The proportion of the dietary energy in the US consumed by dogs and cats was calculated as the sum of the energy consumed by dogs and cats (203 ± 15 PJ y -1 ) divided by human energy intake (1051 ± 9 PJ y -1 ), with the result that dogs and cats consume about 19.4 ± 1.6% of the energy that humans in America do ( Table 1 ).

Cats require ~544 kJ (kg BW) -0.67 d -1 energy [ 29 ]. The body weight of cats varies less than that of dogs, so the average and standard deviation of cat weight in Bermingham et al. [ 33 ] (4.2 ± 0.2 kg) were used to represent average cat weight, resulting in a total cat energy requirement of 1,426 ± 79 kJ d -1 (341 ± 19 kcal d -1 ). Multiplied by the estimated number of owned cats in the US ( Eq 1 ), this results in an estimate of 45 ± 2.5 PJ y -1 consumed.

The American Pet Products Association (APPA) estimates that there were 77.8 million dog and 85.6 million cats owned as pets in the United States in 2015 ( Table 1 ) [ 8 ]. Dogs’ energy requirements are taken as ~544 kJ (kg BW) -0.75 d -1 [ 29 ]. Dogs’ body weight (BW) varies greatly by breed. To estimate the average BW of dogs, the average weight of the American Kennel Club (AKC)’s list of the 10 most popular dog breeds in the US was used [ 30 ]. Average breed weights were taken either from the AKC or other sources [ 31 ]. This resulted in an average US dog BW of 22 kg. The standard deviation of the average breed weights represents the variability among breeds, rather than uncertainty in the average dog weight and is therefore inappropriate for the uncertainty analysis done here. To estimate the uncertainty in the average dog weight, data from Meyer et al. [ 32 ] were taken for 10 breeds of different sizes. For each breed, Meyer et al. [ 32 ] reports the mass and standard deviation of the samples (n = 4 to 9). The standard deviation was regressed against the mass (r 2 = 0.87) and standard deviation at 22 kg was estimated as 1.2 kg. Therefore, the estimated average US dog BW that will be used hereafter is 22 ± 1.2 kg giving an average energy requirement of 5,594 ± 443 kJ d -1 (1337 ± 106 kcal d -1 ). Multiplied by the estimated number of owned dogs in the US ( Eq 1 ), this results in an estimate of 159 ± 13 PJ y -1 consumed by dogs [ 29 ].

The Census Bureau estimates that the total population of the US was 321 million in 2015, with roughly equal proportions of men and women [ 27 ] ( Table 1 ). The USDA Agricultural Research Service estimates that on average, US males (age 2+) consume 10,330 ± 91 kJ d -1 (2,469 ± 81 kcal d -1 ) and US females (age 2+) consume 7,607 ± 64 kJ d -1 (1,817 ± 15 kcal d -1 ). Therefore, the average daily energy consumption for both males and females is 8,966 ± 155 kJ d -1 (2,143 ± 37 kcal d -1 ) [ 28 ]. Using Eq 1 , these estimates result in a total human energy intake of 1,051 ± 9 PJ y -1 .

Energy from animal sources

For humans, the fraction of energy that is derived from animal sources, F A , can be calculated as: (2) where E A,C is the energy consumed by humans from animal sources (subscript A). E A,C can be calculated from data available from the U.S. Department of Agriculture (USDA) (Table 2): the total amount of red meat (including beef, veal, pork, and lamb), poultry (including chicken and turkey) and fish (including fish and shellfish) eaten by each Americans is 59.6 kg yr-1. Given the energy density of each food used by the USDA (Table 2), and with the conservative assumption that this meat provides the only animal-derived energy consumed by Americans, it is calculated that Americans consume 206 PJ yr-1 from animal sources, which constitutes 20% of their total energy intake.

For dogs and cats, direct data on consumption is not available and therefore F A cannot be calculated directly using Eq 2. Instead, new calculations must be made based on available data: ingredient lists for dog and cat foods and the composition of these ingredients in terms of substrates which have well-known energy densities (i.e., Atwater factors for protein, carbohydrate, and fat).

To do this, the ingredient lists for individual pet foods were used. Individual ingredients were considered in terms of the content of energy-providing substrates, protein, fat, and carbohydrate and non-energy providing components like water, ash, and fiber. Compositional data analysis is required for these calculations because the substrate components must sum to unity [34]. For a particular pet food, m, the center (analogous to the arithmetic mean) dry mass fraction of substrate k (protein, fat, carbohydrate, other), expressed as average grams of k per gram of m, was calculated as the closed geometric mean: (3) where is the mass fraction of substrate k in one of the first five ingredients, i, in a particular food (i.e., grams of k per gram of i). For these calculations, the category ‘other’ was included to provide closure [35], that is, so that the fractions of all categories would sum to unity. was estimated for each ingredient by equating it with a general ingredient category for which substrate content is available (Table 3) [29, 36].

Similarly, the average dry mass fraction of animal-derived substrate k for a particular food (i.e., average grams of animal-derived k per gram of m) was calculated as the closed geometric mean: (4) where is the mass fraction of animal-derived substrate k in one of the first five ingredients, i, in a particular food (Table 3 asterisks indicate animal-derived). For these calculations, the same approach was used in calculation of , except non-animal derived protein, fat, and carbohydrates were added to the ‘other’ category to maintain closure. and are (geometric) average mass fractions and therefore explicitly assume that the first five ingredients in a food are present in equal proportions and that they constitute nearly all of the mass of pet food m. This assumption is wrong, but conservative, as explained below. Uncertainty in was calculated as the variance across all m for each substrate k [35].

The fraction of energy derived from animal products in a food m (animal-derived joules per total joules) was calculated as: (5) where E k is the energy density of the substrates (i.e., Atwater factors: E protein = E carbohydrate = 4J/g, E Fat = 9 J/g [29]). E other was set to zero in for both total and animal-derived calculations. In the former case, water, ash, and fiber, which provide no dietary energy, comprised the ‘other’ category. In the latter, ‘other’ contained water, ash, and fiber as well as non-animal derived protein, fat, and carbohydrates, on the logic that these do not provide animal-derived dietary energy. The total animal-derived energy was calculated as (6) which is the weighted average fraction of animal-derived energy in four categories: premium dog food (n = 102), market-leading dog food (n = 9), premium cat food (n = 163), and market-leading cat food (n = 9). is the annual total energy consumed by dogs and is the annual total energy consumed by cats (Table 1) P x,y is the proportion of dog or cat owners and (x = Dog and Cat, respectively) who prefer premium or market-leading foods (y = P and N, respectively). Likewise, M x,y is the number of foods considered here in each category. More premium foods were used in these calculations because there is more diversity in this market sector. For dry dog food, nine foods from just five manufacturers constitute 48% of the market [37]. For dry cat food, nine foods from just four manufacturers constitute 49% of the market share [38].

Dry foods were used for these calculations. For both dogs and cats, dry food sales dominate wet food sales (billions of US dollars in sales for various foods in 2012: 8.7 (dry dog food) vs 2.3 (wet dog food) [39], and 3.6 (dry cat food) vs. 2.4 (wet cat food) [40], and thus are more representative of the foods fed to cats, and especially, dogs. The dominance of dry food as the preferred form is especially true when the price per serving is taken into account. One market-leading wet cat food costs approximately $0.83 per serving while a dry food by the same manufacturer costs approximately $0.23 per serving. Using the this per-serving price ratio, dry cat food outsells wet cat food on a per-serving basis by a factor of about 3 to 1. Furthermore, dry food typically has lower animal content (as determined by the list of ingredients in descending order of mass contribution) than wet food. Thus, use of dry food for these calculations provides a conservative estimate of the greatest proportion of dog and cat food sales in the U.S.

USDA labeling rules require that pet food ingredients be labeled in descending order of weight contribution, as they do with foods intended for humans. Calculations were made on the assumptions that 1) each of the first five ingredients contributes, by mass, equally to the mass of the pet food and 2) collectively, these first five ingredients make up nearly all of the mass of the pet food (that is, there are no other ingredients that contribute substantially to the mass of the food). With regard to the former, for marketing purposes, animal-derived ingredients typically appear in in the top couple of places in the ingredient list. This is particularly true of premium foods, where 100% of both dog and cat foods examined here had animal-derived products as the first ingredient (Table 4). For all types of dry food examined here (market-leading v. premium dog and cat foods), animal-derived ingredients appear among the first two ingredients more commonly than among the third and fourth ingredients (Table 4). Thus, the calculations made here over-weight the later ingredients, which are less likely to be animal-derived, compared to the earlier ingredients, which are more likely to be animal derived. Although there is no way to know, in proprietary recipes, the exact proportions of ingredient, by weighting the first five ingredients equally, a minimum overall estimate of animal-derived energy in dog and cat food is produced.

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larger image TIFF original image Download: Table 4. Frequency of an animal derived ingredient in one of the first two positions or one of the two following positions in the ingredient list of dry foods considered here. https://doi.org/10.1371/journal.pone.0181301.t004

With regard to the second assumption, that the first five ingredients make up nearly all of the mass of the pet food, ingredients appearing past the first five in the ingredient list are often nutrients (e.g., tocopherol) added in trace quantities. If ingredients past the fifth are not trace, then given the requirement that ingredients be listed in decreasing mass contribution, the sixth ingredient must contribute less than 16% of the mass of the food. In the case of seven substantive ingredients, the maximum fraction of the mass in the 6th and 7th places is 29%. Among the premium brands that were examined, the proportion of animal-derived product decreased as they occurred later in ingredient lists with only 21% of the sixth ingredients in dry dog food being animal-derived. Thus, even in the extreme case, a maximum of 3–6% (21% of 16% = 3.5%; 21% of 29% = 6%) of the animal-derived content may be missing in the foods examined here. Although the methodology use here cannot give exact amounts of animal-derived content from foods, the potential maximum exclusion of 3–6% of animal-derived products is sufficient to draw important conclusions about the amount of animal-derived energy consumed by dogs and cats.

The APPA’s annual pet-owners survey [8] provides data that can be used understand consumer preferences, thus providing information about ratio of premium vs. non-premium (market leading) foods consumed. Non-premium brands tend to have lower animal-derived content whereas premium brands tend to have higher animal-derived content. The premium brand category used here includes the 'premium' and 'gourmet' survey categories. For dogs of all sizes, the average percent of owners who usually feed these meat-rich dog foods is 38%. For cats, this number is 30% (Table 5).

The final market-wide estimates of the fraction of energy in dog and cat foods that is animal-derived are 34% ± 4% and 31% ± 4%, respectively (Table 5). In total, Eq 6 yields an estimate that animal-derived energy constitutes 33% ± 6% of the diets of dogs and cats in the US. This is significantly higher than the fraction of humans’ dietary energy that is animal-derived (19%). Because dogs and cats consume, together, 203 ± 15 PJ/year, it is estimated that dogs and cats consume a minimum of 67 ± 17 PJ/year in animal-derived energy, which is 33% ± 9% of the animal-derived energy consumed by humans in the US or 25% ± 6% of the total.

An important caveat for the calculations of the relative consumption of pets and humans is that the sources of the data, and mode of calculation, are dramatically different. As a result, their ratios may be systematically biased. Nonetheless, the calculations of absolute amounts (e.g., PJ/yr) are informative, and the relative amounts still provide important insight into the magnitude of pets’ consumption.