# Receptor Noise Limited Models (Vorobyev & Osorio 1998) Receptor noise limited colour vision models (Vorobyev & Osorio 1998; Vorobyev et al. 1998) extended to any number of photoreceptor types. ```r RNLmodel(model = c("linear", "log"), photo=ncol(C)-1, R1, R2=Rb, Rb, I, C, noise = FALSE, v=NA, n=NA, e=NA, interpolate = TRUE, nm = seq(300, 700, 1), coord="colourvision") ``` ## Arguments - `model`: Linear (`"linear"`; Vorobyev & Osorio, 1998), or log-linear (`"log"`; Vorobyev et al. 1998) RNLmodel version. `model="log"` is preferred. `model="linear"` can be used only if comparison is to be made between two very similar colours. - `photo`: Number of photoreceptor types. Model accepts any number of photoreceptor types (`>=2`). For instance, dichromatic: `photo=2`; trichromatic: `photo=3`; tetrachromatic: `photo=4`, etc. Default gets number of photoreceptor types from `C` argument. - `R1`: Reflectance of observed objects. A data frame with first column corresponding to wavelength values and following columns with reflectance values. `R1` must be in the same scale as `R2` and `Rb`(percentage or proportion). - `R2`: Reflectance to be compared against R1. `R2=Rb` if comparison is to be made against the background. A data frame with two columns only: first column corresponding to wavelength values and second column with reflectance values. `R2` must be in the same scale as `R1` and `Rb`(percentage or proportion). - `Rb`: Background reflectance. A data frame with two columns only: first column corresponding to wavelength values and second column with reflectance values. `Rb` must be in the same scale as `R1` and `R2` (percentage or proportion). - `I`: Irradiance spectrum. A data frame with two columns only: first column corresponding to wavelength values and second column with irradiance values. Irradiance values must be in quantum flux units. - `C`: Photoreceptor sensitivity curves, from lowest to longest lambda-max. A data frame: first column corresponding to wavelength values and following columns with photoreceptor sensitivity values (see function `photor`). - `noise`: Logical. Whether receptor noise is provided (`noise = TRUE`) or calculated from photoreceptor relative abundances (`noise = FALSE`). - `e`: Receptor noise of each photoreceptor type. Used when `noise = TRUE` - `n`: Relative number of each photoreceptor type in the retina. Usually increases with lambda-max. Used to calculate `e` when `noise = FALSE`. - `v`: Noise-to-signal ratio of a single photoreceptor. Used to calculate `e` when `noise = FALSE`. - `interpolate`: Whether data files should be interpolated before further calculations. See `approx`. - `nm`: A sequence of numeric values specifying where interpolation is to take place. See `approx`. - `coord`: Whether colour locous coordinates should be calculated by the method (`coord="colourvision"`) by Gawryszewski (2018), or by alternative (`coord="alternative"`; available for 2-4 photoreceptor types only) methods (Hempel de Ibarra et al. 2001; Renoult et al. 2017). ## Returns - **ei**: Noise of photoreceptor channels. - **Qri_R1**: Photoreceptor photon catch values from `R1`, after the von Kries transformation (see function `Qr`). - **Qri_R2**: Photoreceptor photon catch values from `R2`, after the von Kries transformation (see function `Qr`). - **Ei_R1**: Photoreceptor outputs from the stimulus (`R1`) - **Ei_R2**: Photoreceptor outputs from R2 - **Xi_R1**: Coordinates in the colour space for R1 - **Xi_R2**: Coordinates in the colour space for R2. Equals zero when `R1=Rb` - **deltaS**: Euclidean distance from R1 to R2. It represents the conspicuousness of the stimulus (`R1`) in relation to the background when `R1=Rb`. ## Details The receptor noise limited model was originally developed to calculate $deltaS$ between two reflectance curves directly, without finding colour locus coordinates (e.g. `x,y`; Vorobyev and Osorio 1998). This function uses later formulae to find colour loci in a chromaticity diagram (similarly to Hempel de Ibarra et al. 2001; Renoult et al. 2015). In lack of a direct measurement, receptor noise ($ei$) can be estimated by the relative abundance of photoreceptor types in the retina, and a measurement of a single photoreceptor noise-to-signal ratio: $$ e_i=\frac{\nu}{\sqrt{\eta _i}}ei=v/sqrt(n) $$ where $v$ is the noise-to-signal ratio of a single photoreceptor, and $n$ is the relative abundance of photoreceptor i in the retina. Alternatively, noise may be dependent of the intensity, but this possibility is not implement in `colourvision` yet. Noise dependent of intensity usually holds for low light conditions only (Vorobyev et al. 1998). ## References Gawryszewski, F.M. 2018. Colour vision models: Some simulations, a general n-dimensional model, and the colourvision R package. Ecology and Evolution, 10.1002/ece3.4288. Hempel de Ibarra, N., M. Giurfa, and M. Vorobyev. 2001. Detection of coloured patterns by honeybees through chromatic and achromatic cues. J Comp Physiol A 187:215-224. Renoult, J. P., A. Kelber, and H. M. Schaefer. 2017. Colour spaces in ecology and evolutionary biology. Biol Rev Camb Philos Soc, doi: 10.1111/brv.12230 Vorobyev, M., and D. Osorio. 1998. Receptor noise as a determinant of colour thresholds. Proceedings of the Royal Society B 265:351-358. Vorobyev, M., D. Osorio, A. T. D. Bennett, N. J. Marshall, and I. C. Cuthill. 1998. Tetrachromacy, oil droplets and bird plumage colours. J Comp Physiol A 183:621-633. ## Author(s) Felipe M. Gawryszewski f.gawry@gmail.com ## See Also `photor`, `RNLthres`, `CTTKmodel`, `EMmodel`, `GENmodel` ## Examples ```r #1 ## Photoreceptor sensitivity spectra ##with lambda max at 350nm, 450nm and 550nm: C<-photor(lambda.max=c(350,450,550)) ##Grey background ##with 7 percent reflectance from 300 to 700nm: Rb <- data.frame(300:700, rep(7, length(300:700))) ## Read CIE D65 standard illuminant: data("D65") ##Reflectance data of R1 and R2 R1.1<-logistic(x=seq(300,700,1), x0=500, L=50, k=0.04) R1.2<-logistic(x=seq(300,700,1), x0=400, L=50, k=0.04) w<-R1.1[,1] R1.1<-R1.1[,2]+10 R1.2<-R1.2[,2]+10 R1<-data.frame(w=w, R1.1=R1.1, R1.2=R1.2) R2<-logistic(x=seq(300,700,1), x0=550, L=50, k=0.04) R2[,2]<-R2[,2]+10 ## Run model model<-RNLmodel(photo=3, model="log", R1=R1, R2=R2, Rb=Rb, I=D65, C=C, noise=TRUE, e = c(0.13, 0.06, 0.12)) #plot plot(model) #2 #Pentachromatic animal ## Photoreceptor sensitivity spectra ##with lambda max at 350,400,450,500,and 550nm: C<-photor(lambda.max=c(350,400,450,500,550)) ##Grey background ##with 7 percent reflectance from 300 to 700nm: Rb <- data.frame(300:700, rep(7, length(300:700))) ## Read CIE D65 standard illuminant: data("D65") ##Reflectance data of R1 R1<-logistic(x=seq(300,700,1), x0=500, L=50, k=0.04) R1[,2]<-R1[,2]+10 #RNL model RNLmodel(photo=5, model="log", R1=R1, R2=Rb, Rb=Rb, I=D65, C=C, noise=TRUE, e = c(0.13, 0.06, 0.12, 0.07, 0.08)) ```

RNLmodel function