Abstract
Future pandemic risk management requires better understanding of the mechanisms that determine the virulence of emerging zoonotic viruses. Bats host viruses that cause higher case fatality rates upon spillover to humans than those derived from any other mammal, suggesting that reservoir host immunological and life history traits may be important drivers of cross-species virulence. Using a nested population-level and within-host modelling approach, we generate virulence predictions for viral zoonoses derived from diverse mammalian reservoirs, successfully recapturing corresponding virus-induced human mortality rates from the literature. Our work offers a mechanistic explanation for the virulence of bat-borne zoonoses and, more generally, demonstrates how key differences in reservoir host longevity, tolerance, and population density impact the evolution of viral traits that generate severe disease following spillover to humans. We provide a theoretical framework that offers a series of testable questions and hypotheses designed to stimulate future work comparing cross-species virulence evolution in zoonotic viruses derived from diverse mammalian hosts.
Main Text
The devastating impacts of the SARS-CoV-2 pandemic highlight the extreme public health outcomes that can result upon cross-species emergence of zoonotic viruses. Predicting the virulence of an emerging virus is a complex problem since chance will always play a role in dictating the initial spillover that precedes selection1, virulence upon emergence may be maladaptive in novel hosts2,3, and patterns in available data may be muddled by attainment bias if avirulent infections go underreported1. Nonetheless, reservoir host immunological and life history traits may be important drivers of cross-species virus virulence; bats, in particular, host viruses that cause higher human case fatality rates than zoonoses derived from other mammals and birds4,5. Understanding the mechanisms that select for the evolution of unique viral traits in bats compared to those selected in other mammalian reservoirs is essential to accurately predicting virulence for future zoonotic threats.
Although the disproportionate frequency with which the Chiropteran order may source viral zoonoses remains debated6,7, the extraordinary human pathology induced by many bat-borne zoonoses—including Ebola and Marburg filoviruses, Hendra and Nipah henipaviruses, and SARS, MERS, and SARS-CoV-2 coronaviruses8—is not contested. Remarkably, bats demonstrate limited clinical pathology from infection with viruses that cause extreme morbidity and mortality in other hosts8. This may be due, in part, to unique bat resistance mechanisms, which include constitutive expression of antiviral cytokines in some species9 and enhanced autophagy10 and heat-shock protein expression in others11. While these protracted inflammatory responses would be pathological in most mammals, bats have evolved unique mechanisms of mitigating inflammation, including loss of PYHIN12,13 and downregulation of NLRP314 inflammasome-forming gene families, dampened STING-dependent interferon activation15, and diminished caspase-1 inflammatory signaling16. As an apparent by-product of these adaptations that enable flight, bats maintain long lifespans17 and tolerate inflammation incurred by the recruitment of immune cells to viral infections8. The extent to which these unique features of bat immunology and physiology modulate the evolution of the viruses they host, however, remains largely unexplored.
General theory suggests that because viral ‘tolerance’ mitigates virulence (defined here as the virus-induced mortality rate) without reducing viral load, a host strategy of tolerance will select for higher growth rate pathogens that achieve gains in between-host transmission without causing damage to the original host18,19 (Fig. 1). Bat viral tolerance thus predicts the evolution of enhanced viral growth rates, which—though avirulent to bats—may cause significant pathology upon spillover to hosts lacking bat immunology and physiology. Indeed, recent work demonstrates how high virus growth rates easily tolerated in bat cells cause significant pathology in cells derived from hosts lacking bat antiviral defenses20. While tolerance reduces pathogen-induced mortality for a single host, tolerant host populations, with limited checks on virus transmission, may demonstrate high pathogen prevalence. If imperfectly tolerant hosts still experience some virus-induced pathology, high prevalence can consequently elevate total population-level mortality for infected hosts—a phenomenon known as the ‘tragedy of tolerance’18. Reports of virus-induced mortality in bats are rare21, suggesting that bat virus tolerance is likely very effective. We explore the extent to which the immunological and life-history traits of mammalian reservoirs can explain variation in the virulence of zoonotic viruses emerging into human hosts.
To elucidate how immunological and life-history traits of mammalian hosts combine to drive zoonotic virus virulence, we adopted a nested modeling approach, embedding a within-host model of viral and immune system dynamics within an epidemiological, population-level framework (Fig. 1). We examined how the life history traits of a primary reservoir drive the evolution of viral traits likely to cause pathology in a secondary, spillover host—chiefly, a human. Using our nested modeling framework, we first computed the optimal within-host virus growth rate (r*), the corresponding virulence at that growth rate (α*), the population-level infection prevalence, and the total population-level infected host mortality for a virus evolved under differing reservoir host-specific cellular and immunological parameter values (Fig. 2, Extended Data Fig. 1–2, Extended Data Table 1). Our analyses highlight several critical drivers of virus evolution likely to generate significant pathology following spillover to a secondary host (Fig. 2): higher within-host virus growth rates (r*) are selected in reservoir hosts with higher background mortality (μ), more rapid virus clearance (c), and more rapid lymphocyte activation (g) upon infection. Higher r* is also selected in host populations that exhibit higher ρ, corresponding to slower saturation of transmission per virion. Critically, higher tolerance of both virus-induced pathology (Tv) and immunopathology (Tw) also select for higher r*, but the effects of Tw are proportionally greater—suggesting that bat tolerance of immunopathology facilitates the evolution of virulent zoonoses. Of note, changes in the majority of within-host parameters drive corresponding increases in r* and α*, such that reservoir hosts evolving viruses with high growth rates also experience high pathogen-induced mortality. The rate of virus clearance by lymphocytes (c) and the two modeled mechanisms of tolerance (Tv and Tw), diverge in this regard, permitting evolution of high r* viruses that incur minimal virulence (α*) on reservoir hosts. By extension, we predict that viruses evolving optimal r* in reservoir hosts with high c, Tv, or Tw might incur substantial pathology upon spillover to secondary hosts exhibiting lower values for these same parameters. Unique among mammals, at least two species of bat constitutively express the antiviral cytokine, IFN-α9, which would manifest as elevated c in our model, and several sources indicate heightened tolerance of immunopathology in bats, modeled here as high Tw12,15,16,22.
We next made broad predictions of the evolution of zoonotic virus virulence across eight mammalian reservoir orders, based on order-specific variation in four key parameters from our within-host nested model: the reservoir host background mortality rate (μ), the rate at which between-reservoir host transmission saturates with increasing viral load (ρ), the reservoir host tolerance of immunopathology (Tw), and the spillover (human) host tolerance of pathology induced by a virus derived from a non-human reservoir (TvS). Within-host immunological data needed to quantify these parameters is lacking across most mammalian orders; thus, we used order-specific life history traits to proxy these metrics for the eight mammalian orders of interest, while holding all other parameters constant across reservoir taxa (Fig. 3, Extended Data Fig. 3, Extended Data Tables 1–3). Host background mortality rates (μ) were quantified directly and summarized by mammalian order, but the lack of available cross-species immunological data in the literature necessitated significant assumptions for the other three parameters. We modeled ρ as a function of reservoir host population size: since wildlife viruses transmit via predominantly density-dependent mechanisms, large wildlife host populations offer more opportunities for onward transmission at a given viral load, meaning that population-level transmission rates will saturate more slowly with increasing virus density. We represented Tw as proportional to the residual of observed host lifespan (again, summarized across orders) from that predicted by basal metabolic rate (BMR): since longevity is linked to resilience to inflammation23, we hypothesized that extraordinarily long-lived hosts would demonstrate tolerance of immunopathological inflammation, as well. Finally, we represented TvS as proportional to the phylogenetic distance between a given reservoir host order and Primates, assuming that human immune systems would be better adapted to tolerate viruses evolved in phylogenetically-related hosts, as has been suggested in the literature5,6. Though assumptions, these parameter representations enabled us to compare the impact of broad reservoir host life-history trait variation on zoonotic virulence: among mammals considered, orders Eulipotyphla and Rodentia exhibited the fasted background mortality rates (μ); orders Primate, Chiroptera, and Carnivora demonstrated the longest lifespans per BMR, corresponding to higher tolerance of immunopathology in our model (Tw); orders Chiroptera and Cetartiodactyla had the largest group sizes, equating to slowest transmission rate saturation (high ρ); and order Diprotodontia was most distantly related to humans, resulting in low human tolerance of viral pathology (TvS). High estimates for Tw, μ, and ρ and low estimates for TvS all predict high spillover virulence to humans (αS), and virulence rankings between orders are sensitive to the scaling of these within-host parameters. Nonetheless, bats demonstrate uniquely long lifespans per BMR and large group sizes; when combined, as in our analysis, to represent high Tw and high ρ, these reservoir host traits elevate predicted r* and ρS beyond other orders. Thus, our approach successfully recovers the key result from the zoonosis literature: bat-derived zoonoses yield higher rates of virus-induced mortality upon spillover to humans (αS) than do viruses derived from any other mammals (Fig. 3d, Extended Data Fig. 4)24.
Compared with the data4, our model underpredicts cross-order comparative virulence rankings for Carnivora-derived viruses and overpredicts rankings for viruses derived from Rodentia and Cetartiodactyla. For order Carnivora, the discrepancy in our predictions vs. those from the literature is resolved when rabies lyssavirus is excluded from data comparisons (Extended Data Fig. 5)4: though most rabies zoonoses are sourced from domestic dogs, lyssaviruses are Chiropteran by origin25, and viral traits responsible for rabies’ virulence may reflect its bat evolutionary history more than that of any intermediate carnivore host. For order Rodentia, comparatively lower spillover virulence reported in the literature suggests that attainment bias may be less extreme for this clade: rodent-borne hantaviruses and arenaviruses represent some of the best-studied zoonoses, and multiple avirulent species within these families are referenced in our dataset4. Records of avirulent zoonoses are rare for other taxa, excepting Primates, which are also well-studied, and Cetartiodactyla, for which existing data on zoonotic viruses are derived entirely from domesticated livestock4. Our model’s overprediction of virus virulence from Cetartiodactyla squares with hypotheses that the low virulence of zoonoses recorded for this clade may reflect higher research effort and sampling rates for livestock pathogens (thus minimizing attainment bias)—or that centuries of human-livestock cohabitation and development of human immunity to livestock pathogens could have muted the virulence of Cetartiodactyla viruses in human hosts4.
Our model provides a mechanistic explanation for the biological processes that underpin cross-species patterns in the evolution of virus virulence—a major advance for efforts to evaluate zoonotic risk. Of note, we are able to recapture broad patterns in the literature while holding constant many basic immunological parameters, including rates of virus consumption by lymphocytes (c) and lymphocyte activation (g), which almost certainly vary across taxa. By summarizing within-host traits across eight mammalian orders, we also generalize substantial within-clade diversity that likely contributes to heterogeneous patterns in available data. Bats alone make up more than 1,400 species and account for some 20% of mammalian diversity26; only a subset of bats are long-lived27 or gregarious28, suggesting considerable variation in immunopathological tolerance or transmission saturation rates—and consequently, the evolution of virus virulence—which we largely disregard here. As more data becomes available, modeling could be fine-tuned to make more specific, species-level predictions of highly virulent disease risk.
Currently, our work emphasizes the uniqueness of bats as flying mammals and, in consequence, as tolerant viral reservoirs. For the first time, we offer a mechanism for the evolution of bat-derived viruses, which demonstrate significant pathology upon spillover to non-bat, particularly human, hosts. In providing a theoretical framework to explain this phenomenon, we generate a series of testable questions and hypotheses for future comparative immunological studies, to be carried out at in vitro and in vivo scales. Empirical work should aim to determine whether virus growth rates are truly higher when evolved in bat immune systems, whether anti-inflammatory mechanisms in bat cells are equally effective at mitigating virus-induced pathology and immunopathology, and whether comparative taxonomic predictions of virus tolerance, resistance, and virulence evolution apply to non-viral pathogens, too. In light of the emergence of SARS-CoV-2, the field of bat molecular biology has echoed the call for mechanistic understanding of bat immunology29, and the NIH has responded30, soliciting research on the development of tools needed to test the predictions outlined here. We offer a bottom-up mechanistic framework enabling the prediction of emerging virus virulence from the basic immunological and life-history traits of zoonotic hosts.
Methods
1. Population-level dynamics and R0 under SIS assumptions
To begin, we follow Miller et al. (2006)18, assuming a simple population dynamics system which allows for both infection-induced mortality and recovery from infection. Since we are interested in examining virus evolution in reservoir hosts, we assume that hosts maintain long infectious periods, before eventually recovering to return to the susceptible class.
We assume that hosts are born at rate b and die of natural death at rate μ, where b > μ. All hosts are assumed to be born susceptible and population density is regulated via a crowding term (q). Because our goal in this endeavor is to allow for the evolution of rates that link to within-host dynamics (Section 4), we represent transmission, virulence, and recovery as functions of the virus causing the infection (respectively, βr, αr and σr), where r denotes the intrinsic virus growth rate. Our system is described by the following system of Ordinary Differential Equations, where N = S + I.
Solving the equilibria of this system establishes that there is both a disease-free equilibrium (DFE) at , as well as an endemic infection equilibrium, (see below, [2a], [2b]).
We study the dynamics of [1] in the following feasibility region:
This region is positively invariant with respect to [1]. From [1], we can then formulate the Jacobian matrix, J, to decipher the local stability of the DFE:
Next, we evaluate the Jacobian at the DFE:
The DFE is locally unstable when at least one of the eigenvalues of the Jacobian is non-negative. The eigenvalues can be read off the diagonal (JDFE is upper triangular). Clearly, the first eigenvalue is negative: – b ‒ μ < 0. A little algebra will establish that the second eigenvalue is negative when:
Therefore, if R0 > 1, the DFE is no longer locally asymptotically stable, resulting in an increase in infected hosts within the population. When R0 > 1, the EE is globally asymptotically stable in the interior of Ω. We demonstrate this by first establishing the local asymptotic stability of the EE, then by determining that there are no limit cycles in the region, Ω.
If we evaluate the Jacobian, once again, at the EE, we will find that the trace (Trace(JEE)) of that matrix is negative:
Note that b > μ + αr (a necessary condition for the existence of the EE). In addition, the determinant of the JEE is positive:
Note that q « 1.
Therefore, the eigenvalues of the Jacobian matrix (JEE) have negative real parts, and therefore the EE (when it exists) is locally asymptotically stable.
We now use the Dulac criterion to establish that no limit cycles exist in Ω. Consider the Dulac function: φ(S, I) = 1/(βSI), and let the function F(S,I) represent the right hand side of [1a], and let the function G(S,I) represent the right hand side of [1b]. Then we have: since q « 1. Thus, system [1] has no limit cycles present in Ω. Therefore, the EE is globally asymptotically stable in Ω when R0 >1.
2. Invasion of a mutant parasite under SIS assumptions
Next, we aim to establish under what conditions a mutant pathogen can invade this system. We accomplish this task by first re-writing our system [1] to include hosts infected with a resident wild-type pathogen, I1, or a novel mutant pathogen, I2 where, now, N = S + I1 + I2:
Notice that the novel mutant pathogen has a different intrinsic viral growth rate than that of the resident (wild-type) pathogen (r1 ≠ r2). It then follows from [1] that there exists a mutant-free equilibrium (MFE) which recapitulates the endemic equilibrium in system [1]. To evaluate the local stability of the MFE we can again construct the Jacobian matrix of the new system, and evaluate the Jacobian at the MFE (Note: at the MFE while S* and replicate the endemic equilibrium values in [2a] and [2b]):
Notice that the upper left four quadrats of this matrix exactly replicate the 2×2 Jacobian ([3a]) evaluated at the EE, which we now refer to as the resident equilibrium. JMFE is a block-triangular matrix, which we can break down into component parts:
Stability of the MFE requires that all eigenvalues of the Jacobian, evaluated at the MFE, must be negative. Since the matrix is block diagonal, the eigenvalues of the Jacobian are given by the eigenvalues of the two matrices on the diagonal, Jres and Jmut. Since we have already established that the EE is globally asymptotically stable when R0 > 1, we know that the eigenvalues of Jres under this condition must be negative. The local stability of the MFE then depends on the sign of the eigenvalue of Jmut, where . Jmut thus corresponds to the growth rate of a rare mutant in an environment with an endemic resident strain. If the mutant pathogen is able to grow within the population, then:
We can rearrange terms to include mutant terms on one side of the equation and resident terms on the other:
It is evident that the MFE is unstable (allowing for invasion of the mutant strain) when the ratio of transmission over the duration of infection is larger for the mutant strain than the resident strain. In general, a pathogen will evolve to maximize this expression, which is known as the invasion fitness, and is given by:
3. Re-evaluating the invasion fitness under SIR assumptions
We next re-evaluate the population-level dynamics shown in Sections 1 and 2 above, under SIR assumptions to show that different representations of the population-level dynamics will not affect the selection gradient on our within-host parameters in Section 4. Assuming SIR dynamics, the system in the absence of a mutant takes the following form, where N = S + I + R:
We proceed as we did in Sections 1-2. Likewise the EE in model [14] is globally asymptotically stable when R0 > 1, and we can introduce a mutant pathogen as we did in [8] to evaluate the local stability of the MFE. Doing so, we find that the invasion fitness remains unchanged between SIS and SIR model assumptions:
Therefore, just as before, the evolutionary stable pathogen, or the strain that will avoid invasion by any other strain, is the strain that maximizes:
4. Within-host dynamics
Now that we have determined the invasion fitness for a mutant virus, we can write the population-level rates dependent on within-host dynamics in their within-host terms (transmission: βr1/r2, virulence: αr1/r2, and recovery: σr1/r2). This will allow us to derive a selection gradient on the viral growth rate, an intrinsic virus property likely to be carried from one host to another. To do this, we establish a simple within-host model that represents the dynamics of infection within each I1 and I2 host as outlined above. We assume the simplest Lotka-Volterra predator-prey relationship between the virus population (V) and the lymphocyte population (L) within each infected host:
Where r corresponds to the intrinsic virus growth rate, K gives the carrying capacity for virus within its reservoir host, c corresponds to the attack efficacy of the immune system upon contact with the virus, and g signifies the recruitment rate of immune cells with virus density. The parameter d gives the natural lymphocyte death rate.
This system has three equilibria: a virus/immune cell free trivial equilibrium at V* = 0 and L* = 0, a virus at carrying capacity/immune cell free trivial equilibrium at V* = K and L* = 0, and a non-trivial endemic virus equilibrium at and . Assuming K » c, g, d, r, then the non-trivial endemic virus equilibrium is a stable spiral (through a linear stability analysis).
Building from above, we can then rewrite the component terms of the population-level transmission, virulence, and recovery rates dependent on within-host dynamics (βr1/r2, αr1/r2, and σr1/r2) in terms of their within-host components, assuming that the within host dynamics are fast relative to the population-level dynamics.
In line with previous work, we assume transmission to be a bounded increasing function of the virus growth rate18,19,35,36, which we represent as: where ζ is the max transmission rate and ρ corresponds to the rate at which transmission approaches ζ as the virus growth rate (rV*) increases (smaller values of ρ correspond to faster rates of transmission saturation).
We can also assume that: by which infection-induced host mortality (‘virulence’) results from both virus-induced pathology, a function of the intrinsic virulence of the parasite, v, and the parasite growth rate rV*, and immunopathology, which we model as proportional to the growth rate of lymphocytes, gL*, upon infection, multiplied by the host’s susceptibility to immunopathology and inflammation, given as w. The terms Tv and Tw correspond to host tolerance of virus-induced pathology and immunopathology, respectively.
Expression [19] assumes a form of “constant” tolerance, by which both virus pathology and immunopathology are reduced by a constant proportion across the course of infection. After Miller et al. 200618, we can also model these relationships assuming “complete tolerance” [20], whereby virus pathology and immunopathology are completely eliminated up to a threshold value, beyond which pathology scales proportionally with virus and immune cell growth.
We consider both constant and complete forms of tolerance in all subsequent analyses. It is important to note that the predictions of the complete form of tolerance are not dependent on the assumption of complete elimination: a more gradual function shows equivalent results 18.
Lastly, we can represent the recovery rate from infection σr as proportional to the equilibrium immune cell population. This assumes the following expression: where γ scales the rapidity of recovery with the immune cell density.
We can then allow the virus to evolve its within-host growth rate (r) to maximize its reproductive success at the invasion fitness ([13] for the SIS model and [16] for the SIR model, above). In within-host terms, the invasion fitness takes on the following general form, under assumptions of constant tolerance:
And under assumptions of complete tolerance:
5. Selection gradient on within-host virus growth rate
We can then determine the selection gradient on r by differentiating [22] and [23] with respect to r. This gives us the following expression under assumptions of constant tolerance (differentiating [22]):
And assuming complete tolerance (differentiating [23]):
We then set these derivatives equal to 0 and solve for r, which we now refer to as r*. r* corresponds to the optimal within-host virus growth rate, here under assumptions of constant tolerance:
And here under assumptions of complete tolerance:
We can check that this optimum is a locally stable maximum (not a minimum) by proving that the second derivative of the invasion fitness ([22] and [23]) with respect to r is negative at the respective values for r* derived in [26] and [27]. When we do this, we find that this is, indeed, true, under assumptions of both constant and complete tolerance. This means that [26] and [27] represent true evolutionarily stable strategies (ESS).
Furthermore, we can compute a pairwise invasibility plot to visually demonstrate that the derived expression for r* represents an ESS (Extended Data Fig. 1).
In Extended Data Fig. 1, we see that all points along the vertical line through the point of intersection fall within the unshaded regions, corresponding to the conditions for a locally stable ESS37. Additionally, we see that higher degrees of tolerance shift r* higher under both constant and complete tolerance assumptions.
Finally, we can express [19] and [20] in within-host terms to calculate the virulence which a virus incurs on the reservoir host when evolved to its optimal within-host virus growth rate (r*). When we do this, we find that virus-induced virulence at r* (which we call α*) can be expressed as the following, under assumptions of complete tolerance:
And the following, under assumptions of constant tolerance:
There are several important insights to come out of these simple expressions for optimal viral growth r* and virulence α* in a reservoir host. We highlight the relationships between r* and α* and specific within-host parameters under assumptions of constant tolerance in Fig. 2 and under assumptions of complete tolerance in Extended Data Fig. 2.
6. Spillover virulence in the secondary host
Our primary interest in understanding the evolution of the optimal virus growth rate in a reservoir host is to predict the virulence that a virus is likely to cause upon spillover to a novel, particularly human, host. Assuming a virus evolves to an optimal growth rate in its reservoir host and then emerges as a zoonosis in a human, we can adapt [19] to describe the “spillover virulence”, using the following expression, here under assumptions of constant tolerance: where αS corresponds to virulence incurred by the virus in a secondary, spillover host. In this expression, the within-host parameters of immune cell death rate dS, growth rate gS, and clearance rate cS, as well as tolerance to immunopathology, TwS,are expressed as features of spillover host physiology (indicated by subscript “S”), while the intrinsic virus virulence, v, remains unchanged from one host to the next. By contrast, we represent the virus growth rate as optimized on the reservoir host (at least for recent spillovers), now called to clarify its selection on the reservoir (indicated by subscript “R”). Finally, we model spillover host tolerance of virus-induced pathology (TvS) as a function of phylogenetic distance between the reservoir and secondary host, here given as ηR. This term echoes recent work demonstrating increasing zoonotic virus virulence with phylogenetic distance between reservoir hosts and humans5.
The “spillover virulence” remains largely unchanged under assumptions of complete tolerance:
After calculating spillover virulence, we then follow Day 200238 to relate virulence to case fatality rates in the human host, as most widely reported in the literature, following the equation: where σS corresponds to the recovery rate from the spilled-over-virus in the human host. While we previously modeled reservoir host recovery rate as evolved to an optimum that responded to the within-host virus growth rate (as in [18]), this will not be the case for infections of recent spillover hosts. More likely, spillover recovery will scale inversely with rR*. When linking to data (Section 7), we control for this variation by accounting for total duration of infection, DIS:
From [32] and [33], we can then derive expressions for spillover virulence (αS) and spillover recovery (σS), in terms of data commonly reported in the literature (CFRS and DI):
7. Linking to the data to establish order-level parameters
In Fig. 3, we illustrate within-host parameters in possible mammalian reservoir species which could influence the evolution of optimal virus growth rates in the native reservoir host and the corresponding virulence upon spillover to a secondary, human host (αS). In the case of many of these parameters, we currently lack knowledge of these features across a majority of mammals; in particular, to our knowledge, no standardized database of mammalian immune cell parameters (i.e. g, c, and d) exists.
As such, we here focus on four parameters for which some data are available in the literature: the reservoir host mortality rate (μ), the reservoir host tolerance of immunopathology (Tw), the reservoir host transmission saturation rate per virion (ρ), and the phylogenetic distance between the reservoir host and human spillover host (ηR), which, for zoonoses, could influence human tolerance of an animal-derived virus (TvS). Fig. 3 captures both natural host mortality (μ) and tolerance of immunopathology (Tw, the scaled order effect size on the regression residuals) in panel a, the reservoir host population size (a proxy for ρ) in panel b, and the reservoir hosthuman phylogenetic distance by mammalian order (a proxy for TvS) in panel c. We summarize data compiled in Fig. 3 into order-level predictions for the within-host parameters, μ, Tw, ρ, and TvS, in Extended Data Fig. 3 and Extended Data Tables 2–3.
To generate order-level summary terms for μ, we simply took the inverse of host maximum lifespan across all species, then applied a generalized additive model39 to the raw data, modeling mammalian order as a random effect in a single smoothing term (Extended Data Table 3). The order-level prediction for μ is then given as the result of the predict.gam function applied to the fitted model (Extended Data Fig. 3).
To generate order-level summary terms for Tw, we fit a linear mixed effect model to the log10 of maximum lifespan as a response variable with the log10 of BMR as the predictor variable, incorporating a random effect of host order (Extended Data Fig. 3, Extended Data Table 3)40. To maintain the magnitude of differences among orders, we permitted only linear transformations of resulting data. Thus, to obtain order-level estimates of Tw on par with those explored in Fig. 2, we added the absolute value of the lower confidence limit of the minimum estimated partial effect size per order to all partial effect sizes to obtain complete tolerance estimates for Tw (ranging from 0 to 1), such that the least tolerant orders assumed values for Tw close to 0 and the most tolerant orders assumed values for Tw close to 1. For constant tolerance assumptions, we simply added 1 to all estimates, such that Tw ranged from close to 1 for poor tolerance to close to 2 for highly tolerant hosts.
To generate order-level summary terms for ρ, we fit another generalized additive model to the response variable of log10 of the reservoir host population size (from Fig. 3b), modeling mammalian order as a random effect in a single smoothing term (Extended Data Fig. 3/Table 3). We then generated an order-level prediction for the reservoir host population size by applying the predict.gam function to the resulting fitted model. We converted this order-level prediction of group size to an estimate of ρ on par with values explored in Fig. 2 by dividing all group size predictions by the upper confidence limit of the maximum estimated group size x100. This resulted in the prediction that reservoir hosts with larger base population sizes had larger values for ρ and a wider range of transmission capacities per virion. These relationships are consistent with our assumptions of density-dependent transmission rates at the population level: more virions generate more infections in large, gregarious host populations.
Using these order-level summary terms, we then generated an order-level prediction for across all mammalian host orders, following [26] and [27] for, respectively, assumptions of constant and complete tolerance. All other parameters (c, g, d, γ, w, v, and Tv) were held constant across all taxa at values listed in Extended Data Table 1.
Once we had constructed an order-level prediction for , we finally sought to explore the effects of these reservoir-evolved viruses upon spillover to humans, after [30] and [31]. As with the reservoir host taxa, we held immunological parameters, c, g, d, and w, constant in humans (at the same values listed above) due to a lack of informative data to the contrary. Then, to generate an order-level estimate for virus virulence on humans (αS), we combined our order-level predictions for with order-specific values for TvS, the human tolerance of an animal-derived virus, which we scaled such that more closely-related orders evolved more easily-tolerable viruses for humans. Specifically, we represented TvS as the scaled inverse of ηR, the cophenetic phylogenetic distance of each mammalian order from Primates. No summarizing was needed for ηR because, following Mollentze and Streicker 20207, we used a composite time-scaled reservoir phylogeny derived from the TimeTree database, which estimated a single mean divergence date for all clades. Thus, all species within a given mammalian order were assigned identical divergence times from the order Primates. To convert ηR to reasonable values for TvS, we divided all order-level values of ηR by the largest (to generate a fraction), then subtracted that fraction from 1 for assumptions of complete tolerance and from 2 for assumptions of constant tolerance.
See github.com/carabrook/spillover-virulence for detailed code documenting parameter derivation for μ, Tw, ρ, and TvS.
8. Comparing spillover virulence predictions with estimates from the literature
To compare estimates of spillover virulence generated from our nested modeling approach (αS) with estimates from the literature, we next followed [32]-[35] to obtain empirical estimates of αS for each mammalian order, using case fatality rates (CFRS) reported in the literature4 and durations of human infection (DIS) which we collected ourselves by searching the primary literature. Infection durations and associated references are listed in the dataset hosted on our publicly available GitHub repository: github.com/carabrook/spillover-virulence. To obtain a composite order-level prediction for αS from DIS and CFRS as reported in4, we adopted the best-fit generalized additive model used by the authors in4 to estimate CFRS to here estimate αS instead (Extended Data Table 3), then predicted αS from the fitted model while excluding the predictive effects of viral family.
In Fig. 3d, we then compare predictions of αS in humans derived from our nested modeling approach with empirical estimates from the zoonosis literature in4, under assumptions of constant tolerance. Constant tolerance offers a reliable baseline assumption under which virulence is proportionally reduced by a constant extent. From this comparison, we see that both methods predict the highest values for (αS) by far from bats (Order Chiroptera), a pattern recapitulated under assumptions of complete tolerance in Extended Data Fig. 4. Our life history method appears to overpredict αS from the orders Rodentia and Cetartiodactyla, relative to the data in Guth et al. (2021)4. In Extended Data Fig. 5, we compare our order-level predictions of αS with a version recomputed from4 where rabies lyssavirus is excluded from the dataset. This greatly reduces the estimated order-level average CFR for Carnivora, making the data align even more closely to our modeled predictions.
Data availability
All data used in this analysis is publicly available at the following GitHub repository: github.com/carabrook/spillover-virulence
Code availability
All code used in this analysis is publicly available at the following GitHub repository: github.com/carabrook/spillover-virulence
Author contributions
CEB and MB conceptualized the research. CEB carried out the modeling and analysis with contributions from CR and SG. CEB wrote the first draft of the manuscript, which all authors edited and revised.
Competing interests
Authors declare that they have no competing interests.
Materials and correspondence
All correspondence should be addressed to corresponding author Cara E. Brook at cbrook{at}uchicago.edu.
Extended Data Figures
Extended Data Tables
Acknowledgments
The authors thank the Boots Lab at UC Berkeley for helpful comments on this manuscript and acknowledge funding from a National Institutes of Health grant 1R01AI129822-01 to CEB, an Adolph C. and Mary Sprague Miller Institute for Basic Research fellowship to CEB, a Branco Weiss Science in Society fellowship to CEB, a Loréal-USA for Women in Science fellowship to CEB, and a Defense Advanced Research Projects Agency PREEMPT Program subgrant D18AC00031 to CEB.