Bluetongue Virus: Midge Fecundity Analysis

Source: El Moustaid et al. 2021 Supplement | Original experiment: Lysyk & Danyk 2007

This analysis recreates the fecundity thermal performance curve from the Bluetongue virus transmission study, showing how midge reproduction varies with temperature.

Dataset

We analyze 29 fecundity measurements (eggs per female per day) across 5 temperature groups:

Temperature groups:

# A tibble: 5 x 2
      T     n
  <dbl> <int>
1    10     6
2    15     6
3    20     6
4    25     7
5    30     7

Fecundity range: 0.4 to 70 eggs per female per day

Thermal Performance Curve

We fit a Brière model to capture the temperature-dependent fecundity pattern:

Model: F(T) = k × T × (T - T_min) × √(T_max - T)

Creating NIMBLE model:
 - Configuring model.

 - Compiling model.

Creating MCMC:
 - Configuring MCMC.
 - Compiling MCMC.
 - Running MCMC.

Progress:
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Configuring Output:
 - Finding Max. a Post. parameters.

Results

Fecundity Thermal Performance Curve

Key Parameters

**MAP Estimates:**

<U+2022> T_min = 5.01 <U+00B0>C

<U+2022> T_max = 32.01 <U+00B0>C

<U+2022> q = 0.018 

<U+2022> sigma.sq = 66.5715 

bayesTPC MCMC of Type:
  briere

Formula:
  m[i] <- ( q * Temp * (Temp - T_min) * sqrt((T_max > Temp) * abs(T_max - Temp))
* (T_max > Temp) * (Temp > T_min) )

Distribution:
  Trait[i] ~ T(dnorm(mean = m[i], tau = 1/sigma.sq), 0, )

Priors:
  q ~ dunif(0, 200) 
  T_max ~ dunif(32, 36) 
  T_min ~ dunif(5, 15) 
  sigma.sq ~ dexp(1)

Max. A Post. Parameters: 
    T_max     T_min         q  sigma.sq  log_prob 
  32.0051    5.0101    0.0184   66.5715 -249.7617 

MCMC Results:
Iterations = 1:12000
Thinning interval = 1 
Number of chains = 4 
Sample size per chain = 12000 

1. Empirical mean and standard deviation for each variable,
   plus standard error of the mean:

             Mean       SD  Naive SE Time-series SE
T_max    32.28717 0.313422 1.431e-03      6.308e-03
T_min     5.85043 0.762443 3.480e-03      1.126e-02
q         0.01857 0.001904 8.690e-06      2.655e-05
sigma.sq 68.51747 5.743078 2.621e-02      5.614e-02

2. Quantiles for each variable:

             2.5%     25%      50%      75%    97.5%
T_max    32.00680 32.0761 32.18537 32.38196 33.16290
T_min     5.02610  5.2674  5.63096  6.21703  7.80807
q         0.01494  0.0173  0.01853  0.01983  0.02238
sigma.sq 58.00772 64.5654 68.27074 72.25270 80.47774

**Posterior Medians:**

<U+2022> Lower limit (T_min):  <U+00B0>C

<U+2022> Upper limit (T_max):  <U+00B0>C

<U+2022> Scaling factor (q):  

**Optimal Temperature:**

<U+2022> Peak fecundity at:  <U+00B0>C

Biological Interpretation

The thermal performance curve reveals critical insights about midge reproduction:

Thermal Limits

• Lower limit (T_min): Below this temperature, midges cannot reproduce
• Upper limit (T_max): Above this temperature, reproduction ceases due to heat stress

Optimal Range

• Peak performance: Maximum fecundity occurs around the midpoint of the thermal range
• Temperature sensitivity: The curve shows how reproduction drops off rapidly at thermal extremes

Transmission Implications

These results inform disease transmission models by quantifying how temperature affects vector population growth and disease spread potential.