Viable populations in a prey–predator system

 Lotka–Volterra equations are considered a dynamical game, where the phenotypes of the predator and of the prey can vary. This differs from the usual procedure of specifying as a priori laws according to which strategies are supposed to change. The question at stake is the survival of each of the species, instead of the maximization of a given pay-off by each player, as it is commonly discussed in games. The predator needs the prey, while the prey can survive without the predator. These obvious and simplistic constraints are enough to shape the regulation of the system: notably, the largest closed set of initial conditions can be delineated, from which there exists at least one evolutionary path where the population can avoid extinction forever. To these so-called viable trajectories, viable strategies are associated, respectively for the prey or for the predator. A coexistence set can then be defined. Within this set and outside the boundary, strategies can vary arbitrarily within given bounds while remaining viable, whereas on the boundary, only specific strategies can guarantee the viability of the system. Thus, the largest set can be determined, outside of which strategies will never be flexible enough to avoid extinction. Received 2 May 1995; received in revised form 15 August 1995     

Self-organised spatial patterns and chaos in a ratio-dependent predator–prey system

Mechanisms and scenarios of pattern formation in predator–prey systems have been a focus of many studies recently as they are thought to mimic the processes of ecological patterning in real-world ecosystems. Considerable work has been done with regards to both Turing and non-Turing patterns where the latter often appears to be chaotic. In particular, spatiotemporal chaos remains a controversial issue as it can have important implications for population dynamics. Most of the results, however, were obtained in terms of ‘traditional’ predator–prey models where the per capita predation rate depends on the prey density only. A relatively new family of ratio-dependent predator–prey models remains less studied and still poorly understood, especially when space is taken into account explicitly, in spite of their apparent ecological relevance. In this paper, we consider spatiotemporal pattern formation in a ratio-dependent predator–prey system. We show that the system can develop patterns both inside and outside of the Turing parameter domain. Contrary to widespread opinion, we show that the interaction between two different type of instability, such as the Turing–Hopf bifurcation, does not necessarily lead to the onset of chaos; on the contrary, the emerging patterns remain stationary and almost regular. Spatiotemporal chaos can only be observed for parameters well inside the Turing–Hopf domain. We then investigate the relative importance of these two instability types on the onset of chaos and show that, in a ratio-dependent predator–prey system, the Hopf bifurcation is indeed essential for the onset of chaos whilst the Turing instability is not.     

Seasonal, El Niño and longer term changes in flower and seed production in a moist tropical forest

It has recently been reported that humid tropical forests are changing rapidly in response to global anthropogenic change and that these forests experience greater tree mortality and even fire during droughts associated with El Niño events. The former reports are controversial largely because a single method has been used – repeated censuses of tree plots. The latter reports focus on recent extreme El Niño events. Here, we show that flower and seed production both increase during El Niño events in an old-growth tropical forest in Panama. Flower production, but not seed production, has also increased over the past 18 years. The sustained increase in flower production was greater for 33 liana species than for 48 tree species. These results indicate that moderate El Niño events favour seed production, document long-term increases in flower production for the first time, and corroborate long-term increases in the importance of lianas using independent methods. Changes in levels of solar irradiance might contribute to all three patterns.     

Asexual reproduction changes predator population dynamics in a life predator–prey system

Many organisms display oscillations in population size. Theory predicts that these fluctuations can be generated by predator–prey interactions, and empirical studies using life model systems, such as a rotifer-algae community consisting of Brachionus calyciflorus as predator and Chlorella vulgaris as prey, have been successfully used for studying such dynamics. B. calyciflorus is a cyclical parthenogen (CP) and clones often differ in their sexual propensity, that is, the degree to which they engage into sexual or asexual (clonal) reproduction. Since sexual propensities can affect growth rates and population sizes, we hypothesized that this might also affect population oscillations. Here, we studied the dynamical behaviour of B. calyciflorus clones representing either CPs (regularly inducing sex) or obligate parthenogens (OPs). We found that the amplitudes of population cycles to be increased in OPs at low nutrient levels. Several other population dynamic parameters seemed unaffected. This suggests that reproductive mode might be an important additional variable to be considered in future studies of population oscillations.     

Cooperative hunting in a discrete predator–prey system II

ABSTRACT

We investigate a discrete-time predator–prey system with cooperative hunting in the predators proposed by Chow et al. by determining local stability of the interior steady states analytically in certain parameter regimes. The system can have either zero, one or two interior steady states. We provide criteria for the stability of interior steady states when the system has either one or two interior steady states. Numerical examples are presented to confirm our analytical findings. It is concluded that cooperative hunting of the predators can promote predator persistence but may also drive the predator to a sudden extinction.     

Prey–predator mutualism in a tritrophic system on a camphor tree

We report the discovery of a mutualistic system encompassing prey–predator interactions. A domatium is a small space in a vein axil on the underside of leaves of woody angiosperms. Cinnamomum camphora Linn. has domatia that harbor a microphytophagous eriophyid mite (sp. 1). We previously reported that a predatory mite, Euseius sojaensis (Ehara), depends on this eriophyid mite as food. We revealed that E. sojaensis also preyed upon another eriophyid mite (sp. 2) that induces galls on leaves, and that the mean area of C. camphora leaves with galls was usually less than half that of leaves without galls. We experimentally tested the effect of E. sojaensis on galls, and confirmed that the presence of E. sojaensis reduced gall induction. Therefore, C. camphora, eriophyid mite sp. 1, and E. sojaensis comprise a mutualistic system, in spite of the prey–predator interactions among them. The conventional concept of mutualism does not apply to such prey–predator interactions, so we defined them as systematic mutualism. Here, the system consists of three trophic levels, and individuals that constitute this system benefit from the other species that constitute this system.     

Effects of topographic position,leaf litter and seed size on seedling demography in a semi-deciduous tropical forest in Panamá

This study examined whether topography-induced gradients in water potential and leaf litter depth contribute to species coexistence in tropical forests through species-specific effects on seedling emergence and mortality. Seedling emergence and mortality were followed for a period of 12 months in 36 (1 × 2 m) plots on Barro Colorado Island (BCI), Panamá. Plots with and without litter were distributed on slope and plateau sites in three catchments. In the absence of manipulations, the lower litter depth on slopes resulted in approximately four times as many emergent seedlings than on plateau sites. However, litter depth had little effect on seedling community composition. By the end of the first dry-season, post-emergence, there were no significant differences in surviving seedling numbers between any treatments. There were differences in the emergent seedling community between slope and plateau sites within the same catchment as well as differences in composition between catchments, suggesting that both niche partitioning and dispersal limitation might play a role in structuring seedling community composition. During the wet-season seedling mortality was highest on slope sites although this pattern was reversed during the dry-season. In both seasons mortality was higher for small-seeded species. These results demonstrate that gradients in water potential related to topography impact on patterns of seedling emergence and mortality although processes in the first year after emergence may be insufficient to explain observed habitat preferences of adult plants.     

Undamped oscillations in prey–predator models on a finite size lattice

Sustained oscillation is frequently observed in population dynamics of biospecies. The oscillation comes not only from deterministic but also from stochastic characteristics. In the present article, we deal with a finite size lattice which contains prey and predator. The interaction between a pair of lattice points is carried out by two different methods; local and global interactions. In the former, interaction occurs between adjacent sites, while in the latter interaction takes place between any pair of lattice sites. It is found that both systems exhibit undamped oscillations. The amplitude of oscillation decreases with the increase of the total lattice sites. In the case of global interaction, we can present a stochastic differential equation which is composed of two factors, i.e., the Lotka–Volterra equation with density dependence and noise term. The quantitative agreement between theory and simulation results of global interaction is almost perfect. The stochastic theory qualitatively expresses characteristics of sustainable oscillation for local interaction.     

Do seed and microsite limitation interact with seed size in determining invasion patterns in flooding Pampa grasslands?

Additive influences of the invasion ability of species (invasiveness) and the characteristics of the habitat which make it invasible (invasibility) cannot fully explain grassland invasion patterns. We tested the hypothesis that different species assemblages of grassland communities may partly result from interactive influences between the relative invasiveness of available species and community invasibility. During 10 months, we evaluated seed and microsite limitation of seedling emergence, survival, and recruitment of plants belonging to species with different seed size (large-seeded species vs. small-seeded species), with in a two-phase community mosaic typical of semi-natural grasslands in the southern flooding Pampa of Argentina. Seeds of large versus small-seeded species were sown either in species-poor patches dominated by a tall tussock grass (“pajonal”) or in species-rich patches dominated by short grasses (“matrix”), subjected to different levels of canopy disturbance (cut vs. uncut). Seed addition promoted seedling emergence for 7 out of the 10 species sown, and this effect was higher for large than for small-seeded species. After seed limitations were removed, interactive effects among seed size, community state and canopy disturbance reflected a strong positive influence of seed size on plant recruitment only in cut pajonal patches. Therefore, according to the stage of invasion process, relative species success may depend on non-interactive (seed-size effect on seed limitation to seedling emergence) or interactive influences among species invasibility and community invasiveness (from seedling emergence to plant recruitment). As a general conclusion, different assemblages of species are expected to successfully colonize spatially close grassland patches, according to both the available invasible species (seed size) and the community state and stage (species composition and canopy disturbance).     

Evolution towards oscillation or stability in a predator–prey system

We studied a prey–predator system in which both species evolve. We discuss here the conditions that result in coevolution towards a stable equilibrium or towards oscillations. First, we show that a stable equilibrium or population oscillations with small amplitude is likely to occur if the prey''s (host''s) defence is effective when compared with the predator''s (parasite''s) attacking ability at equilibrium, whereas large-amplitude oscillations are likely if the predator''s (parasite''s) attacking ability exceeds the prey''s (host''s) defensive ability. Second, a stable equilibrium is more likely if the prey''s defensive trait evolves faster than the predator''s attack trait, whereas population oscillations are likely if the predator''s trait evolves faster than that of the prey. Third, when the adaptation rates of both species are similar, the amplitude of the fluctuations in their abundances is small when the adaptation rate is either very slow or very fast, but at an intermediate rate of adaptation the fluctuations have a large amplitude. We also show the case in which the prey''s abundance and trait fluctuate greatly, while those of the predator remain almost unchanged. Our results predict that populations and traits in host–parasite systems are more likely than those in prey–predator systems to show large-amplitude oscillations.     

Is fire a selective force of seed size in pine species?

Fire is selectively shaping most of the traits of plants growing in fire-prone environments. However, seed size and other features related to seed production have not been studied in the light of the evolutionary role of fire. Our research tests the hypothesis that larger seeds have a higher chance of surviving wildfires and produce more vigorous seedlings with a lower death rate. To test this hypothesis the germination and early seedling growth of five Spanish pine species were studied. Weight, length and width of all seeds were measured. The biomass (fresh and dry weight) and length (root and total) of subsequent seedlings were also measured after 30 d from emergence. Seeds were submitted to elevated temperatures for periods in which the chance of survival was 50 % (calculated by means of a logistic model for each pine species). The differences observed among species suggests that fire may be adaptively shaping seed size in pines with larger seeds (Pinus canariensis and P. pinaster), because larger seeds are more likely to survive after heat shocks. Furthermore, in P. canariensis, seedlings after heat treatment are even larger than those submitted to control. In P. halepensis, despite being well adapted to fire, our results indicated no relationships between fire and seed characteristics. Finally, although heat treatment has a general adverse effect on seedling growth in the case of the two subalpine pines, we have detected a positive relationship between seed size and seedling growth but only in the largest seeds. This might also suggest the relevance of fire as a selective force for these pines which is outperformed by the relevance of dispersal and emergence time as adaptive traits in the post-fire scenario.     

Pollen selection — past,present and future

 A series of studies, recently reviewed, has established that approximately 60% of the structural genes which are expressed in the sporophytic portion of the angiosperm life cycle are also expressed and exposed to selection in the pollen. Given the haploidy and large population sizes of pollen grains, a substantial portion of the sporophytic genome could thus be periodically exposed to a bacterial type of mass screening. This extraordinary possibility is often subject to some skepticism which may, of course, be justified. However, recent attempts to apply models appear to be inappropriate in this context, in part because these attempts overlook an important source of genetic variation, and also because they assume fixed values for selection and fitness. More recently, studies of pollen/pollen interactions have suggested that what Linskens termed the ”programic phase” may represent an arena for important, and largely unexplored phenomena, some of which are discussed here. Received: 3 June 1996 / Revision accepted: 26 July 1996     

Latitudinal and seasonal patterns in clutch size of some single‐brooded British birds

Capsule Daylength, rather than latitude, was found to be an important determinant of variation in clutch size.

Aims To describe the nature of spatial and temporal variation in clutch size, and explore the ecological correlates of these patterns.

Methods We tested the prediction that seasonal declines in clutch size will be greater at higher latitudes. The environmental variables focused on were the influence of daylength, plant productivity, seasonality (i.e. Ashmole's hypothesis) and physiological mechanisms that relate clutch size to ambient temperature. We used data from 1980 to 2003 on spatial variation in clutch size across Britain for single‐brooded species, in which clutch size can be taken as a measure of annual reproductive investment. We included all seven species, from five families, with sufficient data in the British Trust for Ornithology's Nest Record Scheme.

Results There are strong seasonal declines in clutch size but little evidence for latitudinal gradients in clutch size or in latitudinal gradients in the rate of seasonal clutch size decline. Of the environmental variables investigated, daylength had the most marked effect on clutch size; this was positive in diurnal species and negative in the one nocturnal species.

Conclusions Although this study was confined to a relatively small latitudinal range of 8°, we found marked latitudinal gradients in a number of factors thought to drive spatial patterns in clutch size. Moreover, such variation is of sufficient magnitude to generate spatial patterns in other ecological variables in Britain. There is thus no simple explanation for the lack of a latitudinal gradient in clutch size. The results concerning daylength indicate that the time available for foraging is an important determinant of variation in clutch size.     

Bottom-up and top-down effects in a pre-dispersal seed predation system: are non-predated seeds damaged?

Seed predators that severely affect seed germination rates are well known for many plant species. Here, we hypothesised that due to differences in resource allocation within fruits, seed predation can negatively affect non-predated seeds in infested fruits when predation occurs during fruit maturation (a ‘top-down’ effect). We addressed this question using a system of bruchid beetles on Mimosa trees and we also investigated whether seed quality (nitrogen concentration) affects beetle body mass, which would have implications for adult fitness (‘bottom-up’ effect). To assess spatial variation, bottom-up and top-down effects were investigated in two plant populations. Nitrogen concentration was significantly higher in seeds from non-infested fruits than from infested fruits. This supports the hypothesis that resource allocation may differ between seeds from infested and non-infested fruits. Germination experiments showed that seeds from non-infested fruits germinated better than non-predated seeds from infested fruits. It was also confirmed that seed quality affected bruchid body mass. There was also evidence that more resources were taken from well-developed seeds. These results showed that seed predation can damage non-predated seeds.     

Pollen Morphology of the Family Zingiberaceae in China—Pollen Types and Their Significance in the Taxonomy

Pollen morphology of 89 species and 3 varieties belonging to 18 genera (out of 150 spcies in 20 genera) of Zingiberaceae in China was studied under both light microscope and scanning electron microscope. Pollen grains of Zingiberaceae are spherical, subspherical, ovoid and prolate, 36-225 μm in size, nonaperturate or aperturate (spiraperturate, porate). Pollen grains are almost not resistant to acetolysis. The wall is composed of a very thin exine and a thick intine. The exine is psilate, spinate, cerebelloid-areolate, striate, verrucate and foveolate. According to the presence or the absence of aperture and differential ornamentations, two types and six subtypes are recognized: I. The type Nonaperturate: (85 species and 3 varieties in 18 genera). Four subtypes can be recognized within the type based on the characteristics of the exine sculpture. These are: (1) The subtype Psilate, in which, the exine is nearly smooth (including: Hedychium, Curcuma, Kaempferia, Caulokaempferia coenobilis, Boesenbergia rotunda, Stahlianthus, Amomum compactum, Etingera, Hornstedtis, Rhynchanthus). (2) The subtype Spinate, which comprises two groups: (A) The group Short-spinate, pollen grains with smaller spines (Globba), (B) The group Long-spinate, pollen grains with longer spines (Alpinia, Amomum, Plagiostachys, Roscoea, Cautleya, Boesenbergia fallax, Caulokaempferia yunnanensis). (3) The subtype Cereblloid-areolate, pollen grains of which are spherical or subspherical, with cerebelloid sculpture (Zingiber Sect. Zingiber). (4) The subtype Striate, pollen grains of which are prolate or oliveshaped, and striate (Zingiber Setc. Cryptanthium). II. The type Aperturate, in which pollen grains are acetilysis-resistant and possess distinct apertures (mixed colpate-porate or forate), including two subtypes: (1)The subtype Mixed colpate and Porate. Pollen grains are both 3-colpate and 1-3-porate, and usually with one long spiral, two short (straight or slightly curved) colpi and 1-3-poris. The exine is verrucate or not, nearly sinuolate (Costus speciosus, C. tonkinensis, C. lacerus). (2) The subtype porate, whose grains are 6-8-porate and exine is foveolate (Costus megalobractea). The taxonomic significance of the pollen types in the family Zingiberaceae is also discussed.     

Effects of perturbation on the predator–prey system in a heterogeneous landscape

Environmental perturbations occur in ecosystems as the result of disturbance, which is closely related to ecosystem stability and resilience. To understand how perturbations can affect ecosystems, we constructed a spatially explicit lattice model to simulate the integrative predator–prey–grass relationships. In this model, a predator (or prey) gives birth to offspring, according to a specific birth probability, when it is able to feed on prey (or grass). When a predator or prey animal was initially introduced or newly born, its health state was set at a given high value. This state decreased by 1 with each time step. When the state of an animal decreased to zero, the animal was considered dead and was removed from the system. In this model, the perturbation was defined as the sudden death of some portion of the population. The heterogeneous landscape was characterized by a parameter, H, which controlled the degree of heterogeneity. When H ≥ 0.6, the predator population size was positively influenced by the perturbation. However, the perturbation had little effect upon the population sizes of prey or grass, regardless of the value of H.     

On the Neimark–Sacker bifurcation in a discrete predator–prey system

A two-parameter family of discrete models describing a predator–prey interaction is considered, which generalizes a model discussed by Murray, and originally due to Nicholson and Bailey, consisting of two coupled nonlinear difference equations. In contrast to the original case treated by Murray, where the two populations either die out or may display unbounded growth, the general member of this family displays a somewhat wider range of behaviour. In particular, the model has a nontrivial steady state which is stable for a certain range of parameter values, which is explicitly determined, and also undergoes a Neimark–Sacker bifurcation that produces an attracting invariant curve in some areas of the parameter space and a repelling one in others.     

Water turbidity affects predator–prey interactions in a fish–damselfly system

Community structure may differ dramatically between clear-water and turbid lakes. These differences have been attributed to differences in the cascading effect of fish on prey populations, owing to the reduced efficiency of fish predation in the presence of macrophytes. However, recent theoretical ideas suggest that water turbidity may shape predator–prey interactions, and it is predicted that prey will relax its antipredation behaviour in turbid water (H1). As a result, the nature of predator–prey interactions is expected to shift from both direct and indirect in clear water to dominantly direct in turbid water (H2). We tested these ideas in a fish–damselfly predator–prey system. In a first behavioural experiment, we looked at antipredation behaviour of damselfly larvae isolated from habitats that differ in turbidity, in the presence of fish in clear and turbid water. As predicted in H1, the larvae were more active in turbid than in clear water. In a complementary enclosure experiment, we reared larvae in a clear-water pond and a turbid pond, respectively, and manipulated the origin of the larvae (clear-water, turbid pond), fish presence (absent, present), and vegetation density (sparse, abundant). In both ponds, fish had a direct negative effect on survival of the larvae, which was mitigated in the presence of vegetation. In the fish treatment, the change in average body mass tended to be higher in the turbid pond than in the clear-water pond, suggesting indirect effects of fish were mitigated in the turbid pond. This was supported by a negative effect of fish on the effective growth rate of larvae in the clear pond, but not in the turbid pond. These results are compatible with the idea that predator–prey relationships are mainly governed by direct effects in turbid water, and by direct and indirect effects in clear water.     

HAY FEVER—A Comparative Clinical Evaluation of Treatment with Aqueous Pollen Extracts,Alum-Precipitated Pyridine Pollen Extracts and Aqueous Pollen in Oil Emulsions

Three different types of pollen extracts are currently being used in the prophylactic treatment of hay fever. A comparative clinical study of their efficacy reveals that all are about equally efficacious. The alum-precipitated pyridine pollen extracts may be slightly better. Since only 14 to 16 injections are required for prophylactic treatment, they may well replace the older aqueous pollen extracts, 20 to 35 injections of which are usually necessary to provide relief.The aqueous pollen in oil repository method of treatment needs only one to four injections for comparable results, but this so-called “one-shot” treatment can only be administered by one who is trained in emulsion therapy and has come to know by experience the proper maximum dose.