How do productivity gradient and diffusion shape patterns in a plant-herbivore grazing system?

Natural systems show heterogeneous patchy distributions of vegetation over large landscapes. Reaction-diffusion systems can demonstrate such heterogeneity of species distributions. Here, we analyse a reaction-diffusion model of plant-herbivore interactions in two-dimensional space to illustrate non-homogeneous distributions of plants and herbivores. The non-spatial system shows bottom-up control, where herbivore density is low under low and high primary productivity but increased at intermediate productivity. In addition, the non-spatial system provides bistability between a dense vegetation state devoid of herbivores and a coexisting state of plants and herbivores. In the spatiotemporal model, we give analytical conditions of occurring diffusion-driven (Turing) instability, where a novel point in our model is the relative dispersal of herbivores, which represents the movement of herbivores from a higher to a lower vegetation state in addition to the self-diffusion of both species. It is shown that heterogeneity in the population distribution does not occur if the relative dispersal of herbivores is low, but it appears in the opposite case. Due to bistability in the underlying non-spatial system, the spatiotemporal model produces initial value-dependent patterns. The two initial values make different patterns despite having the same primary productivity and relative dispersal rate. As productivity increases with a given relative herbivore dispersal, pattern transition occurs from a blend of stripes and spots of low vegetation state to a predominantly low-density vegetation state with smaller patches of densely vegetated states with one initial value. On the contrary, a discernible change in vegetation patterns from cold spots in the dense vegetation to hot stripes in the primarily low-vegetated state is noticed under the other initial population value. Furthermore, the population distributions of plants and herbivores in the entire domain after a long period are heterogeneous for both initial values, provided the relative herbivore dispersal is substantial. We estimated mean population densities to observe species fitness in the whole domain under variable productivity. When productivity is high, the mean population density of plants may go up or down, depending on the herbivore's relative dispersal rate. In contrast to the bottom-up control dynamics of the non-spatial system, the system exhibits a top-down control under high relative dispersal, where the herbivore regulates vegetation growth under high productivity. On the other hand, herbivores are extinct under high productivity if the relative dispersal is low.

Spatial metapopulation dynamics with local and global colonization.

We revisit a spatial metapopulation model on continuous space as a stochastic point pattern dynamics. In the model, local patches as points are distributed with a certain spatial configuration and status of each patch changes stochastically between occupied and empty: an occupied patch becomes empty by local extinction and an empty patch becomes occupied both by local and global colonization. We carry out simulation analysis and derive an analytical model in terms of singlet, pair and triplet probabilities that describe the stochastic dynamics. Using a simple closure that approximates triplet probabilities by singlet and pair probabilities, we show that equilibrium singlet and pair probabilities can be analytically derived. The derived equilibrium properties successfully describe simulation results under a certain condition where the range of local colonization and the proportion of global colonization play key roles. Our model is an extension of the classical non-spatial Levins model to a spatially explicit metapopulation model. We appeal the advantage of point pattern approach to study spatial dynamics in general ecology and call for the need to deepen our understanding of mathematical tools to explore point pattern dynamics.

Simulating Pine Wilt Disease Dispersal With an Individual-Based Model Incorporating Individual Movement Patterns of Vector Beetles.

Individual movements of the insect vector pine sawyer beetles were incorporated into an individual-based model (IBM) to elucidate the dispersal of pine wilt disease (PWD) and demonstrate the effects of control practices. The model results were compared with the spatial data of infested pine trees in the Gijang-gun area of Busan, Republic of Korea. Step functions with long- and middle-distance movements of individual beetles effectively established symptomatic and asymptomatic trees for the dispersal of PWD. Pair correlations and pairwise distances were suitable for evaluating PWD dispersal between model results and field data at short and long scales, respectively. The accordance between model and field data was observed in infestation rates at 0.08 and 0.09 and asymptomatic rates at 0.16-0.17 for disease dispersal. Eradication radii longer than 20 m would effectively control PWD dispersal for symptomatic transmission and 20-40 m for asymptomatic transmission. However, the longer eradication radii were more effective at controlling PWD. Therefore, to maximize control effects, a longer radius of at least 40 m is recommended for clear-cutting eradication. The IBM of individual movement patterns provided practical information on interlinking the levels of individuals and populations and could contribute to the monitoring and management of forest pests where individual movement is important for population dispersal.

Equilibrium properties of the spatial SIS model as a point pattern dynamics - How is infection distributed over space?

We revisit the classical epidemiological SIS model as a stochastic point pattern dynamics with special focus on its spatial distribution at equilibrium. In this model, each point on a continuous space is either susceptible S or infectious I, and infection occurs with an infection kernel as a function of distance from I to S. This stochastic process has been mathematically described by the hierarchical dynamics of the probabilities that a point, a pair made by two points, and a triplet made by three points, etc., is in a specific configuration of status. Using a simple closure thereby triplet probabilities that appear in the dynamics are approximated, we show that the average singlet probabilities and the pair probabilities that describe spatial distributions of Ss and Is at equilibrium can be explicitly derived using the infection kernel; Is are spatially clustered in the same order of the infection kernel. The results highlight the advantage of point pattern approach to model spatial population dynamics in general ecology where local interactions among individuals likely depend on distance between them.

How can distinct egg polymorphism be maintained in the rufescent prinia (Prinia rufescens)-plaintive cuckoo (Cacomantis merulinus) interaction-a modeling approach.

In avian brood parasitism, both the host and the parasite are expected to develop various conflicting adaptations; hosts develop a defense against parasitism, such as an ability to recognize and reject parasitic eggs that look unlike their own, while parasites evolve egg mimicry to counter this host defense. Hosts may further evolve to generate various egg phenotypes that are not mimicked by parasites. Difference in egg phenotype critically affects the successful reproduction of hosts and parasites. Recent studies have shown that clear polymorphism in egg phenotype is observed in several host-parasite interactions, which suggests that egg polymorphism may be a more universal phenomenon than previously thought. We examined the mechanism for maintaining egg polymorphism in the rufescent prinia (Prinia rufescens) that is parasitized by the plaintive cuckoo (Cacomantis merulinus) from a theoretical viewpoint based on a mathematical model. The prinia has four distinct egg phenotypes: immaculate white, immaculate blue, white with spots, and blue with spots. Only two egg phenotypes, white with spots and blue with spots, are found in the cuckoo population. We show that the observed prinia and cuckoo phenotypes cannot be at an equilibrium and that egg polymorphism can be maintained either at stationary equilibrium or with dynamic, frequency oscillations, depending on the mutation rates of the background color and spottiness. Long-term monitoring of the prinia-cuckoo interaction over a wide geographic range is needed to test the results of the model analyses.

Ancient origin and maternal inheritance of blue cuckoo eggs.

Maternal inheritance via the female-specific W chromosome was long ago proposed as a potential solution to the evolutionary enigma of co-existing host-specific races (or 'gentes') in avian brood parasites. Here we report the first unambiguous evidence for maternal inheritance of egg colouration in the brood-parasitic common cuckoo Cuculus canorus. Females laying blue eggs belong to an ancient (∼2.6 Myr) maternal lineage, as evidenced by both mitochondrial and W-linked DNA, but are indistinguishable at nuclear DNA from other common cuckoos. Hence, cuckoo host races with blue eggs are distinguished only by maternally inherited components of the genome, which maintain host-specific adaptation despite interbreeding among males and females reared by different hosts. A mitochondrial phylogeny suggests that blue eggs originated in Asia and then expanded westwards as female cuckoos laying blue eggs interbred with the existing European population, introducing an adaptive trait that expanded the range of potential hosts.

Beyond pairs: definition and interpretation of third-order structure in spatial point patterns.

Spatial distributions of biological species are an important source of information for understanding local interactions at the scale of individuals. Technological advances have made it easier to measure these distributions as spatial point patterns, specifying the locations of individuals. Extensive attention has been devoted to analyzing the second-order structure of such point patterns by focusing on pairs of individuals, and it is well known that the local crowdedness of individuals can thus be quantified. Statistical measures such as a point pattern׳s pair correlation function or Ripley׳s K function show whether a given point pattern is clustered (excess of short-distance pairs) or overdispersed (shortage of short-distance pairs). These notions are naturally defined in comparison with control patterns exhibiting complete spatial randomness, i.e., an absence of any spatial structure. However, there is no rational reason why the analysis of point patterns should stop at the second order. In this paper, we focus on triplets of individuals in an attempt to quantify and interpret the third-order structure of a point pattern. We demonstrate that point patterns with "bandedness", in which individuals are primarily distributed within bands, can be detected by an excess of thinner triplets at a characteristic spatial scale linked to the band׳s width. In this context, we show how the generation of control patterns as a reference for gauging a test pattern׳s triplet frequencies is critical for defining and interpreting the third-order structure of point patterns. Since perfect information on a point pattern׳s second-order structure typically suffices for its unique reconstruction (up to translation, rotation, and reflection), we conjecture that it is essential to minimally coarse-grain such second-order information before using it to generate control patterns for identifying a point pattern׳s third-order structure. We recommend the further exploration of this conjecture for future studies.

Egg arrangement in avian clutches covaries with the rejection of foreign eggs.

In birds, the colour, maculation, shape, and size of their eggs play critical roles in discrimination of foreign eggs in the clutch. So far, however, no study has examined the role of egg arrangement within a clutch on host rejection responses. We predicted that individual females which maintain consistent egg arrangements within their clutch would be better able to detect and reject foreign eggs than females without a consistent egg arrangement (i.e. whose eggs change positions more often across incubation). We tested this "egg arrangement hypothesis" in blackbirds (Turdus merula) and song thrush (T. philomelos). Both species are suitable candidates for research on egg rejection, because they show high inter-individual variation and individual repeatability in egg rejection responses. As predicted, using our custom-defined metrics of egg arrangement, rejecter females' clutches showed significantly more consistent patterns in egg arrangement than acceptor females' clutches. Only parameters related to blunt pole showed consistent differences between rejecters and acceptors. This finding makes biological sense because it is already known that song thrush use blunt pole cues to reject foreign eggs. We propose that a disturbance of the original egg arrangement pattern by the laying parasite may alert host females that maintain a consistent egg arrangement to the risk of having been parasitized. Once alerted, these hosts may shift their discrimination thresholds to be more restrictive so as to reject a foreign egg with higher probability. Future studies will benefit from experimentally testing whether these two and other parasitized rejecter host species may rely on the use of consistent egg arrangements as a component of their anti-parasitic defence mechanisms.

Dynamic regulation of myosin light chain phosphorylation by Rho-kinase.

Myosin light chain (MLC) phosphorylation plays important roles in various cellular functions such as cellular morphogenesis, motility, and smooth muscle contraction. MLC phosphorylation is determined by the balance between activities of Rho-associated kinase (Rho-kinase) and myosin phosphatase. An impaired balance between Rho-kinase and myosin phosphatase activities induces the abnormal sustained phosphorylation of MLC, which contributes to the pathogenesis of certain vascular diseases, such as vasospasm and hypertension. However, the dynamic principle of the system underlying the regulation of MLC phosphorylation remains to be clarified. Here, to elucidate this dynamic principle whereby Rho-kinase regulates MLC phosphorylation, we developed a mathematical model based on the behavior of thrombin-dependent MLC phosphorylation, which is regulated by the Rho-kinase signaling network. Through analyzing our mathematical model, we predict that MLC phosphorylation and myosin phosphatase activity exhibit bistability, and that a novel signaling pathway leading to the auto-activation of myosin phosphatase is required for the regulatory system of MLC phosphorylation. In addition, on the basis of experimental data, we propose that the auto-activation pathway of myosin phosphatase occurs in vivo. These results indicate that bistability of myosin phosphatase activity is responsible for the bistability of MLC phosphorylation, and the sustained phosphorylation of MLC is attributed to this feature of bistability.

Coevolution in action: disruptive selection on egg colour in an avian brood parasite and its host.

BACKGROUND: Trait polymorphism can evolve as a consequence of frequency-dependent selection. Coevolutionary interactions between hosts and parasites may lead to selection on both to evolve extreme phenotypes deviating from the norm, through disruptive selection. METHODOLOGY/PRINCIPAL FINDING: Here, we show through detailed field studies and experimental procedures that the ashy-throated parrotbill (Paradoxornis alphonsianus) and its avian brood parasite, the common cuckoo (Cuculus canorus), have both evolved egg polymorphism manifested in discrete immaculate white, pale blue, and blue egg phenotypes within a single population. In this host-parasite system the most common egg colours were white and blue, with no significant difference in parasitism rates between hosts laying eggs of either colour. Furthermore, selection on parasites for countering the evolution of host egg types appears to be strong, since ashy-throated parrotbills have evolved rejection abilities for even partially mimetic eggs. CONCLUSIONS/SIGNIFICANCE: The parrotbill-cuckoo system constitutes a clear outcome of disruptive selection on both host and parasite egg phenotypes driven by coevolution, due to the cost of parasitism in the host and by host defences in the parasite. The present study is to our knowledge the first to report the influence of disruptive selection on evolution of discrete phenotypes in both parasite and host traits in an avian brood parasitism system.

The importance of clutch characteristics and learning for antiparasite adaptations in hosts of avian brood parasites.

There is considerable variation in rejection rates of parasitic eggs among hosts of avian brood parasites. In this article, we develop a model that can be used to predict host egg rejection behavior in brood parasite-host systems in general, by considering both intra- and interclutch variation in host egg appearance; clutch characteristics that may be important in calculating the fitness of individuals adopting rejecter or acceptor strategies. In addition, we consider the importance of learning the appearance of own eggs during the first breeding attempt and host probability of survival between breeding seasons on evolution of rejection behavior. Based on this model we can predict at which level of parasitism fitness of rejecter individuals is higher than that of acceptor individuals and vice versa. The model analyses show that variation in egg appearance can be a key factor for the evolution of host defense against parasitism. In more detail, analyses show that we should expect to find a prolonged learning period only in hosts that have a high intraclutch variation in egg appearance, because such hosts may potentially experience high costs in terms of recognition errors. Furthermore, learning is in general more adaptive in parasite-host systems in which hosts do have some reproductive success even when parasitized, and when parasitism rates are moderate. By including variables that have not been considered in previous models, our model represents a useful tool in investigations of host rejection behavior in various host-parasite systems.

Modeling biological invasions into periodically fragmented environments.

Range expansion of a single species in a regularly striped environment is studied by using an extended Fisher model, in which the rates of diffusion and reproduction periodically fluctuate between favorable and unfavorable habitats. The model is analyzed for two initial conditions: the initial population density is concentrated on a straight line or at the origin. For each case, we derive a mathematical formula which characterizes the spatio-temporal pattern of range expansion. When initial distribution starts from a straight line, it evolves to a traveling periodic wave (TPW), whose frontal speed is analytically determinable. When the range starts from the origin, it tends to expand radially at a constant average speed in each direction (ray speed) keeping its frontal envelope in a similar shape. By examining the relation between the ray speed and the TPW speed, we derive the ray speed in a parametric form, from which the envelope of the expanding range can be predicted. Thus we analyze how the pattern and speed of the range expansion are affected by the pattern and scale of fragmentation, and the qualities of favorable and unfavorable habitats. The major results include: (1). The envelope of the expanding range show a variety of patterns, nearly circular, oval-like, spindle-like, depending on parameter values; (2). All these patterns are elongated in the direction of stripes; (3). When the scale of fragmentation is enlarged without changing the relative spatial pattern, the ray speed in any direction increases, i.e., the rate of range expansion increases.

Recurrent habitat disturbance and species diversity in a multiple-competitive species system.

To address how species interactions, dispersal and environmental disturbances interplay to affect the spatial distribution and diversity of species, we present a compartment model in which multiple species undergo competitive interaction of Lotka-Volterra type in a patchy environment arranged in a square lattice. Dispersal of species occurs between adjacent patches. Disturbances are periodically imposed on a central part of the environment in a belt-like block or an island-like block of various sizes where each species is killed for a certain time interval and then allowed to recover for the rest of a disturbance cycle. We deal with a case in which the local population dynamics within each patch is analytically determinable and has multiple locally stable equilibrium states in the absence of environmental disturbance. We further assume a trade-off between the reproductive rate of species and its dispersal ability. With these settings, we numerically examine how the spatio-temporal distributions of species are affected by changes in the pattern, size and duration of disturbances. The results demonstrate that: (1) in the undisturbed area, environmental disturbances could generate spatially segregated distributions of species; (2) in the disturbed area, species with higher dispersal abilities quickly invade and preferentially recover their population during the post-disturbance period, being temporarily relieved of competition from other species. These mechanisms collectively lead to increased species diversity in the whole habitat, functioning best when both the size and duration of disturbances are intermediate. In particular, the belt-like disturbance is more effective than the island-like disturbance in sustaining spatial heterogeneity for a wider range of duration of disturbance.