CHAPTER 12 Impact of Grazing on the Ecosystems Daming Huang CONTENTS Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 The Observational Site of an Alpine Meadow Grazing Ecosystem for a Modeling Approach and Its Natural Conditions. . . . . . . . . . . . . . . . . . . 254 Modeling of an Alpine Meadow Grazing Ecosystem . . . . . . . . . . . . . . . . . . 255 Computer Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 Test of the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 Sensitivity Analysis of Rotational Grazing Scheme . . . . . . . . . . . . . 261 A Simulated Rotational Grazing Experiment Using the Alpine Meadow Grazing Ecosystem Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 Maximum Potential Productivity of the Summer-Autumn Pasture under Grazing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 Maximum Potential Productivity of the SAP under Grazing Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 Under Constant Grazing Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 Under Variable Grazing Pressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 INTRODUCTION The alpine meadow grazing ecosystem is a subsystem of the alpine meadow ecosystem in QingZang Plateau, China. Grazing ecosystem research 253 0-8493-0904-2/01/$0.00+$.50 © 2001 by CRC Press LLC 920103_CRC20_0904_CH12 1/13/01 11:06 AM Page 253 has been conducted using an alpine meadow ecosystem matter cycling energy flow biological complex modeling system approach since Shiyomi et al. (1983). The meadow or pasture forms an ecosystem in which matter cycles and energy flows through the constitutive components such as atmosphere, plants, and animals, day by day. The amount of energy and materials passing through or accumulating within these components is affected by factors in complicated relations with each other. A grazing system embraces an entire biological complex of weather, soil, plants, and animals, together with the management imposed upon it by the grazier in order to attain desired objec- tives, and it should be subject to evaluation by Shiyomi’s system approach (1983, 1986). Modeling offers a way of bridging the gap between grazing experiments and real grazing ecosystems, provided the model includes the decision-making processes as well as the biological interactions between the animals and the meadow. Efficient utilization of alpine meadow is one factor of importance. The potential for highly efficient meadow husbandry opti- mizing herd management can be evaluated by using modeling. From this point of view, we are seeking, in the study, a rotational grazing scheme and an optimal grazing pressure for the alpine meadow husbandry by modeling an alpine meadow grazing ecosystem. THE OBSERVATIONAL SITE OF AN ALPINE MEADOW GRAZING ECOSYSTEM FOR A MODELING APPROACH AND ITS NATURAL CONDITIONS Alpine meadows cover vast areas of the QingZang (Tibet) Plateau, espe- cially in the east and on high mountainous ranges. Amounting to 16 million ha, alpine meadows cover 40% of the grassland in Qinghai Province. The alpine meadow ecosystem research station, AFS, is located at Menyuan Stud Ranch of Menyuan Hui Autonomous County, Haibei Tibetan Autonomous Prefecture, Qinghai Province, 37°29Ј N-37°45Ј N and 101°12Ј E-101°33Ј E. The station lies at the foothill on the south slope of Lenglongling Mountains in the eastern part of the Qilian Mountains, in the northwest valley of the Datong River. The lowest lands on the south side range between 3200 m and 3400 m in altitude, forming a natural pasture where the station is situated. The high- est peak of the Lenglongling Mountain range has an altitude of 5076 meters. It is covered with snow all year, and the snow line is at about 4200 meters. The Datong River valley does not vary much in topography and has an altitude of 2800–3000 meters. In some places, the land has been farmed with rape (Brassica campestris) as the main crop. Field surveys were carried out on the experimental pastures of the AFS. There are 11 vegetation communities at the AFS, of which the most important is a Kobresia humilis meadow. It is the most common in the area of the AFS as well as on the Qinghai-Xizang Plateau and is regarded as the best natural pasture. It is found on river banks, slopes, and hills. The dominant species is Kobresia humilis, and subdominant species are 254 STRUCTURE AND FUNCTION IN AGROECOSYSTEMS DESIGN AND MANAGEMENT 920103_CRC20_0904_CH12 1/13/01 11:06 AM Page 254 Elymus nutans, Festuca ovina, Stipa aliena, etc., varying with the grazing pres- sure. As to domestic animals, there are horses, yaks, and sheep. The AFS area is grazed mainly by yaks and Tibetan sheep. The site parameters and pasture conditions are summarized in Table 12.1. MODELING OF AN ALPINE MEADOW GRAZING ECOSYSTEM In the alpine meadow pasture ecosystem, a portion of the solar energy is fixed by pasture plants; some parts of these plants are grazed by grazing ani- mals, and a fraction of the plants is fixed in animal bodies as energy. Energy escaping from this fixation is accumulated as soil organic matter via feces and urine, or diffused into the atmosphere from the animals as heat. Residual plant matter changes into standing dead plant material and then into soil sur- face litter, and finally accumulates in the soil. The system of energy flow in the alpine meadow grazing ecosystem from sun to animals or soil is shown in Fig. 12.1. In this figure, sources and sinks of energy are denoted by flags; compartments in which energy accumulates temporarily are shown by rec- tangles; directions of energy flow are indicated by arrow-heated full lines, and influences, including environmental and artificial effects on the energy flows which impinge upon the points shown by arrow-heated broken lines, are denoted by ellipses. Bows indicated by arrow-headed broken lines denote valves for regulating the energy flow. For example, the leaf area index or total leaf area per given land area affects the amount of energy flowing from the IMPACTS OF GRAZING ON THE ECOSYSTEMS 255 Table 12.1 Site Parameters and Experimental Pasture Conditions for Modeling Approach Item Explanation Latitude 37°29ЈN-37°45ЈN Longitude 101°12 ЈE-101°33ЈE. Altitude 3100–3800m above sea level Mean monthy air temperature minimum Ϫ13°C (January), maximum 12.3°C July), annual average 0°C Mean monthly precipitation minimum 1.87 mm (January), maximum 114.7mm (July), annual total 531.6mm Daily global solar radiation minimum 12558 kJ . m Ϫ2 . day Ϫ1 , maximum 21767.2 kJ . m Ϫ2 . day Ϫ1 , annual average 20930 kJ . m Ϫ2 . day Ϫ1 Pasture dominant plants Kobresia humilis, K. pygmaea, Stipa aliena, Festuca ovina, Carex spp., Poa spp., Elymus nutans, Saussurea superba, Gentiana straminea Grazing conditions no fertilizer application; Tibetan sheep 920103_CRC20_0904_CH12 1/13/01 11:06 AM Page 255 sun to plants. That is, if this valve opens and the leaf area index becomes larger, the amount of energy fixed in plants increases. The amounts of energy accumulated in eight different compartments on the grazing ecosystem are as follows: (1) above-ground live plant portion, V 1 , (2) below-ground live portion including roots, V 2 , (3) underground dead por- tion including roots, V 3 , (4) above-ground litter I (degradable portion includ- ing sugar, starch, protein, animo acid, etc.), V 4 , (5) above-ground litter II (undegradable portion including lignin, fat, tannin and wax), V 5 , (6) sheep intake (pastural plants consumed by grazing animals), V 6 , (7) sheep 256 STRUCTURE AND FUNCTION IN AGROECOSYSTEMS DESIGN AND MANAGEMENT Digestibility Grazing pressure: S Solar light intensity: A Amount of above-ground live portion: V 1 Leaf area index: L Sun: Q 0 Sheep liveweight: V 7 Amount of sheep intake: V 6 Respiration: Air- temperature: T m Amount of feces +urine+methane: V 8 Dead roots: V 3 Live roots: V 2 Soil: Q 10 Amount of litter I: Amount of litter II: V 5 V 4 Q 9 f 79 f 67 f 19 f 29 f 23 f 310 f 810 f 410 f 56 f 46 f 15 f 14 f 145 f 12 f 01 f 16 f 510 f 21 f 68 Figure 12.1 Energy flows of an alpine meadow grazing ecosystem. 920103_CRC20_0904_CH12 1/13/01 11:06 AM Page 256 liveweight, V 7 , (8) feces on the soil surface, V 8 . All these variables are meas- ured in their calorific value and change with time t. Changes in these variables can be formulated by a set of differential equations as follow: dV 1 /dt ϭ f 01 Q 0 ϩ f 21 V 2 Ϫ ( f 145 ϩ f 12 ϩ f 19 )V 1 Ϫ G 16 /S (12.1) dV 2 /dt ϭ f 12 V 1 Ϫ ( f 21 ϩ f 23 ϩ f 29 )V 2 (12.2) dV 3 /dt ϭ f 23 V 2 Ϫ f 39 V 3 (12.3) dV 4 /dt ϭ f 14 f 145 V 1 Ϫ f 410 V 4 Ϫ G 46 /S (12.4) dV 5 /dt ϭ f 15 f 145 V 1 Ϫ f 510 V 5 Ϫ G 56 /S (12.5) dV 6 /dt ϭ (F 16 ϩ F 46 ϩ F 56 ) Ϫ f 67 V 6 Ϫ f 68 V 6 (12.6) dV 7 /dt ϭ D D ϫ C O /E CV (12.7) dV 8 /dt ϭ f 68 V 6 /S Ϫ f 810 V 8 (12.8) In Equations 12.1–12.8, the unit for these variables’ biomass (dry matter 17.752032 kJ/g, Daming et al, 1991), except V 6 and V 7 , is kJ/m 2 . The unit for V 6 is kJ sheep Ϫ1 . day Ϫ1 and for V 7 is kg/sheep. Parameters in Equations 12.1–12.8, f ij , denote energy flow rate from variable i to j, and they generally change with the environmental temperature. The other parameters, G, S, etc., in the equations are explained in the following paragraphs. The main driving variables are functions of time and expressed by following equations. 1. T m is the mean temperature during 1981–1985 (°C) (Daming et al., 1991; Daming and Songling, 1992). T m ϭ 1.11013 ϩ 0.153234 t Ϫ 6.5979 ϫ 10 Ϫ6 t 3 ϩ 4.004 ϫ 10 Ϫ13 t 6 Ϫ 7.9187 ϫ 10 Ϫ16 t 7 where t denotes the number of days counted from 21 April. 2. Global solar radiation on alpine meadow is expressed by a sine func- tion as Q 0 ϭ 17165.88 ϩ 4605.48 {sin [2 ␲ (t ϩ 32)/365]} (kJ . m Ϫ2 . day Ϫ1 ) The maximum and minimum values of Q 0 are 21771.36 and 12560.4 kJ . m Ϫ2 . day Ϫ1 , respectively. 3. f 01 is the energy conversion efficiency of global solar radiation into plant material (aboveground live plant portion), and it is expressed as IMPACTS OF GRAZING ON THE ECOSYSTEMS 257 920103_CRC20_0904_CH12 1/13/01 11:06 AM Page 257 f 01 ϭ 95[1 Ϫ 1/(0.1019LV 1 )]A/(0.2388AQ 0 ϩ 1) where L is the leaf area index and A is a constant which takes a value between 0 and 0.07. A ϭ 0.035 ϩ 0.035 {sin[2 ␲ (t ϩ 32)/365]} L ϭ 3.238 ϫ 10 Ϫ4 ϩ 2.768 ϫ 10 Ϫ6 t ϩ 8.46 ϫ 10 Ϫ8 t 2 Ϫ 3.11 ϫ 10 Ϫ12 t 4 ϩ 1.519 ϫ 10 Ϫ19 t 7 4.f i9 ’s are coefficients of energy loss from the ith compartment, e.g., above- ground plant portion, underground portion, etc., by respiration of plants expressed as linear functions of air temperature (dimensionless). 5. f i10 ’s are coefficients of energy flow from the ith compartment, i.e., soil surface litter or feces, to the soil, and they are functions of air temperature (dimensionless). They and the other coefficients and parameters about pri- mary production are listed in Table 12.2. 6. G i6 (i ϭ 1,4,5. kJ . sheep Ϫ1 . day Ϫ1 ) is the amount of herbage material grazed by Tibetan sheep (Daming, 1993). The highest sheep food required is F (kJ . sheep Ϫ1 . day Ϫ1 ). F ϭ 1725.872 ϫ V 7 0.75 The relationship between herbage intake, H I (kJ . sheep Ϫ1 . day Ϫ1 ), and herbage allowance, A L , for sheep grazing on meadow is given by the follow- ing equations (Daming, 1993): H I ϭ Ά where A L ϭ (V 1 ϩ V 4 ϩ V 5 ) ϫ S and S is the grazing area per sheep (m 2 /sheep). The estimated critical value, M D , is M D ϭ 1904.1 ϫ V 7 0.75 The amount of aboveground live plant portion, V 1 , grazed by sheep is G 16 ϭ Ά The amount of aboveground litter I, V 4 , grazed by sheep is G 46 ϭ Ά 0 S ϫ V 1 Ն M D [V 4 /(V 4 ϩ V 5 )](1725.872 ϫ V 7 0.75 Ϫ G 16 ) S ϫ V 1 Ͻ M D , A L Ն M D Ϫ0.9064 ϫ S ϫ V 4 A L Ͻ M D 1725.872 ϫ V 7 0.75 S ϫ V 1 Ն M D 0.9064 ϫ S ϫ V 1 S ϫ V 1 Ͻ M D 0.9064 ϫ A L A L Յ M D F A L Ͼ M D 258 STRUCTURE AND FUNCTION IN AGROECOSYSTEMS DESIGN AND MANAGEMENT 920103_CRC20_0904_CH12 1/13/01 11:06 AM Page 258 The amount of aboveground litter II, V 5 , grazed by sheep is G 56 ϭ Ά So that F 16 ϭ G 16 /S, F 46 ϭ G 46 /S, F 56 ϭ G 56 /S and f (145)6 ϭ f 16 ϩ f 46 ϩ f 56 7. f 68 is a proportion of feces, urine and methine energy in the herbage grazed by sheep (Nanlin, 1982). f 68 ϭ 0.490914 0 S ϫ V 1 Ն M D [V 5 /(V 4 ϩ V 5 )]/(1725.872 ϫ V 7 0.75 Ϫ G 16 ) S ϫ V 1 Ͻ MD, A L Ն M D 0.9064 ϫ S ϫ V 5 A L Ͻ M D IMPACTS OF GRAZING ON THE ECOSYSTEMS 259 Table 12.2 Parameters for Energy Flow Equations in the Primary Productivity Compartment of the Model Refs. 5, 3 f 12 ϭ Ά f 145 ϭ Ά f 14 ϭ 0.6 ϫ f 145 , f 15 ϭ 0.4 ϫ f 145 f 19 ϭ Ά f 21 ϭ Ά f 23 ϭ 6.738 ϫ 10 Ϫ4 f 29 ϭ Ά f 310 ϭ Ά f 410 ϭ Ά f 510 ϭ Ά 3.153 ϫ 10 Ϫ5 T m ϩ 4.0033 ϫ 10 Ϫ3 (T m ՆϪ12.697) 0( T m Ͻ Ϫ2.697) 1.9062 ϫ 10 Ϫ5 T m ϩ 2.4202 ϫ 10 Ϫ2 (T m ՆϪ12.697) 0( T m Ͻ Ϫ12.697) 6.081 ϫ 10 Ϫ4 T m ϩ 1.56 ϫ 10 Ϫ3 (T m ՆϪ2.565) 0( T m Ͻ Ϫ2.565) 5.5765 ϫ 10 Ϫ7 T m ϩ 21042 ϫ 10 Ϫ6 (T m ՆϪ3.373) 0( T m Ͻ Ϫ3.373) 8.559 ϫ 10 Ϫ4 (t Յ 25) 0( t Ͼ 25) 3.01 ϫ 10 Ϫ5 T m ϩ 1.139 ϫ 10 4 (T m ՆϪ3.784) 0( T m Ͻ Ϫ3.784) 3.6237 ϫ 10 Ϫ4 (t Ͻ 133) 3.0703 ϫ 10 Ϫ2 (133 Ͻ t Ͻ 164) 0.5 ( t Ն 164) 0( t Ͻ 101, t Ͼ 164) 2.6996 ϫ 10 Ϫ2 (101 Ͻ t Ͻ 164) 920103_CRC20_0904_CH12 1/13/01 11:06 AM Page 259 then f 67 ϭ 1 Ϫ f 68 8. The relationship between the metabolic energy, M E , and V 6 is M E ϭ f 67 ϫ V 6 The relationship between the rate of heat production as a multiple of basic metabolism and the environmental temperature (Kleiber, 1961) is expressed as Y ϭ Ά Then D mei ϭ 293.076 ϫ Y ϫ V 7 0.75 where D mei represents the maintenance requirements of sheep, expressed in grams of digestible organic matter per day. 9. When aboveground live biomass is below 2 t/ha, D me is increased to account for greater energy spent in grazing such that (Huang, 1994): D me ϭ D mei ϫ (1.8 Ϫ 0.4 ϫ C TA ) where C TA ϭ (V 1 ϩ V 4 ϩ V 5 )/1775.2032 (t/ha) 10. Converse digestible organic matter intake to liveweight change. The conversion function (E CV ) is that derived by Arnold et al. (1977). E CV ϭ (0.040 ϫ V 7 Ϫ 0.225)/0.54 Liveweight change (D D ) is calculated in g/day as D D ϭ (M E Ϫ D mei )/17752.032 ϭ [0.459 ϫ V 6 Ϫ 203.076 ϫ Y ϫ (1.8 Ϫ 0.6 ϫ C TA ) ϫ V 7 0.75 /17752.032 and C o ϭ Ά 1 D D Ն 0 1.8 D D Ͻ 0 Ϫ0.05856 ϫ T m ϩ 2.167 T m Ͻ 13.125°C 1.3984 T m Ն 13.125°C 260 STRUCTURE AND FUNCTION IN AGROECOSYSTEMS DESIGN AND MANAGEMENT 920103_CRC20_0904_CH12 1/13/01 11:06 AM Page 260 Computer Program The above process was written in BASIC as a program, Manager of Alpine Meadow Grazing Ecosystems (MAMGE). The initial values of the variables on 21 April (t ϭ 42) are given in Table 12.3. The constants and the eight compartment values from which the program directly interpolates to calculate and derive the value of the following function through integration at each daily step: daily values and accumulated values of V 1 , V 2 , V 3 , V 4 , V 5 , V 6 , V 7 , V 8 , Q 0 , Q 9 , Q 10 , T m , amount of biomass aboveground (V 1 ϩ V 4 ϩ V 5 ), amount of biomass underground (V 2 ϩ V 3 ), etc. Test of the Model The predictions of the model were compared with experimental data obtained from a cutting trial carried out at the AMERS, as shown in Figure 12.2(a). The modeling predicted the energy dynamics of the alpine meadow grazing ecosystem as shown in Figure 12.2(b) for one year and in Figure 12.2(c) for four years. The calculated results fit the experimental data well. The model was tested against experimental data from another rotation grazing trial carried out at AMERS. Although the trial was not specifically designed for this purpose, the conditions under which it was undertaken seemed to be appropriate for comparison with the model output. The graz- ing plan is described in Figure 12.3. Predicted and observed results of the alpine meadow and sheep liveweight are shown in Table 12.4. The energy dynamics of aboveground biomass in paddocks of the rotation grazing experiment are shown in Figures 12.4a–e. The liveweight dynamics of sheep in rotation grazing experiment are shown in Figures 12.4f and g. Sensitivity Analysis of Rotational Grazing Scheme Sensitivity analysis was applied to the model. The effects at 100 and 182 days of a 20% increase or decrease of the values of V i (i ϭ 1, 2, 3, 4, 5) are shown in Table 12.5. The effects of a 20% increase or decrease temperature (T m ) or solar radiation (Q 0 ) for 182 days are also shown in Table 12.5. The results show that the system on 10 July (t ϭ 100 day) would be more stable IMPACTS OF GRAZING ON THE ECOSYSTEMS 261 Table 12.3 Initial Values of the Variables on T ؍ 42 (21 April) V 1t ϭ 42 ϭ 916.285 kJ . m Ϫ2 V 6t ϭ 42 ϭ 0 kJ . m Ϫ2 V 2t ϭ 42 ϭ 25534.238 kJ . m Ϫ2 V 7t ϭ 42 ϭ 24.85 kg . sheep Ϫ1 V 3t ϭ 42 ϭ 8128.224 kJ . m Ϫ2 V 8t ϭ 42 ϭ 0 J . m Ϫ2 V 4t ϭ 42 ϭ 15.266 kJ . m Ϫ2 t 0 ϭ 42 (1 June) V 5t ϭ 42 ϭ 271.382 kJ . m Ϫ2 t f ϭ 182 (30 October) 920103_CRC20_0904_CH12 1/13/01 11:06 AM Page 261 262 STRUCTURE AND FUNCTION IN AGROECOSYSTEMS DESIGN AND MANAGEMENT Below-ground biomass Above-ground biomass Plant dry weight (g/m 2 ) Month (a) 4 5 6 7 8 9 10 11 12 1 2 3 4 2200 2000 1800 1600 400 200 0 Month A E B C D (b) Biomass (x4.1868kj/m 2 ) 7500 6500 5500 3000 2000 1000 0 4 5 6 7 8 9 10 11 12 1 2 3 4 Year (c) Biomass (x4.1868kj/m 2 ) A F B C D E 1 234 7000 6000 5000 4000 2000 2000 1000 0 Figure 12.2 The simulation results of MAMGE (a) The aboveground biomass and underground biomass of Kobresia humilis meadow. Solid line repre- sents simulated values; Dotted line represents measured values. (b) For one year. (c) For 4 years. A, live roots; B, dead roots; C, amount of above- ground live portion (G 1 ); D, litter I; E, litter II; F, amount of total above- ground portion (G 1 ϩ G 4 ϩ G 5 ). 920103_CRC20_0904_CH12 1/13/01 11:06 AM Page 262 [...]... SDi, and SEi (i ϭ 1, 2, 3, 4) paddocks under a given grazing pressure The dotted line shows the continuous grazing in SA, SB, SC, SD, and SE paddocks The liveweight dynamics of Tibetan sheep are shown in continuous grazing (f ) and rotational grazing (g) in SA, SB, SC, SD, and SE 920103_CRC20_0904_CH12 Page 265 265 920103_CRC20_0904_CH12 266 1/13/01 11:06 AM Page 266 STRUCTURE AND FUNCTION IN AGROECOSYSTEMS... 162.5 61.6 300.8 209.0 24.9 37.1 MD E 11:06 AM Winter-spring pasture (g mϪ2) Summer-autumn pasture (g mϪ2) Date B 1/13/01 A 264 Table 12. 4 Comparing Model Output (MD) with Observed Data (OD) in the Rotational Grazing Experiment 920103_CRC20_0904_CH12 Page 264 STRUCTURE AND FUNCTION IN AGROECOSYSTEMS DESIGN AND MANAGEMENT Sheep Liveweight kg/sheep Above-ground biomass (V1+V4+V5) (kj/m2) 0 4 A 5 M 1/13/01... 920103_CRC20_0904_CH12 11:06 AM Page 268 STRUCTURE AND FUNCTION IN AGROECOSYSTEMS DESIGN AND MANAGEMENT 3851.49 3551.56 3251.62 2951.69 ACCUMULATED INTAKE ( KJ/m2 ) 4151.42 268 1/13/01 26 00 21 00 16 00 RA 11.00 TIO N LD 6 0 N U 1 M 0 B 0 E R DU 6.0 0 1.0 F 0 IE ING 0 AZ 2 GR Figure 12. 5 The accumulated intake for 270 rotational grazing schemes under critical grazing pressures and the control constraint 0 Յ Fi6... daily food grazing, feces and urine of Tibetan sheep Alpine Meadow Ecosys., 1982, 1:67 –72 10 Noy-Meir, I Rotational grazing in a continuously growing pasture: a simple model Agric Sys., 1976, 10:87 – 112 11 Orsini, J.P.G and Arnold, G.W Predicting the liveweight change of sheep grazing wheat stubbles in a Mediterranean environment Agric Sys., 1986, 20:83–103 12 Rao, S.S Optimization, theory and applications... FUNCTION IN AGROECOSYSTEMS DESIGN AND MANAGEMENT 800 f56 f46 (b) J(1) 4000 J(4) (kj/m2) Maximum accumulated intake 0 8000 J(5) 0 Below-ground biomass (kj/m2) f16 pressure (kjm-2day-1) Optimum variable grazing 1600 Above-ground biomass (kj/m2) 8000 (a) (c) V1 4000 V5 V4 0 40000 (d) V2 20000 V3 0 42 82 122 Time (day) 162 182 42 82 122 Time (day) 162 182 Figure 12. 7 The potential productivity of the summer-autumn... to compartment modeling of energy dynamics in alpine meadow grazing ecosystem (Equations 12. 1 12. 5), with the productivity being regarded as an objective function to be maximized through optimization under the following grazing pressures over the time Maximum Potential Productivity of the SAP under Grazing Pressure Finding the maximum productivity of the SAP under constant grazing pressure mathematically... modeling of an alpine meadow grazing ecosystem Journal of Xiamen University (Natural Science), 1993, 32(6):768 –772 4 Huang, D., Zuwang, W., Nanlin, P and Li, Z A study of energy flow and economic value of a family pasture in an alpine pastoral area Alpine Meadow Ecosys., 1991, 3:381 – 402 5 Huang, D and Songling, Zhao Compartment modeling of energy dynamics in Kobresia humilis meadow Acta Ecologia Sinica,... f145V1 Ϫ dV4/dt (12. 10) f56 ϭ f15 f145V1 Ϫ dV5/dt (12. 11) Computing of modeling systems provided an inference base to support a recommendation concerning the grazing pressure and accumulated intake The recommendation is as follows: under constant grazing pressure, the suboptimal grazing pressure is 25.90 J mϪ2 dayϪ1 with a higher accumulated intake J(1) ϭ 3268.17 kJ/m2, and the optimal grazing pressure... between grazing pressure and accumulated graze (b) ∑10.5∑(G1 ϩ G4 ϩ G5) The maximum accumulated graze (c) J(1) (d) J(145) (e) The energy dynamics of aboveground biomass portion (f ) The energy dynamics of underground biomass portion 920103_CRC20_0904_CH12 Page 270 STRUCTURE AND FUNCTION IN AGROECOSYSTEMS DESIGN AND MANAGEMENT 920103_CRC20_0904_CH12 1/13/01 11:06 AM Page 271 IMPACTS OF GRAZING ON THE... T., Hirosaki, S and Okubo, T A preliminary simulation model of grazing nature ecosystem Bull Nat Grassl Res Inst., 1983, 22:27–43 14 Shiyomi, M., Akiyama, T and Takahashi, S Modeling of energy flows and conversion efficiencies in a grassland ecosystem Ecol Modeling, 1986, 32:119–135 15 Shiyomi, M and Takahashi, S A formulation of the relationship between herbage allowance and herbage intake for animals . Kobresia humilis, and subdominant species are 254 STRUCTURE AND FUNCTION IN AGROECOSYSTEMS DESIGN AND MANAGEMENT 920103_CRC20_0904_CH12 1/13/01 11:06 AM Page 254 Elymus nutans, Festuca ovina, Stipa. Residual plant matter changes into standing dead plant material and then into soil sur- face litter, and finally accumulates in the soil. The system of energy flow in the alpine meadow grazing ecosystem from. consumed by grazing animals), V 6 , (7) sheep 256 STRUCTURE AND FUNCTION IN AGROECOSYSTEMS DESIGN AND MANAGEMENT Digestibility Grazing pressure: S Solar light intensity: A Amount of above-ground live