Mosquitoes cannot control their body temperature, so their survival and performance depend on the temperature where they live. As a result, outside temperatures can also affect the spread of diseases transmitted by mosquitoes. This has left scientists wondering how climate change may affect the spread of mosquito-borne diseases. Predicting the effects of climate change on such diseases is tricky, because many interacting factors, including temperatures and rainfall, affect mosquito populations. Also, rising temperatures do not always have a positive effect on mosquitoes – they may help mosquitoes initially, but it can get too warm even for these animals.

Climate change could affect the Ross River virus, the most common mosquito-borne disease in Australia. The virus infects 2,000 to 9,000 people each year and can cause long-term joint pain and disability. Currently, the virus spreads year-round in tropical, northern Australia and seasonally in temperate, southern Australia. Large outbreaks have occurred outside of Australia, and scientists are worried it could spread worldwide.

Now, Shocket et al. have built a model that predicts how the spread of Ross River virus changes with temperature. Shocket et al. used data from laboratory experiments that measured mosquito and virus performance across a broad range of temperatures. The experiments showed that ~26°C (80°F) is the optimal temperature for mosquitoes to spread the Ross River virus. Temperatures below 17°C (63°F) and above 32°C (89°F) hamper the spread of the virus. These temperature ranges match the current disease patterns in Australia where human cases peak in March. This is two months after the country’s average temperature reaches the optimal level and about how long it takes mosquito populations to grow, infect people, and for symptoms to develop.

Because northern Australia is already near the optimal temperature for mosquitos to spread the Ross River virus, any climate warming should decrease transmission there. But warming temperatures could increase the disease’s transmission in the southern part of the country, where most people live. The model Shocket et al. created may help the Australian government and mosquito control agencies better plan for the future.

Temperature impacts the transmission of mosquito-borne diseases via effects on the physiology of mosquitoes and pathogens. Transmission requires that mosquitoes be abundant, bite a host and ingest an infectious bloodmeal, survive long enough for pathogen development and within-host migration (the extrinsic incubation period), and bite additional hosts—all processes that depend on temperature (Mordecai et al., 2013, Mordecai et al., 2017). Although both mechanistic (Mordecai et al., 2013, Mordecai et al., 2017; Liu-Helmersson et al., 2014; Wesolowski et al., 2015; Paull et al., 2017) and statistical models (Perkins et al., 2015; Siraj et al., 2015; Paull et al., 2017; Peña-García et al., 2017) support the impact of temperature on mosquito-borne disease, important knowledge gaps remain. First, how the impact of temperature on transmission differs across diseases, via what mechanisms, and the types of data needed to characterize these differences all remain uncertain. Second, the impacts of temperature on transmission can appear idiosyncratic—varying in both magnitude and direction—across locations and studies (Gatton et al., 2005; Jacups et al., 2008a; Stewart-Ibarra and Lowe, 2013; Peña-García et al., 2017; Koolhof et al., 2017). Although inferring causality from field observations and statistical approaches alone remains challenging, nonlinear thermal biology may mechanistically explain this variation. As the climate changes, filling these gaps becomes increasingly important for predicting geographic, seasonal, and interannual variation in transmission of mosquito-borne pathogens. Here, we address these gaps by building a model for temperature-dependent transmission of Ross River virus (RRV), the most important mosquito-borne disease in Australia (1500–9500 human cases per year) (Koolhof et al., 2017), and potentially at risk of emerging worldwide (Flies et al., 2018).

RRV in Australia is an ideal case study for examining the influence of temperature. Transmission occurs across a wide latitudinal gradient, where climate varies substantially both geographically and seasonally. Moreover, compared to vector-borne diseases in lower-income settings, RRV case diagnosis and reporting are more accurate and consistent, and variation in socioeconomic conditions (and therefore housing and vector control efforts) at regional and continental scales is relatively low. Previous work has shown that in some settings temperature predicts RRV cases (Gatton et al., 2005; Bi et al., 2009; Werner et al., 2012; Koolhof et al., 2017), while in others it does not (Hu et al., 2004; Gatton et al., 2005). Understanding RRV transmission ecology is critical because the virus is a candidate for emergence worldwide (Flies et al., 2018), and has caused explosive epidemics where it has emerged in the past (infecting over 500,000 people in a 1979–80 epidemic in Fiji) (Klapsing et al., 2005). RRV is a significant public health burden because infection causes joint pain that can become chronic and cause disability (Harley et al., 2001; Koolhof et al., 2017). A mechanistic model for temperature-dependent transmission could help explain these disparate results and predict potential expansion.

Mechanistic models synthesize how environmental factors like temperature influence host and parasite traits that drive transmission. Thermal responses of ectotherm traits are usually unimodal: they peak at intermediate temperatures and decline towards zero at lower and upper thermal limits, all of which vary across traits (Dell et al., 2011; Mordecai et al., 2013; Mordecai et al., 2017). Mechanistic models are particularly useful for synthesizing the effects of multiple, nonlinear thermal responses that shape transmission (Rogers and Randolph, 2006; Mordecai et al., 2013). One commonly used measure of disease spread is R₀, the basic reproductive number, defined as the number of secondary cases expected from a single case in a fully susceptible population. Relative R₀— R₀ scaled between 0 and 1—is a modified metric that captures the thermal response of transmission without making assumptions about other factors that affect the absolute value of R₀ (Mordecai et al., 2013, Mordecai et al., 2017). For mosquito-borne disease, R₀ is a nonlinear function of mosquito density, biting rate, vector competence (infectiousness given pathogen exposure), and adult survival; pathogen extrinsic incubation period; and human recovery rate (Dietz, 1993). To understand how multiple traits that respond nonlinearly to temperature combine to affect transmission, we incorporate empirically-estimated trait thermal responses into a model of relative R₀. Synthesizing the full suite of nonlinear trait responses is critical because such models often make predictions that are drastically different, with transmission optima up to 7°C lower, than models that assume linear or monotonic thermal responses or omit temperature-dependent processes (Mordecai et al., 2013, Mordecai et al., 2017). Previous mechanistic models that incorporated multiple nonlinear trait thermal responses have predicted different optimal temperatures across pathogens and vector species: 25°C for falciparum malaria in Anopheles vectors (Mordecai et al., 2013) and West Nile virus in Culex vectors (Paull et al., 2017), and 29 and 26°C for dengue, chikungunya, and Zika viruses (in Aedes aegypti and Ae. albopictus, respectively) (Liu-Helmersson et al., 2014; Wesolowski et al., 2015; Mordecai et al., 2017).

Here, we build the first mechanistic model for temperature-dependent transmission of RRV and ask whether temperature explains seasonal and geographic patterns of disease. We use data from laboratory experiments with two important vector species (Culex annulirostris and Aedes vigilax) to parameterize the model with unimodal thermal responses. We then use sensitivity and uncertainty analyses to determine which traits drive the relationship between temperature and transmission potential and identify key data gaps. Finally, we illustrate how temperature currently shapes patterns of disease transmission across Australia. The model correctly predicts that RRV disease is year-round endemic in tropical, northern Australia with little seasonal variation due to temperature, and seasonally epidemic in temperate, southern Australia. These results provide a mechanistic explanation for idiosyncrasies in RRV temperature responses observed in previous studies (Hu et al., 2004; Gatton et al., 2005; Bi et al., 2009; Werner et al., 2012; Koolhof et al., 2017). A population-weighted version of the model (assuming a two-month lag between temperature and human cases based on mosquito and disease development times) also accurately predicts the seasonality of human cases nationally. Thus, from laboratory data on mosquito and parasite thermal responses alone, this simple model mechanistically explains broad geographic and seasonal patterns of disease.

Natural history of RRV

The natural history of RRV is complex: transmission occurs across a range of climates (tropical, subtropical, and temperate) and habitats (urban and rural, coastal and inland) and via many vertebrate reservoir and vector species (Claflin and Webb, 2015). Marsupials are generally considered the critical reservoirs for maintaining the virus between human outbreaks, but recent work has argued that placental mammals and birds may be equally important in many locations (Stephenson et al., 2018). The virus has been isolated from over 40 mosquito species in nature, and 10 species transmit it in laboratory studies (Harley et al., 2001; Russell, 2002). However, four species are responsible for most transmission to humans (Culex annulirostris, Aedes [Ochlerotatus] vigilax, Ae. [O.] notoscriptus, and Ae. [O.] camptorhynchus), with two additional species implicated in outbreaks (Ae. [Stegomyia] polynesiensis and Ae. [O.] normanensis).

The vectors differ in climate and habitat niches, leading to geographic variation in associations with outbreaks. We assembled and mapped records of RRV outbreaks in humans attributed to different vector species (Figure 1, Figure 1—source data 1) (Rosen et al., 1981; Campbell et al., 1989; Russell et al., 1991; Yang et al., 2009; Lindsay et al., 1993b; Lindsay et al., 1993a; Lindsay et al., 1996; Lindsay et al., 2007; McManus et al., 1992; Merianos et al., 1992; Whelan et al., 1992; Whelan et al., 1995, Whelan et al., 1997; McDonnell et al., 1994; Russell, 1994; Russell, 2002; Dhileepan, 1996; Ritchie et al., 1997; Brokenshire et al., 2000; Ryan et al., 2000; Harley et al., 2000; Harley et al., 2001; Kelly-Hope et al., 2004a; Frances et al., 2004; Biggs and Mottram, 2008; Jacups et al., 2008b; Schmaedick et al., 2008; Lau et al., 2017). Ae. vigilax and Ae. notoscriptus were more commonly implicated in transmission in tropical and subtropical zones, Ae. camptorhynchus in temperate zones, and Cx. annulirostris throughout all climatic zones. Freshwater-breeding Cx. annulirostris has been implicated in transmission across both inland and coastal areas, while saltmarsh mosquitoes Ae. vigilax and Ae. camptorhynchus have been implicated only in coastal areas (Russell, 2002) and inland areas affected by salinization from agriculture (Biggs and Mottram, 2008; Carver et al., 2009). Peri-domestic, container-breeding Ae. notoscriptus has been implicated in urban epidemics (Russell, 2002). The vectors also differ in their seasonality: Ae. camptorhynchus populations peak earlier and in cooler temperatures than Ae. vigilax, leading to seasonal succession where they overlap (Yang et al., 2009; Russell, 1998). This latitudinal and temporal variation suggests that vector species may have different thermal optima and/or niche breadths. If so, temperature may impact disease transmission differently for each species.

Figure 1

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Figure 1—source data 1

Vector species implicated in RRV disease outbreaks.

Location and year of RRV disease outbreaks and mosquito species identified as likely vectors based on the collection of field specimens. Only the six most important mosquito species are included. Citation key: A: Biggs and Mottram, 2008; B: Brokenshire et al., 2000; C: Campbell et al., 1989; D: Dhileepan, 1996; E: Frances et al., 2004; F: Harley et al., 2000; G: Harley et al., 2001; H: Jacups et al., 2008b; I: Kelly-Hope et al., 2004b; J: Lau et al., 2017; K: Yang et al., 2009; L: Lindsay et al., 1993b; M: Lindsay et al., 1993a; N: Lindsay et al., 1996; O: Lindsay et al., 2007; P: McDonnell et al., 1994; Q: McManus et al., 1992; R: Merianos et al., 1992; S: Ritchie et al., 1997; T: Rosen et al., 1981; U: Russell et al., 1991; V: Russell, 1994; W: Russell, 2002; X: Ryan et al., 2000; Y: Schmaedick et al., 2008; Z: Whelan et al., 1992; AA: Whelan et al., 1995; AB: Whelan et al., 1997.

https://doi.org/10.7554/eLife.37762.004

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Figure 2—source data 1

Trait thermal response functions and data sources for Ross River virus R₀ models (Equations 1 and 2).

‘Par.’=model parameter. Results are given for fits from data-informed priors. Asymmetrical responses fit with Brière function (B): B(T)= qT(T – T_min)(T_max – T)^1/2; symmetrical responses fit with quadratic function (Q): Q(T) = -q(T – T_min)(T – T_max). Function coefficients (and 95% credible intervals) fit via Bayesian inference.

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Figure 2—source data 2

Trait thermal response functions and data sources used to parameterize priors for data-informed trait thermal responses.

‘Par.’=model parameter. Fits were made with uniform priors. Asymmetrical responses fit with Brière function (B): B(T)= qT(T – T_min)(T_max – T)^1/2; symmetrical responses fit with quadratic function (Q): Q(T) = -q(T – T_min)(T – T_max). Function coefficients (and 95% credible intervals) fit via Bayesian inference.

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Vector and pathogen traits that drive transmission consistently responded to temperature (Figure 2), though data were sparse (McDonald et al., 1980; Mottram et al., 1986; Russell, 1986; Rae, 1990; Kay and Jennings, 2002). Although we exhaustively searched for experiments with trait measurements at three or more constant temperatures in the Australian vector species (Cx. annulirostris, Ae. vigilax, Ae. camptorhynchus, Ae. notoscriptus, and Ae. normanensis), no species had data for all necessary traits (Figure 1). Thus, we combined traits from two species to build composite R₀ models. We used mosquito life history traits measured in Cx. annulirostris: fecundity (as eggs per female per day, EFD), egg survival (as the proportion of rafts that hatch, pRH, and the number of larvae emerging per viable raft, nLR), the proportion surviving from larvae-to-adulthood (p_LA), mosquito development rate (MDR), adult mosquito lifespan (lf), and biting rate (a). We used infection traits measured in Ae. vigilax: vector competence (bc) and parasite development rate (PDR). For comparison, we also fit traits for other mosquito and virus species: MDR and p_LA from Ae. camptorhynchus and Ae. notoscriptus, and PDR and bc from Murray Valley encephalitis virus (another important pathogen transmitted by these mosquitoes in Australia) in Cx. annulirostris (Figure 2—figure supplements 2, 3 and 4) (Kay et al., 1989; Barton and Aberton, 2005; Williams and Rau, 2011). We used sensitivity analyses to evaluate the potential impact of this vector mismatch. However, all spatial and temporal predictions of R₀ (Figures 5–7) use the full R₀ model parameterized with mosquito life history traits from Cx. annulirostris and infection traits from Ae. vigilax (as shown in Figure 2).

Thermal optima ranged from 23.4°C for adult lifespan (lf) to 33.0°C for parasite development rate (PDR; Figure 2). The data supported unimodal thermal responses for most traits, though declines at high temperatures were not directly observed for biting rate (a) and parasite development rate. Data from other mosquito species and ectotherm physiology theory imply these traits must decline at very high temperatures, so we used strong priors to make them decline near ~40°C. Because our approach is designed to identify which traits constrain transmission at thermal limits, this choice is conservative since it means R₀ will be limited by other traits with better data. Accordingly, in the absence of data we preferred to overestimate upper thermal limits and underestimate lower thermal limits rather than vice versa.

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Transmission potential (relative R₀ from the full R₀ model) peaked at 26.4°C, and was positive from 17.0–31.5°C (Figure 3). Removing the temperature-dependence of mosquito density [M] did not substantially affect the peak, because the optima for transmission and mosquito density were closely aligned (constant M model: 26.6°C, M: 26.2°C). By contrast, the range of temperatures suitable for transmission is much larger when mosquito density does not depend on temperature because M(T) constrains transmission at the thermal limits (constant M model positive from 12.9–33.7°C). The thermal constraints that mosquito density imposes on transmission are important because, although demographic traits are well-known to vary with temperature in the laboratory, many temperature-dependent transmission models do not assume that temperature influences mosquito density (Martens et al., 1997; Craig et al., 1999; Paull et al., 2017; Caminade et al., 2017; Hamlet et al., 2018, but see Parham and Michael, 2009; Mordecai et al., 2013, Mordecai et al., 2017; Johnson et al., 2015). The moderate optimal temperature for RRV (26–27°C) fits within the range of thermal optima found for other diseases: malaria transmission by Anopheles spp. at 25°C, and dengue and other viruses by Ae. aegypti and Ae. albopictus at 29 and 26°C, respectively (Figure 4) (Mordecai et al., 2013; Mordecai et al., 2017).

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At the upper thermal limit fecundity (EFD) and adult lifespan (lf) constrain R₀, while at the lower thermal limit fecundity, larval survival (pLA), egg survival (raft viability [pRH] and survival within rafts [nLR]), and adult lifespan constrain R₀ (Figure 3—figure supplement 2). All of these traits (except adult lifespan) only occur in, and adult lifespan is quantitatively more important in, the full R₀ model, illustrating the importance of incorporating effects of temperature on vector life history. Correspondingly, uncertainty in these traits generated the most uncertainty in R₀ at the respective thermal limits (Figure 3—figure supplement 2C). The optimal temperature for R₀ was most sensitive to the thermal response of adult lifespan. Near the optimum, most uncertainty in R₀ was due to uncertainty in the thermal responses of biting rate and egg raft viability. For comparison, substituting larval traits from alternative vectors or infection traits for Murray Valley Encephalitis virus did not substantially alter the R₀ thermal response, since Cx. annulirostris life history traits strongly constrained transmission (Figure 3—figure supplement 1).

Temperature suitability for RRV transmission varies seasonally across Australia, based on the full R₀ model (Equation 1) using monthly mean temperatures from WorldClim. In subtropical and temperate locations (Brisbane and further south), low temperatures force R₀ to zero for part of the year (Figures 5A and 6). Monthly mean temperatures in these areas fall along the increasing portion of the R₀ curve for the entire year, so thermal suitability for transmission increases with temperature. By contrast, in tropical, northern Australia (Darwin and Cairns), the temperature remains suitable throughout the year (Figures 5 and 6). Darwin is the only major city where mean temperatures exceed the thermal optimum, and thereby depress transmission. Because most Australians live in southern, temperate areas, country-scale transmission is strongly seasonal. Using the average (1992–2013) seasonal incidence at the national scale, human cases peak two months after population-weighted R₀(T), matching our a priori hypothesized time lag between temperature suitability and human cases (based on empirical work in other mosquito-borne disease systems, see Materials and methods and Discussion; Figure 7).

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Figure 6

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Figure 7

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As the climate warms, it is critical to understand effects of temperature on transmission of mosquito-borne disease, particularly as new mosquito-borne pathogens emerge and spread worldwide. Identifying transmission optima and limits by characterizing nonlinear thermal responses, rather than simply assuming that transmission increases with temperature, can more accurately predict geographic, seasonal, and interannual variation in disease. Thermal responses vary substantially among diseases and vector species (Mordecai et al., 2013; Mordecai et al., 2017; Tesla et al., in press), yet we lack mechanistic models based on empirical, unimodal thermal responses for many diseases and vectors. Here, we parameterized a temperature-dependent model for transmission of RRV (Figure 2) with data from two important vector species (Cx. annulirostris and Ae. vigilax; Figure 1). The optimal temperature for transmission is moderate (26–27°C; Figure 3), and largely determined by the thermal response of adult mosquito lifespan (Figure 3—figure supplement 2). Both low and high temperatures limit transmission due to low mosquito fecundity and survival at all life stages—thermal responses that are often ignored in transmission models (Figure 3—figure supplement 2). Temperature explains the geography of year-round endemic versus seasonally epidemic disease (Figures 5 and 6) and accurately predicts the seasonality of human cases at the national scale (Figure 7). Thus, the model for RRV transmission provides a mechanistic link between geographic and seasonal variation in temperature and broad-scale patterns of disease.

While the thermal response of RRV transmission generally matched those of other mosquito-borne pathogens, there were some key differences. The moderate optimal temperature for RRV (26–27°C) fit within the range of thermal optima found for other diseases using the same methods: malaria transmission by Anopheles spp. at 25°C, and dengue and other viruses by Ae. aegypti and Ae. albopictus at 29 and 26°C, respectively (Figure 4) (Mordecai et al., 2013; Mordecai et al., 2017). For all of these diseases, the specific optimal temperature was largely determined by the thermal response of adult lifespan (Mordecai et al., 2013,;Mordecai et al., 2017; Johnson et al., 2015). However, the traits that set the thermal limits for RRV transmission differed from other systems. The lower thermal limit for RRV was constrained by fecundity and survival at all stages, while the upper thermal limit was constrained by fecundity and adult lifespan. By contrast, thermal limits for malaria transmission were set by parasite development rate at cool temperatures and egg-to-adulthood survival at high temperatures (Mordecai et al., 2013). As with previous models, the upper and lower thermal limits of RRV transmission are more uncertain than the optimum (Figure 3) (Johnson et al., 2015; Mordecai et al., 2017), because trait responses are harder to measure near their thermal limits where survival is low and development is slow or incomplete. Overall, our results support a general pattern of intermediate thermal optima for transmission where the well-resolved optimal temperature is driven by adult mosquito lifespan, but upper and lower thermal limits are more uncertain and may be determined by unique traits for different vector–pathogen systems. Additionally, upper thermal limits of mosquito-borne disease transmission (a major concern for climate change) are primarily determined by vector life history traits with symmetrical thermal performance curves (like fecundity and survival at various life stages) rather than rate-based traits with asymmetrical thermal performance curves (like biting rate or pathogen development rate).

The trait thermal response data were limited in two keys ways. First, two traits (fecundity and adult lifespan) had data from only three temperatures. We used priors derived from data from other mosquito species to minimize over-fitting and better represent the true uncertainty (Figure 2, versus uniform priors in Figure 2—figure supplement 1). However, data from more temperatures would increase our confidence in the fitted thermal responses. Second, no vector species had data for all traits (Figure 1), so we combined mosquito traits from Cx. annulirostris and pathogen infection traits in Ae. vigilax to build composite relative R₀ models. Geographic and seasonal variation in vector populations suggests that Ae. camptorhynchus and Ae. vigilax have different thermal niches (cooler and warmer, respectively) and Cx. annulirostris has a broader thermal niche (Figure 1) (Russell, 1998). We need temperature-dependent trait data for more species to test the hypothesis that these niche differences reflect the species’ thermal responses. If true, the current model, parameterized primarily with Cx. annulirostris trait responses, may not accurately predict the thermal responses of transmission by Ae. camptorhynchus and Ae. vigilax. Hypothesized species differences in thermal niche could explain why RRV persists over a wide climatic and latitudinal gradient. Thus, thermal response experiments with other RRV vectors are a critical area for future research.

The temperature-dependent R₀ model provides a mechanistic explanation for independently-observed patterns of RRV transmission across Australia. As predicted by the model (Figures 5 and 6), RRV is endemic in tropical Australia, with little seasonal variation in transmission potential due to temperature, and seasonally epidemic in subtropical and temperate Australia (Weinstein, 1997). The model also accurately predicts disease seasonality at the national scale (Figure 7), reproducing the a priori predicted lag (8–10 weeks, or 2 months) for temperature to affect reported human cases (Hu et al., 2006; Jacups et al., 2008b; Stewart Ibarra et al., 2013; Mordecai et al., 2017). This lag between temperature and reported human cases arises from the time it takes for mosquito populations to increase, bite humans and reservoir hosts, acquire RRV, become infectious, and bite subsequent hosts; for pathogens to incubate with vectors; for humans to potentially develop symptoms, seek treatment, and report cases. Further, RRV transmission by Cx. annulirostris in inland areas often moves south as temperatures increase from spring into summer (Russell, 1998), matching the model prediction (Figure 6). Although temperature is often invoked as a potential driver for these types of patterns, it is difficult to establish causality from statistical inference alone, particularly if temperature and disease both exhibit strong seasonality and could both be responding to another latent driver. Thus, the mechanistic model is a critical piece of evidence linking temperature to patterns of disease.

In addition to explaining broad-scale patterns, the unimodal thermal model explains previously contradictory local-scale results. Specifically, statistical evidence for temperature impacts on local time series of cases is mixed. RRV incidence is often—but not always—positively associated with warmer temperatures (Tong and Hu, 2001; Tong et al., 2002a; Tong et al., 2004; Hu et al., 2004; Hu et al., 2010; Jacups et al., 2008b, Williams et al., 2009; Werner et al., 2012; Koolhof et al., 2017). However, variation in the effects of temperature on transmission across space and time is expected from an intermediate thermal optimum, especially when observed temperatures are near or varying around the optimum. The strongest statistical signal of temperature on disease is expected in temperate regions where mean temperature varies along the rapidly rising portion of the R₀ curve (~20–25°C). If mean temperatures vary both above and below the optimum (as in Darwin), important effects of temperature may be masked in time series models that fit linear responses. Additionally, if temperatures are always relatively suitable (as in tropical climates) or unsuitable (as in very cool temperate climates), variation in disease may be due primarily to other factors. A nonlinear mechanistic model is critical for estimating temperature impacts on transmission because the effect of increasing temperature by a few degrees can have a positive, negligible, or negative impact on R₀ along different parts of the thermal response curve. Although field-based evidence for unimodal thermal responses in vector-borne disease is rare (but see Mordecai et al., 2013; Perkins et al., 2015; Peña-García et al., 2017), there is some evidence for high temperatures constraining RRV transmission and vector populations: outbreaks were less likely with more days above 35°C in part of Queensland (Gatton et al., 2005) and populations of Cx. annulirostris peaked at 25°C and declined above 32°C in Victoria (Dhileepan, 1996). Future statistical analyses of RRV cases may benefit from using a nonlinear function for temperature-dependent R₀ as a predictor instead of raw temperature (Figure 6B versus Figure 6A).

Breeding habitat availability also drives mosquito abundance and mosquito-borne disease. Local rainfall or river flow have been linked to the abundance of RRV vector species (Barton et al., 2004; Tall et al., 2014; Jacups et al., 2015) and RRV disease cases (Tong and Hu, 2001; Tong et al., 2002a; Hu et al., 2004; Kelly-Hope et al., 2004b; Tong et al., 2004; Gatton et al., 2005; Jacups et al., 2008b; Bi et al., 2009; Williams et al., 2009; Werner et al., 2012), as have high tides in coastal areas with saltmarsh mosquitoes, Ae. vigilax and Ae. camptorhynchus (Tong and Hu, 2002b; Tong et al., 2004; Jacups et al., 2008b; Kokkinn et al., 2009). Overlaying models of species-specific breeding habitat with temperature-dependent models will better resolve the geographic and seasonal distribution of RRV transmission. Relative R₀ peaked at similar temperatures whether or not we assumed mosquito abundance was temperature-dependent (Equation 1 versus Equation 2); however, the range of suitable temperatures was much wider for the model that assumed a temperature-independent mosquito population (Figure 3). Since breeding habitat can only impact vector populations when temperatures do not exclude them, it is critical to consider thermal constraints on mosquito abundance, even when breeding habitat is considered a stronger driver. Nonetheless, many mechanistic, temperature-dependent models of vector-borne disease transmission do not include thermal effects on vector density (Martens et al., 1997; Craig et al., 1999; Paull et al., 2017; Caminade et al., 2017; Hamlet et al., 2018). Our results demonstrate that the decision to exclude these relationships can have a critical impact on model results, especially near thermal limits.

Several important gaps remain in our understanding of RRV thermal ecology, in addition to the need for trait thermal response data for more vector species. First, the relative R₀ model needs to be more rigorously validated using time series of cases to determine the importance of temperature at finer spatiotemporal scales. These analyses should incorporate daily, seasonal, and spatial temperature variation, including aquatic larval habitat and adult microhabitat temperatures (Paaijmans et al., 2010; Cator et al., 2013; Carrington et al., 2013; Thomas et al., 2018). They should also integrate species-specific drivers of breeding habitat availability, like rainfall and tidal patterns, infrastructure (e.g. drainage), and human activities (e.g. deliberate and accidental water storage). Second, translating environmental suitability for transmission into human cases also depends on disease dynamics in reservoir host populations and their impact on immunity. For instance, in Western Australia heavy summer rains can fail to initiate epidemics when low rainfall in the preceding winter depresses recruitment of susceptible juvenile kangaroos (Mackenzie et al., 2000). By contrast, large outbreaks occur in southeastern Australia when high rainfall follows a dry year, presumably from higher transmission within relatively unexposed reservoir populations (Woodruff et al., 2002). Third, as the climate changes, long-term predictions should consider potential thermal adaption of vectors, since transmission at upper thermal limits is currently limited by vector life history traits. To date, we know very little about standing genetic variation for thermal performance or existing local thermal adaptation in vectors for any disease system. Building vector species-specific R₀ models and integrating thermal ecology with other drivers are important next steps for forecasting variation in RRV transmission. These more advanced models are necessary to translate our relative R₀ results into predictions of absolute R₀ (i.e. estimating the secondary cases per primary case, and where and when R₀ >1 for sustained transmission).

Nonlinear thermal responses are particularly important for predicting how transmission will change under future climate regimes. Climate warming will likely increase the geographic and seasonal range of transmission potential in temperate, southern Australia where most Australians live. However, climate change will likely decrease transmission potential in tropical areas like Darwin, where moderate warming (~3°C) would push temperatures above the upper thermal limit for transmission for most of the year (Figure 5). However, the extent of climate-driven declines in transmission will depend on how much Cx. annulirostris and Ae. vigilax can adapt to extend their upper thermal limits and whether warmer-adapted vector species (e.g. Ae. aegypti and potentially Ae. polynesiensis) can invade and sustain RRV transmission cycles. Thus, we can predict the response of RRV transmission by current vector species to climate change based on these trait thermal responses. However, future disease dynamics will also depend on vector adaptation, potential vector species invasions, and climate change impacts on sea level and precipitation that drive vector habitat availability.

All data and R code used for analyses in this study are included in the supporting files and also available via Dryad (http://dx.doi.org/10.5061/dryad.m0603gk).

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Author details

1. Marta Strecker Shocket

   Department of Biology, Stanford University, Stanford, United States

   Contribution

   Data curation, Formal analysis, Investigation, Visualization, Methodology, Writing—original draft, Writing—review and editing

   For correspondence

   mshocket@stanford.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-8995-4446

2. Sadie J Ryan

   1. Department of Geography, University of Florida, Gainesville, United States
   2. Emerging Pathogens Institute, University of Florida, Gainesville, United States
   3. School of Life Sciences, College of Agriculture, Engineering, and Science, University of KwaZulu Natal, KwaZulu Natal, South Africa

   Contribution

   Data curation, Formal analysis, Investigation, Visualization, Writing—review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-4308-6321

3. Erin A Mordecai

   Department of Biology, Stanford University, Stanford, United States

   Contribution

   Conceptualization, Resources, Supervision, Funding acquisition, Methodology, Project administration, Writing—review and editing

   Competing interests

   No competing interests declared

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