DOI: 10.5061/dryad.cnp5hqcdn
title: Modeling phenological and physiological responses to climate warming in a hypothetical migratory songbird-mosquito system

description: Given the strong temperature-dependence of ectothermic vector physiology,
 climate warming is expected to profoundly impact many vector-borne
 diseases. Notably, endothermic hosts can also respond to warming by
 altering the timing of life history events like seasonal migration and
 reproduction, but relatively few predictive models of vector-borne disease
 have considered both phenological and physiological responses to climate
 warming. Here, we extend the Ross-MacDonald model for a vector-borne
 disease to incorporate temperature effects on host and vector phenology
 and physiology. We use this model to understand how projections of
 moderate and severe warming influence the emergence of a hypothetical
 vector-borne disease in a migratory bird. Modeled vector and host
 infection prevalence always increased under warming, and the increase was
 amplified when hosts failed to update their arrival phenology to keep pace
 with breeding site resources. While extreme warming scenarios yielded the
 highest infection prevalence, reduced vector survival in the hottest
 months caused late-season declines in transmission, altering seasonal
 patterns of infection. By considering host, vector, and parasite responses
 to temperature together, our modeling framework could be employed to help
 decipher otherwise non-intuitive wildlife infection outcomes under current
 and future climate conditions.
description: We use differential equations to track population and infection
 dynamics of a migratory avian host and mosquito vector over a single host
 breeding season, following the first introduction of a novel pathogen
 (i.e., assuming no pre-existing immunity in the host). We incorporate
 climate warming impacts on host and vector phenology and vital rates,
 assessing outcomes under moderate and severe warming scenarios. Warming
 affects mosquito emergence timing and, in some scenarios, the arrival date
 of birds (which in turn influences reproductive success). At the same
 time, temperature dependence in transmission traits is incorporated by
 linking mosquito mortality rate, bite rate, and pathogen development rate
 to daily temperature data. For tractability, we assume that only the focal
 host species can acquire and transmit the pathogen, and that mosquitoes
 preferentially bite this host.
description: # Modeling phenological and physiological responses to climate warming in
 a hypothetical migratory songbird-mosquito system Code and data used in a
 model of vector-borne disease under climate warming scenarios. R and
 RStudio are required to run the model. #### Description of the data and
 file structure "VBD_phenology_physiology_2024.Rproj": R project
 that bundles the relevant scripts and data files. **Save project file in
 the same folder as the unzipped data folders and the markdown (.rmd) files
 below**. Open the project in R Studio and then access the markdown and
 data (.csv) files within the project. **RMD files**:
 "Netcdf_temps_Feb23_23.rmd" Converts netcdf files from Liess et
 al. 2022 to averaged, smoothed temperature time series in .csv
 format. Hosted in folder: 'Formatting_CNRM_temp_series' within
 zipped_data_files (see below); **Access necessary files from the Data
 Repository for the University of Minnesota**:
 [https://doi.org/10.13020/YV29-JY19](https://doi.org/10.13020/YV29-JY19) 
 "Temperature_degday_scenarios.rmd" reads in smoothed temperature
 scenarios based on CNRM global climate model for Minnesota - historical
 temperatures (1980-1999), moderate warming (approx. +2.6C, relative
 concentration pathway 4.5 2080-2099) and severe warming (approx. +5.4C,
 relative concentration pathway 8.5 2080-2099). (Ref:
 [https://doi.org/10.1029/2021EA001893](https://doi.org/10.1029/2021EA001893)). Calculates approximate cumulative degree days above 0C for each of the temperature scenarios; creates temperature and degree day data frames with annual patterns repeating for 20 years. Contains code for several figures related to temperature-dependent parameters. \ \ "Model_pre-infection-dynamics_WNVintro.rmd" contains ordinary differential equations (ODEs) that yield 30-year pre-infection dynamics for hosts and vectors and daily temperature-dependent R0; contains ODEs for the 1 year of infection dynamics after a single infected vector is introduced. To run, user needs to actively switch between the 'only vectors advance phenology' (Vadv) and 'both hosts and vectors advance phenology' (BOTHadv) scenarios before running the for loops. ***inputs:*** "Tempramp_MN_Feb27_23.csv", "DD0_20yr_Mar1.csv" ***outputs:*** "OutHosts_Vadv_Nov2023.csv", "OutHosts_BOTHadv_Nov2023.csv", "WNVout_Vadv_Nov2023.csv", "WNVout_BOTHadv_Nov2023.csv"\ \ "Main_VBDmodel_results.rmd" contains a review of the main methods and equations; it reads in data frames that contain pre and post-infection host and vector dynamics. Includes plots used in the main results section of the manuscript.\ \ "sensitivity_fc_theta.rmd" focused sensitivity analysis assessing the impacts of the warming-induced cost to host reproduction and shift in vector emergence rate. To run, user needs to actively switch between the 'only vectors advance phenology' (Vadv) and 'both hosts and vectors advance phenology' (BOTHadv) scenarios, as well as fc and theta scaling parameters.\ \ "physiology_sensitivity_10_27_25.rmd" (older version: "physiology_sensitivity.rmd") focused on sensitivity analysis exploring how holding bite rate, mosquito lifespan, or pathogen development rate constant with temperature impacts transmission potential. Updated version from 2025 holds parameters constant at a scenario-specific value: x at the mean breeding season temperature within each climate scenario. Older version held parameters constant at the same value across scenarios. "01_Mainmod_earlier_end_breeding.rmd" script used to assess differences in model output given an earlier end to host breeding under warming. Appendix figures created.\ \ "02_Mainmod_feccost_dismort.rmd" script exploring model outcomes with/without a host fecundity cost and disease-induced mortality. Used for Appendix figure S6.\ \ "03_Earlier_breed_end_c_vh.rmd" script used to explore the impacts of ending breeding earlier under warming and turning fecundity cost and disease-induced mortality on/off. Appendix figure S7 S1_SupportingInformation_Appendix: contains- 1. 1. Model parameterization - hosts 2. 2. Model parameterization – vector and pathogen 3. 3. Model parameterization – hosts and vector phenology under climate warming 4. 4. Model analysis: calculating Temperature-dependent relative R~0~ 5. 5. Model assumptions - limitations, implications, and potential model modifications 6. 6. Sensitivity analysis – warming impacts on host fecundity cost (c) and maximum vector emergence rate (εmax) 7. 7. Sensitivity analysis – impacts of physiological parameters on R~0~ 8. Sensitivity analyses - eliminating the fecundity cost or disease-induced mortality 9. Sensitivity analyses - breeding season length 10. Sensitivity analyses - effects of non-competent hosts in the community~ ~ #### **DATA** **zipped_data_files.zip** : zip file of data below *For all CSV files generated by RStudio below, the first column (A) is created by the software and is redundant with time or DOY. It does not have a column name and will not be called by RMD files. **'temperature_data' folder** *Column definitions:* 'tempsmooth' = temperature (°C) 'DOY' = day of year (Julian date). *Files:*\ "Hist_1980_CNRM_1yrsmooth.csv": daily historical temperature values for 1 year; values from the MN model smoothed using the stats::loess function in RStudio. \ "RCP45_2080_CNRM_1yrsmooth.csv": 1 year of daily temperature values for the moderate warming (RCP 4.5) scenario; values from the MN model smoothed using the stats::loess function in RStudio. \ "RCP85_2080_CNRM_1yrsmooth.csv": 1 year of daily temperature values for the severe warming (RCP 8.5) scenario; values from the MN model smoothed using the stats::loess function in RStudio. \ \ "Tempramp_MN_Feb27_23.csv": data frame with daily temperatures for all scenarios; columns: 'amb' = historical temperatures (1980-1999), 'rcp45' = moderate warming (relative concentration pathway 4.5), 'rcp85' severe warming (relative concentration pathway 8.5), 'DOY' = day of year (Julian date). This file contains 20 years of repeated temperature vectors; this is extended to 30 years in RMD files.\ \ "DD0_20yr_Mar1.csv": The degree days above 0C accumulated for each day in the temperature scenarios. Each scenario has a column- 'degreeday_hist' = historical, 'degreeday_45' = RCP 4.5, and 'degreeday_85' = RCP 8.5. This file includes 20 years of degree days, and these vectors are extended to 30 years in RMD files. **'data' folder for Main model:** *Column definitions:* Sh.0 = number of susceptible hosts in historical scenario Sh.3 = number of susceptible hosts in moderate warming scenario Sh.5 = number of susceptible hosts in severe warming scenario Ih.0 = number of infected hosts in historical scenario Ih.3 = number of infected hosts in moderate warming scenario Ih.5 = number of infected hosts in severe warming scenario Rh.0 = number of recovered hosts in historical scenario Rh.3 = number of recovered hosts in moderate warming scenario Rh.5 = number of recovered hosts in severe warming scenario Sv.0 = number of susceptible vectors in historical scenario Sv.3 = number of susceptible vectors in moderate warming scenario Sv.5 = number of susceptible vectors in severe warming scenario Ev.0 = number of exposed vectors in historical scenario Ev.3 = number of exposed vectors in moderate warming scenario Ev.5 = number of exposed vectors in severe warming scenario Iv.0 = number of infected vectors in historical scenario Iv.3 = number of infected vectors in moderate warming scenario Iv.5 = number of infected vectors in severe warming scenario prevalence.X = scenario-specific host infection prevalence; Ih.X / (Sh.X+Rh.X), where X is 0, 3, or 5 for historical, moderate warming, or severe warming, respectively. prevalenceV.X = scenario-specific vector infection prevalence; Iv.X / (Sv.X+Ev.X), where X is 0, 3, or 5 for historical, moderate warming, or severe warming, respectively. Bvh.X = scenario-specific transmission probability from vector to host, where X is 0, 3, or 5 for historical, moderate warming, or severe warming Bhv.X = scenario-specific transmission probability from host to vector, where X is 0, 3, or 5 for historical, moderate warming, or severe warming Mv.X = scenario-specific vector mortality rate, where X is 0, 3, or 5 for historical, moderate warming, or severe warming q.X = scenario-specific pathogen development rate, where X is 0, 3, or 5 for historical, moderate warming, or severe warming Nb.X = number of breeding adult hosts in scenario X, where X is 0, 3, or 5 for historical, moderate warming, or severe warming Reff.X = daily, temperature-dependent R0, where X is 0, 3, or 5 for historical, moderate warming, or severe warming DOY = day of year (Julian date) time = daily timestep in 30-year sequence *Files:* "OutHosts_Vadv_Nov2023.csv": pre-pathogen introduction when ONLY vectors advance phenology under warming. Tracks SIR-SEI compartments, host and vector prevalence, temperature-dependent parameters, and daily R0 (Reff) for each of the three temperature scenarios (historic (.0), RCP4.5 (.3) and RCP 8.5 (.5)). Also includes day of year (DOY) and timestep (time) for the 30-year data frame.\ \ "OutHosts_BOTHadv_Nov2023.csv": pre-pathogen introduction when BOTH hosts and vectors advance phenology under warming. Tracks SIR-SEI compartments, host and vector prevalence, temperature-dependent parameters, and daily R0 (Reff) for each of the three temperature scenarios (historic (.0), RCP4.5 (.3) and RCP 8.5 (.5)). Also includes day of year (DOY) and timestep (time) for the 30-year dataset. \ \ "WNVout_Vadv_Nov2023.csv": post-pathogen the introduction when ONLY vectors advance phenology under warming. tracks same compartments and variables as pre-WNV data frame for 1 year of WNV infection\ \ "WNVout_BOTHadv_Nov2023.csv": post-pathogen introduction when BOTH hosts and vectors advance phenology under warming. tracks same compartments and variables as pre-WNV data frame for 1 year of WNV infection **SENSITIVITY ANALYSES:** **Physiology sensitivity analysis - 'sensitivity_data' folder:** The following csv files contain host and vector dynamics and daily R0 calculated when holding one physiological parameter constant; there is a csv file for each phenology scenario (Vadv = vectors advance, BOTHadv = both hosts and vectors advance). Column definitions are the same as 'data' folder files above.  * vector bite rate constant:\ "OutHosts_Vadv_constant_a.csv"\ "OutHosts_BOTHadv_constant_a.csv" * vector lifespan constant:\ "OutHosts_Vadv_constant_ls.csv"\ "OutHosts_BOTHadv_constant_ls.csv" * pathogen development rate constant:\ "OutHosts_Vadv_constant_q.csv"\ "OutHosts_BOTHadv_constant_q.csv" **Reproductive cost (f_c) and emergence rate (theta) scaling:** **pre-infection dynamics - 'sensitivity_data' folder**: The following csv files contain pre-infection host and vector dynamics and daily R0 calculated when varying either the reproductive cost of late arrival (with parameter f_c) or maximum vector emergence (with parameter theta). There are csv files for each phenology scenario (Vadv = vectors advance, BOTHadv = both hosts and vectors advance phenology). Column definitions are the same as 'data' folder files above. "data_fc_sens_Vadv_Nov2023.csv" #only vectors advance phenology, variable cost (f_c); constant emergence "data_fc_sens_BOTHadv_Nov2023.csv" #both hosts and vectors advance phenology, variable cost (f_c); constant emergence "data_theta_sens_Vadv_Nov2023.csv" #only vectors advance phenology, variable emergence (theta); constant cost (f_c) "data_theta_sens_BOTHadv_Nov2023.csv" #both hosts and vectors advance phenology, variable emergence (theta); constant cost (f_c) **post-infection dynamics - 'sensitivity_output' folder:** The following csv files contain post-infection host and vector dynamics when varying either the the reproductive cost of late arrival (with parameter f_c) or maximum vector emergence (with parameter theta). There are csv files for each phenology scenario (Vadv = vectors advance, BOTHadv = both hosts and vectors advance phenology). Column definitions are the same as 'data' folder files above. "output_fc_sens_Vadv_Nov2023.csv" #only vectors advance phenology, variable cost (fc); constant emergence (theta) "output_fc_sens_BOTHadv_Nov2023.csv" #both hosts and vectors advance phenology, variable cost (fc); constant emergence (theta) "output_theta_sens_Vadv_Nov2023.csv" #only vectors advance phenology, variable emergence (theta); constant cost (fc) "output_theta_sens_BOTHadv_Nov2023.csv" #both hosts and vectors advance phenology, variable emergence (theta); constant cost (fc) **Non-focal hosts / bite dilution - 'sensitivity_data' folder**: These two CSV files contain summary data on transmission potential and pre-infection, end-of-season host abundance when non-competent hosts are incorporated in the community (N_c). There are files for each phenology scenario (Vadv = vectors advance, BOTHadv = both hosts and vectors advance phenology). "data_Nc_sens_Vadv_Nov2023.csv" #only vectors advance phenology "data_Nc_sens_BOTHadv_Nov2023.csv" # both hosts and vectors advance phenology *Column definitions: * Nc = number of non-competent hosts (0, 200, or 800) R0day_X = first day of the year (Julian date) sustained transmission is possible (i.e., R0&gt;1); X corresponds to temperature scenario, "hist," "rcp45," or "rcp85" for historical, moderate warming, or severe warming, respectively peakR0_X = maximum value of R0, where X  represents temperature scenario, "hist," "rcp45," or "rcp85" for historical, moderate warming, or severe warming, respectively Shlast_X = final susceptible host abundance value, where X represents temperature scenario, "hist," "rcp45," or "rcp85" for historical, moderate warming, or severe warming, respectively