Download - Donkey Milk

UNIVERSITY OF PALERMO - SICILY (Italy)

Department S.En.Fi.Mi.Zo - Animal production Sector -

ANSC 400, CORNELL UNIVERSITY, 05/04/2006

Dr. Cristina Giosuè

A A System DynamicsSystem Dynamics application: “How to application: “How to increase the total donkey milk production in increase the total donkey milk production in

Italy, producing profitability to the farmers?” Italy, producing profitability to the farmers?”

PhD student in “PRODUZIONI FORAGGERE MEDITERRANEE” XVIII cyclePhD student in “PRODUZIONI FORAGGERE MEDITERRANEE” XVIII cycle

Visiting fellow at Cornell University in the Departmnent of Animal Science Visiting fellow at Cornell University in the Departmnent of Animal Science

OutlineOutline

-Introduction to System Dynamics System Dynamics modelingmodeling

-Examples of System Dynamics applicationSystem Dynamics application on a donkey milk production model

Introduction to System Dynamics modelingSystem Dynamics modeling

What is System Dynamics and why it is important?

- The complexity of the systems in which we live is growing (accelerating economic, technological, social, and environmental changes)

- Many of the problems we now face arise as unanticipated side effect of our own past actions

- All too often the policies we implement to solve important problem fail, make the problem worse, or create new problems

CSDNet

System Dynamics is

- perspective and set of conceptual tools that enable us to understand the structure and dynamics of complex systems

- qualitative modeling method that enables us to build formal computer simulations of complex systems and use them to design more effective policies and organizations

- a rigorous way to help thinking, visualizing, sharing, and communication of the future evolution of complex organizations and issues over time for the purpose of solving problems and creating more robust designs, reducing the likelihood of counterintuitive or unintended consequences

What is System Dynamics and why it is important?

CSDNet

Figure 1-3 in Sterman Assumes a clear and linear response of results to our decision

Why unintended consequences?

• Event-oriented world view• Every event has a (single) cause• Leads to event-oriented problem solving

System Dynamics involve the use of:

• Diagrams, graphs, words, and basic algebra to activate and capture existing knowledge about a particular observed problem situation

• Frameworks to help both researchers and practitioners organize, filter and structure that knowledge

• Mathematical simulation models and learning environments that help researchers and decision makers to identify more sustainable solutions and further refine their conceptual models

CSDNet

“All models are wrong, some models are useful”

• All models are simplifications and must omit elements of reality

• Despite these omissions, “good models” can enhance our thinking and problem solving

All models have “clients”

• Clients are people you must influence for your work to have impact

• Help clients solve their problem……but also challenge their thinking

Examples of System Dynamics applicationSystem Dynamics application on a donkey milk production model

1. Problem Articulation(Boundary Selection)

3. Formulation4. Testing

5. PolicyFormulation& Evaluation

2. DynamicHypothesis

Iteration can occur from any step to any other

Modeling effort will go through each of these step many times

The SD Modeling ProcessThe SD Modeling Process

1. Problem Articulation(Boundary Selection)

3. Formulation4. Testing

5. PolicyFormulation& Evaluation

2. DynamicHypothesis

Iteration can occur from any

step to any other

Modeling effort will go through

each of these step many times

The SD Modeling ProcessThe SD Modeling Process

Real world

Information feedback

Mental models of real world

Strategy, structure, decision rules

Decisions

(Organizational Experiments)

The researchable PROBLEM is:The researchable PROBLEM is:

How to increase the total How to increase the total donkey milk production in Italy, donkey milk production in Italy,

producing profitability to the producing profitability to the farmers?”……..farmers?”……..

Problem articulation

……..and WHY?..and WHY?


General problem (background)

Food Allergies

a) In the last 20 years the population of developed In the last 20 years the population of developed

countries suffering food allergies has increased countries suffering food allergies has increased

(from 5 to 10%), the children and the babies are (from 5 to 10%), the children and the babies are

the most affected the most affected (www.italiasalute.it)(www.italiasalute.it)

b) FA develop when intestinal immune system FA develop when intestinal immune system

doesn’t respond normally to the food proteins or doesn’t respond normally to the food proteins or

protein fragments which have escaped lumen protein fragments which have escaped lumen

hydrolysishydrolysis



Food Allergies

The main foods, that frequently cause allergy, are:

egg (albumin), peanut, walnut,hazelnut, fish,shellfish, cow milk, chocolate, fruit (strawberry, pineapple, orange, tropical fruit ecc), cheese and vegetable (tomate ecc) ecc.

The common symptoms of FA are:

nausea, vomiting, abdominal pain, distension, flatulence and diarrhea; sometime skin and respiratory tract may be involved. Occasionally, severe systemic (anaphylactic) reactions are provoked and these reactions may be fatal (Sampson et al., 1996; Kimber et al., 2002).



Cow Milk Protein Allergy (CMPA)

Cow milk protein allergy (CMPA) is the most relevant with higher social implications in developed countries.

Prevalence: 2-5% of the children and babies in the developed countries (Pizzin et al., 2003; Villoslada et al., 2005) and 1% in the adults (E. Smith, 1997).


CMPA

Most children with CMPA synthesize Most children with CMPA synthesize specific specific

immunoglobulin E to proteinic antigensimmunoglobulin E to proteinic antigens (Iacono et (Iacono et

al., 1992),al., 1992), such as such as αα, , ββ and k caseins, and k caseins, ββ

lactoglobuline, lactoglobuline, αα lactoalbumine and lactoferine lactoalbumine and lactoferine (Teschemacher et al., 1997; (Teschemacher et al., 1997; F. Lara-Villoslada et al., F. Lara-Villoslada et al.,

2005; CMPA in infancy and childhood) 2005; CMPA in infancy and childhood)



CMPA

Actual alternative feeding

systems........ -Dietary products for infants derived from several

different protein sources (such as bovine casein, bovine whey, bovine or porcine collagen, soy, or mixtures of these) exposed to different procedures of hydrolysis and further processing (heat treatment or ultrafiltration)

-Dietary products based on amino acid mixtures

(Fiocchi et al., 2003).



CMPA

……..but..but

Some patients with CMAP can also react to Some patients with CMAP can also react to

these foods these foods ((multiple food allergies) multiple food allergies) (Iannolino (Iannolino

et al., 2005)et al., 2005)



Researchable problemThe donkey milk and CMPA

Since 1990, in Italy, some researches in regard to donkey Since 1990, in Italy, some researches in regard to donkey

milk use on children with strong food allergies have milk use on children with strong food allergies have

started.started. In some regions of Italy the use of donkey milk to feed the

babies is not new (in Sicily until the end of the Second War and in Germany) (Oftedal et al., 1988).

The economical, social changes and the industrial progress have caused an increase in the use of milk substitutes.

Iacono et al. (1992) showed good results by the use of donkey milk on 9 babies with multiple food allergies. The donkey milk was well tolerated and no negative reactions were recorded. These results were confirmed by Carroccio et al. (2000) on 18/21 patients.


SpeciesWate

r%

Total solids

%

Fat%

Protein%

Casein%

Lactose%

Ash%

EnergyKJ/kg

Cow87.6

212.38 3.46 3.43 2.50 4.71

0.78

2983

Sheep80.4

819.52 7.50 6.17 4.50 4.89

0.92

5289

Goat86.7

713.23 4.62 3.41 3.10 4.47

0.73

3399

Cow buffalo

82.2 17.8 7.50 4.80 3.84 4.700.80

4846

Donkey*

91.16

8.84 0.38 1.72 0.38** 6.880.39

1939***

Woman87.5

712.43 3.38 1.64 0.40 6.69

0.22

2855

Milk composition (%) of different species and Energy (KJ/kg)

(Polidori 1994)

*Salimei et al., 1999; **Salimei et al, 2001; ***Polidori 1994*Salimei et al., 1999; **Salimei et al, 2001; ***Polidori 1994

Sheep Goat CowWoma

n

donke

yHorse

Protein (%) 95.3 91.3 95.0 88.6 86.0 90

Casein (%) 78.5 75.6 78.0 30.4 38.0 45

Whey protein

(%)16.8 15.7 17.0 58.2 48.0 45

(Lisozime, ppm) - trace trace 500 4000 700

Non proteic

nitrogen4.66 8.7 – 7.13

5 –

7.4311.4 14.0 10

Average nitrogen composition of the milk in some species

Cow+ Goat+ Horse*Donkey*

*Woman***

β lactoglobuline

(% of total

wheyprotein)

64 56 60 30 No

α lactoalbumine

(% of total

wheyprotein)

28 47 2-15 22 High

αs casein (% of casein) 450 – 5(as1)

12,6(as2)Yes Yes no

K casein (% of casein) 12 8.1 ? ?

γ casein (% of casein) 2.5 3.9 Yes Yes

β casein (% of casein) 30-35 75 Yes Yes

Some Milk Proteic Fractions

+ Jenness, 1980; *Doreau et Boulot, 1989; **Buscemi, 2000;***Ambruzzi, 2003

More investigations are necessary!

Average value

Total saturated % 67.58

volatile, soluble saturated %

0.91

Total Monounsaturated% 15.82

Total Polyunsaturated % 16.60

Polyunsaturated ω3 % 7.45

Polyunsaturated ω 6 % 8.65

Polynsaturated ω 3/ ω 6 0.86

Acidic composition of the donkey milk fat(Chiofalo 2001)

Essential Fatty Acids (EFAs) and human healthEssential Fatty Acids (EFAs) and human health

EFAsEFAs are long-chain polyunsaturated fatty acids derived from are long-chain polyunsaturated fatty acids derived from linolenic (linolenic (Omega-3Omega-3), linoleic (), linoleic (Omega-6Omega-6), and oleic acids ), and oleic acids

((Omega-9Omega-9)) (The number following "Omega-" represents the position of the first double bond,

counting from the terminal methyl group on the molecule)

Omega-9Omega-9 is "non-essential" because the body can manufacture a

modest amount on its own, provided essential EFAs are present

EFAs EFAs are necessary fats that humans cannot synthesize, and are necessary fats that humans cannot synthesize, and must be obtained through diet and support the cardiovascular, must be obtained through diet and support the cardiovascular, reproductive, immune, and nervous systems by the production reproductive, immune, and nervous systems by the production of prostaglandinesof prostaglandines (they are fundamental for growth in fetuses (by (they are fundamental for growth in fetuses (by mother’s dietary intake) and children, particularly for neural mother’s dietary intake) and children, particularly for neural development and maturation of sensory systemdevelopment and maturation of sensory system (www.goodfats.pamrotella.com(www.goodfats.pamrotella.com))

Essential Fatty Acids (EFAs) and human healthEssential Fatty Acids (EFAs) and human healthFoods that contain omega 3:Foods that contain omega 3: Foods that contain omega 6:Foods that contain omega 6:

Flaxseed oil (flaxseed oil has the highest linolenic content of any food), flaxseeds and flaxseed meal

Flaxseed oil, flaxseeds and flaxseed meal

hempseed oil and hempseeds hempseed oil and hempseeds

walnuts Grapeseed oilpumpkin seeds pumpkin seedsBrazil nuts pine nuts

sesame seeds pistachio nutsAvocados sunflower seeds (raw)some dark leafy green vegetables olive oil, olives, borage oilcanola oil (cold-pressed and unrefined)

evening primrose oil

soybean oil black currant seed oilwheat germ oil chestnut oilFish chicken

Corn, safflower, sunflower, soybean, and cottonseed oils are also sources of linoleic acid, but are refined and may be nutrient-deficient as sold in stores.

Conjugated linoleic acids (CLA) and human healthConjugated linoleic acids (CLA) and human health

Mixture of positional and geometric isomers of linoleic acids Mixture of positional and geometric isomers of linoleic acids with two double bonds, which can be different in the position with two double bonds, which can be different in the position and orientation (and orientation (ciscis or or transtrans) located on adjacent carbons.) located on adjacent carbons.

The main source of CLA in human diets:The main source of CLA in human diets:

-food products derived from ruminants (meat and dairy -food products derived from ruminants (meat and dairy products) products)

The CLA are showingThe CLA are showing impressive range of beneficial health impressive range of beneficial health effects in biomedical studies with animal models, like:effects in biomedical studies with animal models, like:

Anti-carcinogenic Anti-carcinogenic Anti-obesity and altered nutrient partitioning Anti-obesity and altered nutrient partitioning Anti-atherogenic and reduces cholesterol Anti-atherogenic and reduces cholesterol Enhance the immune system Enhance the immune system Enhance bone mineralizationEnhance bone mineralization

(Bauman & Lock, 2006)

Conjugated linoleic acids (CLA)Conjugated linoleic acids (CLA)cis-9, trans-11 CLA and trans-10, cis-12 CLA

cis-9, trans-11 conjugated linoleic acid is the predominant CLA isomer found in ruminant fat including milk fat.

CLA is produced as an intermediate in rumen biohydrogenation of linoleic acid present in the cows diet and a portion of the CLA in milk fat comes from that which has escaped complete biohydrogenation in the rumen.

However, the majority is made by the cow herself using the desaturase enzyme and trans-11 18:1 (vaccenic acid), another fatty acid intermediate produced during rumen biohydrogenation.

With certain diets the rumen environment is changed and a portion of the biohydrogenation produces, trans-10, cis-12 CLA and trans-10 C18:1 as intermediates. trans-10, cis-12 CLA is present at only trace levels in milk fat (Bauman & Lock, 2006)

cis-9, trans-11 CLA

Trans vaccenic and CLA content in milk fat of different species in comparison with human milk fat

(Jahreis et al., 1999)

Collaborative Research projectCollaborative Research project: effect of different diet and oxytocin use on donkey milk fat

yield and fatty acids composition

INVESTIGATORS: INVESTIGATORS: Cornell University Department of Animal Science (USA) ,

Istituto Sperimentale Zootecnico per la Sicilia and University of Palermo Department SEn. Fi.Mi.Zo. (Italy)

OBJECTIVES:OBJECTIVES:– To investigate changes in the pattern of donkey

milk fatty acids, using two different diets, one of them with an extra virgin olive oil integration.

– To investigate changes in donkey milk fat yield and fatty acids composition, using oxytocin

Researchable problem

The donkey as livestock animal

MILKMILK

Medicine:

- PEDIATRICS- PEDIATRICS

- GERIATRICS- GERIATRICS

- CARDIOLOGICS- CARDIOLOGICS

- FOR SOME TUMORS- FOR SOME TUMORS

Cosmetic industry Cosmetic industry


Researchable problem

The donkey as livestock animal

MEATMEAT

- brasato- brasato- StracottoStracotto

- Smoked meat - Smoked meat -Cold meat and Cold meat and -salamisalami


Researchable problemThe EU is showing a particular attention to promote the livestock production in marginal areas, to prevent and to stop the abandon of these rural areas, which can cause very relevant and negative consequences on the environment, the economical and social aspect.

The donkey is a breed in extinction in developed countries, and this animal is presented in marginal areas, thanks its high resistance and adaptation capacity


Donkey breeds in Italy

6 main donkey breeds

Martina Franca Sardo



Amiata Asinara

Romagnolo



Ragusano Pantesco

Sicilian

The donkey, which has used in the past to work

the land and to transport, now as a livestock animal can be an

alternative profitability resource for the

marginal areas of the Mediterranean as well as

for many agriculture areas of the developing countries, In relationship with the other income by the sale of donkey for meat and by other possible utilizations

(trekking, brain gym, pet therapy)

Problem of Donkey milk sale in Italy

• The donkey milk is not included in the DPR 54/97

• The sale can be only direct (from the farmer to the consumer) through autorization from the ASL (local sanitary agency) (Regio Decreto 9Regio Decreto 9thth May 1929 n° 994) May 1929 n° 994)

• The VETERINARY INSPECTORATEThe VETERINARY INSPECTORATE has institued in Sicily a

TECHNICAL AND SCIENTIFIC COMMITTEE TECHNICAL AND SCIENTIFIC COMMITTEE to investigate more to investigate more

donkey milk production and health aspects, to establish donkey milk production and health aspects, to establish

policies and marketing strategies improving this new policies and marketing strategies improving this new

productive sectorproductive sector

Dynamic problem definition Define a “Reference Mode”

Graphs or other information showing the development of the relevant problem over time

The information about the donkey milk production and

donkey milk consume is not registered by the statistical institutions in Italy;

The donkey indeed is not included into animals producing milk but only meat, considering the low incidence of this product and the actual selling and production restrictions.


In Italy, since 1960, donkey number has decreased In Italy, since 1960, donkey number has decreased highly (FAO 2005).highly (FAO 2005).

050,000

100,000150,000200,000250,000300,000350,000400,000450,000500,000550,000

Time (Year)

Donk

ey (h

eads

)

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

Time (Year)

Mil

k p

rod

uct

ion

rat

e (L

iter

/yea

rs)

Qualitative reference mode of donkey milk Qualitative reference mode of donkey milk production (liter/month)production (liter/month)

Qualitative future reference mode of donkey milk Qualitative future reference mode of donkey milk production (liter/month) production (liter/month)

19

95

19

96

19

97

19

98

19

99

20

00

20

01

20

02

20

03

20

04

20

05

20

06

20

07

20

08

20

09

20

06

20

07

20

08

20

09

20

10

20

11

20

12

20

13

Time (Year)

Mil

k p

rod

uct

ion

rat

e (L

iter

/yea

rs)

It is important to define the relevant time horizonenough of past to show problem development

enough into future to show possible delayed effects of potential policies

In this case I have chosen 8 years like time horizon, because I think that this can be enough to evaluate the results of application of different policies and strategies, increasing the milk production and then the milk available for the market

Problem articulation Dynamic problem definition

Dynamic Hypothesis

• A proposed explanation for the A proposed explanation for the behaviorbehavior– Explicit structure that creates behavior– Provisional, subject to revision (working

theory)

• Endogenous focusEndogenous focus– Behavior arising from within the system– Not (just) external shocks

• Avoid “narrow” model boundaries

Tools for Dynamic Hypotheses

• Model Boundary Chart– What variables included, excluded– What variables exogenous, endogenous

• Causal Loop Diagrams (CLD)– Show causal linkages among variables– Focus on feedback structure

• Stock-Flow Diagrams (SFD)– Characterize physical stock-flow structure

Dynamic Hypothesis

Population and birth rate loop

PopulationBirth Rate

++Births

INCREASE in population increases births, INCREASE in births increases population.

This is a POSITIVE feedback loop, which will cause population to grow.

Dynamic Hypothesis

Population and death rate loop

PopulationDeath Rate

+-Deaths

Population INCREASES death rate, death rate DECREASES population

This is a NEGATIVE or BALANCING feedback loop

Dynamic Hypothesis

PopulationDeath RateBirth Rate

++-+Births

Deaths

The simple system has two feedback loops

These operate together to produce the behavior of the system.

Population increases birth rate, birth rate increases population

Population increases death rate, death rate decreases population

Dynamic Hypothesis

Dynamic HypothesisBS sales and

death rate

Breedingstock

-

+

B

BS sale anddeath

Dynamic Hypothesis

BS sales anddeath rate

Breedingstock

-

+

B

BS sale anddeath

Birth rate

+


Breedingstock

-

+

Young stock

B

BS sale anddeath

Birth rate

+

+

Dynamic Hypothesis


Breedingstock

-

+

Young stock

B

BS sale anddeath

Birth rate

+

+

Dynamic Hypothesis

Young stock

YS sales anddeath rate

+


Maturationrate

-


Breedingstock

-

+

Young stock

B

BS sale anddeath

Birth rate

+

+

Young stock


+

Dynamic Hypothesis


Breedingstock

-

+

Young stock

B

BS sale anddeath

Birth rate

+

+

Young stock


+


Maturationrate

-

Dynamic Hypothesis

Breeding stock

+

Maturationrate

+

YS sales anddeath

B


Maturationrate

-


Breedingstock

-

+

Young stock

B

BS sale anddeath

Birth rate

+

+

Young stock


+

Dynamic Hypothesis

Breeding stock

+

Maturationrate

+

YS sales anddeath

B

R

YS decrease

Young stock++

Maturationrate

-

+

-

++

-+

Breedingstock

Donkey milkproduction

+

Milk productionper donkey

+

Breedingstock


+


+Milk available for

the market+

Donkey milkper YS

-

Milk consume peryoung donkey

+

Youngstock

+

Milk available forthe market

Ratio of demand tomilk available for the

market

-Donkey milk

price+

Revenuemilk

++B

Production, demand,price, net margin of

milk

Breedingstock


+


+Milk available for

the market+

Donkey milkper YS

-


+

Youngstock

+


Ratio of demand tomilk available for the

market

-Donkey milk

price+

Donkey milkdemand

+

-

Revenuemilk

++

BDonkey milk

demand

B


milkConsumer

+

+

Breedingstock


+


+Milk available for

the market+

Donkey milkper YS

-


+

Youngstock

+


Breedingstock

Birth rate

+

+


+


+


+

Donkey milkper YS

-


+Young stock+

+


Ratio of demand to milkavailable for the market

-

Donkey milkprice

+

Donkey milkdemand

+

-

Revenuemilk

++

Revenuedonkey sale

Totalrevenue

Donkey price

++ +Maturation

rate

-

B

BS sale and death

B

Donkey milk demand

B


milk Consumer

+

R

YS sales anddeath

+

-

-

+

B

+

YS decrease

++

Net margin forfarmers

Total donkey (YSand BS)


Breedingstock

Birth rate

+

+


+


+


+

Donkey milkper YS

-


+Young stock+

+



-

Donkey milkprice

+

Donkey milkdemand

+

-

Revenuemilk

++

Revenuedonkey sale

Totalrevenue

Donkey price

++ +

+

Total costs

-

Other costs

+

Feed cost+ +

+

Feed resourceper land

-

Maturationrate

-

B

BS sale and death

B

Donkey milk demand

B


milk Consumer

+

R

YS sales anddeath

+

-

-

+

B

+

-

YS decrease

B

Cost

++

Net margin forfarmers

Total donkey (YSand BS)


Breedingstock

Birth rate

+

+Donkey milkproduction

+


+


+

Donkey milkper YS

-


+Young stock+

+



-

Donkey milkprice

+

Donkey milkdemand

+

-

Revenuemilk

++

Revenuedonkey sale

Totalrevenue

Donkey price

+++

+

Total costs

-

Other costs

+

Feed cost+ +

+

Feed resourceper land

-

Maturationrate

-

B

BS sale and death

B

Donkey milk demand

B


milk Consumer

+

R

YS sales anddeath

+

-

-

+

B

+

-

YS decrease

B

Cost

++

DesiredBreeding stock

+

- -

R

Effect of desiredbreeding stock on Net

margin

Explicit delineation of stocks and flows

Stocks (states) are accumulations– Material or information– Can be counted at a given time– Change only through flows

Flows (rates) are quantities per some amount of time- Change states- Cannot be measured instantaneously- Can be affected by many other variables

Dynamic Hypothesis

• “State-rate” structure

Rates affect states, states affect ratesRates affect states, states affect rates

• Units consistency for variables, equations– Explicit specification of units for each

element

Dynamic Hypothesis

Graphical Representation

PopulationBirthRate

DeathRate

StockFlow Flow

Dynamic Hypothesis

Graphical Representation

FBR and AL are Auxiliary Variables (neither stocks nor flows)

PopulationBirthRate

DeathRate

StockFlow Flow

Stock

Fractional BirthRate

AverageLifespan

Population also determines the birth and death rates in this case

Dynamic Hypothesis

Stock and flows diagrams AGING CHAIN DONKEYS

YoungStock

BreedingStockMaturation

rateBirth rate

YS Sales rate

YS Death rate

BS Sales rate

BS Death rate

Exports

ImportsFoaling Interval

Maturation Delay

BS Mortality Rate

BS AverageLifetime

YS MortalityFraction

YS Sales Fraction

<MaturationDelay>

Effect of desiredbreeding stock on YS

sales fraction

Effect of desired breedingstock on BS average

lifetime

Effect of desired breedingstock on YS mortality

fraction

Effect of desiredbreeding stock on BS

mortality rate

Stock and flows diagrams

MILK PRODUCTION, MILK DEMAND AND MILK PRICE

Donkey MilkDemand

Donkey MilkPrice

Reference DonkeyMilk Price

Reference DonkeyMilk Demand

Sensitivity ofDemand to Price

Ratio of Demand to MilkAvailable for Market

Sensitivity of Priceto the Ratio

Smooth of Ratio

Smooth Time



Total MilkProduction

Milk Consumedby YS Milk Available for

the Market

Breedingstock

Youngstock

Initial sales perconsumers

Initial demand

Adoptionrate

Repeated demand

Consumer Averageconsumption per

consumer

Stock and flows diagrams CONSUMER

Potentialconsumers

Consumers

Adoption rate

Adoption fromdoctor's advertising

+

Advertisingeffectiveness

Adoption fromword of mouth

++ Total population

Adoption fraction

Contact rate

-+

Discard rate

Average productuse

-

+

C/TP

Stock and flows diagrams FEED RESOURCE

Feedresourcesper land

Growth rate Consumptionrate

Land area

Relative Rainfall

+

Fractional growthrate

Carrying capacity

FRPL to CCRatio Stocking rate

Minimum feed onland time

Feed Per DonkeyPer Month

Losses rate

Proportional losses

Pulse height1

Reference RainfallAverage Land Area

Per Farm

Effect of Rainfallon CC

Observed Rainfall

Effect of FRPL toCC Ratio on FGR

Total donkeys

Number offarm

Youngstock

Breedingstock

Purchased feed

Max FeedConsumption Rate from

FRPL

Stock and flows diagrams DONKEY FARM SYSTEM

Number ofFarms Exit RateEntry Rate

Reference NetMargin

Lookup Functionfor Entry

Reference ExitRate

Lookup Functionfor Exit

Minimum Time inFarm

Donkey per farm

Entrance Delay

Farm carryingcapacity

Number of farmsto FCC

Fractional entryrate

Effect of number offarms to FER

Breedingstock

Smooth of actualnet margin

Donkey MeatPrice

Donkey Price

Carcass YieldMarketing Costs

Total revenue

Total costs

Non feed unit variablecost per donkey

Milk Availablefor the Market

Actual NetMargin

Purchasedfeed

Feed price

Feed costs

Desired BreedingStock

Relative net margin

Effect of Net Margin ondesired Breeding stock

Smooth of ActualNet Margin

NM smooth time

Milk Revenues

Meat Revenues

Breedingstock

Youngstock Donkey milk

price

Reference netmargin

YS salesrate

BS salesrate

Stock and flows diagrams REVENUE, COSTS AND NET MARGIN

Mathematics of SD models

• System of ordinary differential equations• Solved by numerical integration

– St = ∫(Inflow-Outflow) ds + S0

– Inflow = f(S, other variables)

– Outflow = f(S, other variables)

• Many software programs available

– Vensim® is good for research purposes

Dynamic Hypothesis

Testing (Formulate Simulation Model)

• An explicit mathematical representationhelps to:

– Identify vague concepts– Resolve contradictions previously unnoticed

• Provides a real test of understanding of the problem and its elements– Specification must be complete and

consistent• Many softwares available

– I’m using Vensim® from Ventana Systems

Model Evaluation

• Begins with first equation• Comparison of behavior in model to real world• Concepts in model should correspond to a

meaningful real world concept• Check for

– Dimensional consistency– Sensitivity to parameter changes– Response to “extreme conditions”

Policy Design and Evaluation

• Modifications to relevant parameters• Creation of entirely new strategies and structures

– Modifying the feedback structure– Reducing or eliminating the delays– Changing information flows– Altering decision rules

• Assess sensitivity of policy results

And now a little bit of practice!

Milk production model

Thank you !

Download - Donkey Milk

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