Biology Reference
In-Depth Information
0.45
0.55
0.78
1.0
0.35
One-
leaved
plant
Two-
leaved
plant
Three-
leaved
plant
Four-
leaved
plant
0.15
0.21
0.19
0.41
seed
seedling
0.05
0.05
0.27
3.90
40.00
FIGURE 7.1
Life stages, transition probabilities, and reproduction (in italics) for a population of Amer-
ican ginseng. Values represent the average number of plants for every one plant that tran-
sition to another stage (or remain in the same stage) from one year to the next. In other
words, for every 1 seed, 0.15 seedlings will be present in the next year, and for every 1
three-leaved plant 3.90 seeds will be present in the next year. Data taken from Population
2, 1986-1987 in [
10
].
With six life stages all possibly transitioning into all other stages, we have 36
different elements to keep track of, and we use a 6
×
6 matrix:
⎛
⎝
⎞
⎠
A
1
,
1
A
1
,
2
A
1
,
3
A
1
,
4
A
1
,
5
A
1
,
6
A
2
,
1
A
2
,
2
A
2
,
3
A
2
,
4
A
2
,
5
A
2
,
6
A
3
,
1
A
3
,
2
A
3
,
3
A
3
,
4
A
3
,
5
A
3
,
6
.
A
4
,
1
A
4
,
2
A
4
,
3
A
4
,
4
A
4
,
5
A
4
,
6
A
5
,
1
A
5
,
2
A
5
,
3
A
5
,
4
A
5
,
5
A
5
,
6
A
6
,
1
A
6
,
2
A
6
,
3
A
6
,
4
A
6
,
5
A
6
,
6
Each row and column in the matrix represents a life stage; the columns are for
the life stage in a given year (time
t
0
), and the rows represent the life stages in the
next year (time
t
0
+
1). Each element in the matrix represents the average number
of new plants in the next year that are produced by a single plant in the current year.
In other words, if the value in the second column (representing seedlings) and third
row (representing one-leaved plants) is
A
3
,
2
=
21, we expect for every one seedling
at time
t
0
there will be 0.21 one-leaved plants in the population at time
t
0
+
0
.
1. To put
it another way, 21% of the seedlings will survive to be one-leaved plants in the next
year.
The first column in the matrix represents the transition from the stage of being a
seed to all other possible stages. Seeds can only become seedlings in the first year;
therefore all but one of the values in the first column will be zero. More formally, and
drawing from the data presented in Figure
7.1
:
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