Help me define a function to fit this curve?

[researcher605]

I'm a scientist studying the biology of reproduction. I have data from an animal species for a phenotype that changes over the course of a few days. I've plotted the averages [here]:

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What I'd like to do is have a singular function to describe the shape of this curve. I've tried my hand at some well-treaded functions like the Gompertz, Weibull, and logisitic, but I feel like each one alone misses certain properties of the shape that I think (might) have particular biological significance.


In the end, I'd like to use the function to describe these elements:


1) The rate at which the phenotype increased in the initial stage.


2) the rate at which the phenotype decreases in the subsequent stage.


3) the non-zero plateau at which the phenotype eventually comes to rest.


The first two I bring up became the parameters of the Gompertz function can be combined into a singular metric (mean doubling time) which is more intuitive and comparable between populations. Ultimately, that's the goal: to have a singular function that any researcher can use to help reveal variation across species.


Just some more information: the phenotype theoretically starts at 0, but in the plot there are some animal use restrictions that keep us from measuring the phenotype any earlier than the first data point shown. Second: the longitudinal study continues until the animals' death.


Thanks for your help!