Biology Reference
In-Depth Information
Table 2.4
Exponential growth rates for each pathway, incorporating all data
Time span
(years)
Doubling
time (years)
Pathway
Period
Growth equation
R
2
Biocontrol
1850-1969
120
y = 2.7980e
0.3000x
0.9547
23.0
Cargo
1850-1999
150
y = 6.0163e
0.2215x
0.9301
31.2
1890-1999
80
y = 10.991e
0.2943x
0.9888
23.4
Food
1850-1989
140
y = 3.0237e
0.2492x
0.9476
27.7
“Intentional”
1850-1999
150
y = 11.147e
0.2136x
0.9795
32.3
1890-1999
80
y = 42.370e
0.1766x
0.9801
39.1
Nursery
1850-1999
150
y = 2.0542e
0.1677x
0.8193
41.1
1930-1999
70
y = 3.6361e
0.3844x
0.8755
17.9
Pet trade
1920-1999
80
y = 17.367e
0.4501x
0.9949
15.3
Overall
1850-1999
150
y = 23.709e
0.2567x
0.9948
26.9
Fig. 2.16
Cumulative growth in reptile and amphibian introductions via the nursery-trade path-
way, 1930-1999. Blue line = data for nursery-trade introductions; red line = best-fitting exponen-
tial equation for those data, modelled by the function y = 3.6361e
0.3844x
, with R
2
= 0.8755
Similarly changeable dynamics characterize the cargo pathway and explain why
it has surpassed the “intentional” pathway in numerical importance despite the latter's
considerable and long-standing lead (Fig. 2.15). Visual inspection of the fit of the
equation to the cumulative growth curve for the cargo pathway (Fig. 2.17) shows
that the equation is being constrained by the simultaneous need to explain relatively
low growth rates in the 1850s as well as significantly higher ones later in the 20th
century. One can provide a better-fitting model by focusing only those data since
the 1890s, the point at which the cargo-pathway data and the exponential model
begin to diverge. Doing this (Fig. 2.18) indicates that throughout the 20th century
the cargo pathway has actually maintained a higher exponent (0.2943) and, conse-
quently, shorter doubling time (23.4 years) than has the “intentional” pathway
