Models predicting disease transmission are vital tools for long-term planning of malaria reduction efforts, particularly for mitigating impacts of climate change. We compared temperature-dependent malaria transmission models when mosquito life history traits were estimated from a truncated portion of the lifespan (a common practice) to traits measured across the full lifespan. We conducted an experiment on adult female Anopheles stephensi, the Asian urban malaria mosquito, to generate daily per capita values for mortality, egg production, and biting rate at six constant temperatures. Both temperature and age significantly affected trait values. Further, we found quantitative and qualitative differences between temperature-trait relationships estimated from truncated data versus observed lifetime values. Incorporating these temperature-trait relationships into an expression governing the thermal suitability of transmission, relative R₀(T), resulted in minor differences in the breadth of suitable temperatures for Plasmodium falciparum transmission between the two models constructed from only An. stephensi trait data. However, we found a substantial increase in thermal niche breadth compared to a previously published model consisting of trait data from multiple Anopheles mosquito species. Overall, this work highlights the importance of considering how mosquito trait values vary with mosquito age and mosquito species when generating temperature-based suitability predictions of transmission.

Life history experiment

We ran a life history experiment on the urban type form Anopheles stephensi, which was initiated three days after adult emergence to permit mating. After they were presented with an initial blood meal for 15 minutes via a water-jacketed membrane feeder, we randomly distributed 30 host-seeking females into individual cages (16 oz. paper cup; mesh top) to one of six constant temperature treatments (16°C, 20°C, 24°C, 28°C, 32°C, 36°C ± 0.5°C, 80% ± 5 RH, and 12L:12D photoperiod). Each individual adult cage contained an oviposition site: a petri dish secured to the bottom of the housing containing cotton balls to retain liquid, overlaid with filter paper for egg removal and counting. Individual mosquitoes were offered a blood meal for 15 min each day. Blood meals were scored through visual verification of the abdomen immediately after the feeding period. Oviposition sites were rehydrated and checked for the presence of eggs daily. We followed populations of individual females in each temperature treatment until all mosquitoes had died or when less than 7% of the starting population remained. At least two biological replicates were performed at each temperature (N= 390).

Statistical analyses

We used generalized linear mixed models (GLMM) R package <lme4::glmer() (29) > to estimate the effects of temperature, mosquito age, and their interaction on the proportion of females that imbibed blood on a given day (i.e., the number of females that took a blood meal on a given day out of the total number of females alive on that day for each temperature treatment) and the mean daily egg production (i.e., the number of eggs laid on a given day divided by the total number of females alive on that day in a given temperature treatment). We used a Log-rank test with R package <survival::survdiff() (30)> on Kaplan-Meier estimates to determine if survivorship differed with temperature. Lastly, to determine if the daily survival rate changed across the lifespan of the mosquito, we fit a variety of survival distributions, which allow either for a constant (exponential) or variable daily mortality rate (log-normal, gamma, Gompertz, and Weibull) with R package <flexsurv (31)> to the Kaplan-Meier estimates.

Fitting thermal responses in a Bayesian framework

To predict the thermal limits (T_min, T_max) and optimum (T_opt) for each parameter, we used Bayesian inference to fit either a symmetric (quadratic; -c(T-T_min)(T-T_max)) or an asymmetric (Briere; cT(T-T_min)(T_max-T)^1/2) unimodal non-linear function to each trait versus temperature (T, in degrees Celsius) as in Johnson et al. 2015 (10). Note the parameter c is a fit parameter that controls the shape of each respective function. These functions were further restricted to be non-negative. That is, all traits are assumed to be zero if T < T_min or T > T_max). We assumed that data are distributed as truncated normal distributions with the means for each block and temperature described by either the quadratic or Briere function as above. We selected the best-fitting functional form for the mean between quadratic or Briere using the Deviance Information Criterion (DIC). We chose to fit thermal responses to the data means across individuals for each replicate as opposed to the raw individual data due to 1) the data exhibiting extreme non-normality for some traits (e.g., lifetime egg production, estimated daily eggs, and lifespan) and thus 2) to ensure compliance with the central limit theorem (CLT) when fitting truncated normal distributions. Developing methodology to account for the non-normal distributions associated with observing individual level data is a key research gap to refine predictions of thermal suitability of transmission events and is an area of future work.

For each parameter in the mean function (i.e., c, T_min, T_max) and the variance of the truncated normal distribution, we assumed relatively uninformative uniform priors that restrict the range of parameters to biologically meaningful values.  More specifically, we first fit curves with uninformative priors restricted to biologically informed ranges (T₀ ~ uniform (0, 24), T_m ~ uniform (25, 45), c ~ uniform (0, 1)) , followed by informative priors derived from traits estimated in a previous study (assuming a gamma distribution over each component trait). A direct comparison of each temperature-trait response using either uninformative or informative priors is provided to illustrate the influence of informative priors on our trait fits presented in the main text. No fit with informative priors was conducted for lifetime egg production (B) as Johnson et al. 2015 did not fit this trait and thus appropriate priors did not exist. Further, we choose to use the fit using uninformative priors for estimated daily eggs (EFD*) as informative priors altered the thermal response outside the observed data and drastically increased the credible intervals. This is likely associated with the large uncertainty associated with the prior fit observed in Johnson et al. 2015.

Models were fitted in R using JAGS/rjag, which implements Markov Chain Monte Carlo (MCMC). For each thermal trait, posterior draws for the parameters were obtained from three concurrent Moarkv chains. In each chain, a 5,000-step burn-in phase was followed by 20,000 samples of the stationary chain, for a total of 60,000 posterior samples. These samples were then thinned by saving every eigth sample, in order to further reduce autocorrelation in the chain and to reduce computation in the following analyses.

We also defined temperature-trait responses for mosquito and parasite traits not directly measured in this study to assess the impact incorporating multiple trait thermal responses from a single mosquito species (An. stephensi), rather than aggregated from several different mosquito species, has on relative R₀(T). An. stephensi data in Paaijmans et al. 2013 and Shapiro et al. 2017 were used to construct temperature-trait relationships for mosquito development rate (MDR), probability of egg to adult survival (pEA), P. falciparum development rate (PDR) and vector competence (bc). In contrast, for the Multi-species estimated model we used the thermal relationships defined in Johnson et al. 2015.

Description of the data is included in the associated metadata file that is uploaded in the Miazgowiczetal_ProcRoySoc_Data zip file.