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FYI: A Sample of Multivariate Temporal Dynamic Analysis
Dear Colleagues,
Attached is a sample of multivariate temporal dynamic analysis.
When I was preparing this mail, I have already received a response
from Mr. Marco Canepa from Italy. He said in his mail:
" ..the 15th observation data are:
A: 520
B: 234
C: 1120
D: 1404
E: 370
I immediately noticed a correct prediction for C and D,
A is correct as far as trend, B and E are not very correct.."
The multidimensional sphere model (MDSM) was originally developed
for vegetation data. Thanks Mr. Marco, who shed a light to the
model: it could also be used on microbiology or entomology for data
synthesis and analysis. Data in these fields are more accurate and
with a shorter time intervals. It might be easier to conduct a time
series analysis in these fields. Thus, I posted my communications
with Mr. Marco here to share with you what we discovered and am
looking for more comments and application opportunities.
Thank you for your attention and interest.
T. Jay BAI, Ph.D.
Quantitative Ecologist
970-490-8345
Bai@gpsr.colostate.edu
http://lamar.colostate.edu/~jbai
==========================
Dear Marco,
Please find enclosed multivariate temporal dynamic analysis output
that you requested.
Your variables A, B, C, D, and E were represented by numbers, 1, 2,
3, 4, and 5, respectively. I am not sure what they represent. Just
as an example, I assumed that these species were plant species, and
the values were their productions, and I further assumed that your data
were vegetation data, i.e., all five species were collected from the
same community. Under these presumptions, I performed a multivariate
temporal dynamic analysis. If these data were other ecological data,
then you can convert them to responded species accordingly.
There are two tables attached. The first table, MarcoData, is your
original data. The second table, Marcoout, is the output of the
computer software of MultiDimensional Sphere Model (MDSM).
The MDSM treats your vegetation data as 5 component vectors, 5-vector,
and every species as a component of the vector. For example, the five
values, 504, 280, 1453, 1344, and 368 together made the 5-vector that
represents the vegetation of the first year. In other words, the
column D is a 5-vector representing the observation of the vegetation
at given year, and same as the column P (projection), E (expectation),
R (prediction error), and T (multivariate instantaneous trend, see below).
There are 14 identical tables inside the Marcoout for each year of the
14 years. There are eight columns and they are explained briefly below:
The first column is the variable names, such as plant species, 1, 2, 3,
4, and 5; or V-SUM, Cos, and SMC.
P: projection values of the given year based on the previous information.
(But for the first year, the projection values are the same as the original
vegetation observation data.)
D: Observation Data. These are the values that the program read from
the input vegetation data that you supplied.
E: Expectation. Expected true values of the vegetation at given year
(E=P+D, it is weighted averages from projections and observations).
IV: Importance Values. It is the importance values, or relative composition,
of the plant species in the vegetation.
R: Projection Error. (R=E-P. Please notice that, the error definition is
the difference between the projections and expectations, instead of
between the projections and observations.)
T: Multivariate Instantaneous Trend.
[T=IV(k)/IV(k-1). This model analyzes the composition change of the
vegetation. It considers the composition change is the essential change
of the vegetation, or any community.]
P(k+1): Vegetation Projection for the next year.
(k is the index of the year.)
The first five rows of the output describe the five species. The last
three rows describe the general condition of the vegetation.
V-SUM: vector sum, or vector lengths, describe the general situation
of the vegetation
Cos: Cosine values between the two vectors describing the correlation
between the two vectors. (The Cosine values under column D express the
correlation between the observations: cosine<D(k), D(k-1)>, while the
values under column E express the correlation between the observation
and expectation: cosine<D,E>.)
SMC: System Monitoring Coefficient, SMC=Cos<E,D>/Cos<D,D>. When the
SMC value is greater than or close to one, we consider that the model is
working for system monitoring and it's projections were over fitting or
correct fitting the observations.
The lowest SMC value during the 14 years is the year of 11: 0.9981,
and the highest SMC values occurred on year of 10: 1.0030. As both of
them are not much less than one, we consider the projections are
fitting with the observations.
In your original email, you asked that:" What would the next sequence
of number will be ?" As a temporal dynamic analysis model, the MDSM
projected the values for the 15th year's vegetation. The values for
the plant species 1, 2, 3, 4, and 5, are:
597.59, 255.02, 1133.47, 1408.26, and 410.30, respectively.
How close is this projection? We have to wait till next year to
find out. But from the history of the analysis, i.e., the year of
2-13, we can expect that it would be a very close projection.
For your second question: "Is there a software available able to work
this out?" The answer is yes. A DOS executable computer program,
SMM52 based on MDSM performing temporal dynamic analysis, can be
down loaded from my webpage:
http://lamar.colostate.edu/~jbai
(You can just click the webpage address, instead of typing it, as you
mentioned that there is no "wave" key on your keyboard. Furthermore,
there are some other references about this model that you may be
interested to check out from the web page. )
If you have any more questions, please contact us or send your message to
MDSM@grpsr.colostate.edu
Best Wishes,
T. Jay Bai, Ph.D.
USDA-ARS GPSR
Ft. Collins, CO 80521
(970)490-8345
bai@gpsr.colostate.edu
http://www.gpsr.colostate.edu/GPSR/higraph/people/jaybai.htm
Table One MarcoData
A 504 466 485 465 436 473 516 481 531 620 624 670 639 621
B 280 271 275 267 261 260 265 253 235 232 241 236 241 247
C 1453 1460 1520 1459 1523 1440 1600 1536 1442 1270 1248 1071 1149 1112
D 1344 1368 1352 1361 1429 1415 1388 1347 1387 1406 1438 1425 1454 1417
E 368 374 410 430 430 409 434 406 384 361 388 381 411 404
Table Two MarcoOut (This was a computer output ASCII file. Readers may need
to aligned them to read it.)
K=1 P D E IV R T Pk+1
------------------------------------------------------------------
1 504.00 504.00 504.00 0.2407 0.00 1.0000 504.00
2 280.00 280.00 280.00 0.1337 0.00 1.0000 280.00
3 1453.00 1453.00 1453.00 0.6938 0.00 1.0000 1453.00
4 1344.00 1344.00 1344.00 0.6418 0.00 1.0000 1344.00
5 368.00 368.00 368.00 0.1757 0.00 1.0000 368.00
V-SUM 2094.13 2094.13 2094.13
Cos 0.0000 0.0000
SMC 0.0000
k=2 P D E IV R T Pk+1
------------------------------------------------------------------
1 504.00 466.00 473.60 0.2252 -30.40 0.9356 436.00
2 280.00 271.00 272.80 0.1297 -7.20 0.9701 262.89
3 1453.00 1460.00 1458.60 0.6935 5.60 0.9995 1459.29
4 1344.00 1368.00 1363.20 0.6481 19.20 1.0099 1381.55
5 368.00 374.00 372.80 0.1773 4.80 1.0087 377.24
V-SUM 2105.59 2103.22 2107.07
Cos 0.9998 0.9999
SMC 1.0001
k=3 P D E IV R T Pk+1
------------------------------------------------------------------
1 436.00 485.00 475.20 0.2220 39.20 0.9860 478.23
2 262.89 275.00 272.58 0.1274 9.69 0.9819 270.03
3 1459.29 1520.00 1507.86 0.7045 48.56 1.0159 1544.18
4 1381.55 1352.00 1357.91 0.6345 -23.64 0.9789 1323.48
5 377.24 410.00 403.45 0.1885 26.21 1.0635 436.04
V-SUM 2148.78 2140.20 2151.25
Cos 0.9996 0.9995
SMC 0.9999
k=4 P D E IV R T Pk+1
------------------------------------------------------------------
1 478.23 465.00 467.65 0.2208 -10.58 0.9943 462.35
2 270.03 267.00 267.61 0.1263 -2.42 0.9919 264.85
3 1544.18 1459.00 1476.04 0.6968 -68.15 0.9890 1443.02
4 1323.48 1361.00 1353.50 0.6390 30.01 1.0071 1370.65
5 436.04 430.00 431.21 0.2036 -4.83 1.0799 464.35
V-SUM 2110.31 2118.23 2112.00
Cos 0.9996 0.9995
SMC 0.9998
k=5 P D E IV R T Pk+1
------------------------------------------------------------------
1 462.35 436.00 441.27 0.2028 -21.08 0.9186 400.53
2 264.85 261.00 261.77 0.1203 -3.08 0.9523 248.56
3 1443.02 1523.00 1507.00 0.6926 63.98 0.9940 1513.83
4 1370.65 1429.00 1417.33 0.6514 46.68 1.0195 1456.82
5 464.35 430.00 436.87 0.2008 -27.48 0.9863 424.12
V-SUM 2191.96 2175.77 2194.55
Cos 0.9997 0.9996
SMC 0.9999
k=6 P D E IV R T Pk+1
------------------------------------------------------------------
1 400.53 473.00 458.51 0.2140 57.98 1.0554 499.19
2 248.56 260.00 257.71 0.1203 9.16 1.0000 259.99
3 1513.83 1440.00 1454.77 0.6791 -59.06 0.9805 1411.92
4 1456.82 1415.00 1423.36 0.6645 -33.45 1.0200 1443.34
5 424.12 409.00 412.02 0.1923 -12.10 0.9579 391.80
V-SUM 2129.42 2142.13 2132.38
Cos 0.9995 0.9994
SMC 1.0000
k=7 P D E IV R T Pk+1
------------------------------------------------------------------
1 499.19 516.00 512.64 0.2313 13.45 1.0806 557.61
2 259.99 265.00 264.00 0.1191 4.01 0.9901 262.38
3 1411.92 1600.00 1562.38 0.7049 150.47 1.0380 1660.85
4 1443.34 1388.00 1399.07 0.6313 -44.27 0.9500 1318.64
5 391.80 434.00 425.56 0.1920 33.76 0.9983 433.25
V-SUM 2238.61 2216.31 2250.49
Cos 0.9982 0.9980
SMC 0.9998
k=8 P D E IV R T Pk+1
------------------------------------------------------------------
1 557.61 481.00 496.32 0.2285 -61.29 0.9880 475.25
2 262.38 253.00 254.88 0.1174 -7.50 0.9853 249.27
3 1660.85 1536.00 1560.97 0.7188 -99.88 1.0196 1566.12
4 1318.64 1347.00 1341.33 0.6176 22.68 0.9784 1317.92
5 433.25 406.00 411.45 0.1895 -21.80 0.9867 400.60
V-SUM 2152.65 2171.72 2153.63
Cos 0.9999 0.9991
SMC 0.9992
k=9 P D E IV R T Pk+1
------------------------------------------------------------------
1 475.25 531.00 519.85 0.2447 44.60 1.0706 568.50
2 249.27 235.00 237.85 0.1120 -11.42 0.9539 224.17
3 1566.12 1442.00 1466.82 0.6904 -99.29 0.9605 1385.07
4 1317.92 1387.00 1373.18 0.6463 55.26 1.0464 1451.41
5 400.60 384.00 387.32 0.1823 -13.28 0.9622 369.49
V-SUM 2118.44 2124.63 2129.55
Cos 0.9986 0.9984
SMC 0.9998
k=10 P D E IV R T Pk+1
------------------------------------------------------------------
1 568.50 620.00 609.70 0.2964 41.20 1.2115 751.11
2 224.17 232.00 230.43 0.1120 6.27 1.0007 232.17
3 1385.07 1270.00 1293.01 0.6286 -92.05 0.9105 1156.39
4 1451.41 1406.00 1415.08 0.6880 -36.33 1.0645 1496.63
5 369.49 361.00 362.70 0.1763 -6.79 0.9673 349.19
V-SUM 2039.19 2056.87 2077.77
Cos 0.9963 0.9993
SMC 1.0030
k=11 P D E IV R T Pk+1
------------------------------------------------------------------
1 751.11 624.00 649.42 0.3155 -101.69 1.0643 664.13
2 232.17 241.00 239.23 0.1162 7.07 1.0374 250.01
3 1156.39 1248.00 1229.68 0.5974 73.29 0.9503 1185.94
4 1496.63 1438.00 1449.73 0.7043 -46.90 1.0237 1472.05
5 349.19 388.00 380.24 0.1847 31.05 1.0475 406.44
V-SUM 2055.08 2058.49 2059.65
Cos 0.9998 0.9978
SMC 0.9981
k=12 P D E IV R T Pk+1
------------------------------------------------------------------
1 664.13 670.00 668.83 0.3383 4.69 1.0724 718.53
2 250.01 236.00 238.80 0.1208 -11.21 1.0394 245.31
3 1185.94 1071.00 1093.99 0.5534 -91.95 0.9264 992.19
4 1472.05 1425.00 1434.41 0.7256 -37.64 1.0303 1468.21
5 406.44 381.00 386.09 0.1953 -20.35 1.0573 402.85
V-SUM 1956.38 1976.81 1969.47
Cos 0.9970 0.9996
SMC 1.0025
k=13 P D E IV R T Pk+1
------------------------------------------------------------------
1 718.53 639.00 654.91 0.3264 -63.62 0.9646 616.41
2 245.31 241.00 241.86 0.1205 -3.45 0.9978 240.46
3 992.19 1149.00 1117.64 0.5570 125.45 1.0064 1156.40
4 1468.21 1454.00 1456.84 0.7260 -11.36 1.0006 1454.80
5 402.85 411.00 409.37 0.2040 6.52 1.0446 429.31
V-SUM 2017.33 2006.61 2018.86
Cos 0.9994 0.9976
SMC 0.9983
k=14 P D E IV R T Pk+1
------------------------------------------------------------------
1 616.41 621.00 620.08 0.3141 3.67 0.9623 597.59
2 240.46 247.00 245.69 0.1244 5.23 1.0325 255.02
3 1156.40 1112.00 1120.88 0.5677 -35.52 1.0193 1133.47
4 1454.80 1417.00 1424.56 0.7215 -30.24 0.9938 1408.26
5 429.31 404.00 409.06 0.2072 -20.25 1.0156 410.30
V-SUM 1963.24 1974.32 0.00
Cos 1.0000 0.9999
SMC 0.9999
-----Original Message-----
From: marco [SMTP:sandeco@MBOX.VOL.IT]
Sent: Tuesday, June 09, 1998 3:23 AM
To: ECOLOG-L@UMDD.UMD.EDU
Subject: number of species -Mathem. predetermination-
Hello everyone,
Who could be useful for this problem.
I am a biologist and in my ecology researches I try to forecast what the
evolution in the number of animal species will be assumed there is an
interrelation with cohabitant living organisms. Example:
In a pond we find 4 species of living organisms : A, B, C, D, In monthly
surveys we observe if their number increased, decreased, or remained constant
thus assessing them respectively 1, 2, X.
After 10 observations the result will be:
1 1 1 2 1 2 1 X X 2 for specie A
2 1 1 1 2 1 1 2 1 2 for B
1 2 1 X 1 2 2 2 1 1 for C
2 1 2 1 1 2 1 2 2 2 for D
What would the next sequence of number will be ?
There always is a law which is non-visible to the eye but identifyable
through a system. Is there a software available able to work this out
?. Thanks. Marco/Italy