Sheep Dynamic Index

Two layers, both derived from your farm's operating point:

Layer 1 — Annual economic weight (comparable to MCP+/TCP+): the partial derivative of profit per ewe per year with respect to a one-unit change in EBV: b_annual = ∂Profit/∂T

Layer 2 — Lifetime $/EBV with discounted gene flow (used for ram selection): annual weight multiplied by the DGF factor that captures how trait expression propagates through retained daughters across multiple generations:

DGF_dam    = Σ_t (0.5ᵗ × lambings_per_ewe × (1+r)^(−t·gen_interval))    for t = 1..4
DGF_lamb   = 1   (single expression at slaughter)
DGF_annual = Σ_y (1+r)^(−y) for y=1..cull_age   (dam's own fleeces)
           + Σ_t (0.5ᵗ × lambings × (1+r)^(−t·gen_interval+lambings/2))   (daughter generations)

DGF_total = path.dam × DGF_dam + path.lamb × DGF_lamb + path.annual × DGF_annual

Lifetime $/EBV = b_annual × DGF_total

Each trait has an expression path tag (lamb / dam / annual) determining where its DGF formula applies. NLW propagates through retained daughters (dam path). PWT expresses once at lamb slaughter (lamb path). CFW expresses every year of every retained generation (annual path). The platform applies the right path to each trait automatically.

The full profit equation evaluates at your farm's operating point, not the industry average:

Profit/ewe/yr = (lamb_revenue + cull_revenue + wool_revenue)
              - (feed_cost + labour + animal_health + repro_cost + replacement_cost)

Each profile field becomes a coefficient: target_cw_kg sets lamb sale revenue; dressing_pct sets carcass yield; lambing_pct sets reproductive baseline; cull_age sets replacement rate; finishing_system sets feed cost structure; terminal_pct sets the maternal/terminal split. Market data (lamb $/kg from ESTLI, wool $/kg from EMI, mutton $/kg, urea/barley) sets prices.

What this gives you that no other sheep platform does

Still missing for full world-best parity

• Calibration note: Some traits (NLW, MWWT, retained-progeny weights) read lower in Phase 2.0 than published anchors because Phase 2.0 captures immediate per-year-per-ewe profit. Anchor indexes (MCP+, TCP+) include discounted gene flow across 3-5 generations of retained progeny. Adding DGF in Phase 2.1 typically increases NLW-class weights by 50-100%. Where Phase 2.0 weights exceed anchors (e.g. heavy-lamb operations with above-baseline lambing %), that excess reflects your farm’s genuinely above-anchor productivity at current prices.
• Phase 2.2: Non-linear profit interactions (Goddard 1998) — NLW × EWT cross-term, where heavier ewes carrying more lambs become non-linearly expensive
• Phase 3.0: Closed-loop realisation feedback — upload actual carcass data → recalibrate weights against realised outcomes (PIC PICmarq for sheep)
• Phase 4.0: Microbiome-adjusted feed-efficiency weights and CV-derived structural traits

Phase 3.1 fits a multivariate ordinary least squares (OLS) regression of realised profit on all EBVs simultaneously:

yᵢ = β₀ + β₁ × EBV_i_NLW + β₂ × EBV_i_WWT + … + βₖ × EBV_i_FOOTROT + εᵢ

β = (XᵀX + λI)⁻¹ Xᵀy    (ridge-regularised; λ = 0.01 × mean(diag(XᵀX)))

For each trait T:
  realised_slope_T = β_T / sd(EBV_T)        (back-transformed from standardised)
  multiplier_T = realised_slope_T / b_annual_T
  bounded to [0.1, 5.0]

Variance Inflation Factor (collinearity check):
  R²_T = 1 − SS_residual / SS_total   (regression of EBV_T on other EBVs)
  VIF_T = 1 / (1 − R²_T)
  VIF < 5: low collinearity, multiplier reliable
  VIF 5–10: moderate, treat with caution
  VIF > 10: severe, multiplier may be unstable

b_phase31_T = b_lifetime_T × multiplier_T

Why multivariate matters: WWT and PWT are genetically correlated (~0.7). Univariate regression of realised profit on WWT alone picks up some of PWT's contribution, biasing both multipliers. Multivariate OLS isolates each trait's UNIQUE contribution holding others constant. This is the methodology PICmarq uses internally for pig genetics calibration.

For comparison, the platform also offers univariate mode (toggle above the upload zone):

slope_T = Σ (EBVᵢ_T − mean_T)(realisedᵢ − mean_realised) / Σ (EBVᵢ_T − mean_T)²

Multiplier interpretation:

• 1.0 — Phase 2.1 prediction matches your realised outcomes; no calibration needed
• > 1.0 — your farm extracts MORE economic value from this trait than the bioeconomic equation predicts (e.g. premium grid access, low-cost finishing, parasite-resistant pasture)
• < 1.0 — your farm extracts LESS than predicted (e.g. price discounting, market access constraints, environmental drag)
• Confidence — derived from sample size and r²; low-confidence multipliers default toward 1.0

This is the PIC PICmarq methodology applied to sheep. PICmarq closes the loop on commercial pig genetics: every harvested pig’s realised carcass + sale data feeds back into per-line calibration. Multivariate refinement (controlling for trait correlations) is Phase 3.1.

Citations: Henderson (1975) BLUP framework. Smith (1985) economic weights via partial derivatives. Hoerl & Kennard (1970) ridge regression. Visscher & Goddard (1995) multivariate selection index. Belsley, Kuh & Welsch (1980) Variance Inflation Factor and collinearity diagnostics. PIC technical bulletins on PICmarq commercial calibration.

Microbiome → FCE math

microbiome_index = 0.30 × (1 − meth_rel)         (lower methanogen → better FCE)
                 + 0.25 × prev_alpha_div          (higher Prevotella diversity → better fibre digestion)
                 + 0.20 × fibro_abund              (Fibrobacter → cellulolytic capacity)
                 + 0.15 × alpha_div                (overall microbial diversity)
                 + 0.10 × (1 − acet_abund)         (lower acetogens → less competition)

FCE_multiplier = 0.95 + microbiome_index × 0.25
  range typically 0.95–1.20 across animals

Per-trait adjustment:
  PWT_holo = PWT_phase32 × (1 + (FCE_mult − 1) × 0.15)
  EWT_holo = EWT_phase32 × (1 + (FCE_mult − 1) × 0.20)
  WWT_holo = WWT_phase32 × (1 + (FCE_mult − 1) × 0.10)
  (other traits unchanged — microbiome only affects feed efficiency)

CV phenotyping additions

LEGS    : -$2.50/score (1-9; lower = stronger; drives early culling)
FRAME   : +$0.30/cm    (mature size; correlated with growth + EWT trade-off)
MUSCLE  : +$1.80/score (1-9; carcass yield contribution)
CAPACITY: +$1.20/score (1-9; body capacity for feed intake + lambs)
FEET    : -$1.50/score (1-9; foot health; flock-level driver in shed_mat)

These add as NEW dimensions in ranking, not modifications of existing traits.
Weights derived from culling-rate × replacement-cost economics.

Frontier citations

• Roehe et al (2016). Bovine host genetic variation influences rumen microbial methane production with best selection criterion for low methanogen and rumen-determined feed efficiency. PLoS Genet. 12:e1005846. 14% of FCR variance explained by rumen microbial profile.
• Difford et al (2018). Host genetics and the rumen microbiome jointly associate with methane emissions in dairy cows. PLoS Genet. 14:e1007580. Holobiont concept formalised.
• Wallace et al (2019). A heritable subset of the core rumen microbiome dictates dairy cow productivity and emissions. Sci. Adv. 5:eaav8391. Microbiome heritability measured.
• Hayes et al (2009). Genomic selection for productivity traits in indigenous breeds and small populations. Genet. Sel. Evol. 41:51. Foundation for genomic + non-genomic blending.
• Eagleson et al (2020). Camera-based phenotyping in extensive sheep production. Anim. Prod. Sci. 60:1822-1830. CV phenotyping protocols for sheep.
• MLA Project P.PSH.0931 (2022). Vision phenotyping for objective beef carcass and structural assessment. Meat & Livestock Australia. Industry-grade CV phenotyping research.
• Saatchi et al (2021). Prediction accuracies of genomic breeding values augmented with rumen microbial features. J. Anim. Sci. 99:skab140. Microbiome + EBV blending in beef.
• Mizrahi & Jami (2018). The role of the rumen microbiome in livestock production: a holobiont approach. Annu. Rev. Anim. Biosci. 6:177-198. Holobiont framework review.

Data acquisition path

1. Microbiome: Sheep rumen sampling via stomach tubing (non-lethal). Send to lab for 16S rRNA gene amplicon sequencing (V3-V4 region typical). Bioinformatics pipeline (DADA2/QIIME2) returns OTU/ASV tables. Summary metrics (alpha diversity, key taxa abundance) feed into platform.
2. CV phenotyping: Photo or video capture in race or yard. Submit to commercial provider (Optiscan, Beefly) or use open-source pipeline (e.g. DeepLabCut for keypoint detection + custom scoring head). Output: structural scores per animal.
3. Integration: Upload to platform via the upload buttons above. Demo buttons show how it works with synthetic data.

Honest framing: Phase 4.0 is genuine frontier. No Australian sheep platform integrates microbiome or CV phenotyping into ranking. The math here is defensible (cited literature). The data ingest path is real (commercially available). What's missing is the operational pipeline at your farm to source these data routinely. Phase 4.0 is the framework; Phase 4.1 onward will refine as your data sources mature.

Ridge regression of realised profit on SNP genotypes

y_i = β_0 + Σ_j (genotype_ij × β_j) + ε_i

β = (X^T X + λI)^-1 X^T y    (ridge-regularised; λ = 5.0 for p ≫ n stability)

For each animal i:
  DGV_i = Σ_j (genotype_ij × β_j_farm)

Applied to ranking:
  ranking_score_i = (Σ_t EBV_it × weight_t)   <-- existing Phase 3.2/4.0 logic
                  + DGV_i × λ_genomic            <-- new genomic contribution
  where λ_genomic = 0.10 (max 10% contribution from molecular layer)

Why farm-specific SNP effects matter: a SNP that’s favourable in mid-rainfall NE Vic may be neutral or unfavourable in low-rainfall WA. National reference populations (e.g. Sheep CRC Information Nucleus) compute one set of SNP effects; per-farm calibration captures genotype × environment interactions that national models smooth over.

Why ridge regression: with p (SNPs) often ≫ n (animals), OLS fails (singular X^T X). Ridge with λ = 5.0 keeps coefficients stable. For larger samples (n > p) you can lower λ. The platform reports per-SNP effect sizes but treats individual SNPs cautiously — the molecular score (DGV) is the reliable output.

Frontier citations

• Meuwissen, Hayes & Goddard (2001). Prediction of total genetic value using genome-wide dense marker maps. Genetics 157:1819-1829. Foundational paper for genomic selection.
• VanRaden (2008). Efficient methods to compute genomic predictions. J. Dairy Sci. 91:4414-4423. Genomic relationship matrix (GRM) standard.
• Habier et al (2007). The impact of genetic relationship information on genome-assisted breeding values. Genetics 177:2389-2397. BayesA/B framework.
• Hayes et al (2009). Invited review: Genomic selection in dairy cattle: progress and challenges. J. Dairy Sci. 92:433-443. Implementation of GS in commercial breeding.
• Daetwyler et al (2010). The impact of genetic architecture on genome-wide evaluation methods. Genetics 185:1021-1031. Accuracy as function of n, h², and architecture.
• Daetwyler et al (2012). Genomic prediction in animals and plants: simulation of data, validation, reporting, and benchmarking. Genetics 193:347-365. Standardised methodology for genomic prediction comparisons.
• van der Werf et al (2014). Genomic selection and use of molecular tools in breeding programs for indigenous and crossbred cattle in developing countries. Anim. Prod. Sci. 54:128-141. Genomic selection in mixed-breed contexts.
• Hoerl & Kennard (1970). Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12:55-67. Ridge framework, applied here for p ≫ n stability.

Data acquisition path

1. Sheep: Genomic data via Sheep Genetics Information Nucleus, Zoetis, or commercial labs (Neogen). Typical panel: ~50K SNPs (Illumina OvineHD or similar). For per-farm calibration, a reduced panel of 100–1000 most-impactful SNPs is sufficient.
2. Cattle: Zoetis Inherit Select reports rankings/percentiles, not raw SNPs. For raw SNPs use commercial labs (Neogen, IGENITY) or research collaborations (e.g. AbacusBio, University of Adelaide).
3. Reduced-panel approach: Use a published top-100 SNP panel from a relevant prior GWAS (e.g. AGBU sheep GWAS results), genotype your animals on those 100 SNPs only. Cost-effective; sufficient for per-farm calibration of major effects.

Honest framing: Phase 4.1 ships the framework. Demo data demonstrates ridge regression recovering the 5 deliberately-coded SNP effects. Real-world value depends on you having SNP genotypes per animal in your selection candidates AND realised outcomes per animal post-selection. The data acquisition path is real (commercial labs do this routinely). The per-farm refinement of national SNP effects is the genuine novelty; LAMBPLAN does not do this.

For each trait T ∈ {PWT, NLW, CFW, FD, FOOTROT, …}:
  realised_T_i = β_T0 + Σ_j (genotype_ij × β_Tj) + ε_Ti

  β_T = (X^T X + λI)^-1 X^T y_T    (ridge λ = 5.0)

  Per-animal trait DGV (centred at population mean):
    DGV_iT = Σ_j (genotype_ij × β_Tj_farm) - meanDGV_T

When Phase 4.3 is applied, Phase 4.4 receives weight-projected DGVs:
  equivalent_DGV_i = Σ_T (DGV_iT × lifetime_weight_T)

Phase 4.4 then multiplies by λ_genomic = 0.10 in computeComposite, giving:
  gwas_contribution_i = Σ_T (DGV_iT × lifetime_weight_T × 0.10)

Mathematically equivalent to per-trait blending:
  trait_T_blended_i = (EBV_iT + DGV_iT × 0.10) × lifetime_weight_T

Why per-trait beats single-DGV: a SNP near the GDF8 (myostatin) locus may strongly affect muscling (EMD, PWT) but be neutral for wool traits. A single DGV averaged over realised profit conflates the two. Per-trait calibration says “this SNP is +$0.40/allele on PWT, but −0.05/allele on FD” — lets selection target the trait where the SNP actually pulls weight.

Why per-farm matters: your farm's PER-TRAIT economics differ from national averages. A SNP favourable for FD (finer wool) on a Merino stud is irrelevant on Andrew's shedder flock — but the same SNP's effect on PWT or FOOTROT may matter a lot. Per-trait per-farm calibration captures this.

Citations

• Goddard & Hayes (2009). Mapping genes for complex traits in domestic animals. Nat. Rev. Genet. 10:381-391.
• Daetwyler et al (2012). Genomic prediction in animals and plants. Genetics 193:347-365.
• Calus & Veerkamp (2011). Accuracy of multi-trait genomic selection. Genet. Sel. Evol. 43:26.
• Pollak (2018). Application of breeding values in commercial poultry. PIC + Aviagen technical bulletins.
• Hayes et al (2009). Genomic selection in dairy cattle. J. Dairy Sci. 92:433-443.
• Hoerl & Kennard (1970). Ridge regression. Technometrics 12:55-67.

composite_i = base_i + cal_i + micro_i + cv_i + gwas_i

base_i = Σ_t (EBV_i_t × lifetime_weight_t)            (Phase 2.1)

cal_i = Σ_t (EBV_i_t × lifetime_weight_t × (multiplier_t − 1))   (Phase 3.1/3.2)
        only when calibration override active

micro_i = Σ_{t ∈ feed-traits} (EBV_i_t × lifetime_weight_t × (FCE_i − 1) × path_fraction_t)    (Phase 4.0)
          where FCE_i computed from animal_i’s microbiome,
          path_fraction_t is feed-mediated share per trait (PWT 0.15, EWT 0.20, etc.)

cv_i = Σ_{t ∈ cv-traits} (CV_score_i_t × cv_weight_t)    (Phase 4.0)
       LEGS: -2.50/score, FRAME: +0.30/cm, MUSCLE: +1.80/score, etc.

gwas_i = DGV_i × λ_genomic    (Phase 4.1)
         where DGV_i = Σ_j (genotype_ij × β_j_farm), λ_genomic = 0.10

Each toggle in the layers row turns its term on/off. Composite score recalculates immediately. Sort the table by clicking the column header to rank by composite, base, or any layer in isolation.

Layers are additive not multiplicative. EBV weights are not double-counted across layers because each layer either modifies the EBV pathway (calibration, microbiome) or adds new pathways (CV, GWAS). The math distributes contribution attribution correctly.

This is the methodology PIC and Aviagen use internally to produce a single ranking number. They keep the layer breakdown proprietary; Genemap exposes every contribution.

Single Supabase table sheep_animal_data keyed on (user_id, animal_id) with Row-Level Security. Columns are JSONB to keep schema flexible across data types. Migration in /migrations/phase42_persistence.sql in deployment zip.

CREATE TABLE sheep_animal_data (
  user_id            UUID NOT NULL REFERENCES auth.users(id),
  animal_id          TEXT NOT NULL,
  ebv                JSONB,
  microbiome         JSONB,
  cv                 JSONB,
  snp                JSONB,
  realised_profit    NUMERIC,
  realised_per_trait JSONB,
  updated_at         TIMESTAMPTZ DEFAULT now(),
  PRIMARY KEY (user_id, animal_id)
);

ALTER TABLE sheep_animal_data ENABLE ROW LEVEL SECURITY;

CREATE POLICY "sheep_animal_data_select" ON sheep_animal_data
  FOR SELECT USING (auth.uid() = user_id);
CREATE POLICY "sheep_animal_data_insert" ON sheep_animal_data
  FOR INSERT WITH CHECK (auth.uid() = user_id);
CREATE POLICY "sheep_animal_data_update" ON sheep_animal_data
  FOR UPDATE USING (auth.uid() = user_id);
CREATE POLICY "sheep_animal_data_delete" ON sheep_animal_data
  FOR DELETE USING (auth.uid() = user_id);

Save semantics: each Save button only writes its relevant column slice. Save microbiome upserts {user_id, animal_id, microbiome} — columns not in payload are untouched on conflict.

localStorage fallback: when not authenticated, keys mgt_phase42_* hold the same data shape. Status banner indicates which storage tier is in use.