Chapter 2 Introduction to nutritional models

Figure 2.1: Cattle painted circa 7000 years ago in the Libyan Sahara (Sapienza University of Rome)

Learning Objectives

Explain the usefulness and history behind nutrient models.
List and differentiate common dairy nutritional models.
Describe how nutritional models are developed, step-by-step.

2.1 A brief history

Deliberate animal feeding began before recorded history with the advent of agriculture in Asia and Africa 12,000 years ago (Coffey, 2016). Since this time, humans have carefully considered how to manage forages, grains, minerals, and other natural resources to provide nourishment for domesticated animals. In regions throughout the world, traditional and indigenous knowledge systems contain a wealth of information on animal nutritional management, yet very little of it is recorded in publications and books.

Primarily in the last 200 years, animal nutrition developed as a scientific discipline. The use of scientific methods enabled researchers to isolate the chemical components of feeds and to quantitatively relate dietary intakes to physiological effects. As nutrition science progressed, nutritional diseases that had once harmed or killed thousands of animals (and people) began to be curable. The productivity of agricultural animals began to increase. As per the scientific method, advances were recorded with detailed publications in the scientific literature to enable cumulative progress.

In the United States, nutrition science was spurred by government efforts to reconstruct and reduce poverty after wars. In the aftermath of the Civil War and World Wars, the U.S. government chartered the National Academies of Sciences, Engineering, and Medicine (NASEM) and its subsidiary organization the National Research Council (NRC, Ullrey, 2001). NASEM is a non-governmental, non-profit organization of academics whose mission is to translate scientific information into domestic policy and practice. In animal nutrition, NASEM is famous for organizing efforts to consolidate nutritional science knowledge into animal feeding recommendations by publishing consensus reports.

The first edition of "Nutrient Requirements of Dairy Cattle" was published by the NRC (NASEM's subsidiary) in 1945. In the eight decades following, researchers created seven more editions of this consensus report. Each edition uses the most up-to-date research on dairy cattle nutrition generated by researchers at universities and government institutions.

Test yourself

The 7th edition is the most recent version of the Nutrient Requirements of Dairy Cattle.
The National Academies publishes consensus reports for other species besides dairy cattle.

2.2 Definition

Test Yourself: Before proceeding, we need to ask ourselves...what are nutritional models, and what do they have in common with the cave paintings shown at the beginning of the chapter?

The cave painting of cattle is a two-dimensional representation of three-dimensional animals. It conveys some information about cattle and how they are shaped. Although we cannot know the intention of its artist(s), perhaps they meant to use the cave painting to communicate some information about cattle they had observed. The painting is a "snapshot" in time that summarizes and communicates about cattle.

A nutritional model (for example, the NASEM dairy model) is also a representation of cattle. Instead of a two-dimensional artwork, nutritional models are generally represented mathematically. The tens or hundreds of mathematical expressions that comprise a nutritional model are intended to summarize and communicate what we know about cattle nutrition. Similar to the painting, a model is a representation of reality.

2.3 Usefulness

Models are mathematical and/or statistical descriptions of inputs, processes, and outputs. Nutritional models function as decision-support tools that can use known information (e.g., feed composition, animal characteristics) to predict how nutritional processes will unfold and what outcomes will result. They can be used to answer various types of questions.

Scenario 1

A dairy nutritionist has access to many different feedstuffs with known chemical composition. They have several different pens of animals to feed (e.g., calves, dry cows, lactating cows, high-producing lactating cows). How do they create diets for each pen of animals?

A nutritional model can help determine the requirements for each pen of animals. Additionally, the nutritional model can determine which feeds can be combined to create diets that meet the requirements.

Scenario 2

A group of dairy producers aims to reduce greenhouse gas emissions from their farm so they can reach carbon-neutral production goals. How can they select diets that contribute to their environmental goals?

A nutritional model could help these producers predict the environmental impact of their current production practices, or explore hypothetical alternative diets and scenarios.

Scenario 3

A dairy nutritionist has a suspicion that a group of cows is not producing as much milk fat as they could be, given the diet and animal characteristics. How does the nutritionist test their hypothesis?

A nutritional model can be used to benchmark production. Benchmarking means comparing the observed value against a reference value to evaluate its adequacy. In this case, the nutritionist could enter the diet and cow information to predict the expected milk fat production under these conditions. Then, they could compare this reference (expected) value to their observed value to benchmark.

Scenario 4

Feed costs for certain ingredients have changed, and a nutritionist wants to ensure they can meet animal needs and maintain performance at the least possible cost. How can they create a diet that minimizes feed costs?

A nutritional model can be used to optimize diets based on certain constraints. For example, least cost formulation is a common approach. It involves finding the combination of ingredients that will create a diet that meets animal requirements and costs the least amount.

2.4 NASEM (2021) and other dairy nutrition models

NASEM is one of several dairy cattle nutrition models. In most cases, models are intended to serve as decision support tools. In other words, the model estimates are intended to help dairy stakeholders, especially dairy farm managers, make more-informed decisions. The Cornell Net Protein and Carbohydrate System (CNCPS) is an alternative model upon which commercial ration formulation programs such as AMTS have been built. CNCPS also influence the development of The Large Ruminant Nutrition System (LRNS) by Texas A&M researchers. In recent years, the importance of evaluating the environmental and economic impacts of dairy production have led to the development of models not just focused on the animal-level variables (as with NASEM), but instead integrating information about the entire farm system. These models, for example, the Ruminant Farm Systems (RuFaS) model, incorporate detailed information about local weather, soil characteristics, crop growth and storage, and prices of feedstuffs.

Some programs allow users to optimize the inclusion rate of selected diet ingredients (e.g., least cost ration formulation; AMTS program). In contrast, NASEM is designed to evaluate existing diets rather than formulate new diets that optimize user-defined parameters or meet user-defined constraints. Additionally, NASEM predicts selected environmental impacts at the individual animal, predominantly based on dietary factors. Thus, NASEM predictions of environmental impacts do not integrate farm system information to the same extent as other models, e.g., RuFaS.

Other ruminant diet evaluation models

The Cornell Net Protein and Carbohydrate System (CNCPS) https://cals.cornell.edu/animal-science/outreach-extension/publications-resources-software/cncps

The Large Ruminant Nutrition System (LRNS) https://animalscience.tamu.edu/the-utility-of-applied-nutrition-models-a-brief-history-and-future-perspectives/

Ruminant Farm Systems (RuFaS) http://rufas.org

Test Yourself The NASEM model is designed to diets.

2.5 Let's develop a simple nutritional model

Nutritional models are developed through scientific processes. To get a sense of how nutritional models work, let's go through a fictional example and develop our own (very simple!) nutritional model. We need to follow the following steps:

Hypothesis generation
Data collection (through observation and experimentation)
Model development
Model verification and generation of new hypotheses
...repeat the process ad infinitum

2.5.1 Hypothesis generation

Imagine that a researcher has some cattle in individual stalls. They ensure each cow has as much feed as she wants to consume (ad libitum feeding). Over time, the researcher starts to notice that the larger cattle seem to eat more. They write this observation into their notebook.

What the researcher has just done is the rough beginning of generating a hypothesis:

Larger cows seem to consume more feed than smaller cows.

After thinking about it some more, they can refine their hypothesis to make it more testable. For example, rather than "larger cows", which is somewhat vague, they can be more specific and say "greater bodyweight." Rather than saying "eat more," they can say "consume more dry matter on a daily basis." Now, we have a testable hypothesis:

In lactating cows, greater bodyweight is associated with greater dry matter intake on a daily basis.

By gathering empirical data, we can test this hypothesis. If we find evidence that this relationship is true, we can use it to build a nutritional model.

2.5.2 Data collection through observation (or experimentation)

To learn more about the hypothesized relationship between body size and feed intake, the researcher decides to find a larger group of cattle to collect observational data. They collect two pieces of information in each observation: 1) the animal's body weight (BW), and 2) the animal's dry matter intake (DMI). They use the data to create a plot:

Figure 2.2: DMI vs BW for 300 observations from lactating cows

Think to Yourself: What would you conclude from the plot?

After looking at the plot, the researcher believes that it supports their hypothesis: DMI and BW are positively related. In other words, if an animal's BW is known, its DMI can be guessed with some accuracy. The researcher decides to convert this observed relationship to a mathematical model. Because the relationship seems to follow a line, they fit a regression with the linear form \(y = mx + b\).

Figure 2.3: Fitted regression model predicting DMI from BW for lactating cows

2.5.3 Model development

By fitting a regression model to the observed points, they get an estimate of the slope (0.03) that relates BW and DMI. In other words, the average DMI observed was 3% of the animal BW. This single mathematical expression is a very simple nutritional model: \(DMI = 0.03 * BW\)

We can think of our example model as an expression relating three parameters:

\(DMI\) a predicted value

\(0.03\) a coefficient relating DMI and BW

\(BW\) a user input describing the animal

The researcher thinks the model will be useful for prediction. They decide to test the predictive performance of the model by buying a new lactating cow. They record the cow's BW as 625 kg.

Figure 2.4: Fitted regression model predicting DMI from BW for lactating cows

Test Yourself: Using our simple nutritional model, what is this cow's predicted DMI?

2.5.4 Model verification

To predict the DMI of the new cow, the researcher enters the known information (cow's BW) into the nutritional model: \(DMI = 0.03 * 625\). The model predicts the cow's DMI will be 18.75 kg. Tracing up from the x-axis, the intersection of the red dashed line with the blue line shows the predicted DMI for an animal with BW = 625.

Next, the researcher decides to verify their model by measuring the animal's actual DMI.

Figure 2.5: Actual DMI for a new observation (red point) of a cow with BW = 625 kg

Uh oh.... the actual DMI observed is shown with the large red point. It is greater than the prediction. This means that the model under-predicted the actual DMI for this cow based on her BW. This causes the researcher to go back to their original model, \(DMI = 0.03 * BW\). The variable BW seems to explain some, but not all of the variation in DMI.

Test Yourself: What should the researcher do next?

There are several courses of action to be considered. First, the researcher could leave the model as-is, and attribute the error in prediction to un-explainable variation. Un-explainable variation comes from unknown and un-measurable sources, including the intrinsic randomness of the universe. Second, the researcher could try to gather more information to find other measurable predictors of DMI besides BW. Then, they could revise the nutritional model to include other variables that determine the DMI.

2.5.6 Reflecting on our example model

Congratulations - you created and used your first nutritional model! 🎉

Just like the two-dimensional cow paintings at the beginning, our simple nutritional model conveyed some information about cattle. Instead of a painting, we used a mathematical expression to communicate it. We showed how a researcher could use empirical observations (data collection) to create a model expression, check it against new data, and refine the model.

2.6 Scaling up and adding complexity

How do we get from our simple example model, to a huge and complex model like NASEM?

In our example, one researcher was working alone. In actuality, thousands of animal nutritionists and researchers contribute to developing nutritional models such as NASEM (2021). Many researchers have a specific focus area (e.g., fatty acid nutrition, rumen function) and dedicate their efforts to improving methods and collecting data for this specific topic area. An individual researcher can only collect a limited amount of data on a few parameters. Still, when thousands of researchers publish their findings, these models and data can be aggregated into larger models. In fact, some researchers ("modelers") specialize in aggregating and modeling data collected by other scientists!

The NASEM model is a conglomeration of many smaller models (sometimes called sub-models) into one larger model. The entire NASEM model is massive: it represents all nutrients and energy for all nutritional processes. It contains hundreds of parameters, related by many types of mathematical expressions. In contrast, any given piece (a sub-model) of the NASEM model is simpler. A sub-model could represent only one nutrient (e.g., protein) or a specific process (e.g., ruminal degradation). Many of the sub-models can be further divided into smaller sub-models. Each of these tiny pieces of the NASEM model was created and refined through scientific processes similar to our example model. Modelers worked to connect together these tiny sub-models to create the much larger NASEM model.

Test yourself A NASEM sub-model is someone else's duplicate of the original model.

2.7 Conclusion

Nutritional models serve practical goals: they can make animal feeding practices more economical, more environmentally-sound, and more aligned with human needs and available resources. Nutritional models are developed through scientific processes. They use mathematical expressions to represent information about how nutritional processes work. Nutritional models can appear quite complex, but it's important to remember that they are the collective effort of many people, across long periods of time, as documented in the scientific literature.

2.8 Questions

What historical events spurred the development of animal nutrition sciences in the U.S.?
Explain why nutritional models can be useful to dairy producers.
Give an example of a situation when a nutritional model could help make decisions related to environmental impacts.
Give an exmaple of how a nutritional model could be used in farm economic decisions.
How many editions of the "Nutrient Requirements of Dairy Cattle" consensus report have been published?
Explain how a cave painting can be thought of as similar to a nutritional model, metaphorically.
Explain the steps involved in developing a nutritional model, using a different example than the one discussed in this chapter.
What are some possible courses of action when a nutritional model does not adequately explain the observed variation? Discuss the options available to researchers for model refinement and improvement.
Would you say the process used to develop nutritional models is linear or circular (recursive)? Explain your reasoning.

2.9 R code for figures

R code used for this chapter is given below.

# Set the seed for reproducibility
set.seed(765)

# Load required packages
library(dplyr)
library(magrittr)
library(ggplot2)

# Set the ggplot2 theme
theme_set(theme_bw())

# Generate data
res <- rnorm(300, 0, sd = 3) # generate normally distributed residuals
bw <- rnorm(300, 600, sd = 40) # generate normally distributed body weights
parity <- rep(c(1, 7), 150) # generate parity effect using integers
dmi <- 0.03 * bw + parity + res # create dry matter intake (DMI) as a function of observed and residual

# Create a data frame with the generated data ,create parity values
df <- data.frame(DMI = dmi, BW = bw, Parity = parity) %>%
  mutate(
    Parity = ifelse(
      Parity == 1,
      "Primiparous (first calf)",
      "Multiparous (2+ calves)"
    )
  )

# Create a scatterplot of BW and DMI
p <- ggplot(df, aes(x = BW, y = DMI)) +
  geom_point() +
  labs(x = "BW, kg", y = "DMI, kg/d")

p + theme_bw()

# Add a linear regression line to the scatterplot and label the equation
p + geom_smooth(method = "lm", se = F) +
  annotate(
    geom = "text",
    x = 540,
    y = 35,
    label = "DMI = 0.03*BW",
    color = "blue",
    size = 5
  ) + theme_bw() +
  labs(x = "BW, kg", y = "DMI, kg/d")

# Create a scatterplot of BW and DMI, with an additional vertical red dashed line

p2 <- ggplot(df, aes(x = BW, y = DMI)) +
  geom_point(color = "grey") +
  geom_smooth(method = "lm", se = F) +
  annotate(
    geom = "text",
    x = 540,
    y = 35,
    label = "DMI = 0.03*BW",
    color = "blue",
    size = 5
  ) +
  annotate(
    geom = "segment",
    x = 625,
    xend = 625,
    y = -Inf,
    yend = Inf,
    color = "red",
    lty = "dashed"
  ) +
  theme_bw() +
  labs(x = "BW, kg", y = "DMI, kg/d")

p2

# Add a red point to the scatterplot
p2.1 <- p2 + annotate(
  geom = "point",
  x = 625,
  y = 25,
  size = 4,
  color = "red"
) + theme_bw()

p2.1

# Create a scatterplot of BW and DMI, with color based on parity, and label the linear regression lines
p <- ggplot(df, aes(x = BW, y = DMI, color = Parity)) +
  geom_point() +
  theme_bw() +
  theme(legend.position = "bottom")

p + geom_smooth(method = "lm", se = F) +
  annotate(
    geom = "text",
    x = 555,
    y = 35,
    label = "DMI = 0.03*BW + (multiparous effect)",
    color = "#F8766D",
    size = 5
  ) +
  annotate(
    geom = "text",
    x = 555,
    y = 32,
    label = "DMI = 0.03*BW + (primiparous effect)",
    color = "#00BFC4",
    size = 5
  ) +
  labs(x = "BW, kg", y = "DMI, kg/d")

Learning from the narrative and model in NASEM (2021) 'Nutrient Requirements of Dairy Cattle'