Differential Loss Rates and Invadability of Equilibria
169
This means that isolines of the functional response will be straight lines
in the C I - C 2 plane corresponding to C I + (J C 2 being constant.
In accordance with Section 4.4, we can assume that ingestion is a
piecewise linear function of the effective food concentration (C), such that
1= I'Min(1.C!C'),
(6.10)
with I' and C' being the maximal ingestion rate and the incipient limiting
food level, respectively, as in Eq. (4.9). Ifwe define C'I as the incipient limiting food level for grazing on species i alone, then we must have C'I = C'
and C'2 = (lc', which again implies that (J = C'!C'2' This means that the
ingestion rate will be constant and equal to I' for all biomass pairs C I and C 2
located above the line from C I to C 2 in the C I - C 2 plane (Fig. 6.6), while the
isolines of the functional response will be parallel to this line. Comparing
Fig. 6.6 with the resource classification scheme of Leon and Thumpson
(1975) suggests that a pair of phytoplankton species subject to invariant
selective grazing can be regarded as perfectly substitutable resources.
Food Selection in Daphnia. Although the issue is not entirely settled, several recent studies (DeMott 1982; Knisely and Geller 1986; Sommer 1988b)
indicate that selectivity in Daphnia (and closely related genera) is of the
invariant type. This should also be expected from the mechanics of cladoceran filter-feeding, which lacks the sophisticated mechanisms for selection
of individual particles that are found, for example, in calanoid copepods
(see, e.g., the review by Sterner 1989).
Knisely and Geller (1986) performed an impressive series of food selection experiments on naturally occurring phytoplankton species by two
species of Daphnia (D. hyalina and D. galeata) over a seasonal cycle in Lake
Constance. In a somewhat different approach, Sommer (1988b) studied
food selection in two Daphnia species (D. longispina and D. magna) in a
two-stage chemostat system inoculated with natural phytoplankton communities. In both studies, the selectivity index (J was calculated from loss
rates estimated directly from decreases in cell counts. Since there was
apparently low similarity between the phytoplankton communities used in
the two studies, they must be considered complementary. Figure 6.7 suggests that the investigated phytoplankton genera cannot be separated into
two disjunct groups of edible and inedible species, but instead form a continuum from high to low edibility. It also appears that no genus was uniformly the preferred food (mean ; < 1 for all genera) and no genus was
completely inedible (all genera have mean; > 0).
169
This means that isolines of the functional response will be straight lines
in the C I - C 2 plane corresponding to C I + (J C 2 being constant.
In accordance with Section 4.4, we can assume that ingestion is a
piecewise linear function of the effective food concentration (C), such that
1= I'Min(1.C!C'),
(6.10)
with I' and C' being the maximal ingestion rate and the incipient limiting
food level, respectively, as in Eq. (4.9). Ifwe define C'I as the incipient limiting food level for grazing on species i alone, then we must have C'I = C'
and C'2 = (lc', which again implies that (J = C'!C'2' This means that the
ingestion rate will be constant and equal to I' for all biomass pairs C I and C 2
located above the line from C I to C 2 in the C I - C 2 plane (Fig. 6.6), while the
isolines of the functional response will be parallel to this line. Comparing
Fig. 6.6 with the resource classification scheme of Leon and Thumpson
(1975) suggests that a pair of phytoplankton species subject to invariant
selective grazing can be regarded as perfectly substitutable resources.
Food Selection in Daphnia. Although the issue is not entirely settled, several recent studies (DeMott 1982; Knisely and Geller 1986; Sommer 1988b)
indicate that selectivity in Daphnia (and closely related genera) is of the
invariant type. This should also be expected from the mechanics of cladoceran filter-feeding, which lacks the sophisticated mechanisms for selection
of individual particles that are found, for example, in calanoid copepods
(see, e.g., the review by Sterner 1989).
Knisely and Geller (1986) performed an impressive series of food selection experiments on naturally occurring phytoplankton species by two
species of Daphnia (D. hyalina and D. galeata) over a seasonal cycle in Lake
Constance. In a somewhat different approach, Sommer (1988b) studied
food selection in two Daphnia species (D. longispina and D. magna) in a
two-stage chemostat system inoculated with natural phytoplankton communities. In both studies, the selectivity index (J was calculated from loss
rates estimated directly from decreases in cell counts. Since there was
apparently low similarity between the phytoplankton communities used in
the two studies, they must be considered complementary. Figure 6.7 suggests that the investigated phytoplankton genera cannot be separated into
two disjunct groups of edible and inedible species, but instead form a continuum from high to low edibility. It also appears that no genus was uniformly the preferred food (mean ; < 1 for all genera) and no genus was
completely inedible (all genera have mean; > 0).