View source for Canadian lynx data

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The Canadian lynx data set used in [[Time series|time series]] modelling is the annual record of the number of the Canadian lynx  "trapped"  in the Mackenzie River district of the North-West Canada for the period 1821–1934. These data are actually the total fur returns, or total sales, from the London archives of the Hudson's Bay Company in the years of 1821–1891 and 1887–1913; and those for 1915 to 1934 are from detailed statements supplied by the Company's Fur Trade Department in Winnipeg; those for 1892–1896 and 1914 are from a series of returns for the MacKenzie River District; those for the years 1863–1927 were supplied by Ch. French, then Fur Trade Commissioner of the Company in Canada. By considering the time lag between the year in which a lynx was trapped and the year in which its fur was sold at auction in London, these data were converted in [[#References|[a2]]] into the number that were presumably caught in a given year for the years 1821–1934 as follows:

269, 321, 585, 871, 1475, 2821, 3928, 5943, 4950, 2577, 523, 98, 184, 279, 409, 2285, 2685, 3409, 1824, 409, 151, 45, 68, 213, 546, 1033, 2129, 2536, 957, 361, 377, 225, 360, 731, 1638, 2725, 2871, 2119, 684, 299, 236, 245, 552, 1623, 3311, 6721, 4254, 687, 255, 473, 358, 784, 1594, 1676, 2251, 1426, 756, 299, 201, 229, 469, 736, 2042, 2811, 4431, 2511, 389, 73, 39, 49, 59, 188, 377, 1292, 4031, 3495, 587, 105, 153, 387, 758, 1307, 3465, 6991, 6313, 3794, 1836, 345, 382, 808, 1388, 2713, 3800, 3091, 2985, 3790, 674, 81, 80, 108, 229, 399, 1132, 2432, 3574, 2935, 1537, 529, 485, 662, 1000, 1590, 2657, 3396.

The above time lag was not constant. It depended on the month in which the animal was trapped and the date of shipment. It was also noticed that the catchment area of the animal did not remain constant throughout the period 1821–1934.

M.G. Bulmer [[#References|[a1]]] observed that the data on many animal populations in North Canada were periodic with a period of  $  9.63 $
years for each cycle. The lynx population was one of them having this cycle. He also found that the tendency to cycle is most pronounced in the Midwest of Canada but this tendency became weaker (and later) as one moved away from this region. The simplest explanation for the cause of the cycle in all species which is acceptable to biologists is their relation, through the food chain, with the corresponding cycle in the snowshoe hare population. For example, the snowshoe hare is a dominant item in the food of the lynx, coyote, red fox, and fisher.

In the cycle of the Canadian lynx data it is noticed that the ascent periods exceed the descent periods as below:<table border="0" cellpadding="0" cellspacing="0" style="background-color:black;"> <tr><td> <table border="0" cellspacing="1" cellpadding="4" style="background-color:black;"> <tbody> <tr> <td colname="1" style="background-color:white;" colspan="1">ascent</td> <td colname="2" style="background-color:white;" colspan="1">descent</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"></td> <td colname="2" style="background-color:white;" colspan="1"></td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"> $  \geq  $
7</td> <td colname="2" style="background-color:white;" colspan="1"></td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"></td> <td colname="2" style="background-color:white;" colspan="1">4</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1">6</td> <td colname="2" style="background-color:white;" colspan="1"></td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"></td> <td colname="2" style="background-color:white;" colspan="1">4</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1">6</td> <td colname="2" style="background-color:white;" colspan="1"></td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"></td> <td colname="2" style="background-color:white;" colspan="1">4</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1">5</td> <td colname="2" style="background-color:white;" colspan="1"></td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"></td> <td colname="2" style="background-color:white;" colspan="1">4</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1">5</td> <td colname="2" style="background-color:white;" colspan="1"></td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"></td> <td colname="2" style="background-color:white;" colspan="1">3</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1">6</td> <td colname="2" style="background-color:white;" colspan="1"></td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"></td> <td colname="2" style="background-color:white;" colspan="1">4</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1">6</td> <td colname="2" style="background-color:white;" colspan="1"></td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"></td> <td colname="2" style="background-color:white;" colspan="1">4</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1">6</td> <td colname="2" style="background-color:white;" colspan="1"></td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"></td> <td colname="2" style="background-color:white;" colspan="1">3</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1">6</td> <td colname="2" style="background-color:white;" colspan="1"></td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"></td> <td colname="2" style="background-color:white;" colspan="1">4</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1">5-8</td> <td colname="2" style="background-color:white;" colspan="1"></td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"></td> <td colname="2" style="background-color:white;" colspan="1">6-3</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1">6</td> <td colname="2" style="background-color:white;" colspan="1"></td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"></td> <td colname="2" style="background-color:white;" colspan="1">4</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"> $  \geq  $
5</td> <td colname="2" style="background-color:white;" colspan="1"></td> </tr> </tbody> </table>

</td></tr> </table>

The marginal histogram of the data shows obvious bimodality and more analysis of the data can be found in [[#References|[a3]]].

The Canadian lynx data also often serve as a testing ground for predator-prey models (cf. also [[Predator-prey system|Predator-prey system]]). See also [[Canadian lynx series|Canadian lynx series]].

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  M.G. Bulmer,   "A statistical analysis of the 10-year cycle in Canada"  ''J. Anim. Ecol.'' , '''43'''  (1974)  pp. 701–715</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  C. Elton,   M. Nicholson,   "The ten-year cycle in numbers of the lynx in Canada"  ''J. Anim. Ecol.'' , '''11'''  (1942)  pp. 215–244</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top">  H. Tong,   "Nonlinear time series: a dynamical system approach" , Clarendon Press  (1990)</TD></TR></table>