Why is there a ~ symbol in front of some values in the best-fit values of nonlinear regression?

If a value of a parameter in nonlinear regression results is preceded by ~, it means the results are 'ambiguous'. Changing the value of any parameter will always move the curve further from the data and increase the sum-of-squares. But when the fit is 'ambiguous', changing other parameters can move the curve so it is near the data again. In other words, many combinations of parameter values lead to curves that fit equally well.

The parameter values preceded by ~ define the curve that Prism plots, but these values aren't actually useful in other ways. Other values would generate the same curve, or one that fits just as well. When the best fit value is preceded by ~, so is the standard error. The corresponding confidence intervals are shown as "very wide" with no numerical range (the range would be infinitely wide).