Clarks 2Dt function in R

<bialozyt <at> biologie.uni-marburg.de> writes:

you answerd to Nancy Shackelford about Clarks 2Dt function.
Since the thread ended just after your reply,
I would like to ask, if you have an idea how to use this function in R

I got started on your problem, but I didn't finish it.
I got a plausible answer to start with, but when checking
the answer I ran into some trouble.  Unfortunately, fitting
these functions is a bit harder than one might expect ...
it takes quite a bit of fussing to get a good, reliable answer.

  My partly-worked solution is below.

## fixed
clark2Dt <- function(x , p, u=1) {
   (p/(pi*u))/(1+(x^2/u))^(p+1)
 }

it might be easier to read this way (but is basically the same):

clark2Dt <- function(x , p, u=1) {
    p/(pi*u*(1+(x^2/u))^(p+1)))
}

It might be preferable to define this in terms of s=sqrt(u)
instead (then s would be a scale parameter with the same units
as x, more easily interpretable ...

Maybe, we discuss about that later on.

## assume these are traps/samples with unit size
## (if not, it will get absorbed into the "fecundity" constant
sorry, the data I presented had been values from an histogram.
The original values are distances of a seed to the mother tree (collected
at the ground and analysed by genetic methods)
distance.g <- c(9.47232811914168, 11.5630878232601, 17.3827098005335,
17.5600939627878, 
18.654398944747, 19.275178339348, 21.8818486421527, 24.7435850272904, 
24.7435850272904, 26.7718434185444, 27.0590058941556, 29.6521854169334, 
31.1320799176942, 35.3820703187569, 35.3820703187569, 37.8337534486551, 
39.1764342432586, 42.2206217394529, 42.2206217394529, 46.6070488232746, 
47.0958352718993, 47.879233494707, 48.2387406553514, 50.8665115768823, 
52.6980549929627, 61.1531879793733, 64.2214247742698, 77.1263333762711, 
77.202254500777, 77.3194477483065, 79.4948180709245, 79.5726567345014, 
79.5726567345014, 88.0804024742081, 89.2390553520044, 91.2574654483515, 
114.565764954916, 114.565764954916, 116.17115175455, 117.152046504188, 
117.268056179105, 117.453800704495, 119.837877150803, 120.140648408006, 
121.44946356442, 122.510601174015, 126.837244136672, 126.837244136672, 
127.566961633094, 129.663329048668, 133.908240597828, 136.759605878483, 
139.003489164914, 139.50556763001, 139.50556763001, 139.50556763001, 
146.974468871303, 147.755130536613, 147.755130536613, 162.676537028077, 
162.866514667679, 166.683866645741, 167.76249998129, 169.292965300547, 
181.234937305426, 184.245751646494, 184.245751646494, 184.274614639389, 
186.352049626362, 186.515863399008, 187.015197509915, 189.430673862562, 
192.365315220583, 192.365315220583, 193.952885258349, 197.375515451871, 
198.543778799249, 200.520691201501, 205.542393680856, 225.561660084303, 
231.752325770962, 233.023285532692, 233.023285532692, 233.023285532692, 
233.759118752746, 235.325997289608, 239.854566353462, 240.991578690945, 
242.360865240119, 245.316493737478, 250.607074322132, 255.339762865456, 
255.339762865456, 255.373878851326, 259.681179333143, 262.909634855639, 
274.461480903967, 274.461480903967, 275.408697211377, 278.603449547446, 
279.386382094669, 283.251948979172, 283.251948979172, 285.64952739357, 
285.948766389864, 287.336178892847, 293.919249114593, 296.684681943866, 
318.22059219857, 321.528407765743, 321.528407765743, 328.199413922994, 
329.256885273328, 336.700014849395, 340.813815007235, 344.155248252501, 
355.036094643507, 369.731635108215, 413.34522726085, 437.163468053688, 
486.081993289409, 511.989800874079, 513.42775947575)

So, I thought I could just use these values instead of the other ones.

but non of my settings worked:

Would it help to use these data?

Thanks
Ronald