diff --git a/app/static/src/app/components/mixins/selectVariables.ts b/app/static/src/app/components/mixins/selectVariables.ts
index ade2ef79..908ca341 100644
--- a/app/static/src/app/components/mixins/selectVariables.ts
+++ b/app/static/src/app/components/mixins/selectVariables.ts
@@ -53,14 +53,15 @@ export default (
         const variable = dataTransfer!.getData("variable");
         const srcGraphConfig = dataTransfer!.getData("srcGraphConfig");
         if (srcGraphConfig !== thisSrcGraphConfig) {
-            if (srcGraphConfig !== "hidden") {
-                removeVariable(parseInt(srcGraphConfig, 10), variable);
-            }
-            // add to this graph if necessary
+            // add to this graph if necessary - do this before remove so it is not unlinked if linked variables
             if (!hasHiddenVariables && !selectedVariables.value.includes(variable)) {
                 const newVars = [...selectedVariables.value, variable];
                 updateSelectedVariables(graphIndex!, newVars);
             }
+
+            if (srcGraphConfig !== "hidden") {
+                removeVariable(parseInt(srcGraphConfig, 10), variable);
+            }
         }
     };
 
diff --git a/app/static/src/app/components/run/RunPlot.vue b/app/static/src/app/components/run/RunPlot.vue
index 658731ce..e334a27a 100644
--- a/app/static/src/app/components/run/RunPlot.vue
+++ b/app/static/src/app/components/run/RunPlot.vue
@@ -85,7 +85,7 @@ const allPlotData = (start: number, end: number, points: number): WodinPlotData
     const plotOptions = { showLegend: true, includeLegendGroup: true };
     const allData = [
         ...odinToPlotly(filterSeriesSet(result, selectedVariables.value), palette.value, plotOptions),
-        ...allFitDataToPlotly(allFitData.value, palette.value, start, end)
+        ...allFitDataToPlotly(allFitData.value, palette.value, start, end, props.graphConfig.selectedVariables)
     ];
 
     // 2. Parameter sets
diff --git a/app/static/src/app/components/sensitivity/SensitivityTracesPlot.vue b/app/static/src/app/components/sensitivity/SensitivityTracesPlot.vue
index 63976e5f..53ee6e4e 100644
--- a/app/static/src/app/components/sensitivity/SensitivityTracesPlot.vue
+++ b/app/static/src/app/components/sensitivity/SensitivityTracesPlot.vue
@@ -200,7 +200,8 @@ export default defineComponent({
                 });
 
                 if (allFitData.value) {
-                    result.push(...allFitDataToPlotly(allFitData.value, palette.value, start, end));
+                    result.push(
+                        ...allFitDataToPlotly(allFitData.value, palette.value, start, end, props.graphConfig.selectedVariables));
                 }
             }
 
diff --git a/app/static/src/app/plot.ts b/app/static/src/app/plot.ts
index bdee7674..8c3e3450 100644
--- a/app/static/src/app/plot.ts
+++ b/app/static/src/app/plot.ts
@@ -141,15 +141,21 @@ export function allFitDataToPlotly(
     allFitData: AllFitData | null,
     paletteModel: Palette,
     start: number,
-    end: number
+    end: number,
+    selectedVariables: string[]
 ): WodinPlotData {
     if (!allFitData) {
         return [];
     }
     const { data, linkedVariables, timeVariable } = allFitData;
+    console.log("linked variables")
+    console.log(JSON.stringify(linkedVariables))
     const filteredData = filterData(data, timeVariable, start, end);
     const palette = paletteData(Object.keys(linkedVariables));
-    return Object.keys(linkedVariables).map((name: string) => ({
+    // Display column data if it is not linked OR if its linked variable is selected
+    const columns = Object.keys(linkedVariables)
+        .filter((column) => !linkedVariables[column] || selectedVariables.includes(linkedVariables[column]!));
+    return columns.map((name: string) => ({
         name,
         x: filteredData.map((row: Dict<number>) => row[timeVariable]),
         y: filteredData.map((row: Dict<number>) => row[name]),