Temperature explains broad patterns of Ross River virus transmission
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 . Transmission depends on a suite of vector , pathogen , and human traits , including mosquito density ( M ) . Our main model ( ‘full R0 Model , ’ Equation 1 ) assumes temperature drives mosquito density and includes the relevant life history trait thermal responses ( Parham and Michael , 2009; Mordecai et al . , 2013; Mordecai et al . , 2017 ) . We initially compare this model to an alternative ( ‘constant M model , ’ Equation 2 ) where mosquito density does not depend on temperature . We make this comparison because many transmission models do not include the thermal responses for mosquito density , assuming it depends primarily on habitat availability . Here , we focus on the relative influence of temperature on transmission potential , recognizing that absolute R0 also depends on other factors . Accordingly , we scaled model output between zero and one ( ‘relative R0’ ) . Relative R0 describes thermal suitability for transmission . Combined with factors like breeding habitat availability , vector control , humidity , human and reservoir host density , host immune status , and mosquito exposure , relative R0 can be used to predict disease incidence . In this approach , only the relative thermal response of each trait influences R0 , which is desirable since traits can differ substantially due to other factors and in laboratory versus field settings ( particularly mosquito survival: Clements and Paterson , 1981 ) . Relative R0 does not provide a threshold for sustained disease transmission ( i . e . where absolute R0 = 1 ) , since this threshold is not controlled solely by temperature . Instead , relative R0 preserves the temperature-dependence of R0 to provide three key temperature values: upper and lower thermal limits where transmission is possible ( R0 >0; a conservative threshold where transmission is not excluded by high or low temperatures ) and the temperature that maximizes R0 .
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 ( pLA ) , 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 pLA 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 . 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 ) . 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 ) .
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 .
The ‘full R0 model’ ( Equation 1 ) assumes temperature drives mosquito density and includes vector life history trait thermal responses ( Parham and Michael , 2009; Mordecai et al . , 2013; Mordecai et al . , 2017 ) . The ‘constant M model’ ( Equation 2 ) assumes mosquito density ( M ) does not depend on temperature ( Dietz , 1993 ) . There is disagreement in the literature over whether the equation for R0 should contain the square root ( Dietz , 1993; Heffernan et al . , 2005; Smith et al . , 2012 ) . We use the version derived from the next-generation matrix method ( Dietz , 1993 ) in order to be consistent with our previous work in other mosquito-borne disease systems ( Mordecai et al . , 2013; Mordecai et al . , 2017; Johnson et al . , 2015 ) . R0 ( T ) = ( a ( T ) 2bc ( T ) e− μ ( T ) PDR ( T ) EFD ( T ) pEA ( T ) MDR ( T ) N r μ ( T ) 3 ) 1/2R0 ( T ) = ( a ( T ) 2bc ( T ) e− μ ( T ) PDR ( T ) MN r μ ( T ) ) 1/2 In both equations , ( T ) indicates that a parameter depends on temperature , a is mosquito biting rate , bc is vector competence ( proportion of mosquitoes becoming infectious post-exposure ) , µ is adult mosquito mortality rate ( adult lifespan , lf = 1/µ ) , PDR is parasite development rate ( PDR = 1/EIP , the extrinsic incubation period ) , N is human density , and r is the recovery rate at which humans become immune ( all rates are measured in days−1 ) . The latter two terms do not depend on temperature . In the full R0 model , mosquito density ( M ) depends on fecundity ( EFD , eggs per female per day ) , proportion surviving from egg-to-adulthood ( pEA ) , and mosquito development rate ( MDR ) , divided by the square of adult mortality rate ( µ ) ( Parham and Michael , 2009 ) . We calculated pEA as the product of the proportion of egg rafts that hatch ( pRH ) , the number of larvae per raft ( nLR , scaled by the maximum at any temperature to calculate proportional egg survival within-rafts ) , and the proportion of larvae surviving to adulthood ( pLA ) . We digitized previously published trait data ( Figure 2—figure supplement 1; McDonald et al . , 1980; Mottram et al . , 1986; Russell , 1986; Rae , 1990; Kay and Jennings , 2002 ) using the free web-based tool Webplot Digitizer available at: https://automeris . io/WebPlotDigitizer/ . We fit thermal responses of each trait using Bayesian inference with the ‘r2jags’ package ( Plummer , 2003; Su and Yajima , 2009 ) in R ( R Core Team , 2017 ) . Traits with asymmetrical thermal responses were fit as Brière functions: qT ( T–Tmin ) ( Tmax–T ) 1/2 ( Briere et al . , 1999 ) . Traits with symmetrical thermal responses were fit as quadratic functions: -q ( T–Tmin ) ( T–Tmax ) . In both functions of temperature ( T ) , Tmin and Tmax are the critical thermal minimum and maximum , respectively , and q is a rate parameter . For priors we used gamma distributions with hyperparameters derived from thermal responses fit to data from other mosquito species ( Figure 2—source data 2 ) ( Davis , 1932; Jalil , 1972; McLean et al . , 1974; Watts et al . , 1987; Rueda et al . , 1990; Focks et al . , 1993; Joshi , 1996; Teng and Apperson , 2000; Tun-Lin et al . , 2000; Alto and Juliano , 2001; Briegel and Timmermann , 2001; Kamimura et al . , 2002; Calado and Navarro-Silva , 2002; Focks and Barrera , 2006; Wiwatanaratanabutr and Kittayapong , 2006; Lardeux et al . , 2008; Delatte et al . , 2009; Beserra et al . , 2009; Yang et al . , 2009; Westbrook et al . , 2010; Muturi et al . , 2011; Carrington et al . , 2013; Tjaden et al . , 2013; Eisen et al . , 2014; Xiao et al . , 2014; Ezeakacha , 2015; Morin et al . , 2015 ) . These priors allowed us to more accurately represent the fit and uncertainty . Our data did not include declining trait values at high temperatures for biting rate ( a ) and parasite development rate ( PDR ) . Nonetheless , data from other mosquito species ( Mordecai et al . , 2013; Mordecai et al . , 2017 ) and principles of thermal biology ( Dell et al . , 2011 ) imply these traits must decline at high temperatures . Thus , for those traits we included an artificial data point where the trait value approached zero at a very high temperature ( 40°C ) , allowing us to fit the Brière function . We used strongly informative priors to limit the effect of these traits on the upper thermal limit of R0 ( by constraining them to decline near 40°C ) . Because our approach is designed to identify which traits constrain transmission at thermal limits , this choice is conservative by allowing R0 to be limited by other traits with better data . Accordingly , in the absence of data we favored overestimating Tmax and underestimating Tmin over the alternative . For comparison , we also fit all thermal responses with uniform priors ( Figure 2—figure supplement 1 ) ; these results illustrate how the priors affected the results . Bayesian inference produces estimated posterior distributions rather than a single estimated value . Because these distributions can be non-normal and asymmetric , we report and apply medians rather than means , since medians are less sensitive to outlying values in extended tails . However , we plot mean values in the figures because they show a smoother and more visually intuitive representation of where trait and R0 thermal responses go to zero at the upper thermal limit . The means and medians are not substantially different , except at this thermal limit ( see example in Figure 3—figure supplement 3 ) . We conducted sensitivity and uncertainty analyses of the full R0 model ( Equation 1 ) to understand how trait thermal responses shape the thermal response of R0 . We examined the sensitivity of R0 two ways . First , we evaluated the impact of each trait by setting it constant while allowing all other traits to vary with temperature . Second , we calculated the partial derivative of R0 with respect to each trait across temperature ( ∂R0/∂X · ∂X/∂T for trait X and temperature T; Equations 3-6 ) . To understand what data would most improve the model , we also calculated the proportion of total uncertainty in R0 due to each trait across temperature . First , we propagated posterior samples from all trait thermal response distributions through to R0 ( T ) and calculated the width of the 95% highest posterior density interval ( HPD interval; a type of credible interval ) of this distribution at each temperature: the ‘full R0 ( T ) uncertainty’ . Next , we sampled each trait from its posterior distribution while setting all other trait thermal responses to their posterior medians , and calculated the posterior distribution of R0 ( T ) and the width of its 95% HPD interval across temperature: the ‘single-trait R0 ( T ) uncertainty’ . Finally , we divided each single-trait R0 ( T ) uncertainty by the full R0 ( T ) uncertainty . The partial derivatives are given below for all traits ( x ) that appear only once in the numerator of R0 ( bc , EFD , pRH , nLR , pLA , MDR; Equation 3 ) , biting rate ( a , Equation 4 ) , parasite development rate ( PDR , Equation 5 ) , and lifespan ( lf , Equation 6 ) . ( 3 ) ∂R0∂x= R02x ( 4 ) ∂R0∂a= R0a ( 5 ) ∂R0∂PDR= R02 lf PDR2 ( 6 ) ∂R0∂lf= R0 ( 1+3PDR ) 2 PDR lf2 We took monthly mean temperatures from WorldClim for seven cities spanning a latitudinal and temperature gradient ( from tropical North to temperate South: Darwin , Cairns , Brisbane , Perth , Sydney , Melbourne , and Hobart ) and calculated the posterior median R0 ( T ) for each month at each location . We also compared the seasonality of a population-weighted R0 ( T ) and nationally aggregated RRV cases . We used 2016 estimates for the fifteen most populous urban areas , which together contain 76 . 6% of Australia’s population ( Australian Bureau of Statistics , 2017 ) . We calculated R0 ( T ) for each location ( as above ) and estimated a population-weighted average . We compared this country-scale estimate of R0 ( T ) with data on mean monthly human cases of RRV nationwide from 1992 to 2013 obtained from the National Notifiable Diseases Surveillance System . We expected a time lag between temperature and reported human cases as mosquito populations increase , bite humans and reservoir hosts , acquire RRV , become infectious , and bite subsequent hosts; after an incubation period , hosts ( potentially ) become symptomatic , seek treatment , and report cases . Empirical work on dengue vectors in Ecuador identified a six-week time lag between temperature and mosquito oviposition ( Stewart Ibarra et al . , 2013 ) . Subsequent mosquito development and incubation periods in mosquitoes and humans likely add another 2–4 week lag before cases appear , resulting in an 8–10 week lag between temperature and observed cases ( Hu et al . , 2006; Jacups et al . , 2008b; Mordecai et al . , 2017 ) . With monthly case data , we hypothesize a two-month time lag between R0 ( T ) and RRV disease cases . To illustrate temperature suitability for RRV transmission across Australia , we mapped the number of months for which relative R0 ( T ) >0 and >0 . 5 for the posterior median , 2 . 5 and 97 . 5% credibility bounds ( Figure 5—figure supplement 1 ) for the full R0 model ( Equation 1 ) . We calculated R0 ( T ) at 0 . 2°C increments and projected it onto the landscape for monthly mean temperatures from WorldClim data at a 5 min resolution ( approximately 10 km2 at the equator ) . Climate data layers were extracted for the geographic area , defined using the Global Administrative Boundaries Databases ( GADM , 2012 ) . We performed map calculations and manipulations in R with packages ‘raster’ ( Hijmans , 2016 ) , ‘maptools’ ( Bivand and Lewin-Koh , 2017 ) , and ‘Rgdal’ ( Bivand et al . , 2017 ) , and rendered GeoTiffs in ArcGIS version 10 . 3 . 1 . In 2000 there was a proposed shift in mosquito taxonomy: several subgenera within the genus Aedes were elevated to genus status ( Wilkerson et al . , 2015 ) . This change affected Aedes vigilax and Aedes camptorhynchus , which were called Ochlerotataus vigilax and Ochlerotatus camptorhynchus for a time by some researchers . More recently , there has been a consensus to return to the previous naming system , so we use Aedes here , although many of the papers we cite use Ochlerotatus instead . The fecundity and adult survival data in McDonald et al . ( 1980 ) were published as time series of one experimental population at each temperature . The resulting data needed to be transformed to fit the corresponding trait thermal responses . For survival , McDonald et al . reported the percent surviving approximately every other day ( hereafter: ‘semi-daily’ ) . We used these data—along with the number of female adults alive on the first day of oviposition at each temperature—to generate a semi-daily time series estimating the number surviving . To generate the dataset that we used to directly fit the thermal responses , we converted this time series into the number of female individuals who died on each day ( i . e . lifespan data ) . For fecundity , McDonald et al . reported semi-daily fecundity data for entire population . Because the population was synchronized , and because mosquitoes lay discrete clutches of eggs separated by several days ( the gonotrophic cycle duration ) , there were many data points when the populations did not produce offspring . These zero-inflated fecundity data are not ideal for fitting thermal responses . Therefore , after digitizing the semi-daily fecundity time series , we binned periods of several days ( the bin size varied by temperature , since the gonotrophic cycle duration varies with temperature ) and took a survival-weighted average within each bin ( so days with more individual mothers contributing to offspring production counted more ) . To generate the dataset that we used to directly fit the thermal responses , we weighted the values within each bin by the mean number of surviving mothers in that bin . This approach allowed us to more accurately reflect daily fecundity averaged over a non-synchronized mosquito population . Note that the variation captured by these data and this approach is not variation between individual adult females , but rather variation by age for the whole population .
Thermal biology predicts that vector-borne disease transmission peaks at intermediate temperatures and declines at high and low temperatures . However , thermal optima and limits remain unknown for most vector-borne pathogens . We built a mechanistic model for the thermal response of Ross River virus , an important mosquito-borne pathogen in Australia , Pacific Islands , and potentially at risk of emerging worldwide . Transmission peaks at moderate temperatures ( 26 . 4°C ) and declines to zero at thermal limits ( 17 . 0 and 31 . 5°C ) . The model accurately predicts that transmission is year-round endemic in the tropics but seasonal in temperate areas , resulting in the nationwide seasonal peak in human cases . Climate warming will likely increase transmission in temperate areas ( where most Australians live ) but decrease transmission in tropical areas where mean temperatures are already near the thermal optimum . These results illustrate the importance of nonlinear models for inferring the role of temperature in disease dynamics and predicting responses to climate change .
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 .