Markov Decision Processes Case example sow replacement Anders - PowerPoint PPT Presentation

Department of Large Animal Sciences Markov Decision Processes Case example – sow replacement Anders Ringgaard Kristensen Presented by Leonardo de Knegt

A sow replacement model At every weaning or return to oestrus it is decided whether or not to cull the sow. The decision is based on a prediction of the future performance of the sow. The prediction is compared to the expected performance of a gilt. Only based on existing registrations. Toft, N. & E. Jørgensen. 2002. Estimation of farm specific parameters in a longitudinal model for litter size with variance components and random dropout. Livestock Production Science 77 , 175-185. Kristensen, A.R. & T.A. Søllested. 2004. A sow replacement model using Bayesian updating in a three-level hierarchic Markov process I. Biological model. Livestock Production Science 87 , 13-24. Kristensen, A.R. & T.A. Søllested. 2004. A sow replacement model using Bayesian updating in a three-level hierarchic Markov process II. Optimization model. Livestock Production Science 87, 25-36.

Prediction of sow performance Based on • Individual conditions • Age • Litter size results (all) • Re-matings • Herd specific conditions • Litter size profile of the herd • Level of involuntary replacement • Piglet mortality • Prices • Feed intake • Standard conditions • Weight of sows

What do we know about litter size in sows? The profile for a herd: • It is lower for a gilt than for a second parity sow • A maximum is reached at parity 3, 4, 5 • It is decreasing for older sows • Some herds produce at a higher level than others Within herd: • Some sows produce at a higher level than others • The repeatability over parities is rather low • Large random variation

Department of Veterinary and Animal Sciences Litter size profiles of sows in different herds Slide 5

Litter size profiles Estimated by Toft & Jørgensen (2002). Censored data: • Only the best sows are kept. • The results for high parities are unknown for sows that have already been culled. • Must be taken into account by the estimation procedure. • If ignored, the expected litter size is over-estimated for high parities.

Department of Veterinary and Animal Sciences A litter size model Based on Toft & Jørgensen (2002), Bono et al. (2012) suggested the following litter size model meeting the demands mentioned on the previous slide: Y it = µ t + M i ( t ) + ε it , where • Y it is the litter size of sow i at parity t • µ t = is the litter size profile of the herd (average litter size at parity t ) described by 5 parameters, θ 1 , θ 2 , θ 3 , θ 4 , θ 5 • M i ( t ) ~ N(0, σ 2 ) is the effect of sow i at parity t • ε it ~ N(0, τ 2 ) is random variation (noise) The sow effect is auto correlated over parities: Cov( M i ( t ), M i ( t+u )) = exp(- u α ) σ 2 , in other words • • M i ( t ) = ρ M i ( t -1) + η it , where • ρ = exp(- α ) η it ~ N(0, (1- ρ 2 ) σ 2 ) • Described by 8 herd specific parameters: θ 1 , θ 2 , θ 3 , θ 4 , θ 5 , τ , σ , α Slide 7

Litter size profile for a specific herd: 5 parameters 16 θ 4 14 θ 3 Slope = θ 5 θ 2 Litter size 12 θ 1 10 8 0 1 2 3 4 5 6 7 8 9 10 11 12 Parity

Litter size profile for a specific herd Estimated from herd data Herd level productivity 15 Censoring: • Only the best sows are kept 13 • Profile will be biased if simple Litter size averages are used 11 • A maximum likelihood estimation technique is used 9 7 1 2 3 4 5 6 7 8 9 10 11 12 Parity

Litter size profile for a specific herd Estimated from herd data Herd level productivity 15 Individual sows are compared to that 13 • Sow 1 is below average Litter size • Sow 2 is above average 11 9 7 1 2 3 4 5 6 7 8 9 10 11 12 Parity Sow 1 Sow 2

Department of Veterinary and Animal Sciences Prediction for an individual sow Based on: • Litter size profile of the herd • Individual deviations from the litter size profile • All previous litter sizes are taken into account • Risk of return to oestrus • Previous matings Uncertainty about the prediction is taken into account • Not just “average” Slide 11

Department of Veterinary and Animal Sciences The decision influences the future 1 1 Present sow is a parity 5 sow. 2 2 Depending on the decision made, we may “next 1 1 1 1 time” have a: 1 1 • 6th parity sow (if we keep) 2 2 3 3 • 1st parity sow (if we replace) 5 5 6 6 1 1 1 1 Looking two cycles forward, we may have a: 2 2 7 7 • 7th parity sow (if we still keep) 1 1 • 2nd parity sow (if we replaced last time) 8 8 • 1st parity sow (if we replaced this time) Looking three cycles forward, we may have an 8th Right now: Choose between parity sow, a 1st parity sow, a 2nd parity sow • The red tree or a 3rd parity sow. • The green tree Slide 12

Department of Veterinary and Animal Sciences Why is it difficult? What we observe is not what we wish to know: • Litter size versus productivity potential • The selection problem Many traits must be considered Combinatorical explosion Herd differences Slide 13

Department of Veterinary and Animal Sciences Illustration of the hierarchy Stage length: lifespan of a sow Founder Sow 1 Sow 2 Sow 3 No state nor action Stage length: Reproductive cycle (parity) Child 1 3 4 3 4 1 2 1 2 1 2 Action: Mating method Stage length: Duration of “Mating”, “Gestation” and “Suckling” Child 2 M G S M G S M G S M G S M G S M G S M G S M G S M G S M G S Actions Mating: allow 1…5 matings Gestations: none Suckling: keep or cull after weaning Slide 14

Department of Veterinary and Animal Sciences Model structure: follow with page 28 of paper II Founder level • Stage: Lifespan of a sow (variable) • No state and action Child 1 • Stage: Reproductive cycle (weaning) • State space: • 1st parity: None • 2nd parity: Litter size + culled • 3rd parity (and older): Updated estimate for M ( t ) + culled • Action: Mating method Child 2: • Stage: Mating, gestation, suckling • State space: • Mating: Healthy/Diseased • Gestation: Pregnant/Open/Diseased • Suckling Litter size + diseased • Actions • Mating: Allow 1,…,5 matings • Gestation: None • Suckling: Keep/Cull Slide 15

Department of Veterinary and Animal Sciences Summary, state space A sow is described by: • Parity • Reproductive state (mating/gestation/suckling) • Estimated value of M ( t ) based on all litter size results • Present litter size (if suckling) A herd is described by • Litter size parameters • Mortality • Involuntary culling • Conception rates • Prices Slide 16

Department of Veterinary and Animal Sciences Decisions Number of (re-)matings before culling Keep/Replace • Binary decision • Economic value for ranking Slide 17

Department of Veterinary and Animal Sciences Calibration of biological parameters Slide 18