This study aims to understand the cause of the recent observation that humans with a 25 higher diversity of virulence genes in their metagenomes tend to be precisely those with 26 higher diversity of antibiotic-resistance genes. We simulated the transferring of 27 virulence and antibiotic-resistance genes in a community of interacting people where 28 some take antibiotics. The diversities of the two genes types became positively 29 correlated whenever the contagion probability between two people was higher than the 30 probability of losing resistant genes. However, no such positive correlations arise if no 31 one takes antibiotics. This finding holds even under changes of several simulations' 32 parameters, such as the relative or total diversity of virulence and resistance genes, the 33 contagion probability between individuals, the loss rate of resistance genes, or the social 34 network type. Because the loss rate of resistance genes may be shallow, we conclude 35 that the contagion between people and antibiotic usage is the leading cause of 36 establishing the positive correlation mentioned above. Therefore, antibiotic use and 37 something as prosaic as the contagion between people may facilitate the emergence of 38 virulent and multi-resistant bacteria in people's metagenomes with a high diversity of 39
Since the 1940s, antibiotics have been used in health contexts in medicine and 46 veterinary and as growth promoters in livestock and agriculture (Castanon, 2007) . As an 47 incredible example of Darwinian selection, bacteria worldwide have gradually become 48 resistant to several antibiotics. Such spread of resistance has had terrible consequences. 49
For example, there were about 875 500 disability-adjusted life-years and more than 33 50 000 deaths in European Economic Area due to antibiotic resistance in 2015 (Cassini et 51 al., 2019) . 52
Bacterial communities are often very complex, eventually comprising both pathogenic 53 and non-pathogenic bacteria. The human microbiome, defined as the set of 54 microorganisms that colonize humans (body's surfaces and biofluids, including tissues 55 such as skin, mucosa, and, most importantly, the gastrointestinal tract) comprises about 56 3.8 × 10 13 bacterial cells (Sender et al., 2016) , spanning thousands of taxa. 57
Virulence factors are proteins that help bacteria in colonizing a host or biome. These 58 traits are easily spread in bacterial populations or microbiomes by horizontal gene 59 transfer, which can potentially convert mutualistic or commensal bacteria into 60 pathogens able to progress into new tissues, triggering an infectious disease. We 61 recently found a positive correlation between antibiotic resistance genes' diversity and 62 virulence genes' diversity across human gut microbiomes (Escudeiro et al., 2019) . 63
Could this positive correlation result from administering antibiotics in sick people due 64 to bacterial infections, eventually selecting bacteria encoding virulence and resistance 65 determinants simultaneously? This hypothesis is unlikely to be adequate because, even 66 when the objective of taking antibiotics is to kill or inhibit the growth of pathogenic 67 bacteria, many non-pathogenic (mutualistic or commensal) strains and species are 68 undoubtedly affected. Therefore, an explanation for the positive correlation mentioned 69 above is still missing. 70
Both virulence and resistance genes present in commensal bacteria and pathogenic 71 bacteria spread between people's metagenomes. This dissemination may contribute to 72 the accumulation of virulence and resistance genes in some people when themselves or 73 their contacts take antibiotics. Meanwhile, pathogenic bacteria's presence triggers the 74 administration of antibiotics. Therefore, contagion (the dissemination of bacteria and 75 their genes) between people should play a role in keeping the correlation between 76 resistance and virulence genes' diversity. Microbes' transmission from mother to child 77 is already well documented (Blaser and Falkow, 2009 We simulated a network where each node represents a person or, more precisely, a 101 person's metagenome. To simplify language, sometimes we use the words person or 102 people, meaning a person's metagenome or people's metagenomes, respectively. The 103 edges represent possible transmission avenues of microorganisms. 104
We built the social contact network following the Watts and Strogatz method (Watts 105 and Strogatz, 1998). In a regular network, each node links to the n nearest nodes. In 106 non-regular networks, each node's link has a certain probability p of being reconnected 107 to another randomly chosen node. The parameter p represents the probability of each 108 connection to be modified. We defined the network type by the value assigned to the 109 parameter p (for example, a regular network when p = 0, whereas p = 1 results in a 110 random network). Unless noted, we performed simulations with p = 0.5. 111 112
The model considers the transmission of bacterial pathogens (capable of causing  114 infections), as well as virulence and antibiotic resistance genes, between people. These 115 non-housekeeping genes are present in the metagenome. We focused on the presence or 116 absence of genes encoding different functions, irrespectively of its copy-number in the 117 metagenome. In the simulations, each gene represents a gene family (with similar 118 functions). We divided resistance genes into groups, each group having the same 119 number of families. Each group represents genes associated with resistance to an 120 antibiotic. Of note, we did not consider resistance to multiple drugs in our simulations. 121
Therefore, there will be as many groups as there are antibiotics accounted for in the 122 simulations. We define the diversity of a specific gene kind as the number of genes of 123 that type present in a human metagenome. 124
To simulate the migration of bacteria from individuals outside the network or the 125 contagion from sources such as food or contaminated water, we inserted five different 126 bacterial pathogenic species into random individuals per cycle. To simplify language, 127 we assume that pathogenic bacteria belong to different species, but, in reality, some of 128 them may constitute different strains of the same species. In this model, the only 129 difference between species is the antibiotic to which they are susceptible, as explained 130 below. 131
Individuals infected by pathogenic bacteria feel sick and take an antibiotic. The 132 antibiotic administered is specific for the bacteria that caused the illness. The antibiotic 133 selects cells carrying resistance genes by eliminating the remaining susceptible bacteria. 134
In this work, we assume that all families of resistance genes are present in all 135 metagenomes, but in two different possible states: in some metagenomes, they are 136 present in low copy number, so they are not transmissible to other individuals in the 137 network; in other metagenomes, the copy number of resistance genes is high due to the 138 selective pressure of antibiotics to which they were previously submitted. In the latter 139 case, resistance genes are transmissible from person to person. 140
Moreover, upon antibiotic consumption, the following events can occur: (i) elimination 141 of a pathogenic bacterial species; (ii) selection in the metagenome of resistance genes 142 belonging to the same group of resistance to an antibiotic, which means their copy 143 number gets so high that they become transferable; (iii) loss of resistance genes 144 associated with other antibiotics with a given probability (becoming non-transferable 145 but still present in minute copy number); (iv) virulence genes disappear from the 146 metagenome with a given probability. 147
Several processes lead to gene loss. Genes are lost because of the selective pressure by 148 antibiotics and because we assume that resistance determinants impose a fitness cost (in 149 the absence of antibiotics). To include this cost in the simulations, we consider that each 150 metagenome may lose specific resistance genes according to a "loss rate" (with this 151 process, these genes become non-transferable). 152 153
Each simulation is composed of several cycles. In each cycle, we considered all 155 procedures described in the pseudocode (Table 1 ; see also the flowchart in Fig. 1) . We 156 performed exploratory simulations to parameterize our model. We fixed a set of 157 parameters as default ( Table 2 ). The main steps of the program in each cycle are: 158 i) Transfer of pathogenic bacteria, virulence and resistance genes between people (i.e., 159 between linked nodes), according to specific contagion probabilities of pathogens and 160 virulence and resistance genes of the metagenome. With this process, the diversity of 161 genes present in the recipient metagenome increases. 162
ii) To look for people infected by at least one pathogenic bacterial species. These people 163 take antibiotics (chosen according to the pathogen). The antibiotic eliminates the 164 pathogenic species and selects the resistance genes associated with the antibiotic used. 165
According to a certain probability, the antibiotic also eliminates virulence genes and 166 resistance genes unrelated to the administered antibiotic. Finally, the metagenome loses 167 a few more resistance genes not associated with the antibiotic, according to the loss rate 168 probability. The cause of this loss is the fitness cost of resistance genes. 169
iii) The metagenomes of people that did not take an antibiotic in this cycle lose 170 resistance genes according to the loss rate probability. This loss is a consequence of the 171 fitness cost imposed by resistance genes on their hosts, which is not happening with 172 virulence genes. Given the complexity of human interactions, it is paramount to simplify the computer 183 simulations. A simplified model allows us to comprehend the effect of specific factors 184 in our simulations, which would otherwise be extremely difficult to detect. As these 185 simplifications do not allow us to make quantitative inferences, we make qualitative 186 analyses. The focus is always on the correlation or linear regression slope signal 187 between the diversity of virulence and antibiotic resistance genes and whether the 188 correlation is significantly different from zero. Accordingly, the null hypothesis is that 189 there is no correlation between antibiotic resistance genes' diversity and virulence 190 genes' diversity. The alternative hypothesis is that there is a correlation between 191 antibiotic resistance genes' diversity and virulence genes. We define ߙ = 1x10 -6 , 192 rejecting the null hypothesis if P-value < ߙ . 193
We performed the data analyses described above, and the Student's t-tests (see In principle, the bacterial pathogen contagion probability parameter could have any 210 value in the simulations. Given the importance of this parameter, we must calibrate its 211 value according to the model's other conditions. We assumed that individuals are not 212 affected by more than two infectious diseases at the same time. Therefore, we started 213 this study searching for the parameters that led individuals to have a maximum of two 214 pathogenic bacterial species or strain simultaneously at a given cycle. 215
We performed simulations with different bacterial pathogen contagion probabilities, and 216 counted the number of pathogenic bacterial species that each individual has per cycle. 217
As we can see in Table 3 , when the bacteria pathogen contagion probability is 0.2, some 218 individuals in a specific cycle (out of two million possibilities) became infected by three 219 pathogenic bacteria. For this reason, we settled the bacterial pathogen contagion 220 probability to be less than 0.2 in our simulations. 221
In each cycle of the simulation, we introduced five pathogenic bacterial species into the 222 population. Then, we counted the total number of pathogenic species present in the 223 population. If this number is equal to five, then the only pathogenic species in the 224 population are those that were inserted (simulating immigration into the network), 225 which means that, before the insertion, all pathogenic bacterial species had disappeared 226 in that cycle. As it is unrealistic that all bacterial species disappear simultaneously, we 227 looked for a contagion value below 0.2 that minimizes the number of times that all 228 bacteria disappear at the same time. As shown in Table 4 , the number of times that 229 pathogenic species disappear increases with a bacterial pathogen contagion probability 230 of 0.1 or less. Therefore, we defined that this probability is 0.15 in the simulations. 231 232
As previously explained, individuals take antibiotics whenever pathogenic bacteria 234 infect them. However, antibiotics remove other bacteria present in the microbiome 235 carrying antibiotic-resistance and virulence genes, beyond pathogenic bacteria. 236 Therefore, it is essential to calibrate the probability of passing these genes by avoiding 237 their population's loss. These genes disappeared from the community when the number 238 of eliminated genes was higher than the number of genes passed between individuals. 239
To better understand the impact of the gene contagion probability parameter, we then 240 studied the simpler case: only antibiotics can eliminate genes, and there is no fitness 241 cost for harboring resistance genes (hence, loss rate = 0). 242
As we can see in We studied the correlation between virulence genes' diversity and the diversity of 253 resistance genes effect for different combinations of gene contagion probability and 254 resistance gene loss rate. For that, we fixed all the other parameters (see Table 2 ). Fig. 3  255 shows that if the gene contagion probability is higher, the same or only slightly lower 256 than the loss rate, the correlation between the diversity of virulence genes and the 257 diversity of resistance genes is positive (Supp. Table 1 In the previous sections, we showed that if the gene contagion probability is higher than 278 the loss rate, the outcome is a positive correlation between virulence and resistance 279 genes' diversity. Here we show that taking antibiotics is crucial for this outcome (Supp. 280 Fig. 3.1) . 281
If no one takes antibiotics, there is no counter-selective pressure on commensal bacteria 282 encoding virulence genes. The result is that virulence genes' diversity gets the 283 maximum possible value in everyone's metagenome in the community (in Supp. We have seen that the positive correlation between virulence and resistance genes' 297 diversity is positive if the gene contagion probability is higher than the loss rate (Fig.  298 3C). We then analyzed the robustness of this result. The next five subsections show the 299 impact of changing the simulations' parameters or changing the network itself. We 300 studied the following parameters: population size, the ratio between virulence genes and 301 antibiotic resistance genes, the elimination probability under antibiotic intake, the 302 proportion of the population harboring antibiotic-resistance genes in their metagenome, 303 and the network type. 304
Due to computer power constraints, we had to assume that the population has just a 307 thousand people. Therefore, it is essential to understand whether population size 308 impacts the correlations' signals. We performed simulations with a population size of 309 3000 individuals, instead of 1000 individuals, for the 14 conditions shown in Fig. 3C . 310
Although there were significant differences between the slopes in three cases, we didn't 311 observe a change of the correlation's signal from the cases where the population size 312 was 1000 individuals (Supp. Table 4 .1 and Supp. Fig. 4.1 ). An increase in the 313 population size leads to a rise in the number of intermediaries between two distant 314 individuals. Therefore, for virulence genes and antibiotic resistance genes to be 315 transferred between these two faraway individuals, more contacts are needed and, 316 consequently, more time is required to achieve a stable correlation. 317 318
In all the other sections, we considered that virulence and resistance genes have the 321 same total diversity. Here, we studied the effect of assuming that the diversity of 322 virulence genes is different from that of resistance genes for the same 14 conditions of 323 gene contagion probability and loss rate studied in the previous section. For that, we 324 performed simulations similar to the previous ones, but with the following ratios 325 between virulence and antibiotic resistance genes: 1:2, 1:4, 2:1, 4:1. Although there 326 were significant differences between the slopes in 48 out of 56 cases, we didn't observe In the previous sections, we considered that every individual carries all the antibiotic 351 resistance genes in two alternative states at the beginning of the simulation. Either 352 resistance genes were present at low copy numbers (hence being unable to be 353 transmitted to other people) or at high copy numbers because they previously selected 354 by antibiotic exposure (thus transmitting to other people). In this section, we study the 355 effect of considering that, initially, only 10% of the metagenomes contain antibiotic-356 resistance genes. With this parameter changed, the simulations take more time to 357 stabilize because 90% of the population receives resistance genes only through 358 contagion. We performed simulations similar to the ones shown in Figure 3 , but with 359 5000 cycles. The final slopes are not significantly different from the case where all 360 metagenomes initially contain antibiotic-resistance genes (Supp. The simulations leading to Fig. 3 were performed in a network with a rewiring 365 probability of p = 0.5 (see Methods). We then performed similar simulations but in a 366 regular (p = 0) and in a random (p = 1) networks. This parameter did not change the 367 correlation signals (see Suppl. Tables 9.1 and 9.2). However, the time needed (number 368 of cycles) to reach a stable distribution was lower for higher values of p (Supp. Fig. 9 . 5.1 -5.4, 6.1, 6.2, 7.1 -7.6, 8.1, 9.1 and 9.2) show that if the contagion rate is 398 higher than the loss rate, a positive correlation emerges between the diversity of 399 antibiotic resistance genes and virulence genes. 400
At first, one might expect to see a negative correlation whenever the contagion 401 probability is lower than the loss rate, but that is not always the case. Indeed, when the 402 contagion probability is only slightly lower than the loss rate, the correlation is positive. 403
For example, if the contagion probability is 0.005 and the loss rate is 0.01, the 404 correlation is still positive (Fig. 3A and 3C , Supp. Table 1 ). The reason for these 405 counter-intuitive cases is that, in each cycle, one individual contacts with four other 406 individuals, and during each of these contacts they share bacteria from its microbiomes. 407
In turn, each individual can only be medicated with antibiotics once (at the end of a 408 cycle). That implies that the rate of loss of resistance genes applies only once in a cycle. 409 Therefore, the impact of the contagion rate is higher than the loss rate of resistance 410 genes. Together, these six factors suggest that the fitness cost of resistance determinants is 474 often very low or null, allowing the permanence of resistance determinants in 475 microbiomes for long periods. This stability of resistance determinants implies that their 476 loss rate, the probability that a metagenome loses a particular resistance gene or 477 mutation, is undoubtedly lower than the contagion probability. Therefore, antibiotic 478 consumption and contagion between people lead to a positive correlation between the 479 diversity of resistance genes and virulence genes. 480 481
The simple fact that people contaminate between themselves, and antibiotic use, is chief 483 to explain the positive correlation between antibiotic resistance gene diversity and 484 virulence gene diversity across human metagenomes. This result is robust and general 485 because we made very few assumptions. This result also has worrying health 486 implications: people with a higher diversity of resistance genes in their metagenomes 487 have a higher diversity of virulence genes. Such co-presence may potentiate the 488 appearance of plasmids or bacteria encoding virulence and resistance genes 489 simultaneously. Meanwhile, the current restrictive measures due to the COVID-19 490 pandemic may weaken this correlation between the diversity of resistance genes and 491 antibiotics and virulence factors due to a decrease in the contagion rate (Domingues et  492 al., 2020). 493
The authors declare that the research was conducted in the absence of any commercial 495 or financial relationships that could be construed as a potential conflict of interest. 
Choose an antibiotic randomly. Select all resistance genes associated with the chosen antibiotic.
Eliminate resistance genes not associated with the chosen antibiotic according to the probability of eliminating genes under antibiotic intake. Eliminate virulence genes according to the probability of eliminating genes under antibiotic intake.
Loss rate of resistance genes under antibiotic consumption Eliminate resistance genes not associated with the chosen antibiotic according to the loss rate probability.
Loss rate of resistance genes without antibiotic consumption Eliminate resistance genes according to the loss rate probability. 