Quantification of Openness

Openness is proportional to the area available for exchange of energy and matter, relative to the volume = the inverse

1 h 1 day 1 week 1 month 1 year 10 years 100 years

Generation time

1 h 1 day 1 week 1 month 1 year 10 years 100 years

Generation time

Figure 1 Length and generation time plotted on log-log scale: (a) Pseudomonas, (b) Daphnia, (c) bee, (d) housefly, (e) snail, (f) mouse, (g) rat, (h) fox, (i) elk, (j) rhino, (k) whale, (l) birch, (m) fir.

Figure 1 Length and generation time plotted on log-log scale: (a) Pseudomonas, (b) Daphnia, (c) bee, (d) housefly, (e) snail, (f) mouse, (g) rat, (h) fox, (i) elk, (j) rhino, (k) whale, (l) birch, (m) fir.

Figure 2 Intrinsic rate of natural increase against weight for various animals.

space scale (L1). It may also be expressed as the supply rate = k x gradient x area relative to the rate of needs, which is proportional to the volume or mass. Table 1 illustrates the relationship between hierarchical level, openness, and the four scale-hierarchical properties presented.

Openness also determines the diversity, which can be seen by the following realtionships between species diversity, SD, on islands and the area of the islands, A:

where C and z are constants.

10-1

10-3

+ Phytoplankton

+ Oysters

+ Homo sapiens

1 cm

10 cm

Figure 3 Excretion of Cd (day-1) plotted against the length of various animals: (1) Homo sapiens, (2) mice, (3) dogs, (4) oysters, (5) clams, (6) phytoplankton.

Length

Figure 4 Uptake rate (mgg-1 per day) plotted against the length of various animals: (1) phytoplankton, (2) clams, (3) oysters.

Length

Figure 4 Uptake rate (mgg-1 per day) plotted against the length of various animals: (1) phytoplankton, (2) clams, (3) oysters.

Table 1 Relationship between hierarchical level, openness (area/volume ratio), and approximate values four scale-hierarchical properties: energy/volume, space scale, timescale, and behavioral frequency

Hierarchical

Opennessac

Energy3

Space scalea

Timescalea

Dynamicsc

level

(A/V, m-1)

(kJm-3)

(m)

(s)

(gm3s-1

Molecules

109

109

10-9

<10-3

104-106

Cells

105

105

10-5

10-103

1-102

Organs

102

102

10-2

104-106

10-3-0.1

Organisms

1

1

1

106-108

10-5-10-3

Populations

10-2

10-2

102

108-1010

10-7-10-5

Ecosystems

10-4

10-4

104

1010-1012

10-9-10-7

aOpenness, spatial scale, and timescale are inverse to hierarchical scale.

bEnergy and matter exchange at each level depend on openness, measured as available exchange area relative to volume. cOpenness correlates with (and determines) the behavioral frequencies of hierarchical levels.

aOpenness, spatial scale, and timescale are inverse to hierarchical scale.

bEnergy and matter exchange at each level depend on openness, measured as available exchange area relative to volume. cOpenness correlates with (and determines) the behavioral frequencies of hierarchical levels.

See also: Generation Time.

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