Optimal harvesting of an age-structured population

Here we investigate the optimal harvesting of an age-structured population. We use the McKendrick model of population dynamics, and optimize a discounted yield on an infinite time horizon. The harvesting function is allowed to depend arbitrarily on age and time and its magnitude is unconstrained. We obtain, in addition to existence, the qualitative result that an optimal harvesting policy consists of harvesting at no more than three distinct ages.     

Alternative dynamical states in stage-structured consumer populations

The population dynamics of a consumer population with an internal structure is investigated. The population is divided into juvenile and adult individuals that consume different resources and do not interfere with each other. Over a broad range of external conditions (varying mortality and different resource levels), alternative stable states exist. These population states correspond to domination of juveniles and domination of adults, respectively. When mortality is varied, hysteresis between the alternative states only occurs if juveniles have more resources than adults. In the opposite case the juvenile-dominated state is stable for all values of mortality, but the adult-dominated state is not. When the population is modelled with more than one juvenile stage, the adult-dominated state becomes a periodic orbit due to a delay in the regulatory mechanism of the population dynamics. It is shown numerically that the stage-structured model converges to a model with continuous size structure for very large numbers of successive juvenile stages.     

Harvest-induced maturation evolution under different life-history trade-offs and harvesting regimes

The potential of harvesting to induce adaptive changes in exploited populations is now increasingly recognized. While early studies predicted that elevated mortalities among larger individuals select for reduced maturation size, recent theoretical studies have shown conditions under which other, more complex evolutionary responses to size-selective mortality are expected. These new predictions are based on the assumption that, owing to the trade-off between growth and reproduction, early maturation implies reduced growth. Here we extend these findings by analyzing a model of a harvested size-structured population in continuous time, and by systematically exploring maturation evolution under all three traditionally acknowledged costs of early maturation: reduced fecundity, reduced growth, and/or increased natural mortality. We further extend this analysis to the two main types of harvest selectivity, with an individual's chance of getting harvested depending on its size and/or maturity stage. Surprisingly, we find that harvesting mature individuals not only favors late maturation when the costs of early maturation are low, but promotes early maturation when the costs of early maturation are high. To our knowledge, this study therefore is the first to show that harvesting mature individuals can induce early maturation.     

The impact of maturation delay of mosquitoes on the transmission of West Nile virus

We formulate and analyze a delay differential equation model for the transmission of West Nile virus between vector mosquitoes and avian hosts that incorporates maturation delay for mosquitoes. The maturation time from eggs to adult mosquitoes is sensitive to weather conditions, in particular the temperature, and the model allows us to investigate the impact of this maturation time on transmission dynamics of the virus among mosquitoes and birds. Numerical results of the model show that a combination of the maturation time and the vertical transmission of the virus in mosquitoes has substantial influence on the abundance and number of infection peaks of the infectious mosquitoes.     

Interaction of maturation delay and nonlinear birth in population and epidemic models

 A population with birth rate function B(N) N and linear death rate for the adult stage is assumed to have a maturation delay T>0. Thus the growth equation N′(t)=B(N(t−T)) N(t−T) e⁻ d ₁ T−dN(t) governs the adult population, with the death rate in previous life stages d ₁≧0. Standard assumptions are made on B(N) so that a unique equilibrium N _e exists. When B(N) N is not monotone, the delay T can qualitatively change the dynamics. For some fixed values of the parameters with d ₁>0, as T increases the equilibrium N _e can switch from being stable to unstable (with numerically observed periodic solutions) and then back to stable. When disease that does not cause death is introduced into the population, a threshold parameter R ₀ is identified. When R ₀<1, the disease dies out; when R ₀>1, the disease remains endemic, either tending to an equilibrium value or oscillating about this value. Numerical simulations indicate that oscillations can also be induced by disease related death in a model with maturation delay. Received: 2 November 1998 / Revised version: 26 February 1999     

Stage-structured interactions between seasonal and permanent residents of an estuarine nekton community

Estuarine assemblages of fishes and natant decapod crustaceans (i.e. nekton) comprise both permanent resident species and juveniles of coastal marine species that use estuaries primarily as nurseries. In an attempt to understand how the young of marine species successfully invade communities of permanent estuarine residents we studied potential interactions between two of the most abundant decapod crustaceans in nekton assemblages of the southeastern United States. Three years of quantitative samples from an intertidal marsh on Sapelo Island, Georgia showed that densities of the resident daggerblade grass shrimp Palaemonetes pugio were reduced during the time that juvenile white shrimp Penaeus setiferus used the estuary as a nursery. Results of a field enclosure experiment showed that white shrimp had no significant lethal or sublethal effects on adult grass shrimp. However, they did reduce survival of both juvenile and larval grass shrimp in laboratory experiments, suggesting the potential importance of a stage-dependent predatorprey interaction between the two shrimp species. The mortality rate of young grass shrimp in the presence of white shrimp was unaffected by grass shrimp density, but larvae (2.6–3.0 mm) suffered higher mortalities than did juveniles (5.0–15.0 mm). We suggest that the vulnerability of grass shrimp to predation by white shrimp is related to their molting cycle. The window of vulnerability opens more often for younger grass shrimp because they molt more frequently. When combined with losses due to other predators and competitors, the impact of early white shrimp cohorts on grass shrimp larvae and juveniles may prevent the resident species from maintaining its population at high densities, thereby freeing resources in the nursery for subsequent cohorts of juvenile white shrimp.     

Microhabitat segregation and cannibalism in an endangered freshwater isopod, Thermosphaeroma thermophilum

Intraspecific microhabitat segregation is expected to arise when there are age- or sex-specific differences in predation risk. The degree to which conspecific predation (cannibalism) can generate this risk, however, is poorly understood. In this paper, we examine microhabitat use, cannibalism, and individual responses to the presence of conspecifics in Thermosphaeroma thermophilum, an endangered isopod crustacean species that is endemic to a single, thermal spring in Socorro, N.M. USA. In samples from the natural habitat, juveniles (mancas) were found mainly on vegetation, whereas adults were found predominantly on bottom sediments. Females were found on vegetation more often than males. In laboratory containers without refuges, males cannibalized females, males and females cannibalized mancas, and mancas cannibalized each other, even in the presence of alternative food. When placed in containers provided with refuges, mancas actively avoided adults. We suggest, therefore, that cannibalism in T. thermophilum generates age-, size-, and sex-specific predation risks which are responsible for microhabitat segregation between mancas and adults, and between males and females. Since interspecific predation in the spring is negligible, cannibalism appears to play a significant role in population regulation and behavioral evolution in this species. We recommend, given the current “endangered” status of this species, that microhabitat heterogeneity be maintained in its native spring because it provides refuges from cannibalism and may support a larger and more viable natural population. Received: 28 June 1996 / Accepted: 24 February 1997     

Post-settlement effects of habitat type and predator size on cannibalism of glaucothoe and juveniles of red king crab Paralithodes camtschaticus

Postlarval (glaucothoe) and juvenile (first crab stage, C1) red king crab Paralithodes camtschaticus actively select structurally complex substrata for settlement. Such habitats may provide them with shelter from predation during critical early stages. We tested this hypothesis by placing glaucothoe and juvenile crab in aquaria with or without natural or artificial habitats, and with or without predators (1-3-year-old red king crab) of two different sizes. Predators caused increased mortality of glaucothoe, but predator size, habitat presence and habitat type had no effect on survival. Predators caused significant mortality of C1 crabs in the absence of habitat, and mortality was inversely related to predator size. Density of glaucothoe on habitats was similar with or without predators, but density of C1 crab on habitats was higher than that of glaucothoe, and increased in the presence of large predators. Active selection for complex substrata by settling glaucothoe does not reduce cannibalism, but may pre-position them for improved survival after metamorphosis. In contrast, juvenile crabs modify their behavior to achieve higher densities in refuge habitats, which tends to dampen the effect of predation. These survival strategies may have evolved to compensate for the greater risk of predation in open habitats.     

New records of within-group infanticide and cannibalism in wild chimpanzees

Two cases of within-group infanticide and cannibalism were observed among the M Group chimpanzees of the Mahale Mountains, Tanzania. In both cases, victimized infants were male, 5 – 6 months of age, and in good health when killed. Four to five years have passed since the mothers of the victims immigrated into M Group as nulliparous immigrants. In one case the 2nd-ranking male was observed to detach the infant from the mother's belly. Both infants were finally killed by the alpha male after several adult males scrambled for the bodies. There was no evidence that the mothers had mated with males other than those of M Group. Nor was there evidence that the mothers had restrictive mating relationships with some of the M Group adult males. What little evidence is available shows that the mothers had mated mostly with adolescent and other immature males during their conception cycles. However, at least in one case, the mother began to mate more with adult males rather than with immature males after the infanticide. It is proposed that the function of within-group male infanticide can be explained by the male-male competition hypothesis developed for hanuman langurs and other nonhuman primates.     

Population dynamics and harvesting of semelparous species with phenotypic and genotypic variability in reproductive age

We study the evolution of polymorphic life histories in anadromous semelparous salmon and the effects of harvesting. We derive dynamic phenotypic and genetic ESS models for describing the evolutionary dynamics. We show in our deterministic analysis that polymorphisms are not possible in a panmictic random mating population. Instead, genetic or behavioral polymorphisms may be observed in populations with assortative mating systems. Positive assortative mating may be supported and generated by behavioral and phenotypic traits like male mate choice, spawning ground selection by phenotype, or within-river homing-migration-distance by size. In the case of an evolutionarily stable dimorphism, the ESS is characterized by a reproductive ideal free distribution such that at an equilibrium the individuals are indifferent from the fitness point of view between the two life histories of early and late reproduction. Different strategy models - that is, phenotypic and genetic ESS models - yield identical behavioral predictions and, consequently, genetics does not seem to play an important role in the present model. An evolutionary response to increased fishing mortality is obvious and may have resource management implications. High sea fishing mortalities drive the populations toward early spawning. Thus it is possible that unselective harvesting at sea may eliminate, depending on the biological system, behavioral polymorphisms or genetic heterozygozity and drive the population to a monomorphic one. If within-river homing migration distances depend on the size of fish, unselective harvesting at sea, or selective harvesting of spawning runs in rivers, may reduce local population sizes on spawning grounds high up rivers. Finally, harvesting in a population may cause a switch in a dominant life-history strategy in a population so that anticipated sustainable yields cannot be realized in practice.     

Parasite transmission and cannibalism in an amphipod (Crustacea)

In its freshwater amphipod host Gammarus duebeni celticus, the microsporidian parasite Pleistophora mulleri showed 23% transmission efficiency when uninfected individuals were fed infected tissue, but 0% transmission by water-borne and coprophagous routes. Cannibalism between unparasitised and parasitised individuals was significantly in favour of the former (37% compared to 0%). In addition, cannibalism between parasitised individuals was significantly higher than between unparasitised individuals (27% compared to 0%). Thus, parasitised individuals were more likely to be cannibalised by both unparasitised and parasitised individuals. We discuss the conflicting selective forces within this host/parasite relationship, the implications of parasite mediated cannibalism for host population structure and the impacts this may have on the wider aquatic community.     

Differential cannibalism and population dynamics in a host-parasitoid system

The effects of host cannibalism on a host-parasitoid system were explored through experiment and modelling. In individual encounters between parasitized and unparasitized Plodia interpunctella larvae, parasitized larvae were more likely to be cannibalized. Inclusion of this differential cannibalism into a simple Lotka-Volterra-type model of host-parasitoid population dynamics generates alternative stable states-including stable coexistence and extinction of the parasitoid — which depend on starting conditions. Possible mechanisms for differential cannibalism, and its implications for studies of host-parasitoid populations and biological control programmes are discussed.     

Effects of zooplankton availability and foraging mode on cannibalism in three dragonfly larvae

Summary Cannibalism is likely to operate as a form of population control in dragonfly larvae. I performed aquarium experiments to investigate the effect of foraging activity and zooplankton availability on cannibalism in three dragonfly larvae. Large Cordulia aenea larvae showed low activity, and large Leucorrhinia dubia larvae showed high activity irrespective of zooplankton availability. In contrast, large Coenagrion hastulatum larvae changed from high activity in the absence to low activity in the presence of zooplankton. Small Cordulia aenea larvae were active in the absence of large conspecifics irrespective of zooplankton availability. In the presence of large conspecifics they showed a reduced activity when zooplankton were present. Small L. dubia larvae showed high activity and small Coenagrion hastulatum larvae low activity irrespective of pressence or absence of zooplankton and large conspecifics. In all three species cannibalism was highest in the absence of zooplankton. In the absence of zooplankton cannibalism was low in Coenagrion hastulatum compared to the other two species. On the contrary, in the presence of zooplankton, cannibalism did not differ between the three species.     

Harvesting on a stage-structured single population model with mature individuals in a polluted environment and pulse input of environmental toxin

In the natural world, there are many species whose individual members have a life history that they take them with two distinct stages: immaturity and maturity. In particular, we have in mind mammalian populations and some amphibious animals. We improve the assumption of a single population as a whole. It is assumed that the immature individuals and mature individuals are divided by a fixed period. This paper concentrates on the study of a stage-structured single population model with mature individuals in a polluted environment and pulse input of environmental toxin at fixed moments. Furthermore, the mature individuals are harvested continuously. We show that the population goes extinct if the harvesting rate is beyond a critical threshold. Conditions for the extended permanence of the population are also examined. From the biological point of view, it is easy to protect species by controlling the harvesting amount, impulsive period of the exogenous input of toxin and toxin impulsive input amount, etc. Our results provide reasonable tactics for biological resource management.     

The effects of cannibalism on Amazonian poison frog egg and tadpole deposition and survivorship in Heliconia axil pools

This study investigated the influence of cannibalism on egg and larval mortality, and on the deposition strategies of adults, in a tropical anuran breeding in very small leaf axil pools. Patterns of egg and tadpole deposition and mortality in the Amazonian poison frog, Dendrobates ventrimaculatus, were monitored in rainforest near Pompeya in Sucumbios Province, Ecuador. Oviposition and tadpole deposition typically ocurred in leaf axils of Heliconia plants. Pools typically received more than one oviposition. Egg survivorship was low, and significantly lower when eggs were deposited in pools with large tadpoles, indicating that cannibalism is an important source of mortality. Tadpole survivorship was also associated with the presence of other tadpoles: most pools ended with only one surviving tadpole, regardless of the number of tadpoles deposited in the pool. Egg deposition was signifcantly less likely for pools that had a tadpole in them, suggesting that adults can detect the presence of tadpoles and avoid ovipositing in pools that contain them. This hypothesis was tested with a series of pool choice experiments, which revealed that D. ventrimaculatus avoid placing either eggs or tadpoles into a pool which contains a large tadpole. Several hypotheses which could explain multiple deposition in this species are discussed. Received: 14 September 1998 / Accepted: 25 January 1999     

Emergent impacts of cannibalism and size refuges in prey on intraguild predation systems

Many organisms undergo ontogenetic niche shifts due to considerable changes in size during their development. These ontogenetic shifts can alter the trophic position of individuals, the type and strength of ecological interactions across species, and allow for cannibalism within species. In this study we ask if and how the interaction of a size refuge and cannibalism in the prey alters the dynamics of intraguild predation (IGP) systems. By manipulating the composition of large cannibalistic (Aeshna umbrosa) and predatory (Anax junius) dragonfly larvae in mesocosms we show that the interaction of cannibals and predators was non-linear and increased the survival of prey. The structure of the final resource community shared by prey and predator differed between small and large dragonfly treatments but not within size classes across species. In general, the small prey stage showed similar shifts in microhabitat use and refuge use when exposed to either conspecific cannibals or predators, while large cannibals showed no clear anti-predator response. However, further behavioral experiments revealed that specific behavioral components, such as distances between individuals or number of movements, differed when individuals were exposed to either cannibals or predators. This indicates that individuals discriminated between conspecific or heterospecific predators. Furthermore, in similar experiments large cannibals and predators showed different behaviors when exposed to conspecifics rather than to each other. These changes in behavior are consistent with the observed increase in prey survival. In general, the results indicate that cannibalism and ontogenetic niche shifts can result in behavior-mediated indirect interactions that reduce the impact of the predator on the mortality of its prey and alter the interactions of IGP systems. However, they also indicate that size is not the sole determinant and that we also need to account for the species identity when predicting the dynamics of communities.     

Optimization of harvesting age in an integral age-dependent model of population dynamics

The paper deals with optimal control in a linear integral age-dependent model of population dynamics. A problem for maximizing the harvesting return on a finite time horizon is formulated and analyzed. The optimal controls are the harvesting age and the rate of population removal by harvesting. The gradient and necessary condition for an extremum are derived. A qualitative analysis of the problem is provided. The model shows the presence of a zero-investment period. A preliminary asymptotic analysis indicates possible turnpike properties of the optimal harvesting age. Biological interpretation of all results is provided.     

Dynamics of an age-structured population with Allee effects and harvesting

We propose a discrete-time, age-structured population model to study the impact of Allee effects and harvesting. It is assumed that survival probabilities from one age class to the next are constants and fertility rate is a function of weighted total population size. Global extinction is certain if the maximal growth rate of the population is less than one. The model can have multiple attractors and the asymptotic dynamics of the population depend on its initial distribution if the maximal growth rate is larger than one. An Allee threshold depending on the components of the unstable interior equilibrium is derived when only the last age class can reproduce. The population becomes extinct if its initial population distribution is below the threshold. Harvesting on any particular age class can decrease the magnitude of the possible stable interior equilibrium and increase the magnitude of the unstable interior equilibrium simultaneously.     

Age-related cannibalism and horizontal transmission of a nuclear polyhedrosis virus in larval Spodoptera frugiperda

1. Experiments were carried out to investigate the incidence of cannibalism throughout the larval development of the noctuid moth Spodoptera frugiperda, and to examine the risk of infection from consuming conspecifics infected with a nuclear polyhedrosis virus (SfNPV). 2. Cannibalism was observed commonly even when food was not limiting, but occurred more frequently at low food quantities and/or high rearing densities. The sex of the larvae had no effect on the incidence of cannibalistic behaviour, however the probability of cannibalism occurring was affected by larval stage. The frequency of cannibalism was significantly higher among fifth- and sixth-instar larvae than among earlier instars, and larvae were more likely to consume younger conspecifics than larvae of the same stage. 3. Fifth-instar larvae offered fourth-instar victims fed equally on healthy larvae, virus-infected larvae (2 days post-infection), uninfected corpses, and virus-killed corpses (6 days post-infection). Horizontal transmission of SfNPV was only recorded in larvae offered virus-killed corpses, however, and total mortality in this treatment was only 32%. 4. In a similar experiment, fourth-instar larvae avoided cannibalising virus-killed corpses. Horizontal transmission of SfNPV was recorded in fourth-instar larvae that consumed 2-day post-infected larvae. The low incidence of cannibalism observed in fourth-instar larvae, however, suggests that this is unlikely to provide an important route for the transmission of SfNPV.