

0.48 0.56

0.48 0.55

0.48 0.54

0.47 0.54

0.47 0.53

0.47 0.53

0.47 0.52

0.29 0.37

0.25 0.33

0.24 0.28

0.23 0.25

0.22 0.23

0.21 0.22

0.21 0.20

0.20 0.20

3.4. Relative grass growth rate Table 5 aims to test the robustness of the hypothesized MP grazing advantage when relative grass growth rate differs from the baseline assumption. A comparison between Tables 5 and 2 shows that for both grazing practices, biomass indices increase under all stocking rates. This is largely due to the higher growth rate of the unpalatable grass, which to a large degree is grazed much less compared to palatable grass.

Meanwhile, composition index decreases precipitously for both grazing strategies, which indicates that palatable grass is not able to compete with the less palatable grass even at the very low stocking rate.

Nevertheless, the composition index for MP grazing has a relative advantage over continuous grazing, especially at lower stocking rate, as the higher grazing pressure on less palatable grass reduces its competition edge to a certain degree.

Lower composition index, together with the assumption of higher forage conversion rate of the palatable grass (which is to be tested later on in Section 3.7), results in a drop in both ending weight and 30-year NPV for both grazing strategies. The advantage of MP grazing still remains, however, and even strengthens in this scenario when compared to the baseline scenario. For example, at the stocking rate of 30, MP grazing increases the 30-year NPV by 90.6% when compared to continuous grazing for the baseline case (Table 2), compared to 160% for the current scenario (Table 5). This shows the more uniform grass utilization under MP grazing helps counter the dominating effect of less palatable grass.

Table 4 Effect of grazing practice on 30-year steer selling weight, Net Present Value (NPV), biomass index and composition index at growth rate g1 = 0.04; g2 = 0.032. Otherwise as for Table 2.

15

20

scenario compared to the baseline scenario as depicted in Table 2. For example, the stocking rate of 30, compared to continuous grazing the MP grazing strategy increases the 30-year NPV by 90.6% in baseline conditions (Table 2), yet only by 26.7% in mesic conditions (Table 4).

This underscores the importance of using an effective MP grazing strategy to minimize the impact of drought years as indicated by Teague et al. (2013), Jakoby et al. (2014) and Jakoby et al. (2015).

3.3. Absolute grass growth rate

Stocking rate (# of steers per 100 ha)

15

3.5. Initial grass biomass index Table 6 shows the impact of a lower initial forage biomass index of 0.6 (compared to the baseline of 0.8; Table 2), with other conditions remaining the same. Comparing Table 6 with Table 2, we see the impact from the initial biomass index change not observable at the end of the 30-year period, in that the animal performance and ecological condition exactly resemble that of the baseline case. There is a slight decrease in NPV for each stocking rate, though, due to the reduced animal performance in the first couple of years as a result of the initially low grass biomass. Therefore, a one-time shock to total biomass amount 203

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Table 6 Effect of grazing practice on 30-year steer selling weight, Net Present Value (NPV), biomass index and composition index when initial biomass index is 0.6.

Otherwise as Table 2.

Stocking rate (# of steers per 100 ha)

15

20

25

30

35

40

50

55

Ending Weight (kg steer−1) Continuous 340 MP 353

337 352

331 351

323 349

311 348

300 345

285 337

279 330

30-year NPV ha−1 ($ × 102) Continuous 3.13 MP 3.97

3.79 5.27

4.11 6.48

3.95 7.57

3.90 8.50

2.53 9.21

−0.54 9.58

Biomass Index Continuous MP

0.43 0.52

0.42 0.51

0.42 0.51

0.40 0.50

0.39 0.50

0.39 0.49

Composition Index Continuous MP

0.93 0.89

0.87 0.87

0.78 0.84

0.68 0.80

0.57 0.77

0.51 0.73

Table 8 Effect of grazing practice on 30-year steer selling weight, Net Present Value (NPV), biomass index and composition index when the relative conversion rate of less palatable grass is 1.25. Otherwise as for Table 7.

Stocking rate (# of steers per 100 ha)

20

25

30

35

40

50

55

Ending Weight (kg steer−1) Continuous 335Z MP 352

329 353

317 353

304 352

294 352

287 350

275 342

270 335

−2.13 8.91

30-year NPV ha−1 ($ × 102) Continuous 3.06 MP 4.30

3.33 5.77

3.63 7.18

2.69 8.49

1.53 9.66

0.21 10.6

−2.64 11.1

−4.23 10.7

0.38 0.47

0.37 0.46

Biomass Index Continuous MP

0.42 0.52

0.41 0.51

0.39 0.50

0.38 0.50

0.38 0.49

0.37 0.48

0.37 0.45

0.36 0.43

0.44 0.62

0.42 0.55

Composition Index Continuous MP

0.84 0.88

0.69 0.85

0.54 0.81

0.47 0.77

0.43 0.73

0.41 0.67

0.38 0.50

0.37 0.43

than continuous grazing and therefore compensates the initial low ratio of palatable grass. In addition, a more uniform grazing behavior for MP grazing increases overall grass availability and spreads grazing pressure over the entire management unit in contrast to continuous grazing which concentrates grazing pressure on the preferred plant species.

Therefore, the animal performance is affected to a much lesser degree by the initially low palatable grass ratio.

will not alter the ecological condition in the long term, and therefore its impact on long term economic returns is also very small.

3.6. Initial grass composition index Table 7 considers a lower initial composition index of 0.3 (from the baseline 0.5) with all the other conditions the same as the baseline case in Table 2. Compared to a lower initial biomass index, a lower initial composition index has more serious negative influence. For MP grazing, the composition index at the end of the 30-year period is less affected at lower stocking rates, but is more seriously affected as stocking rate increases. Comparatively, the composition index for continuous grazing is much more severely affected, even at the low stocking rate. Despite the lower composition index, the biomass index is affected to a much lesser degree. This is mainly caused by the prevalence of less palatable grass and weeds, which generally have a lower growth rate and consumption compared to the palatable grass.

When the palatable grass ratio is initially low, MP grazing generates more robust long-term economic returns than continuous grazing strategy. For example, a comparison between Table 2 and Table 7 reveals that, at the stocking rate of 30 steers per 100 ha, the 30-year NPV ha−1 (Unit: $ × 102) decreases from 4.04 to 0.83 for continuous grazing, a 79.5% decrease; while it decreases from 7.70 to 7.11 for MP grazing, a 7.66% decrease. This is due to the less selective grazing behavior and periods of adequate recovery with MP grazing, which under moderate stocking rate results in much higher grass composition index

3.7. Higher forage conversion rate for less palatable grass In the previous scenario, it is found that if palatable grass is less abundant, then the animal performance is seriously affected, especially under continuous grazing. To check the robustness of this conclusion, we consider another case, where less palatable grass has a higher forage conversion coefficient, which is l = 1.25 (Table 8).

Compared to Table 7, higher forage conversion rate for less palatable grass in Table 8 increases animal performance and economic profit for both grazing strategies, especially for those scenarios where the composition indices are low. In those cases, the animal has to consume mainly less palatable grass and the increased forage conversion rate will promote the animal weight gain to a greater degree. The ecological indices for both grazing strategies are barely influenced though, since there is no change in grass growth and competition behavior. The minimal changes in ecological indices are caused solely by the increase in animal daily consumption, due to slightly increased steer weight gains over time.

For MP grazing, as the stocking rate increases from 15 to 35, the ending weight does not show a pattern of decrease as it usually does.

This is because the overall biomass stay fairly stable for these stocking rates, while the portion of less palatable grass, which has a higher conversion coefficient, increases. Compared to continuous grazing, the advantage of MP grazing remains robust for each of the stocking rates.

This is attributed to the planned grass recovery period for MP grazing, which results in higher biomass index. However, as MP grazing generally results in a lower ratio of less palatable grass, especially at higher stocking rates, the advantage of MP grazing diminishes by a small degree under the higher forage conversion rate for less palatable grass.

For example, at the stocking rate of 20, compared to continuous grazing, MP grazing increases the steer ending weight and 30-year NPV per hectare by 8.0% and 95% respectively when l = 0.75 (Table 7), versus the corresponding 7.3% and 73% increase when l = 1.25 (Table 8).

Table 7 Effect of grazing practice on 30-year steer selling weight, Net Present Value (NPV), biomass index and composition index when initial composition index is 0.3. Otherwise as for Table 2.

Stocking rate (# of steers per 100 ha)

15

20

25

30

35

40

50

55

Ending Weight (kg steer−1) Continuous 335 325 MP 352 351

308 350

294 348

284 345

276 341

266 327

261 318

30-year NPV ha−1 ($ × 102) Continuous 2.61 2.62 MP 3.90 5.12

2.23 6.21

0.83 7.11

−0.66 7.76

−2.22 8.05

−5.51 7.12

−7.24 6.55

Biomass Index Continuous MP

0.42 0.52

0.41 0.51

0.39 0.50

0.38 0.50

0.38 0.49

0.37 0.48

0.37 0.45

0.37 0.44

Composition Index Continuous MP

0.84 0.88

0.70 0.85

0.55 0.82

0.47 0.78

0.43 0.73

0.40 0.67

0.38 0.53

0.37 0.46

15

3.8. Plant selection rules In this section we assume less selective behavior for continuous 204

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Table 9 Effect of grazing practice on 30-year steer selling weight, Net Present Value (NPV), biomass index and composition index at defoliation rate 80% for palatable grass and 40% for less palatable grass under continuous grazing.

Otherwise as for Table 2.

Stocking rate (# of steers per 100 ha) Ending Weight (kg steer−1) Continuous MP 30-year NPV ha−1 ($ × 102) Continuous MP Biomass Index Continuous MP Composition Index Continuous MP

15

20

25

30

35

40

50

Table 10 Effect of different initial installment costs on 30-year and 5-year NPV, all other parameters are the same as Table 2.

Stocking rate (# of steers per 100 ha)

55

341 353

339 352

337 351

334 349

331 348

326 345

312 337

305 330

3.37 4.03

4.30 5.35

5.06 6.59

5.60 7.70

5.84 8.65

5.79 9.39

5.88 9.78

4.73 9.12

0.44 0.52

0.43 0.51

0.43 0.51

0.42 0.50

0.41 0.50

0.40 0.49

0.38 0.47

0.38 0.46

0.94 0.89

0.91 0.87

0.87 0.84

0.83 0.80

0.78 0.77

0.73 0.73

0.62 0.62

0.58 0.55

15

20

25

30

35

40

50

55

30-year NPV ha−1 ($ × 102) Continuous 3.22 MP (low cost) 4.21 MP (Baseline) 4.03 MP (high cost) 3.54 MP (extremely 2.55 high cost)

3.91 5.53 5.35 4.86 3.87

4.20 6.76 6.59 6.10 5.11

4.04 7.87 7.70 7.21 6.22

4.00 8.83 8.65 8.16 7.17

2.64 9.56 9.39 8.90 7.91

−0.29 9.96 9.78 9.29 8.30

−1.86 9.30 9.12 8.63 7.64

5-year NPV ha−1 ($ × 102) Continuous 0.90 MP (low cost) 1.18 MP (baseline) 1.00 MP (high cost) 0.51 MP (extremely −0.48 high cost)

1.06 1.55 1.37 0.88 −0.11

1.11 1.88 1.71 1.22 0.23

1.22 2.18 2.00 1.51 0.52

1.12 2.43 2.25 1.76 0.77

0.85 2.61 2.44 1.95 0.96

0.28 2.74 2.57 2.08 1.09

−0.11 2.66 2.48 1.99 1.00

surpass that under continuous grazing, reached at a stocking rate of 30.

Notice that the extremely high cost scenario only applies for small ranches of less than 41 ha, not for large commercial ranches. In addition, the competitive edge of MP grazing over continuous grazing has been reduced when 5-year NPV is considered, in comparison to the 30year NPV. When making comparisons among grazing strategies it is very important to continue such studies for sufficient time to allow potential differences to be manifest. An example illustrating this relates to work reported by Whitson et al. (1982), which reported that in the last 4 years of a 14-year study the heavier stocking rate with continuous grazing resulted in degradation of the grazing resource, reduced animal productivity and income stability, when compared with MP grazing.

This indicated that, given sufficient time, MP grazing resulted in better conservation of the resource and generated more net income. This is problematic for ranch operators that lease the land, since with no security of tenure, the incentive to adopt MP grazing is greatly reduced.

grazing when compared to the baseline, while that for MP grazing remains the same. Specifically, defoliation rate under continuous grazing is assumed as 80% for palatable grass and 40% for less palatable grass, compared with 80% for palatable grass and 10% for less palatable grass in baseline case.

Table 9 shows that when selective behavior diminishes for continuous grazing, while biomass indices only slightly increase when compared to those in Table 2, composition indices for continuous grazing demonstrate a significant increase under moderate to high stocking rates. Consequently, the advantage of MP grazing becomes much less obvious when it comes to ending weight and 30-year NPV. This indicates that for those smaller ranches where selective behavior is not a big issue, the advantage of MP grazing will be decreased.

3.9. Different initial installment costs, short-term vs. long-term To test the robustness of baseline results, we also consider three other cost scenarios: 1) low cost scenario, illustrated in the appendix as $7.40 ha−1; 2) high cost scenario, estimated by Undersander et al.

(2002) as $74 ha−1; and 3) extreme high cost scenario, estimated by Undersander et al. (2002) and Probert (2013) as $173 ha−1. The low cost scenario applies to those experienced producers with large ranches, while extremely high cost scenario applies to those who with extremely small ranches less than 100 acres and with livestock lane construction fee included as well.

With only initial installment costs differing from the baseline case, ending weight, biomass index and composition index remain the same as those in Table 2; however, the 30-year NPV for MP grazing will change accordingly, as Table 10 displays. Except for the extremely high cost scenario, MP grazing is advantageous in terms of 30-year NPV for all stocking rates considered when compared with continuous grazing, especially under the relatively high stocking rates. The extremely high cost scenario lags behind continuous grazing at the stocking rates of 15 and 20, but it still has an obvious advantage when the stocking rate is no less than 25. This implies that the long term economic advantage of MP grazing over continuous grazing remains robust even at the highest cost scenario, as long as the ranch is not understocked.

When it comes to achieving economic rewards in the short term, as the extra cost of MP spreads over a relatively short period, the advantages of MP grazing over continuous grazing diminish in all scenarios, but still positive. With the assessment over the first 5 years (5year NPV), MP grazing still maintains it competitive edge for the low cost, baseline and high cost scenario at its optimal stocking rate.

However, the optimal economic returns under MP grazing for the extremely high cost scenario, reached at a stocking rate of 50, is unable to

4. Conclusions In this paper we extend Wang et al. (2016) by comparing the economic returns of MP vs. continuous grazing strategies through the inclusion of the economic component in the simulation model. The focus of our paper is to compare the two grazing strategies under a variety of scenarios across different stocking rates. Our results show that, compared to continuous grazing, the advantage of MP grazing is more pronounced with: 1) longer grass dormant periods; 2) xeric conditions, or relatively low grass growth rate; 3) higher relative growth rates of the less palatable grass; 4) lower initial palatable grass composition; 5) lower forage conversion rate of less parable grass; 6) larger commercial ranches where selective grazing is more serious for continuous grazing; 7) reduced initial installation cost; and 8) a long-term planning horizon.

Compared to continuous grazing, MP grazing has great potential in increasing long term economic performance, indicated by an optimal 30-year NPV per hectare, by sustaining a much higher optimal stocking density. The economic advantage of MP grazing, however, diminishes with favorable conditions such as shorter grass dormant periods, more favorable rainfall conditions or an initially higher palatable grass ratio.

Higher extra cost incurred with MP grazing, due to factors such as smaller farm size, also reduces the economic competitiveness of MP grazing. In addition, shorter lease terms are also among factors that make the advantage of MP grazing either less obvious or non-existent.

One limitation of our paper is that it has assumed constant weather conditions and cattle prices over the years. Potential future research could focus on (1) determining proactive adjustment of management practices under uncertain weather conditions; and (2) investigating the 205

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supported by Dixon Water Foundation under project number H8179 and the National Institute of Food and Agriculture, U.S. Department of Agriculture, under award number 2017-67024-26279.

impact of stochastic market prices on different proactive adjustments to management practices and stock numbers.

Acknowledgements This article is based upon research work that is financially Appendix A Additional Initial Expense for Multi-paddock (MP) grazing.

9 joule fence charger with remote (replace every 5 years) 6 × 6 ft ground rods with clamps 3 lighting chokes @ $8.00 3 throw switches @ $7.00 poly tape for gates 19.5 miles 12.5 high tensile wire 1287 0.75 in. × 48 in. fiber glass sucker rod line posts @$4.00 48 × 6 in. top × 7 ft cedar posts @ $8.00 48 0.75 × 12 ft fiber glass risers @$12.00 48 double U insulators @ $0.78 100 ft 12.5 insulated wire 2300 gal water troughs with float valves @ $250 2 float valves @ $30 (replace every 10 years) 5280 ft 2 in. SDR11 HDPE pipe @ $1.12

$320 $100 $24 $21 $30 $2265 $5148 $384 $576 $38 $21 $440 $60 $5914 $15,341

Note: Installation to be done with ranch labor. The above figures are based on a 2072 ha (5120 ac) ranch. Data is provided by Walt Davis, Grazing Management Consultant, 262 SR 70E, Calera, OK 74730.

Jakoby, O., Quaas, M.F., Baumgärtner, S., Frank, K., 2015. Adapting livestock management to spatio-temporal heterogeneity in semi-arid rangelands. J. Environ. Manag.

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