Periodic dynamics in a two-stage Allee effect model are driven by tension between stage equilibria

Single species difference population models can show complex dynamics such as periodicity and chaos under certain circumstances, but usually only when rates of intrinsic population growth or other life history parameter are unrealistically high. Single species models with Allee effects (positive density dependence at low density) have also been shown to exhibit complex dynamics when combined with over-compensatory density dependence or a narrow fertility window. Here we present a simple two-stage model with Allee effects which shows large amplitude periodic fluctuations for some initial conditions, without these requirements. Periodicity arises out of a tension between the critical equilibrium of each stage, i.e. when the initial population vector is such that the adult stage is above the critical value, while the juvenile stage is below the critical value. Within this area of parameter space, the range of initial conditions giving rise to periodic dynamics is driven mainly by adult mortality rates. Periodic dynamics become more important as adult mortality increases up to a certain point, after which periodic dynamics are replaced by extinction. This model has more realistic life history parameter values than most 'chaotic' models. Conditions for periodic dynamics might arise in some marine species which are exploited (high adult mortality) leading to recruitment limitation (low juvenile density) and might be an additional source of extinction risk.     

The influence of drug treatment on the maintenance of schistosome genetic diversity

Drug treatment of patients with schistosomiasis may select for drug-resistant parasites. In this article, we formulate a deterministic model with multiple strains of schistosomes (helminth parasites with a two-host life cycles) in order to explore the role of drug treatment in the maintenance of a polymorphism of parasite strains that differ in their resistance levels. The basic reproductive numbers for all strains are computed, and are shown to determine the stabilities of equilibria of the model and consequently the distribution of parasite phenotypes with different levels of drug tolerance. Analysis of our model shows that the likelihood that resistant strains will increase in frequency depends on the interplay between their relative fitness, the cost of resistance, and the degree of selection pressure exerted by the drug treatments.     

Species coexistence and pathogens with frequency-dependent transmission

Pathogens that infect multiple hosts are commonly transmitted by vectors, and their transmission rate is often thought to depend on the proportion of hosts or vectors infected (i.e., frequency dependence). A model of a two-host, one-pathogen system with frequency-dependent transmission is used to investigate how sharing a pathogen with an alternative host influences pathogen-mediated extinction. The results show that if there is frequency-dependent transmission, a host can be rescued from pathogen-mediated extinction by the presence of a second host with which it shares a pathogen. The study provides an important conceptual counterexample to the idea that shared pathogens necessarily result in apparent competition by showing that shared pathogens can mediate apparent mutualism. We distinguish two types of dilution effect (pathogen reduction with increasing host diversity), each resulting from different underlying pathogen transmission processes and host density effects. These results have important consequences for understanding the role of pathogens in species interactions and in maintaining host species diversity.     

Modelling transmission of vector-borne pathogens shows complex dynamics when vector feeding sites are limited

The relationship between species richness and the prevalence of vector-borne disease has been widely studied with a range of outcomes. Increasing the number of host species for a pathogen may decrease infection prevalence (dilution effect), increase it (amplification), or have no effect. We derive a general model, and a specific implementation, which show that when the number of vector feeding sites on each host is limiting, the effects on pathogen dynamics of host population size are more complex than previously thought. The model examines vector-borne disease in the presence of different host species that are either competent or incompetent (i.e. that cannot transmit the pathogen to vectors) as reservoirs for the pathogen. With a single host species present, the basic reproduction ratio R(0) is a non-monotonic function of the population size of host individuals (H), i.e. a value [Formula: see text] exists that maximises R(0). Surprisingly, if [Formula: see text] a reduction in host population size may actually increase R(0). Extending this model to a two-host species system, incompetent individuals from the second host species can alter the value of [Formula: see text] which may reverse the effect on pathogen prevalence of host population reduction. We argue that when vector-feeding sites on hosts are limiting, the net effect of increasing host diversity might not be correctly predicted using simple frequency-dependent epidemiological models.     

A mathematical model of the stress induced during avascular tumour growth

In this paper a mathematical model is developed to describe the effect of nonuniform growth on the mechanical stress experienced by cells within an avascular tumour. The constitutive law combines the stress-strain relation of linear elasticity with a growth term that is derived by analogy with thermal expansion. To accommodate the continuous nature of the growth process, the law relates the rate of change of the stress tensor to the rate of change of the strain (rather than relating the stress to the strain directly). By studying three model problems which differ in detail, certain characteristic features are identified. First, cells near the tumour boundary, where nutrient levels and cell proliferation rates are high, are under compression. By contrast, cells towards the centre of the tumour, where nutrient levels are low and cell death dominant, are under tension. The implications of these results and possible model developments are also discussed. Received: 15 November 1999 / Published online: 5 May 2000     

Two-Host,Two-Vector Basic Reproduction Ratio (R 0) for Bluetongue

Mathematical formulations for the basic reproduction ratio (R ₀) exist for several vector-borne diseases. Generally, these are based on models of one-host, one-vector systems or two-host, one-vector systems. For many vector borne diseases, however, two or more vector species often co-occur and, therefore, there is a need for more complex formulations. Here we derive a two-host, two-vector formulation for the R ₀ of bluetongue, a vector-borne infection of ruminants that can have serious economic consequences; since 1998 for example, it has led to the deaths of well over 1 million sheep in Europe alone. We illustrate our results by considering the situation in South Africa, where there are two major hosts (sheep, cattle) and two vector species with differing ecologies and competencies as vectors, for which good data exist. We investigate the effects on R ₀ of differences in vector abundance, vector competence and vector host preference between vector species. Our results indicate that R ₀ can be underestimated if we assume that there is only one vector transmitting the infection (when there are in fact two or more) and/or vector host preferences are overlooked (unless the preferred host is less beneficial or more abundant). The two-host, one-vector formula provides a good approximation when the level of cross-infection between vector species is very small. As this approaches the level of intraspecies infection, a combination of the two-host, one-vector R ₀ for each vector species becomes a better estimate. Otherwise, particularly when the level of cross-infection is high, the two-host, two-vector formula is required for accurate estimation of R ₀. Our results are equally relevant to Europe, where at least two vector species, which co-occur in parts of the south, have been implicated in the recent epizootic of bluetongue.     

Predicting secretory protein signal sequence cleavage sites by fusing the marks of global alignments

Summary. A newly synthesized secretory protein in cells bears a special sequence, called signal peptide or sequence, which plays the role of “address tag” in guiding the protein to wherever it is needed. Such a unique function of signal sequences has stimulated novel strategies for drug design or reprogramming cells for gene therapy. To realize these new ideas and plans, however, it is important to develop an automated method for fast and accurately identifying the signal sequences or their cleavage sites. In this paper, a new method is developed for predicting the signal sequence of a query secretory protein by fusing the results from a series of global alignments through a voting system. The very high success rates thus obtained suggest that the novel approach is very promising, and that the new method may become a useful vehicle in identifying signal sequence, or at least serve as a complementary tool to the existing algorithms of this field.     

Analysing the effect of movement on local survival: a new method with an application to a spatially structured population of the arboreal gecko Gehyra variegata

Mortality during movement between habitat patches is the most obvious cost of dispersal, but rarely it has been demonstrated empirically. An approach is presented, which uses capture–mark–recapture data of an arboreal gecko species to determine the effect of individual movement on local survival in a spatially structured population. Because capture–mark–recapture data are widely available for a range of animal species, it should be possible to extend their application to other species. The method is based on the assumption that the tendency to be a territorial animal or to be a floating animal is fixed during the study period. The advantage of our approach is that only one additional parameter has to be estimated for describing movement risks. We further tested the power of our approach to detect an association of movement and mortality with simulated capture histories. The study revealed a strong negative effect of movement on local survival. Hence, animals that moved more often between trees had a lower survival rate. Interestingly, the mean movement rate for males was significantly higher than for females, which should lead to a biased sex ratio towards females in the population. As there was an even sex ratio in the population, we discuss not mutually exclusive explanations for this finding like differences in emigration rates between sexes, differences in survival rates between sexes, or a skewed sex ratio in offspring.     

The evolution of larval foraging behaviour in response to host plant variation in a leaf beetle

The evolutionary causes of variation in host specialization among phytophagous insects are still not well understood and identifying them is a central task in insect–host plant biology. Here we examine host utilization of the chrysomelid beetle Oreina elongata that shows interpopulation variation in the degree of specialization. We focus on larval behaviour and on what selection pressures may favour the use of two different larval host plants ( Adenostyles alliariae and Cirsium spinosissimum ) in one population as opposed to specialization onto one of them as is seen in other populations. The results suggest that the degree of exploratory foraging behaviour is higher in larvae from the two-host population than in single host populations, and a field survey of the two-host population also indicated that larvae do move between host species. A field experiment indicated that predation rates on O. elongata larvae in the two-host population are higher on one of the host species, A. alliariae , than on the alternative C. spinosissimum . In combination with earlier results this finding suggest that larvae move between hosts to obtain better food on one host, and to get better protection from predators on the other. It appears that in this two-host situation a single plant species does not provide the most beneficial conditions in all parts of O. elongata life cycle and individuals may obtain different plant-specific benefits by moving between host species. This heterogeneous host situation appears to have selected for the explorative larval foraging strategy seen in the in the two-host population. In general, the results support the notion that to understand patterns of host plant use in insects it is often vital to consider a range of host related selection pressures whose relative importance may vary between life stages of the insect.     

Brucellosis, botflies, and brainworms: the impact of edge habitats on pathogen transmission and species extinction

Ecological interactions between species that prefer different habitat types but come into contact in edge regions at the interfaces between habitat types are modeled via reaction-diffusion systems. The primary sort of interaction described by the models is competition mediated by pathogen transmission. The models are somewhat novel because the spatial domains for the variables describing the population densities of the interacting species overlap but do not coincide. Conditions implying coexistence of the two species or the extinction of one species are derived. The conditions involve the principal eigenvalues of elliptic operators arising from linearizations of the model system around equilibria with only one species present. The conditions for persistence or extinction are made explicit in terms of the parameters of the system and the geometry of the underlying spatial domains via estimates of the principal eigenvalues. The implications of the models with respect to conservation and refuge design are discussed. Received: 10 June 1999 / Revised version: 7 July 2000 / Published online: 20 December 2000     

Toward ecologically explicit null models of nestedness

A community is "nested" when species assemblages in less rich sites form nonrandom subsets of those at richer sites. Conventional null models used to test for statistically nonrandom nestedness are under- or over-restrictive because they do not sufficiently isolate ecological processes of interest, which hinders ecological inference. We propose a class of null models that are ecologically explicit and interpretable. Expected values of species richness and incidence, rather than observed values, are used to create random presence-absence matrices for hypothesis testing. In our examples, based on six datasets, expected values were derived either by using an individually based random placement model or by fitting empirical models to richness data as a function of environmental covariates. We describe an algorithm for constructing unbiased null matrices, which permitted valid testing of our null models. Our approach avoids the problem of building too much structure into the null model, and enabled us to explicitly test whether observed communities were more nested than would be expected for a system structured solely by species-abundance and species-area or similar relationships. We argue that this test or similar tests are better determinants of whether a system is truly nested; a nested system should contain unique pattern not already predicted by more fundamental ecological principles such as species-area relationships. Most species assemblages we studied were not nested under these null models. Our results suggest that nestedness, beyond that which is explained by passive sampling processes, may not be as widespread as currently believed. These findings may help to improve the utility of nestedness as an ecological concept and conservation tool.     

Kidney growth,hypertrophy and the unifying mechanism of diabetic complications

Summary. Michael Brownlee has proposed a ‘Unifying Mechanism’ of hyperglycemia-induced damage in diabetes mellitus. At the crux of this hypothesis is the generation of reactive oxygen species (ROS), and their impact on glycolytic pathways. Diabetes is the leading cause of chronic kidney failure. In the early phase of diabetes, prior to establishment of proteinuria or fibrosis, comes kidney growth and hyperfiltration. This early growth phase consists of an early period of hyperplasia followed by hypertrophy. Hypertrophy also contributes to cellular oxidative stress, and may precede the ROS perturbation of glycolytic pathways described in the Brownlee proposal. This increase in growth promotes hyperfiltration, and along with the hypertrophic phenotype appears required for hyperglycemia-induced cell damage and the progression of downstream diabetic complications. Here we will evaluate this growth phenomenon in the context of diabetes mellitus.     

The hypersensitive response is associated with host and nonhost resistance to Phytophthora infestans

The interaction between Phytophthora infestans (Mont.) de Bary and Solanum was examined cytologically using a diverse set of wild Solanum species and potato (S. tuberosum L.) cultivars with various levels of resistance to late blight. In wild Solanum species, in potato cultivars carrying known resistance (R) genes and in nonhosts the major defense reaction appeared to be the hypersensitive response (HR). In fully resistant Solanum species and nonhosts, the HR was fast and occurred within 22 h. This resulted in the death of one to three cells. In partially resistant clones, the HR was induced between 16 and 46 h, and resulted in HR lesions consisting of five or more dead cells, from which hyphae were occasionally able to escape to establish a biotrophic interaction. These results demonstrate the quantitative nature of the resistance to P. infestans. The effectiveness of the HR in restricting growth of the pathogen differed considerably between clones and correlated with resistance levels. Other responses associated with the defense reaction were deposition of callose and extracellular globules containing phenolic compounds. These globules were deposited near cells showing the HR, and may function in cell wall strengthening. Received: 22 April 1999 / Accepted: 4 November 1999     

Salinity drives growth dynamics of the mangrove tree Sonneratia apetala Buch. -Ham. in the Sundarbans,Bangladesh

Mangroves throughout the world are threatened by environmental changes apart from anthropogenic disturbances. Many of these changes may inhibit the growth and survival of mangrove species. To understand and predict the effects of global change on mangrove forests, it is necessary to obtain insights on the growth dynamics of mangroves in relation to environmental factors. This study was conducted on Sonneratia apetala, a mangrove species which grows under a range of salinity conditions across the Sundarbans in Bangladesh. We studied trees growing under respectively high, medium, and low salinity conditions based on the influence of freshwater discharge. First, the periodicity of radial growth across the year was detected by applying cambial analyses. Based on tree-ring analyses, we calculated the growth response of S. apetala to monthly variation in precipitation and temperature as well as river discharge, as a proxy for salinity. We found the cambium of S. apetala being active during the monsoon and post-monsoon period whereas it was dormant in the pre-monsoon. This periodicity in radial growth leads to the formation of distinct annual rings with ring boundaries being marked by radially flattened fibres. S. apetala trees growing under low salinity conditions generally show higher growth rates indicating the positive impact of river discharge, i.e. freshwater input on mangrove growth. Wet and warm conditions during the monsoon period positively affected S. apetala growth, especially in the low salinity zone. Our results show that salinity is the primary driver of growth dynamics of S. apetala in the Sundarbans. A gradual or seasonal increase in salinity, e.g. as a consequence of sea-level rise may therefore importantly alter the growth of this species, possibly leading to changes in mangrove forest dynamics and zonation.     

Coevolution of dispersal in a parasitoid–host system

Interspecific interactions and the evolution of dispersal are both of interest when considering the potential impact of habitat fragmentation on community ecology, but the interaction between these processes is not well studied. We address this by considering the coevolution of dispersal strategies in a host–parasitoid system. An individual-based host–parasitoid metapopulation model was constructed for a patchy environment, allowing for evolution in dispersal rates of both species. Highly rarefied environments with few suitable patches selected against dispersal in both species, as did relatively static environments. Provided that parasitoids persist, all the variables studied led to stable equilibria in dispersal rates for both species. There was a tendency toward higher dispersal rates in parasitoids because of the asymmetric relationships of the two species to the patches: vacant patches are most valuable for hosts, but unsuitable for parasitoids, which require an established host population to reproduce. High host dispersal rate was favoured by high host population growth rate, and in the parasitoid by high growth rates in both species. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Clumped versus scattered: how does the spatial correlation of disturbance events affect biodiversity?

In this study, we systematically explore the effects of rate and spatial correlation (level of clumping) of disturbance events on a community of sessile species differing in their life history traits. A spatially explicit individual-based model shows that long-term coexistence is very sensitive to spatial correlation when the trade-off in life history traits includes differences in dispersal distances. Highest biodiversity emerges at highly correlated disturbances of intermediate rates. Diversity peaks shift to larger rates when clumping decreases. Scattered disturbances lead to competitive exclusion. Interestingly, we observed additional peaks in the diversity–disturbance curves at certain levels of clumping. Thus, subject to the differences in life history traits, particular combinations of disturbance rate and spatial correlation may enable subsets of species to coexist, which opens new possibilities for explaining diversity. Our results suggest that observation of high biodiversity under spatially correlated disturbances points to a competition–colonisation trade-off, which includes dispersal distances.     

The Biology of Vampyrophrya pelagica (Chatton & Lwoff, 1930), a Histophagous Apostome Ciliate Associated with Marine Calanoid Copepods

ABSTRACT. The histophagous apostome. l'ampyrophrya pelagica , occurs on calanoid copepods in North Carolina. Its life cycle has two pathways: one when the copepod host is injured; the other when the host is ingested by an invertebrate predator. The ciliate, immediately after encysting on a copepod. metamorphoses to a feeding stage. When its host is injured or ingested by a predator, it excysts enters the wound and ingests the host's cytoplasm. In the single-host life cycle, after feeding, the ciliate encysts within the cadaver; in the two-host life cycle, after feeding it encysts upon a substrate. Encysted cells divide into 2–32 migratory tomites. Freed tomites are motionless in the water column until the water is disturbed, at which time they spring in the direction of any vibration, which many times results from a feeding copepod. Tomites select specific hosts, since not all species of copepods are infested. We hypothesize that the single-host life cycle yields many tomites that heavily infest hosts at random, and passage through the predator (two-host life cycle) results in fewer, but more widely dispersed tomites that are released continuously. The two-host life cycle is facultative for the individual, but may be obligate for the continuation of the species.     

Localization of pectins in the pollen tube wall of Ornithogalum virens L. Does the pattern of pectin distribution depend on the growth rate of the pollen tube?

Monoclonal antibodies that recognize pectins were used for the localization of esterified (JIM7) and acidic, unesterified (JIM5) forms of pectin in pollen tube walls of Ornithogalum virens L. (x = n = 3). The results indicated that the distribution of the two forms of pectin in the pollen tube wall depended on the medium (liquid or solid) used for pollen germination. In pollen tubes grown in the liquid medium, the localization of JIM7 was limited to the very tip of the pollen tube, whereas the localization of JIM5 indicated a uniform distribution of unesterified pectins in the very tip of the tube and along the subapical parts of the tube wall. In tubes germinated on the medium stabilized with agar (1–2%) the localization of JIM7 and JIM5 indicated the presence of both forms of pectin in the tube tip and along the whole length of the pollen tube wall in a ring-like pattern. Thus, the localization of esterified pectins in the sub-apical part of the pollen tube wall, below the apex of the tube, is described for the first time. Measurements of the growth rates of pollen tubes growing on the two types of medium indicated that oscillations in tube growth rate occur but these do not coincide with the pattern of pectin distribution in the tube wall. Our results complement the previous data obtained for the localization of JIM5 and JIM7 in pollen tube walls of other plant species. (Y.-Q. Li et al. 1994, Sex Plant Reprod 7: 145–150) and provide new insight into an understanding of the construction of the pollen tube wall and the physiology of pollen grain germination. Received: 25 January 1999 / Accepted: 23 June 1999     

Simple Growth Patterns Can Create Complex Trajectories for the Ontogeny of Constitutive Chemical Defences in Seaweeds

All of the theory and most of the data on the ecology and evolution of chemical defences derive from terrestrial plants, which have considerable capacity for internal movement of resources. In contrast, most macroalgae – seaweeds – have no or very limited capacity for resource translocation, meaning that trade-offs between growth and defence, for example, should be localised rather than systemic. This may change the predictions of chemical defence theories for seaweeds. We developed a model that mimicked the simple growth pattern of the red seaweed Asparagopsis armata which is composed of repeating clusters of somatic cells and cells which contain deterrent secondary chemicals (gland cells). To do this we created a distinct growth curve for the somatic cells and another for the gland cells using empirical data. The somatic growth function was linked to the growth function for defence via differential equations modelling, which effectively generated a trade-off between growth and defence as these neighbouring cells develop. By treating growth and defence as separate functions we were also able to model a trade-off in growth of 2–3% under most circumstances. However, we found contrasting evidence for this trade-off in the empirical relationships between growth and defence, depending on the light level under which the alga was cultured. After developing a model that incorporated both branching and cell division rates, we formally demonstrated that positive correlations between growth and defence are predicted in many circumstances and also that allocation costs, if they exist, will be constrained by the intrinsic growth patterns of the seaweed. Growth patterns could therefore explain contrasting evidence for cost of constitutive chemical defence in many studies, highlighting the need to consider the fundamental biology and ontogeny of organisms when assessing the allocation theories for defence.     

Evolution of trophic transmission in parasites: why add intermediate hosts?

Although multihost complex life cycles (CLCs) are common in several distantly related groups of parasites, their evolution remains poorly understood. In this article, we argue that under particular circumstances, adding a second host to a single-host life cycle is likely to enhance transmission (i.e., reaching the target host). For instance, in several situations, the propagules of a parasite exploiting a predator species will achieve a higher host-finding success by encysting in a prey of the target predator than by other dispersal modes. In such a case, selection should favor the transition from a single- to a two-host life cycle that includes the prey species as an intermediate host. We use an optimality model to explore this idea, and we discuss it in relation to dispersal strategies known among free-living species, especially animal dispersal. The model found that selection favored a complex life cycle only if intermediate hosts were more abundant than definitive hosts. The selective value of a complex life cycle increased with predation rates by definitive hosts on intermediate hosts. In exploring trade-offs between transmission strategies, we found that more costly trade-offs made it more difficult to evolve a CLC while less costly trade-offs between traits could favor a mixed strategy.