General trends in the evolution of high growth rate viruses

To elucidate how immunological and life history traits of mammalian hosts combine to drive zoonotic virus virulence, we adopt a nested modeling approach [45], embedding a simple within-host model of viral and leukocyte dynamics within an epidemiological, population-level framework (Fig 1). We examine 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 model in an adaptive dynamics framework [46], we first express the conditions—called the “invasion fitness”—which permit invasion of an evolutionarily “fitter,” mutant virus into a reservoir host system in within-host terms. From this, we derive an expression for , the optimal within-host growth rate of a persistent virus evolved at equilibrium prevalence in its reservoir host; our modeling framework allows us to express as a function of within-host traits that we might expect to vary across mammalian reservoirs with divergent life histories. We deduce that can, consequently, also be expected to vary as a result of these life history differences, which modulate the optimization process by which a virus maximizes gains in between-host transmission () while mitigating virulence incurred on its reservoir (; Fig 1). From this framework, we next derive an expression for α_S, the virulence incurred by a reservoir-optimized virus immediately following spillover to a novel host. We expressed α_S as a function of the reservoir-optimized virus growth rate (), combined with spillover host tolerance of virus pathology (T_vS), which we model as proportional to the phylogenetic distance between reservoir and spillover host (Fig 1).

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Fig 1. Conceptual mechanistic framework to predict zoonotic virus virulence from reservoir immunology and life history traits.

(A) A within-host predator–prey-like model of leukocyte–virus dynamics is embedded in a population-level transmission model for reservoir hosts. Between-host rates of transmission () and virulence () are expressed as functions of within-host dynamics to derive optimal virus growth rates in the reservoir (). See S1 File and Table 1 for parameter definitions and values. (B) Because most mammalian hosts are relatively intolerant of virus pathology and immunopathology, viruses typically evolve low optimal growth rates in reservoir hosts () that minimize virulence incurred on the reservoir (). Low growth rates should also generate relatively low between-host transmission in the reservoir population (). Zoonotic viruses evolved in a reservoir host spillover to human hosts to generate acute infections. These spillover infections yield spillover host virulence (α_S), which we express as a function of the original growth rate of the reservoir-optimized virus (), combined with the spillover host tolerance of direct virus pathology (T_vS). We model this latter term as inverse to phylogenetic distance between reservoir and spillover (human) host. Zoonoses with low —and those from phylogenetically related hosts (like primates) that result in high human T_vS—should generate correspondingly low spillover virulence (α_S) in human hosts. (C) As a result of unique bat virus tolerance, viruses evolved in bat reservoir hosts may optimize at high values that maximize bat-to-bat transmission () but cause only minimal pathology in the bat host (). Such viruses are likely to generate extreme virulence upon spillover (α_S) to secondary hosts, including humans, that lack bat life history traits. The virulence of a virus in its spillover host is amplified (α_S) in cases where large phylogenetic distance between reservoir and spillover host results in minimal spillover host tolerance of virus pathology (T_vS).

https://doi.org/10.1371/journal.pbio.3002268.g001

Our nested modeling approach first follows Alizon and van Baalen (2005) [45] in derivation of an expression for , the within-host virus growth rate optimized based on endemic circulation in a reservoir host. The equation for can be captured as follows: where μ_R signifies the natural mortality rate of the reservoir host, and all other parameters represent within-host viral and immune dynamics in a persistently infected reservoir. Thus, c_R corresponds to the rate of virus clearance by leukocytes, g_0R is the magnitude of constitutive immunity, m_R is the natural leukocyte mortality rate, and g_R is the rate of leukocyte activation following infection, all in the reservoir host. The parameters v and w correspond, respectively, to the intrinsic virulence of the virus and its propensity to elicit a damaging inflammatory response from its host’s immune system—while T_vR and T_wR respectively represent reservoir host tolerance to direct virus pathology and to immunopathology. From the above expression, we explore a range of optimal within-host virus growth rates () for viruses evolved in reservoir hosts with diverse cellular and immunological parameters (Figs 2, S1 and S2 and Table 1). We subsequently calculate the corresponding transmission () and virulence () incurred by viruses evolved to in their reservoir hosts, then, following Gilchrist and Sasaki (2002) [47], model the nascent spillover of a reservoir-evolved virus as acute infection in a secondary host. In this spillover infection, we assume that the virus retains its reservoir-optimized growth rate () while replicating in the physiological and immunological environment of its novel spillover host. We express this spillover virulence (α_S) as: where corresponds to the average viral load experienced across the timecourse of an acute spillover host infection, and g_S, T_vS, and T_wS represent the spillover host analogues of previously described within-host parameters in the reservoir host equations (Figs 2, S1, and S2 and Table 1). We present all main text results under assumptions by which tolerance manifests as a constant reduction of either direct virus-induced pathology (T_v) or immunopathology (T_w). See S1 File for comparable results under assumptions of complete tolerance, whereby tolerance completely eliminates virus pathology and immunopathology up to a threshold value, beyond which pathology scales proportionally with virus and immune cell growth.

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Fig 2. Optimal virus growth rates—and subsequent spillover virulence—vary across reservoir host immunological and life history parameters.

Rows (top-down) indicate the evolutionarily optimal within-host virus growth rate () and the corresponding between-host transmission rate (), and virus-induced mortality rate () for a reservoir host infected with a virus at . The bottom row then demonstrates the resulting virulence (α_S) of a reservoir-optimized virus evolved to upon nascent spillover to a novel, secondary host. Columns demonstrate the dependency of these outcomes on variable within-host parameters in the reservoir host: background mortality (μ_R), magnitude of constitutive immunity (g_0R), rate of leukocyte activation upon viral contact (g_R), rate of virus consumption by leukocytes (c_R), and leukocyte mortality rate (m_R). Darker colored lines depict outcomes at higher reservoir host tolerance of direct virus pathology (T_vR, red) or immunopathology (T_wR, blue), assuming no tolerance of the opposing type. Heat maps demonstrate how T_vR and T_wR interact to produce each outcome. Parameter values are reported in Table 1. Figure assumes tolerance in the “constant” form. See S2 Fig for “complete” tolerance assumptions and S3 Fig for changes in α_S across a variable range of parameter values for spillover host tolerance of direct virus pathology, T_vS, and immunopathology, T_wS. Data and code used to generate all figure panels are available in our publicly available GitHub repository (github.com/brooklabteam/spillover-virulence-v1.0.0; doi: 10.5281/zenodo.8136864).

https://doi.org/10.1371/journal.pbio.3002268.g002

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Table 1. Default parameter values for population-level and within-host models.

https://doi.org/10.1371/journal.pbio.3002268.t001

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 () are selected in reservoir hosts with higher background mortality (μ_R), elevated constitutive immune responses (g_0R), more rapid leukocyte activation upon infection (g_R), and more rapid virus clearance by the host immune system (c_R). Additionally, higher viruses are selected in hosts exhibiting lower leukocyte mortality rates (m_R), resulting in longer-lived immune cells. Critically, higher reservoir host tolerance of both virus-induced pathology (T_vR) and immunopathology (T_wR) also select for higher . In keeping with trade-off theory, changes in the majority of within-host parameters drive corresponding increases in , and , such that viruses evolved to high growth rates experience high transmission within the reservoir host population—but also generate high virus-induced mortality (Fig 2). By definition, the 2 modeled mechanisms of tolerance (T_vR and T_wR) decouple the relationship between transmission and virulence, permitting evolution of high viruses that achieve gains in between-host transmission (), while simultaneously incurring minimal virulence () on reservoir hosts. By extension, we demonstrate that viruses evolving high optimal values in reservoir hosts incur substantial pathology upon spillover to secondary hosts (α_S). Intriguingly, the virulence that a virus incurs on its spillover host (α_S) accelerates substantially faster than that incurred on its reservoir host () at higher values for certain parameters, chiefly, g_0R, c_R as well as, most critically, T_vR and T_wR. This underscores the important capacity of these within-host traits to drive cross-species virulence in emerging viruses.

Order-specific estimates for optimal virus growth rates evolved in reservoir hosts

We next apply our model to attempt to make broad predictions of the evolution of optimal virus growth rates () across diverse mammalian reservoir orders, based on order-specific variation in 3 key parameters from our nested model: the reservoir host background mortality rate (μ_R), the reservoir host tolerance of immunopathology (T_wR), and the reservoir host magnitude of constitutive immunity (g_0R). Within-host immunological data needed to quantify these parameters is lacking for most taxa; thus, we use regression analyses to summarize these terms across mammalian orders from publicly available life history data. In particular, we use well-described allometric relationships between mammalian body mass and basal metabolic rate (BMR) with lifespan and immune cell concentrations [49–53] to proxy μ_R, T_wR, and g_0R across mammalian orders (Figs 3A–C, S4 and S1 Table). From here, we use our nested modeling framework to predict optimal virus growth rates () across diverse mammalian reservoirs (Fig 3D). Then, we estimate , the spillover host tolerance of direct virus pathology, as proportional to the time to most recent common ancestor (MRCA) between the human primate order and each mammalian reservoir order, now focusing our analysis on zoonotic spillover (Fig 3E and 3F and S1 Table). Finally, we combine estimates for and to generate a prediction for α_S, the virulence of a reservoir-optimized virus in a human spillover host, which we can compare against case fatality rates for mammalian zoonoses reported in the literature [4,8] (Figs 3G and S5–S9).

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Fig 3. Reservoir host life history traits predict evolution of zoonotic virus virulence.

(A) Variation in log₁₀ maximum lifespan (y-axis, in years) with log₁₀ adult body mass (x-axis, in grams) across mammals, with data derived from Jones and colleagues [54] and Healy and colleagues [55]. Points are colored by mammalian order, corresponding to legend. Black line depicts predictions of mammalian lifespan per body mass, summarized from fitted model (but excluding random effect of mammalian order), presented in S2 Table. (B) Baseline neutrophil concentrations (y-axis, in 10⁹ cells/L) per mass-specific metabolic rate (x-axis, in W/g) across mammals, with data from Jones and colleagues [54] and Healy and colleagues [55] combined with neutrophil concentrations from Species360 [53]. Black line projects neutrophil concentration per mass-specific metabolic rate (excluding random effects of mammalian order), simplified from fitted model presented in S2 Table. (C) Order-level parameters for nested modeling framework were derived from fitting of linear models and linear mixed models visualized here and presented in S4 Fig and S2 Table to data from (A) and (B). Average annual mortality rate (μ_R) was predicted from a linear regression of species-level annual mortality (the inverse of maximum lifespan), as described by a predictor variable of host order; tolerance of immunopathology () was derived from the scaled effect of host order on the linear mixed effects regression of log₁₀ maximum lifespan (in years) by log₁₀ mass (in grams), incorporating a random effect of order. The magnitude of constitutive immunity ( was derived from the scaled effect of order on the regression of log₁₀ neutrophil concentration per log₁₀ body mass (in grams), combined with BMR (in W) (S4 Fig and S1 and S2 Tables). Panels shown here give numerical estimates for μ_R and order-level effects from fitted models that were scaled to numerical values for and , as presented in S4 Fig (S1 Table). Red and blue colors correspond to, respectively, significantly positive or negative order-level partial effects from these regressions. (D) Reservoir-host estimates for μ_R, T_wR, and g_0R were combined in our modeling framework to generate a prediction of optimal growth rate for a virus evolved in a host of each mammalian order (). Here, point size corresponds to the average number of species-level data points used to generate each of the 3 variable parameters impacting , as indicated in legend. (E) Phylogenetic distance from Primates (in millions of years, indicated by color) on a timescaled phylogeny, using data from TimeTree [56]. (F) An order-level estimate for the nested model parameter, T_vS, the spillover human host tolerance of pathology induced by a virus evolved in a different reservoir order, was estimated as the scaled inverse of the phylogenetic distance shown in (E) (S4 Fig and S1 Table). (G) Reservoir-host predictions of optimal virus growth rates () from (D) were combined with human spillover host estimates of tolerance for direct virus pathology (T_vS) from (F) in our nested modeling framework to generate a prediction of the relative spillover virulence (α_S) of a virus evolved in a given reservoir host order immediately following spillover into a secondary, human host. Here, the left panel visualizes predictions from our nested modeling framework, using order-specific parameters for μ_R, T_wR, g_0R, and T_vS (S1 Table). The right panel depicts relative human α_S estimates derived from case fatality rates and infection duration reported in the zoonotic literature [8]. For the left panel, point size corresponds to the average number of species-level data points used to generate each of the 4 variable parameters impacting α_S. For the right panel, point size indicates the total number of independent host–virus associations from which virulence estimates were determined. In (C), (D), and (G), 95% confidence intervals were computed by standard error; in (G) for the left panel, these reflect the upper and lower confidence intervals of the optimal virus growth rate in (D). See S1 Table for order-level values for , μ_R, T_wR, g_0R, and T_vS and Table 1 for all other default parameters involved in calculation of α_S. Sensitivity analyses for zoonotic predictions are summarized in S5–S9 Figs and S3 Table. Data and code used to generate all figure panels are available in our publicly available GitHub repository (github.com/brooklabteam/spillover-virulence-v1.0.0; doi: 10.5281/zenodo.8136864).

https://doi.org/10.1371/journal.pbio.3002268.g003

We first fit a simple linear regression to the response variable of the inverse of maximum lifespan across diverse mammalian hosts with a single predictor of reservoir host order (Fig 3A and S2 Table). From this simple model, we can easily make projections that summarize μ_R, the reservoir host annual mortality rate, to an average value for each of 26 mammalian orders. We express μ_R in units of days^-1 on a timescale most relevant to viral dynamics; as a result, even multiyear differences in maximum longevity do little to drive differences in μ_R across mammalian orders. Nonetheless, 8 orders (Afrosoricida, Dasyuromorphia, Didelphimorphia, Eulipotyphla, Macroscelidea, Notoryctemorphia, Peramelemorphia, and Rodentia) demonstrate significantly elevated annual mortality rates using the median order mortality rate (Diprotodontia) as a reference. By contrast, Carnivora, Cetartiodactyla, Primates, and Perissodactyla demonstrate significantly reduced annual mortality rates as compared to the same reference (Fig 3C and S1 and S2 Tables).

Drawing on well-described allometric relationships between mass and lifespan [49] and more recent literature that links longevity with resilience to inflammation [11,44,57–61], we next sought to characterize variation in T_wR, reservoir host tolerance of immunopathology, across mammalian orders. Smaller-bodied organisms are hypothesized to be shorter-lived due to higher metabolic rates, more rapid energy expenditure, and faster accumulation of oxidative damage, which can manifest as inflammation [62]. We hypothesized, then, that organisms that are longer-lived than predicted for their body size might be more resilient to inflammatory stressors—and, therefore, by extension, more tolerant of immunopathology. Building on this hypothesis, we scale T_wR after order-level deviations in lifespan as predicted by body mass. To this end, we fit a linear mixed effect regression with a random effect of host order to the log₁₀ relationship of lifespan (in years) as predicted by body size (in grams), again spanning data representing 26 diverse mammalian orders. From this, we identify 5 orders (Carnivora, Chiroptera, Cingulata, Monotremata, and Primates) with significantly longer lifespans than predicted by body size—which scale to enhanced estimates for T_wR. By contrast, we identify 8 orders (Afrosoricida, Cetartiodactyla, Dasyuromorphia, Didelphimorphia, Eulipotyphla, Notoryctemorphia, Peramelemorphia, and Rodentia) with significantly shorter lifespans than predicted by body size, which scale to lower value estimates for T_wR (Figs 3A, 3C, S4 and S1 and S2 Tables). Because the same data on host lifespan are included in both estimation of μ_R and T_wR, order-level estimates for T_wR largely mirror those for μ_R—such that longer-lived orders are modeled with low values for annual mortality rate and high values for tolerance to immunopathology (and vice versa). However, because mass is not factored into estimation of μ_R, these parameters diverge in select cases: for example, we estimate mid-range mortality rates for order Chiroptera, as compared with other mammals, but very high values for T_wR becase Chiropteran lifespans—though not remarkably long at face value—far exceed those predicted by body size. By contrast, we estimate low values for both μ_R and T_wR for order Cetartiodactyla, as hosts in this order are long-lived but less long-lived than predicted for body size.

Finally, we fit another linear mixed effect regression with a random effect of host order to the log₁₀ relationship of baseline circulating neutrophil concentration (in 10⁹ cells/L) as predicted by mass (in grams) and BMR (W); these data spanned only 19 mammalian orders (Fig 3B). From this, we identify a significant positive association between the orders Chiroptera and Monotremata and the response variable of baseline neutrophil concentration, indicating that species in these orders may have more enhanced constitutive immune responses than predicted by mass-specific BMR (Fig 3C). The orders Cetartiodactyla, Dasyuromorphia, Diprotodontia, and Scandentia, by contrast, show significant negative associations, representing lower baseline neutrophil concentrations than predicted per mass-specific BMR. We scale these order-level effects to correspondingly high and low estimates for g_0R, the within-host parameter representing the magnitude of reservoir-host constitutive immunity in our nested modeling framework (Figs 3B, 3C, S4 and S1 and S2 Tables).

From life history-derived estimates for μ_R, T_wR, and g_0R, we next generate a prediction of the optimal growth rate of a virus evolved in a reservoir host for each of 19 distinct mammalian orders for which we possess the full suite of proxy data for all 3 variable within-host parameters (Fig 3D). In keeping with results from our general model (Fig 2), we predict the evolution of high viruses from reservoir orders exhibiting high μ_R, T_wR, and/or g_0R. Because our nested model expresses parameters in timesteps most relevant to viral dynamics (days), differences in mortality rates across mammalian orders—though substantial on multiyear timescales of the host—have limited influence on downstream predictions of differences in the evolution of virus growth rates. This result echoes prior observations from Fig 2, which showed reduced sensitivity of to realistic variation in the magnitude of μ_R, as compared with other parameters. As a result, we ultimately recover the highest predicted optimal growth rates for viruses evolved in the orders Chiroptera and Monotremata, which exhibit both long lifespans per body size (corresponding to high estimates for T_wR) and high baseline neutrophil concentrations (corresponding to high estimates for g_0R). Data are particularly sparse, however, for order Monotremata, for which complete records are only available for 2 species (the platypus and the short-beaked echidna). As a result, predictions for this order should be interpreted with caution. More data, particularly for baseline neutrophil concentrations, will be needed to evaluate the extent to which these predictions hold across all 5 extant species in the Monotremata order. Additionally, we predict the evolution of the lowest growth rate viruses in reservoir hosts of the orders Scandentia, Cetartiodactyla, Diprotodontia, and Dasyuromorphia, all of which demonstrate significantly low estimates for the magnitudes of constitutive immunity and 2 of which (Cetartiodactyla, Dasyuromorphia) also demonstrate significantly low estimates for tolerance of immunopathology.

Estimating zoonotic virus virulence in spillover human hosts

After establishing optimal growth rates for viruses evolved in diverse reservoir host orders (), we subsequently model the corresponding “spillover virulence” (α_S) of these viruses following emergence into a human host. Zoonotic spillovers are modeled as acute infections in the human, and virulence is calculated while varying only the growth rate of the spillover virus () and the human tolerance of direct virus pathology (T_vS) between viruses evolved in differing reservoir orders. We vary this last parameter, T_vS, to account for any differences in virus adaptation to reservoir host immune systems that are not already captured in estimation of reservoir host T_wR and g_0R. T_vS is thus computed as the inverse of the scaled time to MRCA for each mammalian reservoir host order from Primates (Figs 3E, S4 and S1 and S2 Tables), such that we estimate low human tolerance to viruses evolved in phylogenetically distant orders (e.g., monotreme and marsupial orders), and high human tolerance to viruses evolved in Primate and Primate-adjacent orders. In general, the modulating effects of T_vS do little to alter virulence rankings of zoonotic viruses from those predicted by raw growth rate () alone—with the highest spillover virulence predicted from viruses evolved in orders Monotremata and Chiroptera and the lowest spillover virulence predicted from viruses evolved in orders Cetartiodactyla and Scandentia (Fig 3D and 3G). Notably, modulating T_vS enhances predictions of spillover virulence for some marsupial clades (Peramelemorphia, Dasyuromorphia, Diprotodontia) relative to eutherian orders with similar predicted values. This results in dampened predicted spillover virulence for the eutherian order Perissodactyla as compared with marsupial orders Dasyuromorphia and Diprotodontia, despite lower predicted values for the latter 2 clades (Figs 3D, 3G, and S5). Similarly, this elevates spillover virulence predictions for Peramelemorphia above Eulipotyphla, Afrosoricida, and Hyrocoidea, despite higher predicted in the 3 eutherian orders (Figs 3D, 3G, and S5).

Comparing predictions of spillover virulence by reservoir order with estimates from the literature

Since parameter magnitudes estimated from life history traits are largely relative in nature, we scale predictions of spillover virulence (α_S) by reservoir order in relative terms to compare with estimates gleaned from the zoonosis literature [8] (Figs 3G and S5–S9). For 8 reservoir orders (Chiroptera, Eulipotyphla, Primates, Carnivora, Rodentia, Diprotodontia, Perissodactyla, and Cetartiodactyla), we are able to fit a simple linear regression comparing the relative virulence of zoonoses derived from each order as reported from case fatality rates in the literature [4,8] versus those predicted by our nested modeling approach (S6 and S8 Figs and S3 Table). Our nested modeling framework recovers available case fatality rate data well, yielding an R² value of 0.57 in the corresponding regression of observed versus predicted values (S6 Fig and S3 Table). Critically, we successfully recover the key result from the zoonosis literature: bat-derived zoonoses yield higher rates of virus-induced mortality upon spillover to humans (α_S) than do viruses derived from all other eutherian mammals (Figs 3G and S5–S8). In general, high estimates for T_wR, μ_R, and g_0R, and low estimates for T_vS predict high spillover virulence to humans (α_S). Bats demonstrate uniquely long lifespans for their body sizes and uniquely enhanced constitutive immune responses [21] as compared with other taxa; when combined, as in our analysis, to represent high T_wR and high g_0R, these reservoir host traits elevate predicted and α_S beyond all other eutherian orders (Fig 3D and 3G).

Evaluated against the data [4,8], our model overpredicts cross-order comparative virulence rankings for viruses evolved in order Eulipotyphla (Figs 3G and S6), largely as a result of our parameterization of high values for annual mortality rate (μ_R) and correspondingly low values for tolerance of immunopathology (T_wR) in this order. In addition, our model underpredicts virulence for Carnivora-derived viruses, based on within-host parameter estimates largely inverse to those recovered for Eulipotyphla (e.g., low μ_R and high T_wR). We are able to resolve this underprediction of Carnivora virulence when excluding rabies lyssavirus from data comparisons [4,8] (S8 Fig); though most rabies zoonoses are sourced from domestic dogs, lyssaviruses are Chiropteran by origin [63], and viral traits responsible for rabies’ virulence may reflect its bat evolutionary history more than that of any intermediate carnivore host. Nonetheless, while excluding rabies from comparison improves recovery of literature-estimated relative virulence of Carnivora-derived viruses, it somewhat destabilizes predictions for other orders, such that the overall performance of the model is largely equivalent as to when comparing against all available data (S8 Fig; R² = 0.57).

In all cases, our model successfully reproduces estimates of significantly lower virulence incurred by zoonotic viruses evolved in Cetartiodactyla hosts as compared with all other orders considered [8]. While previous work suggested that low observed virulence for Cetartiodactylan zoonoses might result from overreporting of avirulent zoonoses in domestic livestock with frequent human contact [8], our analysis indicates that viral zoonoses emerging from Cetartiodactylan hosts may truly be less virulent to humans. Our mechanistic framework demonstrates that reduced tolerance of immunopathology (manifest as shorter lifespans than predicted by body size) and limited constitutive immune responses identified in Cetartiodactylan hosts may drive the evolution of low growth rate viruses that cause correspondingly benign infections following zoonotic emergence. Further research into the extent to which Cetartiodactylans are impacted by immunopathology, as well as the degree to which low reported baseline neutrophil concentrations accurately reflect their innate immunity, is needed to evaluate these predictions. Quantification of the natural growth rates of Cetartiodactylan-evolved viruses could offer one means of testing this modeling framework.

Sensitivity analyses demonstrate that, as previously observed in Fig 2, within-host parameters have unequal impacts on the resulting prediction of spillover virulence in our nested modeling framework (S9 Fig and S3 Table). Individually profiling T_wR, g_0R, and T_vS while holding all other parameters constant across host orders is insufficient to recover previously reported estimates of spillover virulence for zoonoses. Nonetheless profiling g_0R—and to a lesser extent T_vS or T_wR—while paired with order-specific estimates generated from life history data for the other 2 parameters greatly improves our recovery of spillover virulence as reported in the literature (yielding an R² value of 0.99 from the corresponding regression of observed versus predicted values; S9 Fig and S3 Table). These findings suggest that no single parameter in our nested modeling framework underpins observed variation in predicted spillover virulence across reservoir host orders; still, g_0R, the magnitude of constitutive immunity attributed to each reservoir order, appears to modulate these resulting differences to a greater extent than do T_vS and T_wR.

Evolutionary framework

Cross-species dynamics.

We next derive an expression to explore the consequences of spillover of a virus evolved to its optimal growth rate in a reservoir host population—which we term —following cross-species emergence into the human population. Contrary to its established persistent infection in the reservoir host, we assume that such a virus will produce an acute infection in the spillover host. To model the dynamics of this acute spillover, we borrow from Gilchrist and Sasaki [47], who developed a within-host parasite–leukocyte model in which an immortal leukocyte successfully eradicates the parasite population to near-zero. We modify their acute model to be more comparable to our chronic infection model ((3a)/(3b)) and to reflect our differing notation for within-host dynamics.

(9a)(9b)

Here, represents the reservoir-evolved virus growth rate, but all other terms reflect within-host conditions of the spillover host: V_S and L_S correspond, respectively, to the spillover host virus and leukocyte populations, c_S is the virus consumption rate upon contact with leukocytes in the spillover host, and g_S is the growth rate of the spillover host leukocyte population in response to virus. We express the model in units of τ, which we assume to be short in comparison to the t time units of dynamics in the reservoir host population. Rather than solving for virus and leukocyte populations at equilibrium (as in the reservoir host population), we follow Gilchrist and Sasaki [47] to instead derive an expression for the virus population at the peak of infection (), where we anticipate maximum pathology for the spillover host. We then extend this prior work to generate an expression for the average viral load () in the spillover host across the timecourse of acute infection, which we can use in comparisons of spillover host virulence with reported case fatality rates for zoonoses in the literature.

If we divide Eq (9a) by Eq (9b), we derive a simple time-independent relationship between virus and leukocyte density: (10)

If we then let L_S (0) = 1, V_S (0) = 1, assuming that both virus and leukocyte populations will be small at τ = 0, we can integrate (10) to establish the following relationship between virus and leukocyte: (11)

Notice that the above (11) is simply a quadratic equation (see (12) below): (12)

Now, we can take the derivative of Eq (12) to formulate an expression for , the maximum viral load, which should precede the end of acute infection and the point of host recovery at the maximum duration of infection: (13)

Then, extending previous work [47], we calculate the average viral load by taking the integral of Eq (12) from V_S(0) to and dividing by the duration of that interval. From this exercise, we express the average value of Eq (12) as: (14)

Now, with this established expression for , we adapt Eq (7) to reflect the acute within-host dynamics of “spillover virulence,” which we model (as before) as a combination of mortality induced from direct virus pathology and from immunopathology. As in the reservoir host system, we also model the mitigating impact of tolerance on the 2 mechanisms of virulence: (15)

This yields the above expression for “spillover virulence.” Here, the growth rate of the virus is expressed at its evolutionary optimum evolved in the reservoir host (), and the virus’s intrinsic virulence (v) and propensity to elicit an inflammatory immune response (w) remained unchanged from one host to the next. Inspired by findings in the literature that report higher virulence in cross-species infections between hosts separated by larger phylogenetic distances [8–12], we model spillover host tolerance of virus-induced pathology (T_vS) as a decreasing function of increasing phylogenetic distance between the reservoir and secondary host. All other immune-related parameters assume characteristics of the spillover host: g_S is the spillover host’s leukocyte growth rate, and T_wS corresponds to the spillover host’s tolerance of immunopathology.

Order-specific estimates for optimal virus growth rates evolved in reservoir hosts

Next, we develop estimates for the optimal virus growth rate () expected to evolve across a suite of diverse mammalian reservoir orders. Because within-host immunological data needed to quantify within-host parameters underpinning the expression for are largely lacking, we proxy a few key within-host parameters from well-described allometric relationships for mammalian life history data. As such, we here focus on 3 key parameters for which data could be gleaned from the literature: the reservoir host mortality rate (μ_R), the reservoir host tolerance of immunopathology (T_wR), and the magnitude of reservoir host constitutive immunity (g_0R).

To generate order-level summary terms for μ_R we fit a simple linear regression to the response variable of the inverse of maximum lifespan (in days) with a single categorical predictor of host order, using data from Jones and colleagues [54] and Healy and colleagues [55] that span 26 mammalian orders and 1,060 individual species (Fig 3A). This first model thus takes the form: (16) where Y_ij corresponds to natural mortality rate observations for i species belonging to j orders; α₀ is the overall intercept; k indicates the total number of available orders (here, 26); β_j is an order-specific slope; δ_ij indicates observations of i species grouped into j orders; and ε_ij is a normally distributed error term corresponding to species i within order j. We estimate μ_R by simply generating predictions from this fitted model across all 26 mammalian orders represented in our dataset (Fig 3C and S2 Table).

We next use the same dataset of 1,060 species grouped into 26 mammalian orders to generate order-level estimates for the reservoir host tolerance of immunopathology (T_wR). Here, we fit a linear mixed effects regression to the log₁₀ relationship of lifespan (in years) as predicted by body mass (in grams). This second model takes the form: (17) where Y_ij corresponds to the log₁₀ value of record of maximum lifespan (in years) for i species belonging to j orders; α₀ is the overall intercept; β₁ indicates the slope of the fixed predictor of log₁₀ mass (in grams), here represented as X₁; u_0j is the order-specific random intercept; and ε_ij is a normally distributed error term corresponding to species i within order j. To estimate T_wR, we extract the relative partial effects of mammalian order on maximum lifespan per body size, and then rescale these effects between 1 and 2 for assumptions of constant tolerance and between 0 and 1 for assumptions of complete tolerance (S1 and S2 Tables). We justify this approach based on literature that highlights links between antiaging molecular pathways that promote longevity and those that mitigate immunopathology [11,44,57–61].

Finally, to generate order-level summary terms for the magnitude of constitutive immunity (g₀), we fit another linear mixed effects regression to the relationship between the predictor variables of log₁₀ mass (in g) and BMR (in W) and the response variable of log₁₀ baseline neutrophil concentration (in 10⁹ cells/L), which offers an approximation of a mammal’s constitutive innate immune response. BMR data for this model are derived from Jones and colleagues [54] and Healy and colleagues [55], while neutrophil concentrations were obtained from zoo animal data presented in the Species360 database [53]; prior work using this database has demonstrated scaling relationships between body size and neutrophil concentrations across mammals [52]. Paired neutrophil and BMR data were limited to just 19 mammalian orders and 144 species. Our model also includes a random effect of host order, resulting in the following form: (18) where Y_ij corresponds to the log₁₀ baseline neutrophil concentrations (in 10⁹ cells/L) for i species belonging to j orders; α₀ is the overall intercept; β₁ indicates the slope of the fixed predictor of log₁₀ mass (in grams), here represented as X₁; β₂ indicates the slope of the fixed predictor of BMR (in W), here represented as X₂; u_0j is the order-specific random intercept; and ε_ij is a normally distributed error term corresponding to species i within order j. Using a similar approach as that employed above for T_wR, we estimate g₀ by extracting the relative partial effects of mammalian order on neutrophil concentration per mass-specific BMR, then rescale these effects between 0 and 1. Because we estimate significantly positive partial effects between the orders Chiroptera and Monotremata and baseline neutrophil concentration (Fig 3C), this generates correspondingly high estimates of g_0R for these two orders (S4 Fig and S1 Table).

Using these order-level summary terms for μ_R, T_wR, and g_0R, we then generate an order-level prediction for across all mammalian host orders, following Eq (8) (Fig 3D). All other parameters (c_R, g_R, m_R, w, v, and T_vR) are held constant across all taxa at values listed in Table 1.

Estimating zoonotic virus virulence in spillover human hosts

Once we have constructed an order-level prediction for , we explore the effects of these reservoir-evolved viruses upon spillover to humans, following Eq (15). As when computing virulence for the reservoir host population, we hold immunological parameters,c_S, g_S, and m_S 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 incurred on humans (α_S), we combine our order-level predictions for with order-specific values for T_vS, the human tolerance of an animal-derived virus, which we scale such that viruses derived from more closely related orders to Primates are more easily tolerated in humans. Specifically, we represent T_vS as the scaled inverse of the cophenetic phylogenetic distance of each mammalian order from Primates. No summarizing is needed for T_vS because, following Mollentze and Streicker [10], we use a composite timescaled reservoir phylogeny derived from the TimeTree database [56], which produces a single mean divergence date for all clades. Thus, all species within a given mammalian order are assigned identical times to MRCA with the order Primates. To convert cophenetic phylogenetic distance into reasonable values for T_vS, we divide all order-level values for this distance by the largest observed (to generate a fraction), then subtract that fraction from 2 for assumptions of constant tolerance (yielding T_vS estimates ranging from 1 to 2) and from 1 for assumptions of complete tolerance (yielding T_vS estimates ranging from 0 to 1).

We then combine reservoir host order-level predictions for with these estimates for human tolerance of virus pathology (T_vS) to generate predictions of the expected spillover virulence of viral zoonoses emerging from the 19 mammalian orders for which we possess complete data across the 4 variable parameters (μ_R, T_wR, g_0R, and T_vS). We scale these α_S estimates—and their 95% predicted confidence intervals—in relative terms (from 0 to 1) to compare with estimates from the literature.

Comparing predictions of spillover virulence by reservoir order with estimates from the literature

To compare estimates of spillover virulence generated from our nested modeling approach (α_S) with estimates from the literature, we follow Day (2002) [87] to convert case fatality rates of viral zoonoses in spillover human hosts (CFR_S) reported in the literature [8] to empirical estimates of α_S for each mammalian order, using data on the duration of human infection (D_IS) for each viral zoonosis. For this purpose, we collected data on D_IS by searching the primary literature; raw data for infection durations and associated references are reported in our publicly available GitHub repository (github.com/brooklabteam/spillover-virulence-v1.0.0; doi: 10.5281/zenodo.8136864). Briefly, Day (2002) [13] notes that the equation for case fatality rate in the spillover host (CFR_S) takes the form: (19) where σ_S corresponds to the recovery rate from the spilled-over virus in the human host. We also note that the total duration of infection, D_IS, is given by: (20)

Therefore, we translated human case fatality rates of viral zoonoses (CFR_S) into estimates of spillover virulence (α_S) using the following equation: (21)

To obtain a composite order-level prediction for α_S from D_IS and CFR_S as reported in [8], we adopt the best-fit generalized additive model (GAM) [88] used by the authors in [8] to summarize CFR_S by order and, here, apply it to α_S estimates converted from CFR_S reported in the literature (S2 Table). This best-fit GAM estimates the response variable of spillover virulence (α_S) from corresponding predictor variables of reservoir host order, virus family, virus species publication count (a measure of research effort), spillover type (via bridge host versus direct), and vector-borne disease status (yes or no). Following [8], we summarize α_S at the order-level from the fitted GAM, excluding the effects of viral family, to yield a literature-derived value for α_S across disparate mammalian orders, against which to compare predictions from our nested modeling approach. Because the majority of the within-host parameters underpinning α_S predictions in our nested modeling approach (μ_R, T_wR, g_0R, and T_vS) are quantified only in a relative fashion, we were unable to compare direct magnitudes of virulence (e.g., in terms of host death per unit time). To account for this, we rescale α_S estimates from both our nested modeling approach and from the empirical literature from 0 to 1 and compare the relative rank of virulence by mammalian order instead. We predict α_S for 19 discrete mammalian orders, though data from the literature are available for only 8 orders against which to compare.

Finally, because bats are the most likely ancestral hosts of all lyssaviruses [63], and it may be more appropriate to class carnivores as “bridge hosts” for rabies, rather than reservoirs (as the authors discuss in Guth and colleagues (2022) [8]), we recompute literature-derived estimates of relative α_S by fitting the same GAMs (S2 Table) to a version of the dataset excluding all entries for rabies lyssavirus. We rescale these new estimates of spillover virulence between 0 and 1 and compare them again to predictions from our nested modeling approach.

To quantitatively evaluate the extent to which our nested model accurately recaptures estimates of relative spillover virulence (α_S) recovered from the literature, we fit a simple linear regression to the relationship between observed and predicted virulence across the 8 mammalian orders for which we possess comparative data (S6 and S8 Figs and S3 Table). We then determine the sensitivity of our predictions for α_S across reservoir orders to changes in the parameters we estimated from the literature. Because reservoir host natural mortality rate (μ_R) has minimal influence on optimal virus growth rates ()—and because we assume mortality data to be the most likely to be accurately reported in the literature—we focus this sensitivity analysis on the extent to which variation in estimation of reservoir host tolerance of immunopathology (T_wR), reservoir host magnitude of constitutive immunity (g_0R), and spillover host tolerance of reservoir-derived virus pathology (T_vS) impacts the resulting prediction for spillover virulence (α_S) (S9 Fig and S3 Table). To this end, we undertook 2 different analyses: first, we replaced order-specific values of T_wR, g_0R, and T_vS with constant values across all orders and profiled each of these 3 parameters in turn across a range of reasonable values; our aim here was to determine whether perturbation of a single parameter could replicate α_S estimates from the literature. Because this single parameter modulation was largely unsuccessful in recapturing order-specific differences in α_S, we next individually profiled T_wR, g_0R, and T_vS in turn while paired with life history-derived, order-specific values for the other 2 parameters, as presented in the main text (S9 Fig and S3 Table). To quantify the impact of this profiling on the accuracy with which we estimated spillover virulence across orders, we refit linear regressions of observed versus predicted spillover virulence using both parameter profiling approaches (S9 Fig and S3 Table).