How can I tell if a photodetector is thermal noise limited or shot noise limited? Most datasheets for photodetectors only specify the noise equivalent power, making no distinction between thermal noise (Johnson noise) and shot noise. For modelling purposes, how do I know whether the photodetector is shot-noise limited or thermal noise limited?
 A: Noise equivalent power (NEP) is a parameter that depends on thermal noise only.
From RP Photonics,

When a photodetector does not get any input light, it nevertheless produces some noise output with a certain average power, which is proportional to the square of the r.m.s. voltage or current amplitude. The noise-equivalent power (NEP) of the device is the optical input power which produces an additional output power identical to that noise power for a given bandwidth (see below).

Note that NEP also depends on the bandwidth considered, and that a receiver's specified NEP is often only 1 Hz. For your application, you must scale the NEP by the square root of your system's bandwidth to get the noise measure appropriate for your system.
Shot noise ideally doesn't depend on the detector used (a non-unity quantum efficiency will increase the effective shot noise), only on the frequency and power of the signal applied. The shot noise power spectral density is given by
$$S(f) = h\nu\bar{P}$$
where $\nu$ is the optical frequency and $\bar{P}$ is the average power received.
As it doesn't depend on any parameter of the receiver, it wouldn't make sense for it be specified on a receiver datasheet.
Your system is typically considered shot noise limited if the shot noise is greater than the thermal (or other) noise at the detection threshold. Typically (at optical and NIR frequencies) this only happens if you use a detector with internal gain, such as a photomultiplier or avalanche photodetector.
A: The photodetector itself isnt the whole picture. You need to know details about the readout circuit as well as the photon source to know what your dominant noise source is.
If your dominant noise source is shot noise from the photon source you are measuring, then your SNR will be proportional to the square root of irradiance on your detector. If any other noise source is dominant then your SNR will be proportional to irradiance.
If you cant take these measurements you will have to calculate the various noise contributions. But you dont need to consider only one noise source. For modeling purposes I would just calculate them all.
