[R-sig-eco] Relationship between x and latitude
Tom_Philippi at nps.gov
Tom_Philippi at nps.gov
Tue Jan 25 23:08:28 CET 2011
If you are interested in characterizing a constraint, e.g., the maximum
plant functional diversity as a function of latitude, in this context,
quantile regression is probably not a good approximation to extreme value
statistics. Quantiles (percentile rankings) are affected by differences in
the numbers of observations with lower values of functional diversity
affect, while extreme value statistics only characterize the upper tail of
the distribution. Quantile regression would indicate how the shape of the
entire distribution of functional diversity changes as a function of
latitude, but that is not the same as estimating a constraint line.
The environmetrics task view has a section on extreme value statistics.
Unfortunately, the peak over threshold approach to quantifying trends in
extreme values in extRemes and other packages requires equal sample
intensity across time (space in your case), and so probably won't work.
You might find something applicable in Mathieu Ribatet's SpatialExtremes
package; I haven't used it and don't know what it includes.
Tom
-------------------------------------------
Tom Philippi
Quantitative Ecologist
Inventory and Monitoring Program
National Park Service
c/o Cabrillo National Monument
1800 Cabrillo Memorial Dr
San Diego, CA 92106
(619) 523-4562
Tom_philippi at NPS.gov
http://science.nature.nps.gov/im/monitor
-------------------------------------------
Peter Francis
<peterfrancis at me.
com> To
Sent by: Pedro Lima Pequeno
r-sig-ecology-bou <pacolipe at gmail.com>,
nces at r-project.or r-sig-ecology at r-project.org
g cc
Subject
01/25/2011 08:30 Re: [R-sig-eco] Relationship
PM GMT between x and latitude
Thanks Pedro and Zoltan, that is very much appreciated.
I agree the relationship between maximum x and latitude is the strongest.
To put "x" into context, it is plant functional diversity. I have accounted
for species richness i.e there are more plants near the equator therefore
if it is not accounted for there will ultimately be more functional
diversity.
So the fact, despite species number being accounted for it is interesting
that this pattern still occurs.
I have two question if you don't mind?
1. My data is based on WWF Eco-regions, and this probably introduces
spatial autocorrelation into the mix, can this be accounted for in quantile
regression?
2. I have another variable i wish to model phylogenetic diversity - i want
to see - if the patterns observed are the same and try and quantify it. I.e
is there a method to describe (mathematically) the line so i can compare?
Thank,
Peter
On 25 Jan 2011, at 19:55, Pedro Lima Pequeno wrote:
Hi, Peter.
X values seem to be higher near the Equator, on average. Nevertheless, the
strongest relation seems to be between maximum values of X and latitude.
That is, perhaps something associated with latitude limits the potential
size of X. I would try a quantile regression model. Quantile regression
allows you to fit regression lines through any quantile of the response
variable (standard regression relates only the mean value of the response
to predictors). For modeling upper values of the response, you could use
upper quantiles such as 95% or 99%. You could try a non linear quantile
regression model, since the relationship you are interested in is
non-monotonic. Package "quantreg" has functions for fitting quantile
regression models in a frequentist framework. Of course, there are several
functions for modeling non-monotonic relations. Also, you need to guess
starting values for model parameters, since model fitting is iterative.
Here is some code just for illustration; there are probably better
functions for modeling this particular relation.
library(quantreg)
plot(latitude, x)
mod = nlrq(x ~ -a*latitude^2*exp(-b*latitude) + c, start = c(a=0.00001,b =
0.01,c = 0.015), tau = 0.95)
# obs.: this function is an adaptation of Ricker's standard model for
non-monotonic ecological relations
summary(mod)
newvalues = seq(-40, 80, length = 478)
lines(newvalues, predict(mod, list(latitude=newvalues)), col = 3, lw = 2)
Hope it helps,
Pedro A. C. Lima Pequeno
2011/1/25 Peter Francis <peterfrancis at me.com>
Dear List,
I am looking at the relationship between a quantity and the distance from
the equator.
Asking the question does latitude effect the value of x - i.e is x higher
or lower as you move away from the equator
I have plotted x against latitude(plot(latitude,x)) and there seems to be
something there, however i was wanting to investigate in a more
quantitative way. I had thought of models but my experience is relatively
low and i am unsure what method would be best for my pattern of data. Any
advice would be greatly appreciated.
###data###
x <-
c(0.015348175, 0.014102894, 0.013158871, 0.012796208, 0.012547266,
0.012499614, 0.011580142, 0.011274077, 0.011026623, 0.010934845,
0.010866659, 0.01075808, 0.010581273, 0.010548757, 0.010415088,
0.010395809, 0.010328903, 0.009754356, 0.009652272, 0.009533795,
0.009179444, 0.009141853, 0.009140609, 0.008882345, 0.008671247,
0.008426542, 0.008407421, 0.008248698, 0.008228469, 0.008169984,
0.008158929, 0.007978867, 0.007893121, 0.007886193, 0.007785512,
0.007613687, 0.007591255, 0.007542375, 0.007532009, 0.007497797,
0.007487081, 0.007469353, 0.007369905, 0.007169296, 0.007122561,
0.007070457, 0.006975594, 0.006948638, 0.006805148, 0.006791063,
0.006783499, 0.006733242, 0.006733242, 0.006701148, 0.006691116,
0.006672124, 0.006660939, 0.006571554, 0.006552405, 0.006536592,
0.006523875, 0.006480761, 0.006471293, 0.006454864, 0.006365157,
0.006356432, 0.006323978, 0.006260515, 0.006188042, 0.006187938,
0.006181114, 0.006181114, 0.006079529, 0.006017497, 0.006008061,
0.005953895, 0.005920824, 0.005899296, 0.00589274, 0.005862688,
0.005853862, 0.005811885, 0.005778694, 0.005736366, 0.005686819,
0.005686362, 0.005621206, 0.005607628, 0.005567988, 0.005532497,
0.005493249, 0.005433072, 0.005429215, 0.005420174, 0.005408397,
0.005382781, 0.005304967, 0.005298177, 0.005273268, 0.005158224,
0.005135415, 0.005092708, 0.005048508, 0.005048015, 0.005044948,
0.005028163, 0.005028163, 0.005014717, 0.004967595, 0.00489943,
0.004887419, 0.004887419, 0.004887419, 0.004861756, 0.004842995,
0.00476598, 0.004734517, 0.004689229, 0.004657052, 0.004624096,
0.004618037, 0.00460988, 0.004606092, 0.004531219, 0.004527051,
0.004506577, 0.004482963, 0.004476035, 0.004476035, 0.004476035,
0.004476035, 0.004476035, 0.004419306, 0.004413048, 0.004366397,
0.00434048, 0.00434048, 0.004302982, 0.004296803, 0.004290441,
0.004285631, 0.004275535, 0.004254518, 0.004207445, 0.004173182,
0.004155142, 0.004134336, 0.004110218, 0.004106806, 0.004105657,
0.004091356, 0.004018147, 0.004003681, 0.003994852, 0.003993325,
0.003983061, 0.003966886, 0.003918854, 0.003917177, 0.003891429,
0.003842899, 0.003842899, 0.003834539, 0.003832233, 0.003818814,
0.003789309, 0.003707218, 0.003697771, 0.003668882, 0.003668882,
0.003602582, 0.003602582, 0.003602582, 0.003591953, 0.003537737,
0.003513987, 0.003464507, 0.003459366, 0.003437983, 0.003400975,
0.003377825, 0.003366575, 0.003285648, 0.003270708, 0.003260783,
0.00318234, 0.00318234, 0.003151494, 0.0031, 0.003094114, 0.003082046,
0.003081427, 0.003069106, 0.003069106, 0.003052216, 0.003036596,
0.003035941, 0.003032508, 0.003023303, 0.003020964, 0.003019848,
0.002981245, 0.002978949, 0.002969224, 0.002958385, 0.002955199,
0.002954933, 0.002954933, 0.002950752, 0.002918346, 0.002906109,
0.002902979, 0.002901011, 0.002896504, 0.002877516, 0.002849816,
0.002843091, 0.002828998, 0.002817939, 0.002816043, 0.002803956,
0.002798723, 0.002790437, 0.002777884, 0.002777884, 0.002777884,
0.002777884, 0.002777884, 0.002777884, 0.002777884, 0.002777555,
0.002776965, 0.002771398, 0.002752354, 0.00272757, 0.002717057,
0.002701395, 0.002687727, 0.002635401, 0.002635401, 0.002635401,
0.002635401, 0.002631182, 0.002623146, 0.002616387, 0.002584465,
0.002578125, 0.002577877, 0.002548996, 0.002488092, 0.002476084,
0.002474694, 0.002451195, 0.002443587, 0.002442069, 0.002439442,
0.002439442, 0.002425784, 0.002418847, 0.002409969, 0.002404593,
0.002401727, 0.002401727, 0.002401727, 0.002400578, 0.002364737,
0.00235511, 0.002326208, 0.002326208, 0.002323944, 0.002317546,
0.002275955, 0.002261807, 0.002219485, 0.002217373, 0.002210748,
0.002208339, 0.002199135, 0.002192113, 0.002171856, 0.002171856,
0.002156217, 0.002126684, 0.002090031, 0.002086738, 0.002086209,
0.002078779, 0.002047235, 0.002040628, 0.002036937, 0.002036773,
0.002036773, 0.002017393, 0.002009864, 0.001999733, 0.001998787,
0.001990045, 0.001986944, 0.001975691, 0.001971625, 0.001945183,
0.001936149, 0.001926163, 0.001919142, 0.001897503, 0.001897503,
0.001887366, 0.001866615, 0.001865528, 0.001860441, 0.001851106,
0.001850471, 0.001807395, 0.001807281, 0.001794796, 0.001790554,
0.001778587, 0.001773777, 0.001770118, 0.001726876, 0.001716987,
0.001705133, 0.001692117, 0.001675794, 0.001605834, 0.001605667,
0.001598937, 0.001575879, 0.001565384, 0.001546179, 0.001534643,
0.001525447, 0.001522089, 0.001502833, 0.001481944, 0.001473202,
0.001452109, 0.001449217, 0.001446246, 0.001446246, 0.001422652,
0.001422652, 0.001375286, 0.001361211, 0.001356151, 0.001347116,
0.001339627, 0.001339627, 0.00133279, 0.001331517, 0.001331517,
0.001331517, 0.001331517, 0.001322368, 0.001306458, 0.001296254,
0.001257304, 0.001238302, 0.001238302, 0.001238302, 0.001223937,
0.001191425, 0.001189038, 0.001180128, 0.001176136, 0.001144119,
0.001122304, 0.001109047, 0.001072805, 0.001072805, 0.001072805,
0.001072805, 0.001072805, 0.001072805, 0.001072805, 0.001072805,
0.001072805, 0.001072805, 0.001072805, 0.001072805, 0.001072805,
0.001072805, 0.001072805, 0.001072805, 0.001072805, 0.001072805,
0.001072805, 0.001072805, 0.001060498, 0.001051146, 0.001051146,
0.001015594, 0.000997827, 0.000979584, 0.000979125, 0.000959362,
0.000932058, 0.000927945, 0.000927867, 0.000909772, 0.000898857,
0.000891068, 0.000816096, 0.000804403, 0.000783013, 0.000781831,
0.000750918, 0.000744673, 0.000739314, 0.000738508, 0.000735344,
0.000712073, 0.000679757, 0.000679757, 0.000674523, 0.000636956,
0.000629264, 0.000623775, 0.000621972, 0.000620247, 0.000617503,
0.000615432, 0.000580207, 0.000548295, 0.000540084, 0.000527764,
0.000518084, 0.000510753, 0.000507758, 0.000493544, 0.000490135,
0.000468122, 0.000468122, 0.000466777, 0.000440226, 0.000420408,
0.000409094, 0.000393234, 0.000373562, 0.000373562, 0.000373562,
0.000373562, 0.000373562, 0.000373562, 0.000373562, 0.000373562,
0.000347605, 0.000344458, 0.000343825, 0.000335533, 0.000315615,
0.000313374, 0.000313148, 0.000246113, 0.000239747, 0.000227964,
0.000224992, 0.000215867, 0.000197565, 0.000196167, 0.000171385,
0.000170994, 0.000156109, 0.000129517, 0.000126808, 0.000126808,
9.35e-05, 6.5e-05, 6.5e-05, 5.95e-05, 5.59e-05, 4.36e-05, 4.36e-05,
4.36e-05, 3.74e-05, 3.34e-05, 2.14e-05, 2.02e-05)
latitude <- c(4.845, -21.9, 6.395, 19.79, 5.385, -25.565, -27.83, 19.93,
-10.995, 6.255, 7.035, 2.51, 15.16, 20.985, -29.59, -10.12, 27.655,
14.405, -0.165, 24.04, 20.765, -12.385, -12.03, 9.955, 11.46,
3.425, 1.01, -4.22, 12.52, 36.325, 8.46, 22.655, 15.11, 41.925,
34.395, 12.12, -30.375, -0.535, 17.47, -11.415, 30.11, 4.84,
-32.045, -18.435, 36.37, 20.55, 2.395, 1.895, -1.17, 35.7, 24.72,
-1.365, -1.035, 37.045, 17.745, 0.955, -15.34, 4.65, -22.675,
-34.015, -23.56, 39.615, -4.415, 28.98, 36.96, 16.39, 41.26,
-0.75, 18.58, 4.395, -32.605, -0.365, 4.975, -17, 40.67, 7.43,
5.07, 2.125, 1.25, 21.28, 3.695, -6.16, 11.13, -35.655, 21.905,
10.54, 5.145, 1.615, 10.29, 13.345, 42.71, 10.405, 39.17, -6.625,
7.845, 19.115, 23.295, 18.065, 7.31, -5.53, 56.1, 10.23, -25.705,
44.31, 17.135, -20.11, -6.87, -5.21, 15.635, -11.675, -46.71,
39, 42.845, -11.505, 18.855, -6.895, 29.55, 11.865, 16.875, -32.09,
-14.44, 32.46, 33.49, -11.655, 7.275, -12.305, -3.35, -34.16,
-3.855, 33.455, 38.615, 54.455, 10.63, 30.775, 37.525, 25.325,
30.935, 43.085, 7.69, -2.235, 11.225, 10.51, 22.26, 9.005, 40.255,
-11.045, 6.33, -1.46, 33.385, -26.69, 9, 29.405, -29.125, 6.57,
34.56, -4.67, -17.94, 28.615, -28.205, 10.95, -2.545, 30.49,
26.935, -4.45, -7.855, -14.835, 29.88, 7.95, 34.84, 39.8, -28.745,
38.275, 43.15, -19.85, 10.695, 0.43, -0.78, -5.69, -5.285, 38.085,
0.685, -3.385, -2.515, 15.44, -20.16, 40.185, 50.705, -6.71,
-37.8, 28.555, -1.58, -0.065, -10.97, 36.505, 48.14, -19.835,
-5.755, 18.3, 14.4, 7.28, 6.965, 36.95, 24.62, -29.885, 16.33,
10.795, -12.5, -0.58, -7.085, 14.885, -14.515, 0.53, 5.84, -32.88,
29.945, -13.44, 23.045, 65.91, 31.525, 20.04, 17.94, -7.855,
-27.86, -8.355, 15.41, 18.165, 18.425, 47.655, 51.59, 56.745,
-2.39, -42.475, 18.05, -14.01, 23.055, -42.19, -24.14, 26.935,
66.305, 68.565, 71.13, 74.72, 38.305, -6.09, -14.18, 31.73, 5.025,
-4.035, -22.18, -16.525, -15.675, 37.645, 23.95, 36.48, -12.39,
47.24, 48.425, -37.45, 18.13, 6.78, 22.71, -40.75, -17.15, 30.16,
41.445, -1.52, 8.795, -2.91, 27.955, 22.075, -12.75, -19.575,
-20.53, 12.665, -7.415, -12.54, 16.46, 23.89, 41.805, -13.615,
-1.475, 38.37, 33.15, 46.965, 33.04, 18.575, -6.08, 10.935, 19.14,
17.165, 38.645, 40.49, 25.725, 25.785, 16.285, 46.095, 8.95,
15.15, -18.045, 45.095, 26.115, 37.54, -0.295, -2.77, -3.445,
46.19, -10.32, 11.33, -6.09, -5.435, 17.76, -26.505, -24.855,
-2.89, 31.965, 42.825, -19.13, 30.43, 29.525, -13.855, 22.8,
0.29, 33.635, 19.055, 37.14, 4.755, -5.4, -1.7, 26.87, -7.1,
19.81, 33.005, 15.805, 1.15, 42.47, 10.73, -15.695, 32.38, 27.93,
45.155, -26.425, -21.545, 36.165, -21.265, 5.775, 20.55, -0.885,
2.82, 8.16, -7.37, 19.11, 39.72, 40.5, -7.91, 19.43, 23.605,
16.935, -11.65, 8.99, 9, 18.845, 41.575, 33.51, -29.935, 37.055,
-28.54, -31.89, 18.34, -32.745, -15.29, -0.96, 0.41, 3.235, 4.12,
12.505, 22.675, 26.05, 35.625, 38.825, 39.015, 40.825, 42.075,
43.48, 44.33, 46.735, 53.115, 57.18, 60.945, 42.555, 21.825,
30.85, 37.205, -26, -28.705, -25.1, 13.195, 22.515, 17.925, -24.31,
-3.495, 3.08, 20.91, -34.72, 18.98, 22.035, 41.88, -1.83, 7.37,
17.175, 39.735, -21.705, 4.835, -28.215, -21.96, 29.755, -5.74,
32.945, 35.14, 21.065, 20.885, -19.72, -5.18, 8.745, 36.335,
17.01, 46.885, 16.285, 27.935, -36.145, -0.85, 12.935, 18.34,
26.99, 26.335, 14.32, 32.01, 5.675, -25.82, -32.665, 4.035, 14.055,
16.65, 20.585, 30.365, 38.725, 46.025, -42.595, 81.835, -32.405,
24.455, 12.87, 30.595, 20.505, -29.405, 19.99, 42.565, 6.78,
12.84, 39.43, 20.065, 35.13, 35.91, 18.39, -34.33, -5.805, 20.715,
18.18, 19.575, 20.535, 44.73, 42.605, -13.615, 7.745, 11.37,
9.455, 42.595, 31.305, 9.835)
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