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1 Anders Ringgaard Kristensen, I PH Anders Ringgaard Kristensen, I - - PDF document

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Anders Ringgaard Kristensen, I PH KVL Anders Ringgaard Kristensen, I PH Outline Short survey of animal replacement models A 4-level model for optimal feeding level, fattening policy and slaughtering of organic steers (BKN): Model

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Advanced Herd Management 2006 1

Animal replacement models

Anders Ringgaard Kristensen

KVL Advanced Herd Management 2006 2 Anders Ringgaard Kristensen, I PH Anders Ringgaard Kristensen, I PH

Outline

  • Short survey of animal replacement models
  • A 4-level model for optimal feeding level, fattening

policy and slaughtering of organic steers (BKN):

Model structure Decisions being optimized

  • A 3-level model for optimal replacement of sows

Model structure Integration with Dynamic Linear Model

  • A dairy cow model with one calving disease

Model structure Decisions being optimized

Advanced Herd Management 2006 3 Anders Ringgaard Kristensen, I PH Anders Ringgaard Kristensen, I PH

Anim al replacem ent m odels: Breeding anim als

  • Dairy cows:

Traits:

Age (lactation number and stage) Milk yield Pregnancy status Diseases

Decisions

Replace Inseminate Treat (for diseases)

  • Sows

More or less like cows (except milk yield … )

Short survey of animal replacement models Advanced Herd Management 2006 4 Anders Ringgaard Kristensen, I PH Anders Ringgaard Kristensen, I PH

  • Dairy heifers
  • Slaughter pigs
  • Steers
  • Traits considered:

Age Weight Pregnancy status (heifers … )

  • Decisions considered:

Feeding level Insemination (heifers) Slaughter (pigs, steers)

Short survey of animal replacement models

Anim al replacem ent m odels: Grow ing anim als

Advanced Herd Management 2006 5 Anders Ringgaard Kristensen, I PH Anders Ringgaard Kristensen, I PH

Sow m odel: Litter size and Markov property

  • Litter size at next parity depends on all previous litter

size observations.

  • In other words, the Markov property is not satisfied.

A 3-level model for optimal replacement of sows Advanced Herd Management 2006 6 Anders Ringgaard Kristensen, I PH Anders Ringgaard Kristensen, I PH

Circum venting the Markov violation

  • Define the state as the combined value of present and

previous litter size.

  • If each may be “Low”, “Average”, “High” (9

combinations):

Low, Low Low, Average Low, High Average, Low Average, Average Average, High High, Low High, Average High, High

  • Only a computational problem – the “curse of

dimensionality” once again.

A 3-level model for optimal replacement of sows

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Advanced Herd Management 2006 7 Anders Ringgaard Kristensen, I PH Anders Ringgaard Kristensen, I PH

A com prehensive exam ple

  • A sow replacement model

Developed for practical use at prototype level 3 levels: Decisions at 2 levels Estimation at herd level Bayesian updating (Dynamic linear model) Decision making

A 3-level model for optimal replacement of sows Advanced Herd Management 2006 8 Anders Ringgaard Kristensen, I PH Anders Ringgaard Kristensen, I PH

State space

  • Litter size
  • Age (parity)
  • Rematings

A 3-level model for optimal replacement of sows Advanced Herd Management 2006 9 Anders Ringgaard Kristensen, I PH Anders Ringgaard Kristensen, I PH

Litter size, age dependence

A 3-level model for optimal replacement of sows Advanced Herd Management 2006 10 Anders Ringgaard Kristensen, I PH Anders Ringgaard Kristensen, I PH

The Markov property

  • Let in be the state at stage n
  • The Markov property is satisfied if and only if

P(in+ 1| in, in-1, … , i1) = P (in+ 1| in) In words: The distribution of the state at next stage depends

  • nly on the present state – previous states are not relevant.
  • This property is crucial in Markov decision processes.

A 3-level model for optimal replacement of sows Advanced Herd Management 2006 11 Anders Ringgaard Kristensen, I PH Anders Ringgaard Kristensen, I PH

The Markov property in sow s

  • Does ”Age” satisfy the Markov property
  • Yes!
  • Does ”Rematings” satisfy the Markov property?
  • Yes, almost. The probabilty of conception hardly depends on

previous results at all.

  • Does ”Litter size” satisfy the Markov property?
  • No, certainly not. Several high (or low) will further increase (or

decrease) our expectations to future litter size. Example:

  • Sow 1: 12 – 14 – 16 – 15 – 16 piglets
  • Sow 2: 6 – 5 – 7 – 6 – 16 piglets
  • We prefer sow 1

A 3-level model for optimal replacement of sows Advanced Herd Management 2006 12 Anders Ringgaard Kristensen, I PH Anders Ringgaard Kristensen, I PH

Lacking Markov property:

  • The lacking Markov property must be considered when

the state is defined

  • Straight forward solution:

Define the state as in = (y1, y2, … , yn) For a sow in parity 8 this means e.g. 158 = 2.5 x 109 state combinations. Prohibitive

A 3-level model for optimal replacement of sows

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Advanced Herd Management 2006 13 Anders Ringgaard Kristensen, I PH Anders Ringgaard Kristensen, I PH

From registration to inform ation

A 3-level model for optimal replacement of sows Advanced Herd Management 2006 14 Anders Ringgaard Kristensen, I PH Anders Ringgaard Kristensen, I PH

From registrations to inform ation

  • Interpretation
  • Registration: Litter size λi = yi
  • Data: Λ = { y1, y2, … , yn}
  • Processing: Ψ() - Kalman filtering, DLM
  • Information: I = Ψ(Λ) = (i1, i2)
  • Decision: Θ
  • Decision strategy: I → Θ
  • Ψ(): As little loss of information as possible (preferably none).

A 3-level model for optimal replacement of sows Advanced Herd Management 2006 15 Anders Ringgaard Kristensen, I PH Anders Ringgaard Kristensen, I PH

Litter size m odel ( Toft & Jørgensen) :

Y M n I M n Y n n M n aM n e M n N N

n n n n n n n n M n

= + + = + = − = − − − + − = − + → →

µ ε ε µ µ θ θ θ θ σ ε τ ( ) ( ) exp( ( ) ) ( ) ( ) ( ) ( , ) ( , )

1 2 2 3 4 2 2

1 1

A 3-level model for optimal replacement of sows Advanced Herd Management 2006 16 Anders Ringgaard Kristensen, I PH Anders Ringgaard Kristensen, I PH

Observation equation

[ ]

I Z M n

n n n

= = ⎡ ⎣ ⎢ ⎤ ⎦ ⎥

θ ε 1 1 ( )

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System equation

θ θ ε ε σ τ

n n n M n

F e a M n e e N a

= + = ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ − ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ + ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ → ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ − ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟

− − 1 1 2 2 2

1 1 ( ) , ( )

A 3-level model for optimal replacement of sows Advanced Herd Management 2006 18 Anders Ringgaard Kristensen, I PH Anders Ringgaard Kristensen, I PH

DLM: Kalm an filtering Each time an observation yn is made, the current estim ate of M(n) is updated according to the Kalman filtering method. I = Ψ(y1,y2,… ,yn) = (M(n)) E(yn+ 1| y1,y2,… ,yn)= E(yn+ 1| M(n)) = ZF (M(n),0)’ V(yn+ 1| y1,y2,… ,yn) is known (Eq. (12)) The processing of data into information reduces the dimension from n to 1 without loss of information (given the litter size model)

A 3-level model for optimal replacement of sows

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Advanced Herd Management 2006 19 Anders Ringgaard Kristensen, I PH Anders Ringgaard Kristensen, I PH

Biological param eters

  • Litter size parameters:
  • Herd level estimation
  • Censoring
  • Other assumptions
  • Conception rates (parity, remating)
  • Piglet mortality (parity)
  • Sow weight (parity)
  • Involuntary culling (parity)
  • Feed intake

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Model structure

  • Founder level

Stage: Life span of a sow State: Dummy Decision: Dummy

  • Child level 1

Stage: Production cycle from weaning State: M(n) Decision: Mating method

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Model structure

  • Child level 2
  • Stages: ”Mating”, ”Gestation”, ”Suckling”
  • State:
  • Mating: ”Healthy”, ”Diseased”
  • Gestation: ”Pregnant”, ”Infertile”, ”Diseased”
  • Suckling: Present litter size
  • Decision:
  • Mating: Allow m matings, m ∈ { 1,…

,5}

  • Gestation: Dum my
  • Suckling: ”Keep”, ”Replace”

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Prototype

  • A plug-in for the MLHMP software
  • Herd interface

Herd specific parameters and prices Reads sow data Presents results

  • Built for use in practice
  • Demonstration

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DLM and MDP

  • First processing: Monitoring & filtering
  • Second processing: Decision making
  • MDP with DLM integrates both parts

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Estim ating Disease Costs using MLHMP

The follow ing slides are m ade by Doron Bar, Cornell University, NY

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Advanced Herd Management 2006 25 Anders Ringgaard Kristensen, I PH Anders Ringgaard Kristensen, I PH

The Traditional Approach

Estimate disease effects

  • Milk losses.
  • Increased culling hazard.
  • Decreased fertility.
  • Repeatability.
  • Cost of treatment (discarded milk, drugs and extra labor

costs).

1. Assign to each parameter a cost and add them to get the total disease cost. 2. The result is a fixed cost for all cows in the herd, and for all herds!

Advanced Herd Management 2006 26 Anders Ringgaard Kristensen, I PH Anders Ringgaard Kristensen, I PH

I f cow s could talk..

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How should it be done

  • In evaluating economic figures we have to compare them to

alternative options (opportunities).

  • A correct comparison will weight our option against the best

alternative option.

  • In a dairy we always have the option to replace the diseased

cow with a new heifer or keep but not to inseminate this cow.

  • So, the first step is to find the best option in each situation

(policy map).

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Desired answ ers

  • Optimal management of diseased cows
  • Cost of being in a diseased state
  • Herd dynamics (especially economic figures) in relation

to disease frequency

  • Sensitivity analysis of the above points

Then we can decide:

  • To treat or not to treat
  • To vaccinate or not (or similar preventive measures)

Advanced Herd Management 2006 29 Anders Ringgaard Kristensen, I PH Anders Ringgaard Kristensen, I PH

Prototype DP m odel: modeling a calving disease

  • 6 permanent traits (“Permanent milk yield potential”)
  • 8 possible lactations
  • 20 stages per lactation (0-3 days, month in milk (18) and dry period
  • 9 pregnancy states (0,1,2…

,7,8+ months pregnant)

  • 5 temporary (relative to permanent) milk yield levels
  • 2 disease states (healthy diseased)
  • 3 actions (keep, inseminate, replace)

State space ca. 84,000

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Exam ple: retained placenta

  • Milk loss (-360 lb, -570 lb, -640 lb)
  • Increased culling (OR= 2)
  • Repeatability (OR= 2)
  • Pregnancy rate (OR= .75)
  • Treatment cost ($50)
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New : perm anent cow potential

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Stages, States and Actions

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Keep em pty cow

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I nsem inate em pty cow

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Cull em pty cow