Hi, from the graph it seems that you have three different pattern thus the easiest way to use three functions and the daily temperature as a model option, a regression-tree analysis could underline this decision or use more complicated modelling techniques such as NNets and use temperature as a parameter too.

I´m sorry I don´t know

Have you tried using degree-days rather than mean daily temps to drive your model? Using DDs you can accommodate most all temperature responses using one function. Your lower threshold looks like around 6-8C, and you could use an upper threshold of 30-32C if needed.

The above answers are good, my only other suggestion, looking at your graph, is to add a dimension for temperature to your model to account for the interaction (nonlinear multiple regression really). In other words, by only using time you'll get an average function that doesn't really work because of the confounding effect of temperature.

I mean if you only need to describe the process a simple non linear regression (or GAM maybe) with a 3D regression plane for a graph should do, right?

The way we model oviposition is, first, to account to potential oviposition as a function of temperature. Second, we model de physiological age of females as a funtion of temperature. Third, to model the relative oviposition as function of physiological age with a -usually- left skewed curve.

A comprehensive description and comparison should be based on life table. Because life table can take the effect of age into consideration. The "relative" cumulative oviposition is not a good idea, because it ignores the total fecundity. The "relative" oviposition period is also not a good idea, because it ignores the length of oviposition duration. The "time-specific" idea is also not good. The "age-specific" will be better, because it shows the effect of "reproductive age" on the population growth. Fitting data to any "model" is only statistical game. You can certainly find a variety of equations for your data. But you will unable to define all parameters of those equations. "Moving average" is absolutely not good. I hope these comments are useful to you. Please don't mind my straight suggestions.

I could add that your degree-day based oviposition function could be age- or stage- based, where response curves (DD vs OV rate) are age or stage dependent. This should neatly encapsulate all the dynamics needed, with the compromise of settling upon some number of stages (or ages). 8-10 sub stages generally should work without compromising too much precision.

I think, because degree days are based on lineal models, some precision on physiological age of the mother is lost. On the opposite, non linear models are more realistic and withou over parametrization. Linear models doesn't imply just 2 parameters because the 2 thermal thresholds add more paramaters; some non linear models use 3 or 4 paramters keeping the parsimony principle. But its my point of view and not necessarily a clear cut on the dicision of what kind of models can be used. Anyway, it's important to describe the oviposition curve through the life of the mother.

It sounds like, Julio, we are in agreement more or less. I would agree that the oviposition response to temperature may be best modeled using non-linear functions (but do we have access to hourly weather data, or just daily?), but that the physiological age of the mother may be best tracked using heat units, to simplify modeling the entire life cycle which is also modeled readily using heat units. Also, I point out that most temperature-rate of response sigmoid curves (attracting modelers to try to fit nonlinear functions) are developed only from lab data which produces unrealistic artifacts, especially at the cool and hot extremes, so fitting that part of the response curve is an act of promoting unrealistic behaviors. For example insects may seek shade when it is hot in nature, but cannot escape the heat in a controlled growth chamber. Constant cool temps in growth chambers, similarly, cannot be compared to cool days with normal diurnal fluctuations and a model fitted at this end is also often just an artifact of the experiment.