b-diversity can emerge from stochastic processes
(e.g. local extinctions because of demographic sto-
chasticity; Hubbell 2001), or dispersal limitation
and priority effects, often connected to a patch dy-
namics perspective (Chave and Leigh 2002; Condit
et al. 2002; Chase 2003).
Scale-dependent diversity relationships have
been explicitly observed along gradients of distur-
bance (Chase 2003, 2007; Ostmanet al. 2006) and
gradients of productivity (Mittelbachet al. 2001;
Chase and Leibold 2002; Chase 2003). Scale depen-
dence will occur whenever responses ofa- andg-
diversity do not scale linearly, i.e.b-diversity varies
along the gradient. For example, in a meta-analysis
of the well-studied relationship between productiv-
ity and species diversity, Mittelbachet al. (2001)
found that hump-shaped productivity–diversity
relationships tend to emerge more frequently at
local scales, whereas monotonically increasing pro-
ductivity–diversity relationships tended to emerge
more frequently at regional scales. Chase and
Leibold (2002) showed this scale dependence in
surveys of invertebrates and amphibians from
small fishless ponds in Southwestern Michigan,
USA. When considered on a ‘per-pond’ basis
(local scale), they found a hump-shaped relation-
ship between productivity and diversity, whereas
when the same data were considered on a ‘per-
watershed’ basis (regional scale), a monotonically
increasing relationship between productivity and
diversity was observed (Fig. 5.1a).
Such scale dependence is not universal (e.g. Chase
and Ryberg 2004; Harrisonet al. 2006a). For example,
when comparing the ponds discussed above with
regions where ponds were physically closer and
dispersal was more likely among ponds, Chase and
Ryberg (2004) found thatb-diversity was lower in
regions where dispersal was more likely among
ponds, and no such scale dependence emerged
(Fig. 5.1b). This result could have been due to higherMore Connected Regions(^0020406080100120)
10
20
30
40
(a)
(b)
0 20 40 60 80100120
0
10
20
30
40
0
10
20
30
40
0
10
20
30
40
Productivity
(mg cm-2day-1)
Productivity
(mg cm-2day-1)
Species Richness
Species Richness
Species Richness
0 20 40 60 80 100 120 0 20 40 60 80 100 120
Local Regional
Less Connected Regions
Local Regional
Figure 5.1Scale-dependent productivity–diversity relationships in isolated (a) but not connected (b) watersheds.
Redrawn from Chase and Ryberg (2004).
62 SPACE AND TIME