The functional response of a predator describes the number of prey that an individual consumes as the density of the prey increases (1). It is an important concept in the field of ecology and evolution, also useful in the understanding of population dynamics at different trophic levels (2). The predator will consume a greater number of prey as density increases, and the maximum number of prey it can consume is determined by satiety (maximum consumption capacity) or by the maximum time available to manipulate the prey (2). The functional response is considered a criterion that allows the evaluation of the potential of a predator to be used as a biological control agent within a pest management program (3, 4, 5).

There are three types of functional responses, the type I response describes a linear increase in the number of prey consumed until a maximum consumption rate is reached, where the number of consumed prey remains constant despite the increase in prey density. In the type II functional response, the rate of consumption by a predator rises at a decelerating intake rate as prey density increases, until reaching an asymptote (hyperbolic curve) at which the rate of consumption remains constant regardless of increases in prey density. The type III response is described as a sigmoid curve, at low densities the number of consumed prey is reduced, but as the number of prey increases the rate of consumption also increases, until the limit is reached (4, 6, 7).

The attack rate, handling time and exposure time of the prey to the predator are the factors that determine the functional response of a predator (8, 9). Handling time is a term that involves different aspects of the predator's behavior, since it refers to the time it takes for the predator to capture, subjugate, kill, and digest the prey (10, 11). Handling time and attack rate are inversely proportional, high handling time leads to low attack rates, since the predator will spend a longer time on each prey reducing the number of attacks per unit of time. On the other hand, high attack rates are the consequence of short handling time (7).

Novius punicus (Gordon) and Novius cardinalis (Mulsant) (Coleoptera: Coccinellidae) are predators of the Colombian fluted scale Crypticerya multicicatrices Kondo and Unruh (Hemiptera: Monophlebidae: Iceryini), which was reported as an invasive insect in the archipelago of San Andrés, Providencia and Santa Catalina in 2010 (12, 13). After a search for natural enemies in the place of origin of this pest (continental region of Colombia), these two coccinellid species were considered as potential control agents for this fluted scale (13). The species N. punicus is native to the New World (14, 15) and preys on scale insects of the tribe Iceryini such as Icerya purchasi Maskell and Crypticerya montserratensis (Riley and Howard) (16). Novius punicus is an important natural enemy of C. multicicatrices (17), demonstrating a great predatory capacity on this pest. The immature and adult stages of this coccinellid feed preferably on the eggs of the fluted scale; however, it can also feed on nymphs (13). It is common to find larvae of this predator inside the ovisacs of adult fluted scales, where they hold their eggs. This species is the main one responsible for the reduction in the populations of C. multicicatrices on the islands of San Andrés, Providencia and Santa Catalina in 2013 (13). On the other hand, Novius cardinalis, until recently known as Rodolia cardinalis, is a species native to Australia (14, 15) and preys mainly on species of the family Monophlebidae. Novius cardinalis has been used in successful biological control programs for I. purchasi (13, 17). It was introduced to Colombia in 1948 to control I. purchasi in urban areas (12) and it has been reported preying on eggs and nymphs of C. multicicatrices (13). Both species of coccinellid predators play an important role in reducing the population levels of C. multicicatrices in urban areas of Colombia where it occurs. For this reason, the objective of this study was to determine the functional response of N. punicus and N. cardinalis on eggs and first-instar nymphs of C. multicicatrices, respectively.

The results of the logistic regression show that the two species of coccinellids have a type II functional response. For both cases, the estimated value was negative and statistically significant (Table 1), which indicates that the curve of the proportion of eaten prey fits a function with a decreasing rate, characteristic of a type II functional response.

Table 1

Predator	Estimated	S.E.	Z-value	Pr (> |z|)
N. punicus	-0.0117	0.0006	-21.295	< 2.2 e-16 ***
N. cardinalis	-0.0100	0.0008	-12.553	< 2.2 e-16 ***

*** Statistical significance at P < 0.001; Standard Error: S.E.

The functional response adjusted by the random predator equation for N. punicus and N. cardinalis are shown in Figures 1a and 1b, respectively. In the case of N. punicus, it can be observed that the relationship between the number of consumed prey and their density followed the typical curve of the type II functional response, clearly reaching an asymptote that shows the maximum rate of consumption of eggs of the fluted scale by this predator in a 24-hour period. On the other hand, the graph that describes the functional response of N. cardinalis feeding on first-instar nymphs of C. multicicatrices does not clearly show the predation limit in 24 hours, so it can be assumed that this coccinellid reaches its maximum rate of consumption at densities higher than those tested in this study.

Figure 1

The calculated parameters of the random predator equation are shown in Table 2. The attack rate of N. punicus on eggs of C. multicicatrices is higher than that observed in N. cardinalis preying on nymphs of Colombian fluted scale. On the other hand, the calculated handling time for N. cardinalis is 0.34 hours, and for N. punicus is 0.64 hours.

Table 2

Predator	Parameter	Estimate	S.E.	Z-value	Pr (> |z|)
N. punicus	α	0.1191	0.0125	9.487	< 2.2 e-16 ***
	Th	0.6423	0.0268	23.973	< 2.2 e-16 ***
N. cardinalis	α	0.0542	0.0041	13.312	< 2.2 e-16 ***
	Th	0.3441	0.0225	15.263	< 2.2 e-16 ***

*** Statistical significance at P < 0.001; Standard Error: S.E.

Some authors have reported that there may be factors inherent to the experiment that make it difficult to differentiate between the curves that are characteristic of a type II and type III functional response, for example, not offering different numbers of prey at low densities, or not establishing an evaluation time that is in accord with the biological characteristics of the insect (6, 22). Logistic regression is an effective way to distinguish between type II and type III functional responses (21). Carrying out a comparison using the proportion of eaten prey at different densities allows greater sensitivity in the differentiation of the curves that represent type II and type III functional responses.

Different equations can be used to describe the functional response of a predator, each of them is used to estimate different values for the attack rate and handling time. Rogers (22) established that the random predator equation predicts the number of attacks that a predator can carry out in a given period of time, in a system where the exploitation of prey is allowed. This equation is suitable for systems where the density of the prey decreases as the predator consumes them (21); that is, experiments where the prey are not replaced to maintain a constant density throughout the evaluation. It is common to find the type II functional response in predators of the family Coccinellidae [e.g. Sakaki and Sahragard (10)]; this type of functional response is characterized by a decreasing proportion of eaten prey as prey density increases (10); in addition, the maximum rate of consumption is determined by the handling time of the prey (5, 6).

The experiments reported here were carried out in a relatively small area so the prey density per unit area could be very high, increasing the encounter rate between predator and prey and reducing the search time; on the other hand, the sedentary habit and size of the prey does not represent a major challenge for their submission by the predators. Thus, the difference in handling times presented by these species may be mainly due to their ability to consume and digest prey. In addition, Munyaneza and Obrycki (5) mentioned that the resting time can be an important component of the total handling time that a predator has on a given prey.

The differences observed in the parameters (α) and (T_h) in the studied species reflect different feeding strategies. Novius punicus optimized the attack rate (α) by specializing in an immobile and confined prey (eggs in ovisac), but it showed a longer handling time (T_h); in contrast, N. cardinalis had a lower attack rate (α) for a mobile prey (first-instar nymphs), which compensated with a shorter handling time (T_h). This last characteristic is related to high rates of prey consumption.

FoRAGE (Functional Responses from Around the Globe in all Ecosystems) is a specialized database that includes more than 2000 entries of functional response experiments for all kinds of predators (23), among these, multiple coccinellid species. To put into context, the values of the parameters estimated in this experiment for N. punicus and N. cardinalis, the findings reported by other authors for functional response experiments with adults of various coccinellids species and various prey are summarized in Table 3.

The search efficiency values found in this study are similar to those reported by De Bortoli et al. (24) for adults of Cryptolaemus montrouzieri Mulsant (Coleoptera: Coccinellidae) (α = 0.01-0.05) preying on Planococcus citri (Risso) (Hemiptera: Pseudococcidae). In contrast, the handling time values are much lower than those reported for C. montrouzieri (T_h = 0.94-3.36 hours) in the above experiment (24), but much higher than those of other species with more mobile prey (Table 3).

Table 3

Predator (Coleoptera: Coccinellidae)	Prey	α (h-1)	Th (h)	T(°C)	Experimental unit	Information source
Cryptolaemus montrouzieri Mulsant	Planococcus citri (Hemiptera: Pseudococcidae)	0.03	1.47-7.61	25	Petri dish 15 cm diameter	(24)
Cryptolaemus montrouzieri Mulsant	Planococcus citri (Hemiptera: Pseudococcidae)	0.01-0.05	0.94-3.36	30	Petri dish 15 cm diameter	(24)
Cheilomenes sexmaculata (Fabricius)	Aphis craccivora, Myzus persicae (Hemiptera: Aphididae)	1.06 0.9	0.09 0.1	26-28	Glass Beaker 8 x 11 cm	(9)
Propylea dissecta (Mulsant)	A. craccivora, M. persicae (Hemiptera: Aphididae)	0.94 0.7	0.18 0.24	26-28	Glass Beaker 8 x 11 cm	(9)
Coccinella transversalis Fabricius	A. craccivora, M. persicae (Hemiptera: Aphididae)	1.05 0.94	0.09 0.14	26-28	Glass Beaker 8 x 11 cm	(9)
Harmonia axyridis (Pallas)	Myzus persicae (Hemiptera: Aphididae)	2.55	0.16	25	Petri dish 9 cm diameter	(25)

The functional response parameters of the predators N. punicus and N. cardinalis reflect the result of the specialization of these coccinellids in consuming scale insect prey of the tribe Iceryni (13, 16), where the developmental stages on which they carry out the greatest predation (eggs and first-instar nymphs) are of low mobility or are contained in the ovisac of adult females. These characteristics make N. punicus a species with a high affinity to its main prey and less prone to attack other non-target species.

Some authors have pointed out that for functional response studies to be useful to evaluate the potential of a species as a biological control agent, it is necessary to carry out the experiments in such a way as to include the greatest number of conditions that the insect predator will encounter in the field (10, 26, 27). Messina and Hanks (27) showed that the characteristics of the plant where the prey is found can alter the functional response of the predator. These authors found that Propylea quatuordecimpunctata L. (Coleoptera: Coccinellidae), showed a different type of functional response (type II or type III) when feeding on the aphid Diuraphis noxia Mordvilko (Hemiptera: Aphididae) depending on the architecture of the leaf, especially because of the shelter that these structures provide to the prey (27).

The coccinellids N. punicus and N. cardinalis are both important predators of eggs and first-instar nymphs of C. multicicatrices, respectively. Both coccinellids have a type II functional response, in which the proportion of prey consumed decreases as the prey density increases. The attack rate and handling time parameters observed for N. punicus and N. cardinalis reflect the specialization of both species in consuming prey from the tribe Iceryini, in particular, eggs and newly emerged first-instar nymphs of the adult female fluted scales. Taking into account the experimental conditions of the study, it can be said that the differences in the number of consumed prey observed between N. punicus and N. cardinalis are mainly due to their ability to consume the prey. The present experiment is a first step in evaluating the potential of these coccinellid species to be used in a management program for C. multicicatrices.