Density-dependent Functional Response Research Articles

A Predator–Prey Model with Beddington–DeAngelis Functional Response and Multiple Delays in Deterministic and Stochastic Environments

In view of prey’s delayed fear due to predators, delayed predator gestation, and the significance of intra-specific competition between predators when their populations are sufficiently large, a prey–predator population model with a density-dependent functional response is established in a deterministic environment. We research the existence and asymptotic stability of the equilibrium statuses. Then, taking into consideration environmental disturbances, we extend the deterministic model to a stochastic model and research the existence and stationary distributions of stochastic solutions. Finally, we perform some numerical simulations to verify the theoretical results. Numerical examples indicate that fear, delays and environmental disturbance play crucial roles in the system stability of the equilibrium status.

Predator type influences the frequency of functional responses to prey in marine habitats.

The functional response of a consumer to a gradient of resource density is a widespread and consistent framework used to quantify the importance of consumption to population dynamics and stability. Within benthic marine ecosystems, both crustaceans and fishes can provide strong top-down pressure on prey populations. Taxon-specific differences in biomechanics or habitat use, among other factors, may lead to variable functional response forms or parameter values (attack rate, handling time). Based on a review of 189 individual functional response fits, we find that these predator guilds differ in their frequency distribution of functional response types, with crustaceans exhibiting nearly double the proportion of sigmoidal, density-dependent functional responses (Holling type III) as predatory fishes. The implications of this finding for prey population stability are significant because type III responses allow prey persistence while type II responses are de-stabilizing and can lead to extinction. Comparing per capita predation rates across diverse taxa can provide integrative insights into predatory effects and the ability of predation to drive community structure.

SELF-REGULATING MECHANISMS IN CANNIBALISTIC POPULATIONS OF JUVENILE SHORE CRABS CARCINUS MAENAS

Juvenile cannibalism may play an important role in population regulation of marine organisms with juvenile stages that aggregate in nursery habitats. I conducted a series of field and laboratory experiments to assess whether three potential density-dependent mechanisms could regulate local recruitment of juvenile shore crabs Carcinus maenas in Swedish nursery areas: (1) intracohort cannibalism, (2) juvenile cannibals' functional response to smaller conspecific prey densities, and (3) juvenile cannibals' numerical effect on prey survival. Juvenile cannibals in mesocosms displayed a type III (sigmoid) density-dependent functional response, resulting in significantly higher proportional mortality of smaller conspecifics at high prey densities. Consistent with the laboratory result, cage-enclosed juvenile cannibals in a field experiment eliminated conspecific settlement peaks in mussel habitats and decoupled the relationship between larval and settlement abundance within three days. Density-dependent interference between cannibals in mesocosms decreased per capita predation rates, but conspecific prey mortality still increased with cannibal densities when the abundance of cannibals passed a critical threshold, suggesting that the recruitment success of consecutive cohorts may be negatively correlated. This was supported in a field experiment where the abundance of juvenile cannibals explained 71% of the variation in settlement loss from uncaged mussel habitats. Density-dependent cannibalism also occurred within juvenile cohorts even though food was provided in excess, but the resulting mortality was too low to eliminate initial density patterns over a 30-day period. The results demonstrate that cannibalism between juvenile shore crabs can cause high and strongly density-dependent mortality at natural densities, and that both a functional response and a numerical effect of larger cannibals can regulate the recruitment of new cohorts within days of settlement. A coupling of cannibal and settlement densities on a regional scale is expected to decrease recruitment variability within and between local populations. Moreover, the interaction between the type III functional response, mutual interference, and density-dependent dispersal of cannibals is predicted to reduce cannibalistic rates at low prey and high cannibal densities, respectively, and stabilize local population dynamics in relation to the abundance of juvenile habitats, consistent with field observations of shore crab populations in the study area.

Foraging behaviour and mutual interference in the Mediterranean shore crab, Carcinus aestuarii, preying upon the immigrant mussel Musculista senhousia

Predator–prey dynamics between the Mediterranean shore crab Carcinus aestuarii and the immigrant mussel Musculista senhousia were examined in laboratory experiments to assess the effects of varying predator and prey densities upon predator foraging rates and prey survival. The factorial design involved three predator and three prey densities, with four trials per treatment combination. Functional responses were differentiated statistically by analysis of the exponent β of a general functional response model. Shore crabs displayed type II (decelerating rise to an upper asymptote) inversely density-dependent functional responses at low and moderate predator densities, while a non-traditional model was probably more appropriate at high predator density. No density-dependent refuge was observed for M. senhousia, whereas, at high predator density, mutual interference among crabs was evident and prey mortality was lowered. Mediterranean shore crab's combined functional and interference response, by affecting foraging rates, was important to the outcome of interactions between predators and the bivalve prey, and might play an important role in determining crab's predatory behaviour and dispersion, and prey persistence, in the field.

Does oxygen deficiency modify the functional response of Saduria entomon (Isopoda) to Bathyporeia pilosa (Amphipoda)?

The functional response of the predatory isopod Saduria entomon to the prey amphipod Bathyporeia pilosa was measured in normoxia (95% O2 saturation), moderate hypoxia (45% O2 saturation) and hypoxia (35% O2 saturation) in aquarium experiments. The prey densities tested ranged from 400 to 8000 ind m−2. Prey density influenced consumption rates of S. entomon in normoxia and 45% O2 saturation, but there was no difference between consumption rates at these two oxygen levels. Nevertheless the form of functional response differed. In normoxia S. entomon showed a positively density-dependent functional response to B. pilosa, indicating a potentially stabilizing effect on the prey population. In moderate hypoxia the variance in consumption increased, decreasing the statistical power to distinguish between response models. The functional response of S. entomon in moderate hypoxia was best described with a density-independent response, characterized as destabilizing for the prey population. In hypoxia (35% O2) predation by S. entomon did not respond to increasing prey density, as almost no amphipods were eaten at this oxygen level. The results are discussed in terms of the usability of theoretical models to examine predator–prey relationships in stressful environments.

Cannibal–prey dynamics in young juveniles and postlarvae of the blue crab

Although cannibalism can act as a density-dependent regulator of population size in terrestrial systems, little is known of its effects in the marine environment. Herein we investigate the influence of cannibalism upon the early life history stages of the blue crab, Callinectes sapidus Rathbun, emphasizing cannibalism between juveniles and postlarvae (i.e. megalopae) of the same year class. In laboratory mesocosms we examined various factors modulating cannibal–prey dynamics, specifically: (1) the effects of habitat and presence of conspecifics on postlarval metamorphosis rate; (2) the effect of metamorphosis rate on the mortality of postlarvae from both intra- and inter-cohort cannibalism; (3) the effects of habitat and predator density on the functional response of young juvenile blue crab predators to varying densities of postlarval prey, and (4) the effects of prey size and habitat on predation mortality.Inter-cohort cannibalism caused significant mortality in every crab size and habitat type combination, and was lower in grass than sand for all prey smaller than fifth instar. Cannibalism between postlarvae was associated with metamorphosis and was density-dependent in sand, but not present in grass. Metamorphosis rates of postlarvae were inversely density-dependent in sand, but density-independent and higher in grass, indicating that habitat and intra-cohort agonism likely affects postlarval metamorphosis rates. Inter-cohort cannibalism was negatively correlated with metamorphosis rates of postlarvae. The functional response of young juvenile cannibalistic blue crabs differed significantly between sand and grass habitats, and between medium and high predator densities. Juvenile crabs displayed a type II, inversely density-dependent functional response in sand, resulting in very high mortality at low densities of postlarval prey. In grass, the crabs displayed a weak type III, density dependent response, yielding significantly lower mortality at low prey densities. Thus, habitat complexity changes the form of the functional response in cannibal–prey interactions and grass provides a relative habitat refuge from cannibalism. Doubling the number of predators in grass decreased the consumption rates per predator significantly and eliminated the density-dependence, indicating that intraspecific density can qualitatively change the form of the functional response. In the crab size experiment, only prey smaller than fifth instars received a habitat refuge from cannibalism in grass, whereas fifth instars received a relative size refuge in sand.Our results demonstrate that intra-year class cannibalism can cause mortality upon settling megalopae and first juvenile instars that is dependent on prey density. We expect inter-cohort cannibalism to cause local extinction of cohorts settling in sand, especially at low settlement densities, and high mortality at moderate settlement densities in grass. Satiation of predators at high settlement densities in grass suggests that episodic settlement can overwhelm predators locally. Furthermore, density-dependent mutual interference within large cohorts in the grass beds likely reduces their predation efficiency, indicating that aggregation of conspecific predators in grass habitats does not necessary lead to an increase in predation pressure. Finally, a relative size-refuge from inter-cohort cannibalism for fifth instar crabs supports an ontogenetic habitat shift around this crab size, which may be influenced by density-dependent agonistic behavior within cohorts. We suggest that intra-year class cannibalism is a major process regulating both survival and dispersal in megalopae and juvenile blue crabs.

Melon Aphid (Homoptera: Aphididae) Control by Inundative Convergent Lady Beetle (Coleoptera: Coccinellidae) Release on Chrysanthemum

Convergent lady beetles, Hippodamia convergens Guerin-Meneville, collected from aggregations in California were released for control of melon aphids, Aphis gossypii Clover, infesting potted chrysanthemum, Dendranthema grandiflora (Tzvelev) ‘Hurricane’, outdoors. Most beetles dispersed from plants within 1-3 d after a single release during May 1993 and July and September 1993 and 1994. Most dispersing beetles left the study area, although some moved within release plots to adjoining plants or dispersed to nearby plots within ≈40 m. Aggregation-collected beetles that were allowed to drink and fly in a screen tent for 7–10 d before release and insectary-reared beetles dispersed more slowly than aggregation-collected beetles that were stored at 4–10°C until the day of release. Although beetles dispersed within days, releases significantly reduced aphid densities during all trials. A single release of 34–42 adult H. convergens per pot provided 25–84% aphid control, calculated according to the Abbott method. Each beetle consumed ≈25–170 melon aphids per day. There was a density-dependent functional response in predation; beetles consumed more aphids when released on plants with higher aphid densities. Release of commercially available convergent lady beetles can provide augmentative control of relatively high aphid densities on small potted plants.

Functional responses of optimal consumers and the potential for regulation of resource populations

A central issue in studies of consumer-resource interactions is whether consumers regulate resource dynamics. One condition for regulation is that consumption rate of a resource increases positively with increasing resource density, that is, that the consumer's functional response must be positively density dependent. Many mammalian consumers exhibit density-independent or inversely density-dependent functional responses, suggesting that regulation will not occur. However, most studies measure functional responses for a single consumer and resource species in specific feeding trials. Many real-world consumers use more than one resource and resource choices depend on the distribution and nutritional quality of resources as well as abundances. Foragers also actively choose resources in ways that match predictions of optimal foraging theory, that is, they exhibit adaptive behaviour. This paper explores the variety of functional responses of adaptive consumers that arises from optimal choice of resources in a simple, singleconsumer- two-resource system to determine the potential for consumer regulation of resource populations. Optimal consumer behaviour can generate four types of functional responses: (1) density independent, (2) increasing, inverse density dependent, (3) increasing, positively density dependent, and (4) decreasing. A positive density-dependent functional response arises in 3 of 22 possible cases. Moreover, consumers may not exhibit the same functional response to all resources included in the diet, that is, they exhibit mixed responses to resource densities. This suggests that studies that examine the potential for consumer regulation of resources must go beyond the traditional focus (interactions between a consumer and the most dominant or abundant prey) and consider the variety of resource species selected by a consumer in a specified time period.

Functional responses of blue crabs Callinectes sapidus Rathbun feeding on juvenile oysters Crassostrea virginica (Gmelin): effects of predator sex and size, and prey size

Laboratory experiments assessed functional responses (prey consumption-predator −1 as a function of prey density) of male and female blue crabs Callinectes sapidus Rathbun to six densities of juvenile American oysters Crassostrea virginica (Gmelin) as a function of predator sex and size, and prey size. Crusher chela heights of large male and female crabs (135–165 mm carapace width; CW) were compared to identify sex-related differences in cheliped morphology that might account for the different functional responses. Initial identification of the form of the functional response (positively density-dependent, inversely densitydependent) was based on an ANOVA of the pattern of proportional mortality rates with prey density. The fit of several functional response models was compared statistically. Large female blue crabs exhibited a positively density-dependent functional response to large juvenile oysters (35 mm shell-height; SH), whereas large male crabs demonstrated an inversely density-dependent response. These different functional responses were due to specific features of both the predator and prey: (l) the higher crushing strength associated with a larger chela height to carapace width ratio of large male crabs compared to females, and (2) density-dependent prey features involving a reduction in the number of oysters attached to the outside edges of the oyster-shell cultch at low densities, which are easily crushed. Large crabs feeding on small oysters (25 mm SH) exhibited inversely density-dependent functional responses. Large juvenile oysters attained an absolute prey refuge in size from small blue crabs (60–85 mm CW) of both sexes. These results suggest that (1) sex-related differences in claw morphology can lead to different functional responses, and (2) juvenile oysters gradually attain a partial prey refuge at low densities (< 16.7 oysters · m −2) and large shell-heights (> 35 mm SH) prior to attainment of an absolute prey refuge from all crabs at ≈ 45–50 mm SH.

Variable Functional Responses of a Marine Predator in Dissimilar Homogeneous Microhabitats

Adult soft-shelled clams {Mya arenaria) persist at low densities in Chesapeake Bay sandy habitats despite intense predation by blue crabs {Callinectes sapidus). Clam persistence may be a consequence of variation in blue crab foraging rates as a function of clam density and sediment composition. In laboratory aquaria, we measured the functional responses (prey consumption per predator as a function of prey density) of large blue crabs to six densities of adult soft-shelled clams buried at natural depths in two sediment types (mud and sand). Functional responses in sand and mud were differentiated statistically by analyses of (1) residuals and residual sums of squares of discrete and continuous-time models, and (2) the exponent (3 of a general functional response model. Crab predation rates were significantly higher in mud than sand, and functional responses differed significantly between these two substrates. Blue crabs displayed type III (sigmoid) density-dependent functional responses in sand, and type II (decelerating rise to an upper asymptote) inversely density- dependent responses in mud. Risk of mortality for clams decreased sharply in sand at low densities similar to those observed in the field near the end of the annual period of active predation. These observations (1) suggest that variable blue crab functional responses result in microhabitat-specific mortality rates of benthic prey, and (2) indicate that functional responses can differ significantly according to the physical properties of topographically simple habitats.