I read the paper about SCR. Too difficult for me to understand. So searched on YT to find some explanation. After watching this video, I still don't understand SCR
It is pretty complicated. But my best simple-ish explanation is this: SECR and many other wildlife-focused models, are really 2 (or more, possibly) models put together. In SECR, two models are needed bc there are inherently two processes occurring that produce the data you collect, and you have to model both and try to figure out the parameters of each using only the final product of both (your data). There is a state model, which is a model or equation that describes what the animals are doing, and a capture or observation model, which describes the effectiveness and characteristics of how you, the researcher, sample or observe the animals. Dr Royle shows visualizations for these two things around 3:57. The state model in SECR is usually a poisson model where each point in space (cells of a certain size) might contain 0 or more home range centers. The exact parameters of this distribution will be estimated from the data, but it represents the mean # of home range centers (activity centers) in a given space (usually set to whatever plot or area you are sampling with each trap or camera, etc) and how variable they are. However you have the problem that sometimes those cameras will fail to detect an animal that is actually in that point in space (so a 0 should really be a 1). So we need to add in the second model in the system, the capture model, so we can try to tease out, for all the points in space and time, whether the 0’s we got were true (the animal really isn’t there) or false (it was there and we failed to observe it). For SECR we model this detection rate as a function of distance from the animal's "activity center" -- it is easier (higher p) to observe the animal when you put the trap near its AC and harder when it is farther away from the AC. When you run SECR you choose a curve that best fits your system. Usually it is the halfnormal curve, which dr royle shows around 4:44, which has the parameters g0 and sigma. g0 is the detection rate if you stuck the trap right in the center of the AC. sigma is the distance from the y-axis to the point where the curve switches from accelerating to decelerating (halfway through the curve). This helps you scale your capture functions according to your species or system - for elephants sigma might be thousands of meters, for rabbits it would be much smaller. But the shape of the curve is the similar. There are other options for curves, as well as additional parameters that describe different kinds of traps. In most cases, for example, Animal #1 will be caught relatively often at some cameras, sometimes at a few others, and never at others. This set of captures, how they are arranged, when they happened, how far apart consecutive observations are, across all animals and locations and occasions, can help us determine the g0 and sigma parameters, and D (the last one is what we’re usually interested in). Additionally, p (or g0) is never 1 so there are also some number of animals that we never observe, and our capture model has to account for this. They get very long, but you can write out the likelihood statements for all the parameters of your 2 submodels, which would be, in pseudo technical notation: Likelihood of (capture model parameter values C, state model parameters S; given n, the number of animals observed; and their capture histories, w) = (Probability of observing n | C and S) * (Prob of all w’s given n, C, and S) C and S are generic terms representing the vector of values of the parameters for the chosen state and capture models. Eg, half-normal for your capture model (which have the parameters g0 and sigma) and a Poisson point process model for state (which has a parameter called lambda which tells you how many AC’s can be in a certain area and how much does that tend to vary). The values for C and S are derived numerically, meaning we make the computer try many, many combinations of values for C and S, and for each set a likelihood is estimated based on the observed data - in effect, what is the probability that our capture model has values C, and our state model has values S, given the data we observed. The values of C and S with the highest likelihoods are the ones we go with. This paper goes over most of it, and there is more to it, including allowing parameters to vary with certain habitat or geographic variables, etc. www.otago.ac.nz/density/pdfs/Borchers%20&%20Efford%20Biometrics%202008.pdf
I read the paper about SCR. Too difficult for me to understand. So searched on YT to find some explanation. After watching this video, I still don't understand SCR
You're not alone :(
It is pretty complicated. But my best simple-ish explanation is this:
SECR and many other wildlife-focused models, are really 2 (or more, possibly) models put together. In SECR, two models are needed bc there are inherently two processes occurring that produce the data you collect, and you have to model both and try to figure out the parameters of each using only the final product of both (your data).
There is a state model, which is a model or equation that describes what the animals are doing, and a capture or observation model, which describes the effectiveness and characteristics of how you, the researcher, sample or observe the animals. Dr Royle shows visualizations for these two things around 3:57.
The state model in SECR is usually a poisson model where each point in space (cells of a certain size) might contain 0 or more home range centers. The exact parameters of this distribution will be estimated from the data, but it represents the mean # of home range centers (activity centers) in a given space (usually set to whatever plot or area you are sampling with each trap or camera, etc) and how variable they are.
However you have the problem that sometimes those cameras will fail to detect an animal that is actually in that point in space (so a 0 should really be a 1). So we need to add in the second model in the system, the capture model, so we can try to tease out, for all the points in space and time, whether the 0’s we got were true (the animal really isn’t there) or false (it was there and we failed to observe it).
For SECR we model this detection rate as a function of distance from the animal's "activity center" -- it is easier (higher p) to observe the animal when you put the trap near its AC and harder when it is farther away from the AC. When you run SECR you choose a curve that best fits your system. Usually it is the halfnormal curve, which dr royle shows around 4:44, which has the parameters g0 and sigma. g0 is the detection rate if you stuck the trap right in the center of the AC. sigma is the distance from the y-axis to the point where the curve switches from accelerating to decelerating (halfway through the curve). This helps you scale your capture functions according to your species or system - for elephants sigma might be thousands of meters, for rabbits it would be much smaller. But the shape of the curve is the similar. There are other options for curves, as well as additional parameters that describe different kinds of traps.
In most cases, for example, Animal #1 will be caught relatively often at some cameras, sometimes at a few others, and never at others. This set of captures, how they are arranged, when they happened, how far apart consecutive observations are, across all animals and locations and occasions, can help us determine the g0 and sigma parameters, and D (the last one is what we’re usually interested in). Additionally, p (or g0) is never 1 so there are also some number of animals that we never observe, and our capture model has to account for this.
They get very long, but you can write out the likelihood statements for all the parameters of your 2 submodels, which would be, in pseudo technical notation:
Likelihood of (capture model parameter values C, state model parameters S; given n, the number of animals observed; and their capture histories, w) = (Probability of observing n | C and S) * (Prob of all w’s given n, C, and S)
C and S are generic terms representing the vector of values of the parameters for the chosen state and capture models. Eg, half-normal for your capture model (which have the parameters g0 and sigma) and a Poisson point process model for state (which has a parameter called lambda which tells you how many AC’s can be in a certain area and how much does that tend to vary).
The values for C and S are derived numerically, meaning we make the computer try many, many combinations of values for C and S, and for each set a likelihood is estimated based on the observed data - in effect, what is the probability that our capture model has values C, and our state model has values S, given the data we observed. The values of C and S with the highest likelihoods are the ones we go with.
This paper goes over most of it, and there is more to it, including allowing parameters to vary with certain habitat or geographic variables, etc.
www.otago.ac.nz/density/pdfs/Borchers%20&%20Efford%20Biometrics%202008.pdf