Consumer-resource systems are generally characterized by intricacy, driven by the interactions among individuals. Competition is a density dependent process which allows for indirect and direct interactions between foraging individuals, and thus it can be divided in two discrete phenomena (Begon et al. 1996): exploitation competition, where individuals are affected by the amount of remaining resource which has been exploited by others and therefore depleted, and interference competition that occurs via direct interactions between individuals. Furthermore, mutual interference involves individuals of the same species (Hassell 1971).
Modeling consumers’ functional responses, i.e. the number of prey attacked per predator as a function of prey density, is a central goal for ecologists, since the assessment of populations' performance allows for further decisions in environmental management. The density-dependent concept of a single predator’s feeding rate developed by Holling (1959a,b) dealt with early population models’ presumption which requires the number of attacked prey to be proportional to the density of prey (Beddington 1975). Despite its simplicity and questionable assumptions, ecologists often utilize Holling’s disc equation, which descibes an inverse density dependent
88 prey mortality, commonly occurred in invertebrate predators (Hassell 1978), given by (Holling 1959b):
N aT aNP dt
dN
h
1 (1)
where N denotes the prey density; P the predator debsity; a the predator’s attack rate, i.e. the per capita prey mortality at low prey densities and Th the handling time which reflects the time a predator spends on pursuing, subduing, eating and digesting its prey. Eq. (1) states that the predator’s feeding rate is independent of its density.
Crowley and Martin (1989) argued with this independence assumption by developing a model, commonly known as Crowley-Martin model:
1
1
1
aT N bt P aTbt N P aNP
dt dN
w h w
h
(2),
where b denotes the rate of encounter with other predators and tw the time wasted on other predators. Eq. 2 challenged Holling’s assumption of negligible predator- dependence in functional response, and represent reasonable alternative to the disc equation (Skalski and Gilliam 2001).
Predaceous coccinellidae species (Coleoptera: Coccinellidae) are well known predators of insect pests and their role as biocontrol agents has long been recognized (Dixon, 2000). Their ability as biocontrol agents, as well as their abundance in different habitats, renders the careful study of this taxa imperative. Aphidophagous species are widely distributed in both Palearctic and Nearctic region, preying on numerous economicaly imporant aphid species (Homoptera: Aphididae) (Hodek 1996). Their efficiency in suppressing aphids’ populations makes them popular in biological control, especially in short term periods (Obrycki et al. 2009). Ecology of aphidophagous coccinellids suggests that they display aggregation to their prey (Schellhorn and Andow 2005). Additionally, larvae typically stay within a patch during their life, unlike adults which are characterized by their ability to make flights (Dostalkova et al. 2002). As larvae are exposed to each other, frequent encounters may affect their foraging success. Therefore, a study was initiated in order to determine the effect of mutual interference in coccinellids’ feeding rate. The fourteen- spotted ladybird beetle Propylea quatuordecimpunctata, which is widespread throughout Europe and has been established in Nearctic region (Day et al. 1994), was used as model organism.
89 6.3. Materials and methods
6.3.1. Study organisms
An original strain of P. quatuordecimpunctata were collected from Zea mays L. plants in Arta County (Northwestern Greece, 21°0’0’’/39°10’0’’). Adults and immature stages were tranfered to Biological Control Laboratory, Benaki Phytopathological Institute, and reared in Plexiglass cages (50 cm length X 30 cm diameter) at 25 ± 1 ºC, 65 ± 2% RH and a photoperiod of 16L:8D. A stock colony of Aphis fabae Scopoli (Homoptera: Aphididae) fed on potted Vicia faba L. plants and maintained at 20 ± 1 ºC was used as prey for the coccinellid.
6.3.2. Microcosm experiments
Functional response experiments were carried out at 25 ± 1°C, 65 ± 2% R.H., with a photoperiod of 16:8 (L:D) h. The experimental arena consisted of a plastic container (12 cm height x 7 cm diameter) with a potted V. faba plant (at 8-9 cm height, top growth was cut) bearing different densities of A. fabae (3-3.5 day-old, immature aphids to avoid any reproduction during the experiments). Newly emerged first instars of P. quatuordecimpunctata, collected from the stock colony, were kept individualy in plastic cages (5 cm height X 10 cm diameter) and fed ad libitum with intars and adults of A. fabae. We used 0.5-1.5 day-old fourth instar larvae. The prey densities tested were 5, 10, 15, 20 and 25 aphid nymphs for individual predators, 10, 20, 30, 40 and 50 nymphs for couple of predators, 15, 30, 45, 60 and 75 nymphs when predator density was three larvae and 20, 40, 60, 80 and 100 nymphs when predator density was four larvae. Exposure time was 6 h. Ten replicates on each prey density were formed. At the end of each experimental period we counted the number of aphids not eaten by the predator.
6.3.3. Statistical analysis
Data fitted to Crowley-Martin model (eq. 2). Because parameters b and tw are mathematically indistinguisible, i.e. they always appear together, we grouped them into one parameter c which is a positive constant describing the magnitude of interference among predators (Skalski and Gilliam 2001, Kratina et al. 2009):
1
1
1
aT N cP aT cN P aNP
dt dN
h h
(3)
Fitting was performed using the method of maximum likelihood (R Development Core Team 2010). Significant differences between estimated parameters were based
90 upon a 5% significance level. The overall time wasted due to encounters between predators that search for or handling prey is given by:
s w
h ww b P Tt b P T t
T 1 1 (4),
where Ts denotes the time a predator spents searching. Assuming that in high prey densities Ts is equal to zero, eq. 4 becomes:
h ww bP Tt
T 1 (5).
Therefore, the maximum number of prey that can be attacked by a predator during the time interval (maximum attack rate) considered was calculated as T/(Th+Tw), using mean values of Th and c.