BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:Elasticity analysis of random matrices in matrix population model
s
DTSTART;VALUE=DATE-TIME:20180709T094500Z
DTEND;VALUE=DATE-TIME:20180709T100000Z
DTSTAMP;VALUE=DATE-TIME:20241102T171719Z
UID:indico-contribution-247@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Takenori Takada (Hokkaido University)\nProjection ma
trix models are known to provide us with a plenty of population statistics
\, such as population growth rate\, steady size-class distribution\, and s
ensitivity and elasticity for population growth rate. Hundreds of academic
papers using the model have been published these last forty years and a d
atabase on many of their matrices is now available on the internet (COMPAD
RE and COMADRE)\, which contains the demographic data on more than a thous
and species. Silvertown *et al*. (1996) published a famous paper\, where t
hey mapped elasticity vectors of survival\, growth and fecundity for 84 pl
ant species in a triangle simplex and found that they are located in a spe
cific region. The same trend is found on the map for 1230 plant population
s in the above plant database. To understand and clarify why they are loca
ted in a specific region\, we constructed five types of random matrices. 4
by 4 random matrices were composed of two parts: fecundity and transition
probabilities from a stage to another. The distribution of fecundities fo
llowed a Poisson distribution. The transition probabilities range from zer
o to one\, whose row sums are less than 1. The elasticities for survival\,
growth and fecundity were calculated using 3000 random matrices and the e
lasticity vectors were plotted in the triangle map. The five types of matr
ices were as follows: (1) random matrices with no zero-element\, (2) rando
m matrices with no zero-element and the survival probabilities increase as
individuals grow\, (3) random matrices which have non-zero elements only
on diagonal and sub-diagonal positions\, (4) random matrices which have no
n-zero elements only on diagonal and sub-diagonal positions and the surviv
al probabilities increase as individuals grow\, (5) random matrices in sem
elparous species. The results are: (a) the distribution of the elasticity
vectors moves to upper-left region of the triangle map as average of fecun
dity increases\, (b) In the third and fourth types of random matrices\, th
e distribution is located on a line whose slope is equal to 46 degrees. Th
e slope can be described by a formula depending on the matrix dimension\,
*n* and ranges from 30 to 60 degrees with *n* = 2 to infinity. (c) In seme
lparous species\, the distribution moves to the upper left along the 46-de
gree line. (d) There are no elasticity vectors in the bottom half of the t
riangle map.\n\nhttps://conferences.maths.unsw.edu.au/event/2/contribution
s/247/
LOCATION:University of Sydney Holme Building/--The Refectory
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/247/
END:VEVENT
END:VCALENDAR