New insights into the genetic mechanisms of body size evolution in Carnivora

The range of body sizes in Carnivora is unparalleled in any other mammalian order, with more than 130,000 times in body mass and 50 times in length. However, the molecular mechanisms underlying the huge difference in body size of Carnivora have not been explored so far. Herein, we performed a comparative genomics analysis of 20 carnivores to explore the genetic basis of great body size variation in carnivores. Phylogenetic generalized least squares (PGLS) revealed that 337 genes were signicantly related to both head body length and body mass, these genes were dened as body size associated genes (BSAGs). Fourteen positively related BSAGs were found to be associated with obesity and three of which were identied to be under rapid evolution in the extremely large body-sized carnivores, which suggested that these obesity-related BSAGs might have driven the body size expansion in carnivores. Interestingly, 100 BSAGs were examined to be associated with cancer control in carnivores, particularly 15 cancer-related genes were found to be under rapid evolution in extremely large carnivores. These results strongly suggested that large body-sized carnivores might have evolved effective mechanism to resist cancer, which could be regarded as molecular evidence to support for the Peto’s paradox. For small carnivores, we identied 15 rapidly evolving genes and found six genes with xed amino acid changes that were reported to reduce body size.

obesity and three of which were identi ed to be under rapid evolution in the extremely large body-sized carnivores, which suggested that these obesity-related BSAGs might have driven the body size expansion in carnivores. Interestingly, 100 BSAGs were examined to be associated with cancer control in carnivores, particularly 15 cancer-related genes were found to be under rapid evolution in extremely large carnivores. These results strongly suggested that large body-sized carnivores might have evolved effective mechanism to resist cancer, which could be regarded as molecular evidence to support for the Peto's paradox. For small carnivores, we identi ed 15 rapidly evolving genes and found six genes with xed amino acid changes that were reported to reduce body size.

Conclusion
This study brings new insights into the molecular mechanisms that drove the diversifying evolution of body size in carnivores, and provides new target genes for exploring the mysteries of body size evolution in mammals.

Background
Carnivores, or the mammalian order Carnivora, feed primarily or exclusively on animal matter. They represent a highly diverse and successful group of mammals, which is on the top of the food chain. A total of 280 species were included in 11 families of Carnivora [1], which are widely distributed all over the world, covering most of the major land masses, rivers, and all of the oceans. Carnivores are well-known for their dietetic preferences, carnassial dentition, skull shape and body size [2].
Body size is closely related to habitat, life history, metabolism and risk of extinction, and etc. [3]. Previous studies revealed that the basal metabolic rate of carnivores decreased with the increase of body mass [4][5][6]. For feeding habits, the prey size and diversity increase with body size in predatory carnivores.
Interestingly, statistical analysis showed that among terrestrial carnivores, the herbivorous species are relatively large while the insectivorous species are relatively small [7]. A typical case is the Ursidae that may have increased in size due to their diet including a greater proportion of fruits and vegetation [8].
Importantly, the range of body sizes of carnivores is unparalleled in any other mammalian orders [9,10].
The largest carnivore, male southern elephant seal (Mirounga leonina), is more than 4,000 kg in body mass and over 5.8 m in length [11,12], whereas the smallest carnivore, the least weasel (Mustela nivalis), is only 29 g in body mass and 0.114 m in body length [13,14]. Such a huge difference with more than 130,000 times in body mass and 50 times in length makes the carnivores a good target for investigating the mechanism of mammalian body size evolution.
The formation of the discrepant body size of species in carnivores is actually a manifestation of adapting to their respective niche and has their own ecological advantages. For small carnivores, they have access to a wide variety of food resources that not available to larger carnivores, owned improved reproductive e ciency and a greater ability to respond to environmental emergencies [15][16][17]. For example, small carnivores such as Mustelidae and Viverridae, were adapted for exploiting small rodent prey and invertebrates. Their smaller body makes them move swiftly enough to follow and pounce on prey and more unconspicuous in open vegetation during hunt [10]. In contrast, the increased body size brings a large of bene ts including the ability to exploit vast food resources, increased competitiveness, increased defense against predation, and extended longevity [18,19]. However, larger body size with more cells will have a higher risk of cancer in theory assuming that each cell has a consistent risk of mutations [20]. Notably, some extremely large carnivores such as the walrus (Odobenus rosmarus) and polar bear (Ursus maritimus) that can live longer than 40 years was not found have higher risk of cancer than smaller species such as Mustelidae species that have a lifespan of only several years [21]. This phenomenon is well-known as the Peto's paradox [20,22]. And carnivores may be an excellent target for testing the Peto's paradox at the molecular level.
Until now, the molecular mechanisms regulating the body size of carnivores remain poorly explored.
Previous studies mainly focused on the interspeci c variation of body size, especially con ned to the domestic dog (Canis lupus familiaris). A recent study showed that variants in IGF1, COL11A2, ITGA10, and ADAMTS17 contributed to height that segregates within speci c dog breeds [23]. The constantly updated high-quality genomes of carnivores provide new opportunities for insight into the mechanism of huge body size variation among carnivores. In the present study, 20 high-quality genomes of carnivores were used for comparative genomic analysis. First, phylogenetic generalized least squares (PGLS) methods were used to scan the body-size-associated genes (BSAGs). Second, we determined the rapidly evolving genes (REGs) in extremely large or small carnivores, respectively. And xed amino acid changes were also identi ed in different body size groups. Finally, selective pressure variation on cancer-related BSAGs among different carnivores may partly verify the Peto's paradox. From above results, we expect to provide some novel insights into the molecular mechanism of body size evolution in carnivores and mammals.

Results
Genome-scanning of BSAGs and functional enrichment A total of 6,667 one-to-one orthologous genes were identi ed in the 20 carnivores and one cow genomes ( Figure 1; Table S1) by Ortho nder and our in-house Perl scripts. PGLS revealed that 1,132 and 668 genes were signi cantly associated with head body length and body mass, respectively. There were 337 genes were signi cantly related to both head body length and body mass after performing the two-step of the calibration procedure (P value.all/robust/max < 0.05), which were de ned as body size associated genes (BSAGs ; Table S2). According to the tendency or the correlation slope, 256 genes showed positive correlation and 81 genes exhibited negative correlation.
For 256 positively correlated BSAGs, functional enrichment analyses revealed that 61.7% (161/261) genes were enriched signi cantly (P < 0.05) in 164 GO terms (Table S3). There were 28.6% (46/161) genes annotated to metabolic process, such as "NADP metabolic process", "glycoprotein metabolic process" and "cellular amino acid metabolic process" (Figure 2). And 32.3% (52/161) were signi cantly enriched for GO categories that associated with growth and development, including "positive regulation of growth", "cardiac chamber development", "positive regulation of nervous system development" and "epidermis development" (Figure 2), etc. For instance, seven genes (ADAM10, DBN1, NTRK3, PPIB, MAP2K5, WNT2 and ZFPM2) which played key role in maintaining normal development of organ or body were enriched in the GO term of the "positive regulation of growth". However, due to the scattered functions of these BSAGs, there were only 21 (8.2%) genes signi cantly enriched in KEGG pathways (Table S3), like "cytokine-cytokine receptor interaction", "fanconi anemia pathway" and so on.
For negative correlated BSAGs, 29.6% (24/81) genes were de ned in GO categories such as "telomere maintenance", "DNA repair", "negative regulation of DNA metabolic process", "negative regulation of cell activation" and "apoptotic signaling pathway" (Figure 2; Table S3). There were no signi cant enriched terms when mapped these negative correlated genes to KEGG database.
We then manually looked up the biological functions of these BSAGs by searching literature and multiple databases and identi ed 14 positively correlated BSAGs (BRAP, CHCHD5, CPT1C, GPR1, LDLR, MAP2K5, PLEKHS1, SLC30A8, ST3GAL2, STX16, ZFHX3, ZGRF1, ZNF395 and ZPLD1) were associated with "obesity" (Table S4), which is a manifestation of an enlarged-body-sized phenotype. For instance, a signi cant positive association between log (root-to-tip ω) and log (body mass) were tested at the BRAP, STX16, ZGRF1 and ZPLD1 gene (Figure 3) respectively, and these four genes were reported to cause obesity in human. Furthermore, we also found 100 BSAGs were associated with cancer control, including "DNA repair", "cell cycle control, apoptosis, adhesion and autophagy", "immune response" and so on (Table S5) (Table S6). For example, BRCA2 (breast cancer type 2 susceptibility protein) is a tumor suppressor gene that links with an increased risk for breast and ovarian cancers, and it plays a central role in DNA repair, transcription, and cell cycle in response to DNA damage. In addition, 18 genes were related to immune response, development and maturation of immunocyte, such as ITK and TNFRSF17 (Table S5).
REGs in different body sizes groups "Branch model" implemented in Codeml of PAML 4.9e program was used to identify rapidly evolving genes (REGs) respectively in the small and extremely large groups. These results showed that divergent selective pressure might have acted on carnivores with contrasting body size.
In the small-sized group, a total of 15 BSAGs were found to be under rapid evolution (Table S7). Among them, CTLA4 (cytotoxic T-lymphocyte associated protein 4) is a member of the immunoglobulin superfamily and encodes a protein that transmits an inhibitory signal to T cells. In addition, CTLA4 is related to lower body mass index in human, which was in keeping with small-body-sized phenotypes.
By contrast, 55 REGs were determined in extremely large-sized group (Table S7; Figure 4). Fifteen genes were signi cant enrichment in growth and development (such as nerve, muscle and cardiac development), or phenotypic changes in body size (ATP8B1, DIS3, POMGNT1, SLITRK5, ST3GAL2, TENM3, ZGRF1 and ZPLD1). For instance, ST3GAL2 (ST3 beta-galactoside alpha-2,3-sialytransferase 2) encodes a type membrane protein that catalyzes the transfer of sialic acid from CMP-sialic acid to galactose-containing substates, and this gene is associated with increased fat mass and lean body mass, which is consistent with large-body-sized phenotypes. Additionally, fteen genes were associated with cancer control (Table S5), among which, three genes are related to immunity (MAGT1, RFXANK and SKAP2), ADGRL3 and TENM3 are relevant to cell adhesion, and two genes (ADAM11 and TEP1) had been proved to be tumor suppressor genes. For example, ADAM11 (ADAM metallopeptidase domain 11) has been identi ed as a candidate tumor suppressor gene in human breast cancer, it encodes a member of the ADAM (a disintegrin and metalloprotease) protein family which take part in a variety biological process involving cell-cell/matrix interactions, muscle and nerve development.
Fixed amino acid changes in extremely small body size groups Identifying xed amino acid changes in a certain group may help to explain the molecular mechanism of the occurrence of speci c phenotypes. In the present study, we identi ed six xed amino acid changes of six genes in extremely small carnivores (CDC7, ENG, LIG4, MMP2, POLE and TSPAN8; Figure 5) but none was found in the extremely large carnivores. And these sites were located in their functional domains of respective proteins that were identi ed by Pfam. For instance, a unique change, S513L, was located in the protein kinase domain of CDC7 gene and another mutation (S784P) locates in the DNA ligase IV domain of LIG4 gene, both genes were associated with reduced-body-sized phenotype in human or mice.

Discussion
The great difference in body size between the largest and smallest carnivores, with more than 130,000 times in body mass and 50 times in length, is signi cantly shocking in mammals. Reconstructions incorporating fossil data supported small body size (<5kg) for the ancestors of the species in Caniformia [24]. Though a few studies have been conducted to reveal molecular mechanisms for body size variation within species (such as the domestic dog), the genetic mechanisms underlying the huge differences in body size among the living carnivores are not well understood. In the present study, we scanned the whole genomes of 20 carnivores covering contrasting body size and identi ed that 337 genes were signi cantly related with both head body length and body mass. Selective pressure analyses revealed different evolutionary patterns in the extremely large and small species. Furthermore, xed amino acid changes have also been identi ed in extremely small-body-sized carnivores and suggest the potential functions of these loci to restrict body size growth. All these results provide a genetic basis for studying the body size evolution in carnivores.
Obesity-related genes contributing to increasing body size of carnivores In carnivores, some species of Pinnipedia and Fissipedia have evolved relatively large body size, containing some extremely large species such as walrus, northern sea lion, weddell seal and polar bear, even weighed exceed 350kg. Due to the semi-aquatic life habits, species in Pinnipedia had evolved a large body size to increase body surface area to reduce the rapid heat loss in water [25]. Similarly, the polar bear is the largest extant bear to adapt to the cold Arctic regions, which are averagely weighed 372 kg [26]. Interestingly, polar bears and seals have relatively thick subcutaneous fat, which accounted for more than 30% of their body weight and were much higher than that of other wild carnivores [27][28][29]. It has been suggested that pinnipeds and polar bears are covered with a thick layer of fat to protect them from cold environment. In general, obesity refers to certain degree of overweight and a thick fat layer, which is a state caused by excessive fat accumulation [30], and percent body fat ≥ 25% for men and ≥ 30% for women is an indication of obesity [31].
Fourteen positively correlated BSAGs were identi ed in our study and variations of these genes were reported to cause obesity (BRAP, CHCHD5, CPT1C, GPR1, LDLR, MAP2K5, PLEKHS1, SLC30A8, ST3GAL2, STX16, ZFHX3, ZGRF1, ZNF395 and ZPLD1). For instance, SNPs in BRAP (BRCA1 associated protein) were shown to associate with obesity and other metabolic abnormalities [32]. And STX16 (syntaxin 16) encoded a protein that is a member of the syntaxin or t-SNARE family and deletion in this gene may cause obesity and macrosomia in human [33]. Our result revealed that MAP2K5 (mitogen-activated protein kinase kinase 5) was enriched in the GO cluster of "positive regulation of growth (GO:0045927)" and genetic variations in this gene were reported to cause childhood obesity [34]. Furthermore, the evolutionary rates of 14 obesity-related BASGs in large carnivores were higher than that of small ones. Specially, three obesity-related BSAGs (i.e. ST3GAL2, ZGRF1 and ZPLD1) were determined rapid evolution in extremely large carnivores. For instance, the evolutionary rate of ZPLD1 (zona pellucida like domain containing 1) gene is 0.68632 in the extremely large carnivores, 5.5 times of that identi ed in the control group. Deletions in ZPLD1 has been proved to contribute to genetic susceptibility of common childhood obesity [35]. And it was reported that ST3GAL2-null mice have an increase of 50% in fat mass and 9% in lean body mass [36]. For ZGRF1 (Zinc nger GRF-type containing 1), this gene encodes a protein that contains GRF zinc nger (zf-GRF) and transmembrane domains, and a recent genome-wide and exome chip association study revealed its association with adiposity [37]. Thus, the 14 obesity-related BSAGs identi ed in this study may contribute to increased body size and accumulated body fat for the large carnivores.

Molecular evidence for the Peto's Paradox in carnivores?
Animal gigantism is a recurring phenomenon that is seemingly in uenced by available resources and natural selection [19]. Being larger brings an array of advantages for an organism, however, there also exists associated biological tradeoffs, including the increased risk of developing cancer due to with more cells [38]. Surprisingly, empirical cancer rates did not vary with body size, large and long-lived animals have a lower risk of suffering cancer than smaller, shorter-lived animals, and this phenomenon was called the Peto's Paradox [20,22,39]. Recent years, the Peto's Paradox has been studied in many large mammals, such as the bowhead whale and humpback whale [40,41]. Their genomes provided the following two major evidences related to cancer suppression: 1) multiple duplications of tumor suppressor genes; 2) positive selection in genes related to cancer and aging. It was suggested that large species might have evolved multiple mechanisms to suppress cancer.
Carnivores are relatively long-lived mammals, and generally speaking, species in Pinnipedia have a longer lifespan than species in Fissipedia. Some extremely large species in carnivores, such as walrus and polar bears were reported to live 40 or more years in the wild [42]. Within particular taxa in carnivores, body size and lifespan also seem to be positively correlated [21]. For instance, the sea otter (about 27.4kg) may live as long as 27 years in the wild, as compared with the ferret (about 975.6g) which has lifespan much shorter as 11.1 years [21]. The relatively large polar bears (maximum lifespan: 43.8 years) and brown bears (maximum lifespan: 40 years) also live longer than the smaller giant pandas (maximum lifespan: 36.8 years). However, the molecular mechanism for maintaining the longevity of the large carnivores is not very clear, and there have been very few relevant studies on cancer in carnivores so far.
In our study, it was interestingly identi ed a total of 100 BSAGs in carnivores which were related to cancer control process, including tumor suppressor, DNA repair, as well as immunity. In addition, we also identi ed 15 cancer-related REGs in extremely large carnivores. Among them, 21 BSAGs were determined as tumor suppressor genes in previous studies. For example, the APC (APC regulator of WNT signaling pathway) gene encoded a multidomain protein that played a crucial role in tumor suppression by antagonizing the WNT signaling pathway. Variants in APC would induce various kinds of cancer such as colorectal cancer, pancreatic cancer and so on [43,44]. The DSC3 (Desmocollin 3) gene is required for cell adhesion and desmosome formation, and it has been proved that this gene had a tumor suppressive activity through inhibition of AKT pathway in colorectal cancer [45]. ZFHX3 (zinc nger homeobox 3) was essential to regulate myogenic and neuronal differentiation, and it was reported to function as a tumor suppressor in several cancers [46]. The evolutionary rates of these three genes are signi cantly positively correlated with both body size parameters, suggesting the higher evolutionary rate in large carnivores than small ones. Meanwhile, two tumor suppressor genes, ADAM11 and TEP1, exhibited rapid evolution in the extremely large carnivores. The evolutionary rate of ADAM11 is 0.48527 in the extremely large carnivores, 15.4 times of that identi ed in the background group. And this gene has been identi ed as tumor suppressor gene in human breast cancer [47]. The TEP1 (Telomerase associated protein 1) product was a component of the ribonucleoprotein complex responsible for telomerase activity. And alterations in TEP1 has been con rmed to cause several types of human tumors including brain, breast, prostate and lung cancer [48]. These two genes all had relatively higher evolutionary rates in extremely large carnivores and suggested enhanced ability for suppressing cancer.
Additionally, 16 BSAGs were found to be related with "DNA repair" and it was well known that de cits in DNA repair capacity might lead to genetic instability and carcinogenesis [49]. Recent study revealed that loss of a single allele of the CLSPN (claspin) gene in mice was su cient to drive earlier tumorigenesis [50]. And HELQ (Helicase, POLQ like) played a critical role for replication-coupled DNA repair, germ cell maintenance and tumor suppression in mammals [51]. Importantly, 18 immunity related genes were identi ed in BSAGs of carnivores, among which three genes exhibited elevated evolutionary rates (MAGT1, RFXANK and SKAP2). For instance, ITK (IL2 inducible T cell kinase) functions downstream of the T-cell receptor and was important for T-cell activation, development, differentiation, and production of many pro-in ammatory cytokines [52]. Moreover, ITK has been found to be prevalent in all main types of human neoplasia [53,54]. And the evolutionary rate of MAGT1 (magnesium transporter 1) was 0.33127 in extremely large carnivores, 6.1 times of that in background group. Loss of MAGT1 would disrupt T cell signaling and lead to a novel human primary immunode ciency [55], and furthermore, overexpression of MAGT1 was associated with development and metastasis of colorectal cancer [56]. Here, we obtained 100 cancer-related genes that were signi cantly associated with body size evolution in carnivores including 15 cancer-related REGs that identi ed in extremely large group, which might protect them from cancer invasion, special for large and long-lived species. These results might provide novel molecular evidence for the Peto's Paradox with regard to carnivores.
Fixed amino acid changes in extremely small bod-sized carnivores contributing to growth restriction There are some extremely small species in carnivores, such as meerkat and ferret with body mass less than 1 kg and body length less than 50 cm. The smaller size brings multiple superiority to species. For instance, smaller carnivores could take great advantage of food resources that are not available to some large animals to ensure survival when the environment changes dramatically and have more free energy and time to engage in activities that increase mating and reproductive success [15][16][17].
Compared with other carnivores in our dataset, six xed amino acid changes from six genes were identi ed in extremely small-body-sized group: CDC7 (S513L), ENG (V367I), LIG4 (S784P), MMP2 (S579T), TSPAN8(S178T), and POLE (E701D). These six genes have been shown to be related with the phenotype of reduced body size. CDC7 (cell division cycle 7) was very conserved through mammalian evolution but a xed amino acid change (S513L) was identi ed in extremely small carnivores. CDC7 played essential roles in initiation of mitotic DNA replication, and previous study showed that CDC7 -/or low expression of CDC7 protein would lead to reduced body size with decreased cell proliferation in mice [57]. Importantly, the xed changes (S513L) were located in the protein kinase domain that functioned as an on/off switch for many cellular processes including metabolism, cell cycle progression, transcription [58]. Another xed change (V367I) was examined in the Zona_pellucida domain of ENG (endoglin) that was reported Eng -/mice three times smaller than wild type mice at E10.5 of the embryonic period [59]. The unique amino acid mutation (S784P) was determined in the key domain (DNA ligase IV domain) of the LIG4 (DNA ligase 4) gene that was reported mutations in humans or mice would cause growth failure and microcephaly, and this might be the result of activation of the DNA damage response, leading to a large amount of apoptosis during development [60]. Fixed amino acid mutation was separately found in the MMP2 (S579T) and POLE (E701D) gene. Previous studies have shown MMP2 (matrix metallopeptidase 2) knockout in mice and mutations of POLE (DNA polymerase epsilon, catalytic subunit) in human could cause short stature [61,62]. Finally, we found a xed difference at site 178 of the Tetraspannin domain in TPSAN8 between extremely small carnivores and others, this gene was reported that genetic ablation of in mice caused a reduction (-15.6%) in the body weight of male fed a normal chow diet [63]. Furthermore, the changes of S513L in CDC7 and S784P in LIG4 exhibit transitions of polarity might cause radical changes in the three-dimensional structure and function of proteins [64]. These six unique changes examined in the extremely small carnivores might have restricted body size growth. Of course, function experiments are need to further test if these changes cause growth retardation.

Conclusions
Mammalian order Carnivora exhibited the huge variation of body size, with more than 130,000 times in body mass and 50 times in body length, but their molecular mechanism remains poorly explored. Here we scanned the 20 genomes of representative carnivores and found a total of 337 genes to be associated with the body size. Our analyses showed 14 obesity-related genes and three rapidly evolving genes might drive the body size expansion. Importantly, our results provided molecular evidence for the Peto's paradox that lack of correlation between body size and cancer risk, based on 100 BSAGs associated with cancer control and 15 cancer-related genes under rapid evolution in carnivores. By contrast, 15 rapidly evolving genes and unique amino acid change of six genes might have restricted the growth of small carnivores. This study brought some new insights into the molecular mechanisms that drove the diversifying evolution of body size in carnivores, and provided new target genes for exploring the mysteries of body size evolution in mammals.

Phenotypic data and orthologous genesacquisition
High-quality genomes of 20 carnivores and an outgroup cow (Bos taurus) were downloaded from NCBI database. Eight families in Carnivora (i.e. Felidae, Canidae, Mustelidae, Phocidae, Otariidae, Odobenidae, Herpestidae, Ursidae) were chosen to include diverse body sizes. Two kinds of phenotype data, head body length (cm) and body mass (g), were collected from the PanTHERIA database [65] that were used for subsequent correlation analysis. For the missing head body length data of the domestic cat (Felis catus) in the database, we obtained the alternative data from the Animal Diversity Web resource (http://animaldiversity.org/) [66]. Head body length means the length from the snout of the nose to the root of the tail for an animal [67]. All the phenotype data came from adult individuals. High-con dence "one-to-one" orthologous gene clusters were identi ed using the Ortho nder [68] pipeline, which applied all-against-all BLSATP algorithm. For genes with various transcripts, the longest coding sequence was used in our study. And if transcripts shorter than 150bp, or its lengths were not multiples of three were eliminated by our in-house Perl scripts. The sequences were aligned using Prank [69] at the codon level, with poorly aligned regions with gaps and non-homologous fragments removed using Gblocks [70] with relatively strict parameters ("-t=c, -b5=h"). High-quality multiple sequence alignment (MSA) les were used for subsequent analysis.
PGLS scanning the body-size-associated genes (BSAGs) PGLS implemented in the "Caper" package in R [71] was used to test the potential association between evolutionary rates of each gene and each phenotypic data (i.e. head body length and body mass). The ultrametric tree of 20 carnivores for PGLS analysis was obtained from the TimeTree website [72]. The Brownian motion model was applied and the phylogenetic signal (λ parameter) was tested by maximum likelihood (ML) method. The lambda (λ) value was used as a quantitative measure of phylogenetic signals [73]. When λ was estimated to be 1 or near to 1, it indicated that these genes showed a strong phylogenetic signal. To obtain more stringent correlation P values, we further employed an extra two-step calibration procedure as suggested by Ma et al. [74]. On the basis of 'P value.all' from the regression analysis for all carnivores, the following two P values were calculated: 1) 'Pvalue.robust' from regression repeated after discarding the species with largest residual error; 2) 'Pvalue.max' from the PGLS on the remaining species, to calculate the maximal P value after dropping each species on at a time. Genes that were signi cantly related to both head body length and body mass under the most stringent standard (P value.all < 0.05, P value.robust < 0.05, P value.max < 0.05) are de ned as body-size-associated genes (BSAGs).
The evolutionary rate ω means the ratio of non-synonymous (d N ) and synonymous substitutions (d S ), which was estimated by free-ratios model (model = 1) implemented in the CODEML program of PAML 4.9e [75]. The root-to-tip ω of each species was calculated by averaging the ω from the ancestral carnivore to each terminal branch according to the method suggested by Montgomery et al. [76]. And if the value of d N or d S in each single ω is less than 0.0002, we marked it as an outlier "n/a" to prevent its adverse effect on the integral root-to-tip ω. And all root-to-tip ω were log 10 -transformed to improve normality for regression analysis [76].

Functional enrichment analysis
Functional annotation clustering tool Metascape (http://metascape.org/) [77] was used to perform Gene Ontology (GO) and KEGG pathway enrichment for the BSAGs list. GO categories were discovered and grouped into annotation clusters, against a background of human genome. All GO terms with enrichment score (ES) > 1.3 (corresponding to a p-value less than 0.05) were considered for signi cant enrichment for list of BSAGs examined.

Rapidly evolving genes (REGs) test
To detect whether divergent selective pressure acting on carnivores with contrasting body size among the signi cant BSAGs determined above. We divided the 20 species into three groups, small body-sized carnivores (body mass < 12kg and body length < 1m), including ve species: meerkat, Suricata suricatta, ferret Mustela putorius furo, domestic cat Felis catus, Canada lynx Lynx canadensis and red fox Vulpes vulpes, and extremely large body-sized carnivores (body mass > 350kg), such as polar bear Ursus maritimus, walrus Odobenus rosmarus, northern sea lion Eumetopias jubatus and weddell seal Leptonychotes weddellii), and the remaining 11 species as the third group. Two-ratio model (model = 2) that allows different ω values within the foreground and background branches was used to evaluate the selective pressures in the small and extremely large groups, respectively. The two groups were separately regarded as foreground branches and the remaining 11 species as the background branches. The null model, i.e. one-ratio model (model = 0) assumed all branches have the same ω. The likelihood ratio test (LRT) was used to compare nested likelihood models. If the ω of the foreground is higher than that of the background branches with p <0.05, we de ned these genes as REGs.
Identi cation of xed amino acid changes in extremely small/large body size groups To explore the effects of changes in single amino acid sites contribute to body size development, we scanned all the orthologous genes set for the xed amino acid changes in extremely large group (i.e. polar bear, walrus, northern sea lion and weddell seal) and extreme small species (body mass < 1kg, i.e. Meerkat and Ferret, Bekoff et al. 1984). FasParser [81] was used to pick out the xed amino acid changes in these two groups compared with other carnivores. For extremely small groups, the stoat Mustela erminea (mMusErm1.Pri) was added to improve the reliability of identi ed amino acid sites. Amino acid sites that were the same in the three extremely small species and were consistently different in other carnivores were selected. Gaps-containing sites were also excluded, and positions were corrected using human (Homo sapiens) amino acid sequences. Pfam 1.6 [82] was used to determine whether the changes were located in the functional domains of the protein.

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Availability of data and materials
The data generated and analyzed during this study are included in this article and its additional les, including 7 tables and 5 gures.

Competing interests
The authors declare that they have no competing interests. Authors' contributions SX and GY conceived and designed this project. XH and TW performed the data analysis and wrote this paper. SX improved the manuscript. DS and XL put forward valuable opinions and suggestions, assisted with manuscript editing and polished the paper. All authors agree to publish this paper.