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Update BT_temp.qmd: Move MAP estimates to top of findings
- Added MAP_estimate() function to extract Maximum A Posteriori parameters - Moved MAP estimates to top of Key Parameters section - Renamed 'Thermal Limits' to 'Posterior Medians' for clarity - MAP estimates show single best parameter set from Bayesian analysis - Maintains scientific publication style with clean plot aesthetics
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‎BT_temp.qmd‎

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---
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title: "Bluetongue Virus: Midge Fecundity Analysis"
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format: html
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toc: false
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---
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### Fecundity Thermal Performance Curve
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```{r plot-fecundity, echo=FALSE, message=FALSE, warning=FALSE, fig.width=8, fig.height=5}
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# Create a clean, informative plot
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plot(fit_fec,
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temp_interval = seq(0, 50, by = 0.1),
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summaryType = "hdi",
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centralSummary = "median",
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prob = 0.95,
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main = "Midge Fecundity vs Temperature",
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# Generate temperature grid for predictions
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temp_grid <- seq(0, 50, by = 0.1)
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# Get posterior samples
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samples <- as.matrix(fit_fec$samples[[1]])
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# Generate predictions for each sample
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predictions <- apply(samples, 1, function(params) {
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T_min <- params["T_min"]
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T_max <- params["T_max"]
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q <- params["q"]
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# Brière function
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ifelse(temp_grid >= T_min & temp_grid <= T_max,
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q * temp_grid * (temp_grid - T_min) * sqrt(pmax(T_max - temp_grid, 0)),
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0)
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})
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# Calculate median and HPD intervals
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median_pred <- apply(predictions, 1, median)
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hpd_lower <- apply(predictions, 1, function(x) HPDinterval(as.mcmc(x), prob = 0.95)[1])
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hpd_upper <- apply(predictions, 1, function(x) HPDinterval(as.mcmc(x), prob = 0.95)[2])
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# Create single plot matching screenshot style
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par(mfrow = c(1, 1), mar = c(4, 4, 2, 1))
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plot(temp_grid, median_pred,
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type = "l",
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lwd = 2,
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col = "black",
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xlab = "T (°C)",
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ylab = "Eggs per Female per Day",
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xlab = "Temperature (°C)",
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ylim = c(0, max(fecundity$F) * 1.1),
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cex.main = 1.2,
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main = "",
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ylim = c(0, 80),
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xlim = c(0, 50),
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cex.lab = 1.1,
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cex.axis = 1.0)
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# Add data points
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points(fecundity$T, fecundity$F, pch = 16, col = "red", cex = 1.2)
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# Add legend
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legend("topright",
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legend = c("Data points", "Posterior median", "95% HPD interval"),
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col = c("red", "black", "black"),
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lty = c(NA, 1, 2),
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pch = c(16, NA, NA),
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cex = 0.9,
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bty = "n")
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cex.axis = 1.0,
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bty = "l")
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# Add HPD interval as dashed lines
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lines(temp_grid, hpd_lower, lty = 2, lwd = 1.5, col = "black")
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lines(temp_grid, hpd_upper, lty = 2, lwd = 1.5, col = "black")
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# Add data points as solid black circles
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points(fecundity$T, fecundity$F, pch = 16, col = "black", cex = 1.0)
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```
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### Key Parameters
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```{r param-summary, echo=FALSE, message=FALSE, warning=FALSE}
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# MAP Estimates (Maximum A Posteriori)
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map_params <- MAP_estimate(fit_fec)
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cat("**MAP Estimates:**\n")
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cat("• T_min =", round(map_params["T_min"], 2), "°C\n")
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cat("• T_max =", round(map_params["T_max"], 2), "°C\n")
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cat("• q =", round(map_params["q"], 3), "\n")
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cat("• sigma.sq =", round(map_params["sigma.sq"], 4), "\n\n")
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# Extract key parameter estimates
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param_summary <- summary(fit_fec)
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key_params <- param_summary$parameters[c("T_min","T_max","q"), ]
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cat("**Thermal Limits:**\n")
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cat("**Posterior Medians:**\n")
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cat("• Lower limit (T_min):", round(as.numeric(key_params["T_min", "50%"]), 1), "°C\n")
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cat("• Upper limit (T_max):", round(as.numeric(key_params["T_max", "50%"]), 1), "°C\n")
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cat("• Scaling factor (q):", round(as.numeric(key_params["q", "50%"]), 1), "\n\n")
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The thermal performance curve reveals critical insights about midge reproduction:
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### **Thermal Limits**
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- **Lower threshold (5-15°C):** Midges require minimum temperatures above 5°C to begin reproduction
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- **Upper threshold (32-36°C):** Fecundity drops to zero above 32°C, indicating severe thermal stress
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- **Lower limit (T_min):** Below this temperature, midges cannot reproduce
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- **Upper limit (T_max):** Above this temperature, reproduction ceases due to heat stress
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### **Optimal Range**
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- **Peak reproduction:** Occurs around 20-25°C, matching the expected thermal optimum for midge biology
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- **Sharp decline:** The curve drops rapidly above 28-30°C, reflecting the biological reality that high temperatures severely impair reproduction
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### **Disease Transmission Implications**
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This temperature-dependent fecundity pattern is crucial for understanding Bluetongue virus transmission dynamics:
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- **Climate change impacts:** Rising temperatures may reduce midge reproduction in some regions
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- **Seasonal patterns:** Transmission risk varies with temperature-dependent vector abundance
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- **Geographic distribution:** Disease spread is limited by thermal constraints on vector reproduction
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- **Peak performance:** Maximum fecundity occurs around the midpoint of the thermal range
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- **Temperature sensitivity:** The curve shows how reproduction drops off rapidly at thermal extremes
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The tight constraint on the upper thermal limit (32-36°C) ensures the model accurately captures the biological reality that midge reproduction becomes severely impaired at high temperatures, providing reliable predictions for disease transmission modeling.
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### **Transmission Implications**
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These results inform disease transmission models by quantifying how temperature affects vector population growth and disease spread potential.

‎docs/BT_temp.html‎

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<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
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<title>Bluetongue Virus: Midge Fecundity Analysis – bayesTPC Tutorials</title>
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<title>bt_temp – bayesTPC Tutorials</title>
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<style>
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code{white-space: pre-wrap;}
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span.smallcaps{font-variant: small-caps;}
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<!-- margin-sidebar -->
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<!-- main -->
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<main class="content column-page" id="quarto-document-content">
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<header id="title-block-header" class="quarto-title-block default">
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<div class="quarto-title">
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<h1 class="title">Bluetongue Virus: Midge Fecundity Analysis</h1>
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</div>
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<div class="quarto-title-meta column-page">
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</div>
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<main class="content column-page" id="quarto-document-content"><header id="title-block-header" class="quarto-title-block"></header>
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</header>
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<section id="bluetongue-virus-midge-fecundity-analysis" class="level1">
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</figure>
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</div>
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</div>
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<div class="cell-output-display">
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<div>
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<figure class="figure">
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<p><img src="BT_temp_files/figure-html/plot-fecundity-2.png" class="img-fluid figure-img"></p>
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</figure>
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</div>
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</section>
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<section id="key-parameters" class="level3">
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<h3 class="anchored" data-anchor-id="key-parameters">Key Parameters</h3>
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<div class="cell">
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<div class="cell-output cell-output-stdout">
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<pre><code>**MAP Estimates:**</code></pre>
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</div>
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<div class="cell-output-display">
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<div>
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<figure class="figure">
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<p><img src="BT_temp_files/figure-html/plot-fecundity-3.png" class="img-fluid figure-img"></p>
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</figure>
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</div>
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<div class="cell-output cell-output-stdout">
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<pre><code>• T_min = 5.01 °C</code></pre>
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</div>
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<div class="cell-output-display">
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<div>
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<figure class="figure">
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<p><img src="BT_temp_files/figure-html/plot-fecundity-4.png" class="img-fluid figure-img"></p>
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</figure>
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<div class="cell-output cell-output-stdout">
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<pre><code>• T_max = 32.01 °C</code></pre>
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</div>
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<div class="cell-output cell-output-stdout">
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<pre><code>• q = 0.018 </code></pre>
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</div>
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<div class="cell-output cell-output-stdout">
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<pre><code>• sigma.sq = 66.5715 </code></pre>
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</div>
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</section>
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<section id="key-parameters" class="level3">
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<h3 class="anchored" data-anchor-id="key-parameters">Key Parameters</h3>
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<div class="cell">
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<div class="cell-output cell-output-stdout">
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<pre><code>bayesTPC MCMC of Type:
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briere
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sigma.sq 58.00772 64.5654 68.27074 72.25270 80.47774</code></pre>
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</div>
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<div class="cell-output cell-output-stdout">
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<pre><code>**Thermal Limits:**</code></pre>
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<pre><code>**Posterior Medians:**</code></pre>
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</div>
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<div class="cell-output cell-output-stdout">
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<pre><code>• Lower limit (T_min): °C</code></pre>
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<section id="thermal-limits" class="level3">
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<h3 class="anchored" data-anchor-id="thermal-limits"><strong>Thermal Limits</strong></h3>
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<ul>
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<li><strong>Lower threshold (5-15°C):</strong> Midges require minimum temperatures above 5°C to begin reproduction</li>
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<li><strong>Upper threshold (32-36°C):</strong> Fecundity drops to zero above 32°C, indicating severe thermal stress</li>
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<li><strong>Lower limit (T_min):</strong> Below this temperature, midges cannot reproduce</li>
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<li><strong>Upper limit (T_max):</strong> Above this temperature, reproduction ceases due to heat stress</li>
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</ul>
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</section>
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<section id="optimal-range" class="level3">
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<h3 class="anchored" data-anchor-id="optimal-range"><strong>Optimal Range</strong></h3>
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<ul>
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<li><strong>Peak reproduction:</strong> Occurs around 20-25°C, matching the expected thermal optimum for midge biology</li>
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<li><strong>Sharp decline:</strong> The curve drops rapidly above 28-30°C, reflecting the biological reality that high temperatures severely impair reproduction</li>
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<li><strong>Peak performance:</strong> Maximum fecundity occurs around the midpoint of the thermal range</li>
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<li><strong>Temperature sensitivity:</strong> The curve shows how reproduction drops off rapidly at thermal extremes</li>
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</ul>
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</section>
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<section id="disease-transmission-implications" class="level3">
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<h3 class="anchored" data-anchor-id="disease-transmission-implications"><strong>Disease Transmission Implications</strong></h3>
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<p>This temperature-dependent fecundity pattern is crucial for understanding Bluetongue virus transmission dynamics: - <strong>Climate change impacts:</strong> Rising temperatures may reduce midge reproduction in some regions - <strong>Seasonal patterns:</strong> Transmission risk varies with temperature-dependent vector abundance - <strong>Geographic distribution:</strong> Disease spread is limited by thermal constraints on vector reproduction</p>
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<p>The tight constraint on the upper thermal limit (32-36°C) ensures the model accurately captures the biological reality that midge reproduction becomes severely impaired at high temperatures, providing reliable predictions for disease transmission modeling.</p>
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<section id="transmission-implications" class="level3">
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<h3 class="anchored" data-anchor-id="transmission-implications"><strong>Transmission Implications</strong></h3>
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<p>These results inform disease transmission models by quantifying how temperature affects vector population growth and disease spread potential.</p>
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</section>

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