Agricultural Development underAgricultural Development underRisks and UncertaintiesRisks and Uncertainties

CSM’0620th Workshop on Complex

Systems Modeling August 28-30, 2006

IIASA, Laxenburg, Austria

G. Fischer, T. Ermolieva, Y. Ermoliev, H. van Velthuizen

International Institute for Applied Systems Analysis, Laxenburg, Austria.

Livestock (background)Livestock (background) Urbanization, expected large growth of per capita

incomes, and the ongoing demographic transition in China is bringing about major changes in consumption and production of livestock products.

To meet the growing meat demand, China as many other countries, is rapidly moving from traditional natural resource based management to intensified peri-urban and urban production systems.

The choice of options how to expand livestock production determines the vulnerability towards disease risk.

Environmental impacts through nutrient burden from concentrated pig and poultry systems, where insufficient land is available for manure disposal and recycling, can cause land and water pollution.

0

100

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900

2000 2005 2010 2015 2020 2025 2030

Mil

lio

ns

65+

15-64

0-14

China development scenarioChina development scenario

Rural / Urban household incomes

Composition of Rural Population by age Rural/Urban Population

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1500

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lio

ns

Urban

Rural

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60%

70%

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90%

100%

2000 2005 2010 2015 2020 2025 2030

Urban

Rural

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5000

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15000

20000

25000

30000

35000

40000

2000 2005 2010 2015 2020 2025 2030

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40000

Urban - high

Urban - low

Rural - high

Rural - low

Estimation of meat demandEstimation of meat demand

b2=8.07(62.64)

Per-capita Consumption

77 kg

17 kg

9,700 US-$2,200 US-$

b3=0.98(29.7)

b1=3.25(10.85) Dummies:

China 7.32 (5.31)India -9.56 (-7.34)USA 23.81 (6.04)Japan -50.37 (-13.29)

(125 countries, 1975-1997)

Source: SOW-VU, 2002.

Rural

Urban

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20000

40000

60000

80000

100000

2000 2005 2010 2015 2020 2025 2030

1000

mt

Other meat

Pork

Poultry

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20000

40000

60000

80000

100000

2000 2005 2010 2015 2020 2025 2030

10

00 m

t

0.0

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0.6

0.8

1.0

1.2

6 7 8 9 10

log(Income)

Inco

me E

lasti

cit

yMeat demand by income

Per-capita consumption, meat and eggs Meat demand by type

Meat demand by sector

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2000 2010 2020 2030

kg

per

cap

ut

Rural

Urban

Total

Livestock intensificationLivestock intensification The increasing meat demand can only be met through rapid

introduction of intensified livestock systems. Pig stocks in intensified systems are estimated to increase 3 to 3.5 times, broilers 4.4 to 5 times, and layers 2 to 2.4 times.

With high population and animal densities, in a mixture of still large numbers of backyard producers and a rapidly growing specialized meat sector, disease risks are a great concern.

Due to further intensification of agricultural production in both crop and livestock sectors, we estimate that with current rates of efficiency the environmental pressures stemming from nutrient concentration and overload would increase by at least one-third.

It is of high importance to improve fertilizer use efficiency and balance of nutrients, and to plan for environmentally adequate ways of livestock manure treatment and recycling.

Changes in production structureChanges in production structure

0%

10%

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30%

40%

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90%

100%

1985 1993 1996 1999

Ou

tpu

t sh

are

s

Hog enterprises

Specialised farms

Backyard hog farm

Source: Somwaru 2003

Livestock production intensificationLivestock production intensification Increasing intensification and specialization of livestock

production facilities close to markets in urban areas How far can (and should) China expand its production and

increase its intensification? According to Ricardo, … “intensification is beneficial and

trading nations will gain by specialization in goods of comparative advantage.”

Assertion is true if risks are not taken into account. Main risks: - environmental pollution (manure combined with chemical fertilizers) - livestock related diseases and epidemics - market risks - demand uncertainties and instabilities Intensification should take into account various risks The need for co-existence of large- and small-scale

(efficient) producers.

Co-existence of heterogeneous producersCo-existence of heterogeneous producersAbsence of risks: Two producers with production costs c1 < c2 < b

dxaxa 2211

Risk exposure: a1 and a2 are random variables (shocks to production)

2211 xcxc

dx *1 0*

2 x

dxx 21 01 x 02 x

2211 xcxc

},0max{)( 22112211 xaxadbExcxcxF

where bE max{0, d – a1x1 – a2x2} is the expected import cost if demand

exceeds the supply.

minimize

solution

minimize

minimize

of the distribution function describing

contingencies of the Producer 1, i.e., a1 , and the ratio c2 / b.

Optimal production share of Producer 2 is defined by the quantile

The cost efficient producer 1 is active if: c1 – bEa1 < 0

The less-efficient producer 2 stabilizes the aggregate production and the market in the presence of contingencies affecting the “most cost-effective” producer 1.

Market share of the Producer 2 (risk-free producer with higher production costs):

][),( 21222xxadbPcxxFx

0*2 x

bcxxadP /][ 2*2

*11

Take derivative

If Producer 1 is at risk: 0 < E a1 < 1, a2 = 1. Positive optimal decisions exist if:

0)0,0(1

xF 0)0,0(2

xF 11)0,0(1

bEacFx bcFx 2)0,0(2

i.e., less efficient producer 2 is active unconditionally: c2 – b < 0

Co-existence of heterogeneous producersCo-existence of heterogeneous producers

Spatial planning of livestock production Spatial planning of livestock production facilities in China: Main challengesfacilities in China: Main challenges

Contingencies (analytical form of pdfs) are often not known Spatially explicit framework: 2434 China counties Production allocation and intensification levels are projected

from the base year for: - Pigs, poultry, sheep, goat, meat cattle, milk cows) and - Management system (grazing, industrial, specialized, traditional) Production level to be restricted with respect to location-

specific economic & environmental constraints and indicators aggregating information on current environmental conditions, livestock composition, management characteristics, availability of land, etc.

Aggregate or insufficient data for estimation of the risks, indicators and constraints

Need for spatial data estimation procedures: - Upscaling / Downscaling - Data harmonization procedures

1. Survey statistics on livestock at county level: China 1997 year census

2. Statistics on livestock products by province: statistical year books

3. Crop production statistics at province and county level4. Information on fertilizer use5. Land and population statistics6. Expert estimates and survey data on livestock

production systems with different management characteristics, availability of feeds, etc.

7. Expert estimates, available statistics and simulated data on the level of veterinary services, agriculture related pollution, health control, etc.

8. Market conditions and risks: demand, prices, stability, etc.

9. …

Data for livestock production planningData for livestock production planning

Population distributionPopulation distribution(persons per square kilometer)(persons per square kilometer)

0 (%)

3-5 (%)

6-10 (%)

11-15 (%)

16-20 (%)

21-25 (%)

26-30 (%)

31-35 (%)

36-40 (%)

41-45 (%)

46-50 (%)

51-55 (%)

56-60 (%)

61-65 (%)

66-70 (%)

71-75 (%)

76-80 (%)

81-85 (%)

86-90 (%)

91-95 (%)

96-100 (%)

Intensity of cultivated land (in percent)Intensity of cultivated land (in percent)

021426384105125146167188209230251272293314335356376397418439460481>=502

Geographical distribution of Geographical distribution of pig stocks (in 1000)pig stocks (in 1000)

Hot-spots of fertilizer consumption (in kg of

nitrogen / ha cultivated land) projected for 2030

Hot-spots of high intensity of confined livestock (livestock biomass in kg / ha cultivated land) projected for 2030

0

1-150

151-300

301-600

601-1000

1001-1500

>1500

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1-50

51-150

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351-500

>500

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North

Northea

stEas

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l

South

South

west

Northwes

t

kg p

er h

a

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2030

Change of cultivated land(including orchards)

Nitrogen from manure of pigs and poultry in relation to stock of land for crop cultivation and orchards (kg N per ha)

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mil

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Northwest

Plateau

Southwest

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Northeast

North

Disease risk in ChinaDisease risk in China In extensive systems, all animals are exposed to diseases, they favour disease spread (high number of stepping stones), and present a very low proportion of susceptible animals. The working hypothesis is that the distribution of these extensive production units determines the distribution of disease persistence, and the spatial context for disease spread.

Intensification implies producing disease-free production systems, characterised by an increasing proportion of susceptible animals in the herds. The probability of an outbreak decreases as a function of intensification, mostly because the production conditions are more and more isolated from sources of infection. However, the impact of outbreaks also increases as a function of intensification.

Cases reports of disease transmission from extensive to intensive production units are found frequently in the available literature (e.g. Tong & Tong 1995).

The co-existence of highly contrasted production systems is considered as the main risk factor, and serves as a framework to determine risk categories.

Quantifying these patterns is difficult because of the absence of detailed epidemiological data.

Livestock production allocation under risks and uncertainties

id is the expected national supply increase in the livestock product i

ijlx is the unknown portion of the supply increase i related to location j and

management system l In its simplest form, the problem is to find ijlx satisfying the following system

of equations:

ijlijl dx

,, (1)

0ijlx , (2)

jliijl bx , Ll :1 , nj :1 , mi :1 , (3)

where jlb is aggregate risk constraint restricting the expansion of production

in system l and location j .

Apart from jlb , there may be additional limits imposed on ijlx , ijlijl rx ,

which can be associated with legislation, for example, to restrict production i within a production “belt”, or to exclude from urban or protected areas, etc. Thresholds jlb and ijlr may either indicate that livestock in excess of these

values is strictly prohibited or it incurs measures such as taxes or premiums, for eradication of the risks, say, livestock diseases outbreaks or environmental pollution. In this sense, they are analogous to the risk constraints from the catastrophe and insurance theory. Values jlb and ijlr may be reasonably

treated in priors.

Sequential rebalancing procedureSequential rebalancing procedure

iikik dqy 0- expected initial allocation of demand to location i and system k

i ikkk yb 00 /Derive relative imbalance and update000kikik yz

ki

byik

0But may not satisfy the constraint0iky

0ikz may not satisfy the constraint ik ik dz 0

k ikii zd 00 /Calculate and update 001iikik zy

siky i

kik

sik dqy can be represented as

jskik

skik

sik qqq 11 /

ik

ik dy

0ikyki

ik by

1k ikq - prior

Demand for product i

Aggregate constraint on meat production at location k

by applying sequentially adjusted : , 1sikq

iskik

skik

sik qqq /1

The procedure can be viewed as a redistribution of required supply increase di

ikik qq 0e.g., by using a Bayesian type of rule for updating the prior distribution, .

The procedure converges to the optimal solution maximizing

the cross-entropy function ij

ijij q

yy ln

Fischer, G., Ermolieva, T., Ermoliev, Y., and van Velthuizen, H.,“Sequential downscaling methods for Estimation from Aggregate Data”In K. Marti, Y. Ermoliev, M. Makovskii, G. Pflug (Eds.)Coping with Uncertainty: Modeling and Policy Issue, Springer Verlag, Berlin, New York, 2006.

Bregman, L.M. “Proof of the Convergence of Sheleikhovskii’s Method for a Problem with Transportation Constraints”, Journal of Computational Mathematics and Mathematical Physics,Vol. 7, No. 1, pp191-204, 1967 (Zhournal Vychislitel’noi Matematiki, USSR, Leningrad, 1967).

For Hitchcock-Koopmans transportation model the proof is in:

For more general constraints and using duality theorem the proof is in:

Sequential rebalancing procedureSequential rebalancing procedure

Numerical experimentsNumerical experiments An intensification scenario: production is allocated

proportionally to demand increase. A scenario that combines the demand driven preference

structure of the first scenario with information on population densities and its vulnerability to environmental risks.

Environmental risks combine three factors: a. density of confined livestock, b. human population density, c. availability of cultivated land.

2434 counties were classified as follows: - Percentage of land under cultivation (< 10 percent, 10 to

50 percent, > 50 percent),- Livestock-to-cultivated land ratio i.e., total live weight of

confined livestock per ha available cultivated (< 300 kg/ha, 300 to 600 kg/ha, and > 600kg/ha),

- Population density (< 100 persons per square kilometer, 100 to 1000 persons, and > 1000)

The resulting 27 combined classes The resulting 27 combined classes were further reduced to:were further reduced to:A: No confined livestock, counties in scarcely populated areas (desert or mountain/plateau) and with very little confined livestock

B: No environmental pressure, i.e., counties with substantial crop production but with little confined livestock;

C: Slight environmental pressure counties with low environmental pressure from confined livestock production;

D: Moderate environmental pressure, i.e., counties with moderate environmental pressure from confined livestock production;

E: Environmental pressure, i.e., counties with substantial urbanization and environmental pressure from confined livestock production;

F: High Environmental pressure, i.e., counties with substantial urbanization and high environmental pressure from livestock production, and

G: Extreme environmental pressure i.e., counties with high degree of urbanization coinciding with high environmental pressure from confined livestock production.

No confined livestock

No environmental pressure

Slight environmental pressure

Moderate environmental pressure

Environmental pressure

High environmental pressure

Extreme environmental pressure

Environmental pressures from Environmental pressures from confined livestock production, 2000.confined livestock production, 2000.

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Pressure

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Figure 2. (a) Absolute (million people) and (b) relative (share of total population) distribution of population according to classes of severity of environmental pressure from livestock, 2000. The labels on the horizontal axis indicate China regions: N, NE, E, C, S, SW, NW stand for North, North-East, East, Center, South, South-West, North-West, respectively.

(a) (b)

Distribution of population (year 2000) by severity Distribution of population (year 2000) by severity of livestock related environmental pressureof livestock related environmental pressure

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NW

Figure 3. Relative distribution of population according to classes of severity of environmental pressure from livestock, 2030: (a) “intensification” scenario, (b) environmentally more friendly scenario.

Two scenarios are compared with respect to Two scenarios are compared with respect to number of people in China’s regions exposed to number of people in China’s regions exposed to

different categories of environmental risksdifferent categories of environmental risks

ConclusionsConclusions This paper addresses some important aspects of agricultural

production planning under risks, uncertainties and incomplete information.

We illustrate the need for co-existence and cooperation of various agricultural producers with diversified risks, which enhances stability of agricultural markets.

We show that production expansion can not merely follow historical intensification trends which in many cases would lead to environmental and health problems and violate threshold constraints.

In many real-world applications, the distribution functions of contingencies are not tractable analytically due to the complexity of interacting factors and spatial relationships.

To derive estimates of contingencies, production planning relies on modeling of the dependencies and interactions among the processes as well as on appropriate downscaling and upscaling algorithms for estimating variables on required scales using all available information.

For many practical situations the assumption of “average flows” may be rather strong, which calls for more rigorous probabilistic treatments.

Paper published in "Journal of Systems Science and Systems Engineering“, available at: http://dx.doi.org/10.1007/s11518-006-5018-2

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