How PAP-SIM Works

What PAP-SIM Does

PAP-SIM is a forward-projection genetic selection tool. Given a description of your current herd — its average pulmonary arterial pressure, how variable those scores are, and how aggressively you screen bulls on PAP — it projects how your herd's mean PAP is expected to change generation by generation under that selection strategy.

The tool answers two related questions. First: how quickly will consistent PAP selection improve my herd? Second: what does a specific bull I'm considering actually do to my trajectory? The answer to the first question comes from applying the breeder's equation to your herd's parameters. The answer to the second comes from using that bull's EPD or measured PAP as a direct genetic input.

PAP-SIM also compares two selection strategies side by side: selecting on raw measured PAP (what most producers do today) versus selecting on latent z, a boundary-aware mathematical transformation of PAP that recovers additional genetic signal. This comparison is the scientific core of the tool — it demonstrates the practical advantage of latent z selection in terms of mmHg of herd improvement per generation.

Scientific Background

Pulmonary arterial pressure (PAP) is a measure of the pressure in the pulmonary artery, recorded in millimeters of mercury (mmHg) via right heart catheterization. In cattle, elevated PAP is the primary physiological indicator of susceptibility to high-altitude disease (brisket disease, cor pulmonale), which causes substantial mortality and production losses in herds grazing above roughly 5,000 feet.

PAP is moderately heritable — meaning a meaningful proportion of the variation between animals in their PAP scores is due to genetics, not just environment. This makes it tractable as a selection trait. However, raw PAP has a well-documented statistical problem: it is a bounded phenotype. PAP cannot fall below approximately 35 mmHg (the physiological minimum, sometimes called the biological floor) and very high values are also constrained by survivorship (extremely high-PAP animals die before testing). This boundary compression reduces the apparent genetic variance in raw PAP scores, making heritability estimates artificially low and EPDs less accurate than they should be.

The latent z transformation addresses this directly. It transforms raw PAP through a boundary-aware mathematical function that stretches the scale near the edges — where the boundary compression is greatest — and produces a statistically well-behaved phenotype with higher estimated heritability. EPDs derived from latent z records therefore carry more genetic signal per observation. The practical result, demonstrated in the underlying research, is a consistently higher heritability estimate: h² = 0.37 for latent z compared to h² = 0.28 for raw mPAP in Angus sire models.

Grazing Elevation

Elevation affects PAP testing because atmospheric oxygen decreases with altitude. At higher elevations, all cattle experience some degree of hypoxic pulmonary vasoconstriction — a physiological reflex that raises pulmonary arterial pressure in response to low oxygen. This means cattle at 9,000 feet will naturally test higher than genetically identical cattle at 4,000 feet. Elevation does not change the underlying genetic model or calculations in PAP-SIM, but it affects the contextual guidance displayed in the banner below the slider.

Current Herd Mean PAP

If you have PAP testing records on your cowherd, average the scores across animals and enter that value. If you only have records on bulls you've purchased, use those as a rough proxy — but understand that bull records may be biased downward if you've been selecting for low PAP. If you have no records at all, 54 mmHg is a reasonable default for a commercial Angus-influenced herd at moderate elevation.

This value serves as the anchor for all projection math. A higher starting mean means there is more room to improve — the absolute mmHg gain from consistent selection will be larger — but the per-generation rate of improvement depends on the herd's variability (SD) and the heritability of PAP, not the starting mean itself.

Herd Variability — Standard Deviation

Advanced: Enter Exact SD

Why SD matters so much: The breeder's equation response is directly proportional to SD. A herd with σ = 20 mmHg will show twice the per-generation improvement under the same selection intensity as a herd with σ = 10 mmHg, all else equal. This is because there is more genetic variation to select on. As selection proceeds and the herd mean declines, real-world SD tends to decrease too — PAP-SIM does not model this shrinkage and uses a fixed SD throughout, which means long-term projections (10 generations) are modestly optimistic about later generations.

Selection Pressure

Each option corresponds to a specific numeric selection intensity (i), a standard parameter in quantitative genetics that describes how far above average the average selected parent is, expressed in standard deviation units. Higher intensity means you're selecting a smaller, more elite fraction of available bulls.

The cutoff shown on each option's chip reflects the mmHg threshold that corresponds to that level of intensity given typical breed parameters. These are not hard constraints in the model — the selection intensity drives the math, not the cutoff label. The cutoff labels are contextual guides to help you identify which option matches your buying behavior.

Generations to Project

The x-axis of the chart always shows "Start" plus the number of generations selected. Each point on the chart represents the projected herd mean PAP at the end of that generation, assuming consistent selection throughout.

Adding Sires

The sire entry section lets you overlay a specific bull's expected genetic contribution on top of the population-average trajectories. Click + Add a sire to create a sire card. You can add multiple sires and compare them simultaneously on the same chart. Each sire gets a distinct color.

For each sire you can enter any combination of: a measured PAP score, a PAP EPD, and an EPD accuracy. The model uses whichever data you provide, with EPD taking precedence over phenotype when both are entered. You can rename a sire by clicking directly on the name field — use the bull's actual registration name or a shorthand you'll recognize.

Measured PAP — Bull's Own Test Score

A single phenotypic measurement on the bull himself is the least precise way to estimate his genetic merit, for two reasons. First, the measurement contains environmental noise — the elevation at which he was tested, his age, his physiological state on that day, and the skill of the technician all affect the reading. Second, a single record gives only modest accuracy (≈ 0.27) because PAP heritability is moderate, meaning roughly 28% of phenotypic variation is genetic. The remaining 72% is noise that a single observation cannot filter out.

Despite this limitation, a very low measured PAP (e.g., 35–40 mmHg) on a bull tested at high elevation is still meaningful signal. The model appropriately discounts it via the accuracy-weighting in the genetic effect calculation.

PAP EPD — Expected Progeny Deviation

After entering an EPD, the field shows two contextual hints:

• 1
  Possible change range — displayed in blue, this shows how far the bull's true EPD could differ from the published value at the entered accuracy. Calculated from the official AAA formula: ±(2.267 × (1 − accuracy)) mmHg. At acc = 0.70 that is ±0.68 mmHg; at acc = 0.30 it is ±1.59 mmHg. Lower accuracy means higher uncertainty.
• 2
  Breed percentile context — shows where this EPD ranks within the Angus breed (e.g., "Top 5–10% of breed"). Based on official AAA percentile tables. Note: this percentile context is calibrated for Angus. If you are using a different breed's bull, the percentile label may not apply.

Angus breed EPD reference (AAA)

EPD Accuracy

Accuracy reflects how confident the genetic evaluation is in the published EPD. It is primarily a function of how much data underlies the estimate — the bull's own records, parent records, sibling records, and crucially, the number and quality of his progeny PAP records. A young bull with only a few half-sibling PAP records might have accuracy 0.25–0.40. A widely-used AI sire with hundreds of progeny PAP records might have accuracy 0.80 or higher.

What accuracy does in the model: The genetic effect is calculated as dev = EPD × accuracy. This means a high-accuracy EPD is used at nearly face value, while a low-accuracy EPD is shrunk substantially toward zero. An EPD of −2.0 mmHg at accuracy 0.90 produces a gen-1 effect of −1.80 mmHg. The same EPD at accuracy 0.25 produces a gen-1 effect of only −0.50 mmHg — reflecting genuine uncertainty about whether the true EPD is really −2.0 or something much closer to zero.

The Projection Chart

The chart is a line graph with generations on the x-axis (Start, Gen 1, Gen 2, …) and herd mean PAP in mmHg on the y-axis. Each line represents a different selection scenario. All lines start at the same point — your entered herd mean PAP — and diverge from there based on the genetic inputs.

Reading the Chart

The chart y-axis auto-scales to fit all trajectories, with a minimum of 30 mmHg. A purple dashed horizontal line at 35 mmHg marks the biological floor. When any trajectory approaches this line, a yellow warning banner appears below the chart.

Result Cards

Below the chart, a row of summary cards shows the final projected herd mean PAP after your selected number of generations for each scenario. Each card has:

• 1
  Scenario label — e.g., "No PAP selection", "Latent z selection", or the sire's name. Matched to the chart line color by the top border stripe.
• 2
  Final projected value — the herd mean PAP in mmHg after the selected number of generations. This is the headline number.
• 3
  Total change — shown in green (improvement) or red (deterioration). E.g., "−8.4 mmHg over 5 gen". This is the difference between the final projected value and your starting herd mean.
• 4
  Per-generation rate — how many mmHg of improvement per generation. For population-level scenarios this is constant. For named sires it shows the implied rate after Gen 1.

Interpreting the Population-Level Cards

The three population-level cards (No PAP selection, Raw mPAP, Latent z) give you the strategic baseline. The gap between the No PAP selection card and the Latent z card represents the total genetic improvement available from optimal PAP selection over your time horizon. The gap between Raw mPAP and Latent z shows how much additional improvement comes from using the latent z transformation rather than raw scores — this is the direct quantification of the research advantage.

Interpreting Sire-Specific Cards

Sire cards contain more information than population cards because they describe a specific, identifiable genetic contribution.

• 1
  Final projected value — where your herd would be after the selected number of generations if you used this bull as your ongoing sire selection standard. Compare this to the Latent z and Raw mPAP cards to see if this bull is better or worse than population-average screening at your stated intensity.
• 2
  Gen 1 progeny value — the herd mean your first crop of calves by this bull is expected to average. The number in parentheses (e.g., "−3.2") is the change relative to your current mean. This is what you would observe in the first year if you could measure PAP on all his calves.
• 3
  Implied rate after Gen 1 — the per-generation improvement rate for generations 2 and beyond, derived from the bull's own EPD-implied selection differential. If the bull has a positive EPD or tests above your herd mean, this reads "Gens 2+: flat — no implied improvement." See the sire effect model section for full explanation.
• !
  Low accuracy warning — amber badge. EPD accuracy below 0.35 triggers this. The projected effect could be substantially larger or smaller than shown. Treat with appropriate skepticism.
• !
  Positive EPD warning — red badge. Bull has a positive PAP EPD, meaning his progeny will on average have higher PAP than the genetic base animal's progeny. The chart will show his line rising in Gen 1.

Summary Text Box

Below the result cards, a plain-language summary is automatically generated from your inputs and results. It describes your current herd, your selection approach, the projected change under each scenario, and — if sires are entered — a narrative summary for each named bull. This text is designed to be copy-pasteable for farm records, loan applications, or presentations. The final paragraph includes a technical disclaimer about the nature of the projections.

How to Read Your Results

This section addresses the most important — and most commonly misunderstood — aspect of PAP-SIM: what the numbers actually mean and how to use them in real decisions.

The numbers are expectations, not guarantees

Every value in PAP-SIM is an expected value — a probability-weighted average of outcomes across many possible futures. If the model projects your herd mean will reach 46.2 mmHg in five generations, that means: under the stated genetic parameters and consistent selection, the average outcome of running this breeding program many times in many herds would be approximately 46.2 mmHg. In any single real herd, random genetic drift, inconsistent selection, measurement variation, and environmental factors will cause deviation from this expectation. The true outcome might be 43 mmHg or 49 mmHg. The model is directionally accurate and correctly orders strategies, even when absolute values vary.

The gap between lines matters more than individual values

The most reliable interpretation is relative, not absolute. The gap between the Latent z line and the Raw mPAP line — for example, 2.1 mmHg after 5 generations — is more robust than either absolute projection. The relative advantage of latent z over raw PAP selection is less sensitive to parameter assumptions than the absolute trajectory levels. Similarly, the gap between a named sire's line and the population-level lines reliably shows whether that bull is better or worse than your general screening approach, even if the exact mmHg values shift with different SD or heritability assumptions.

Why does progress feel slow?

New users are often surprised by how gradually the trajectories decline. A 2–3 mmHg per-generation improvement rate feels small. This is a genuine feature of beef cattle genetics, not a modeling limitation. Three factors combine to slow progress:

• 1
  Long generation interval. Beef cattle take 4–6 years per generation. What appears as "5 generations" on the chart represents 20–30 years of breeding decisions. The same per-generation rate that seems slow over generations looks substantial when expressed as mmHg per decade.
• 2
  Sire-only selection. In most commercial operations, cows are not selected on PAP — they are kept or culled for reproductive performance, body condition, temperament, and production. Only the sire half of each offspring's genome is actively selected for PAP improvement. This cuts the theoretical maximum response in half compared to two-way selection.
• 3
  Moderate heritability. With h² = 0.28–0.37, only about a quarter to a third of the phenotypic variation between cattle is genetic. The rest is environmental noise that selection cannot change. This means even aggressive bull screening captures only a fraction of the phenotypic differential as permanent genetic improvement.

Despite these constraints, the compounding over a full breeding program lifetime is real and meaningful. A herd mean that declines from 54 to 46 mmHg over 25 years represents a shift in the entire distribution of PAP scores — a meaningfully lower proportion of animals testing above clinical risk thresholds, and meaningfully better outcomes at altitude.

When a sire's line is above the population lines

If a named sire's trajectory runs above the Raw mPAP or Latent z lines, that bull is genetically below average for PAP relative to what consistent population-level screening would achieve. This does not necessarily mean he is a bad bull — he may be exceptional for growth, carcass, or other traits — but PAP-SIM is showing you the PAP cost in mmHg terms. Specifically, using this bull instead of a population-screened bull costs you X mmHg of mean PAP improvement per generation, where X is the gap between his line and the latent z line.

When a sire's line is flat after Gen 1

When a sire's chart line rises or stays flat in Gen 1 and then shows "Gens 2+: flat — no implied improvement," this means the bull's EPD implies he is providing zero or negative selection pressure for low PAP. The trajectory does not continue declining after Gen 1 because continuing to use bulls of this genetic quality provides no ongoing improvement — the herd stays where it landed after the first generation and does not benefit from compounding selection.

The Breeder's Equation

PAP-SIM's population-level trajectories are computed using the breeder's equation, the foundational formula of quantitative genetics for predicting selection response. The breeder's equation states:

This per-generation response R is subtracted from the herd mean each generation. If your starting mean is 54 mmHg and R = 2.50, then Gen 1 projects to 51.50, Gen 2 to 49.00, and so on — a straight declining line when plotted. (In practice, with a fixed SD assumption, R is constant per generation; in reality, R would slowly decrease as the population SD narrows under sustained selection.)

Why h² appears, not √h²

Some formulations of the breeder's equation write R = √h² × i × σ_A, where σ_A = √h² × σ_p is the genetic standard deviation. Substituting gives R = √h² × i × √h² × σ_p = h² × i × σ_p — the same result. The form R = h² × i × σ_p is used directly here because σ_p (phenotypic SD) is what producers can measure and estimate.

Selection intensities and their meaning

These intensities are conservative estimates appropriate for sire-only PAP selection in a commercial operation. The values represent realistic averages across available bulls in a typical sale environment, not the theoretical optimum achievable with unlimited bull choices.

What Is Latent Z?

Latent z is a boundary-aware mathematical transformation of raw PAP that is the scientific centerpiece of the underlying research (Markel et al., University of Wyoming). Understanding it is not required to use PAP-SIM, but knowing what it is clarifies why the latent z line always shows more improvement than the raw mPAP line.

Raw PAP is a bounded phenotype. The measurement cannot fall below approximately 35 mmHg (the physiological minimum) and extremely high values are underrepresented because very high-PAP animals tend to die before testing. This boundary compression creates a statistical problem: the observed distribution of PAP scores appears narrower at both extremes than the underlying genetic distribution truly is. Standard EPD models that treat PAP as a normally distributed phenotype are therefore working with a distorted picture — they underestimate genetic variance near the boundaries, which means they underestimate heritability and produce EPDs with less predictive power than they should have.

The latent z transformation applies a boundary-aware function that expands the scale near the edges — stretching the compressed region near 35 mmHg and near the upper biological limit — and compresses the scale in the middle where the distribution is already well-behaved. The result is a transformed phenotype whose distribution is closer to normal, whose heritability estimate is higher (h² = 0.37 vs. 0.28), and whose EPDs carry more genetic signal per observation.

PAP-RIDGE is the companion software tool that calculates latent z and other bounded PAP derivatives from raw PAP records. Contact markellivestock@gmail.com for access.

Sire Effect Model

When a specific sire is entered, his trajectory is computed in two phases: a Gen 1 effect and an ongoing rate for generations 2 through N.

Generation 1: the immediate shift

Generations 2+: implied ongoing rate

The model assumes that if you enter a sire, you are describing your ongoing bull selection standard — not just a one-time purchase. For generations 2 and beyond, the sire's trajectory continues at an implied per-generation rate derived from his Gen 1 shift:

This design means a bull with EPD = −2.0, acc = 0.85 produces dev = −1.70 mmHg, and his trajectory declines at 1.70 mmHg per generation after Gen 1. A bull with EPD = +1.5, acc = 0.80 produces dev = +1.20, and his trajectory is flat from Gen 2 onward — accurately reflecting that continued use of below-average bulls produces no ongoing improvement.

The Biological Floor

All trajectories in PAP-SIM are constrained to a minimum of 35 mmHg. This value is shown as a purple dashed horizontal line on the chart, labeled "Biological floor ~35 mmHg."

The biological floor reflects the fact that bovine pulmonary arterial pressure cannot fall below approximately 35 mmHg and still support normal cardiovascular function. Below this threshold, cardiac output would be insufficient to perfuse the pulmonary capillary bed adequately under normal metabolic demand. In practice, no cattle population will select below this value because there is no genetic variation below the physiological minimum — you cannot select for something that doesn't exist.

When one or more trajectories approach the biological floor, a yellow warning banner appears below the chart: "One or more trajectories are approaching the biological floor (~35 mmHg). Genetic progress slows and eventually stops as the population runs out of low-PAP variation to select on." This warning is practically relevant for strong selection scenarios run over 10 generations, and reminds users that the model's linear projection becomes increasingly optimistic as the herd mean approaches the floor.

Model Assumptions and Limitations

PAP-SIM makes several simplifying assumptions that are standard in applied selection response modeling. Understanding them helps you know when to trust the projections and when to be cautious.

• 1
  Fixed phenotypic SD. The model uses a constant σ_p throughout all generations. In reality, sustained selection reduces genetic variance and therefore phenotypic variance over time, causing R to shrink in later generations. This means long-horizon projections (especially 10 generations) are modestly optimistic. The effect is small in early generations.
• 2
  Sire-only selection. The model assumes cows are not selected on PAP. If your operation also culls cows for high PAP, your actual response will be faster than projected — roughly double for equal selection intensity on both sexes.
• 3
  Constant heritability. h² = 0.28 (raw) and h² = 0.37 (latent z) are fixed estimates from Angus sire models. These are the best available values from the underlying research. If your herd is not Angus-influenced, or if your management differs substantially, actual heritability may differ.
• 4
  No linkage disequilibrium or epistasis. The breeder's equation assumes additive gene action — alleles act independently and additively. PAP likely has some non-additive genetic architecture; this assumption introduces modest error that is small relative to other sources of uncertainty.
• 5
  No genetic drift or inbreeding. In small herds, random genetic drift can cause herd mean PAP to move up or down by chance, independent of selection. PAP-SIM projects the expected value — the average trajectory — not the full distribution of possible outcomes. The variance around the projected mean is larger for small herds.
• 6
  Consistent selection every generation. The model assumes the stated selection pressure is applied every generation without interruption. Years where PAP testing is skipped, or where a bull is purchased for other reasons without PAP data, reduce realized response proportionally. Intermittent selection produces slower progress than the consistent projection suggests.
• 7
  Angus breed EPD context. The breed percentile labels (Top 5%, breed average, etc.) and possible change values are derived from official American Angus Association data. If you are working with a different breed, the EPD scale, average, and SD may differ. The genetic effect calculations remain valid but the percentile labels should be interpreted cautiously for non-Angus bulls.

Model Constants

Angus Breed EPD Data

EPD percentile data and possible change values are sourced from official American Angus Association publications. PAP EPD trait summary: 37,428 phenotypic records, 2,608,374 EPDs published, breed avg = +1.16 mmHg, SD = 1.59 mmHg (published EPDs), SD of true EPDs = 2.267 mmHg.

PAP-RIDGE — Companion Tool

PAP-RIDGE is a companion software tool to PAP-SIM that performs the actual mathematical transformations described in the underlying research. Where PAP-SIM projects forward genetic change, PAP-RIDGE works backward from existing records — it takes raw PAP data and computes latent z scores, bounded PAP derivatives, and other transformations described in Rethinking pulmonary arterial pressure as a bounded and dynamic phenotype in cattle.

PAP-RIDGE is designed for:

• 1
  Breed associations wanting to evaluate or implement latent z as a submitted phenotype for genetic evaluation.
• 2
  Veterinarians and herd consultants with PAP testing records who want to translate raw scores into EPD-ready transformed phenotypes.
• 3
  Researchers evaluating the statistical properties of PAP transformations in their own datasets.

Contact markellivestock@gmail.com for access to PAP-RIDGE.