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Pine wilt disease is a serious pest for pine trees in many countries, especially in Asia (e.g., South Korea, Japan, China and Taiwan). In this study, we characterised dispersal patterns (e.g., direction and area) of pine wilt disease in the southern part of Korea in four-year period based on the cross-correlation function. The most likely distance of the highest infestation probability after one year is around 1.2 km from the disease source according to the distribution of pairwise distance. Subsequently, a spatially explicit model was developed in two dimensions by incorporating biological and environmental events, including influence of infested neighbourhoods, short- and long-distance dispersal, asymptomatic carriers and typhoon. The model results were in good agreement with field data when evaluated using the receiver operating characteristics and pair-correlation functions. Asymptomatic carrier played an important role in the spread of PWD. The infestation probabilities based on the spatially explicit model provided the map of spatial conformations that would be effective in addressing disease occurrence in both local and global aspects.

The common cuckoo Cuculus canorus is a brood parasite that utilizes many host species. These have evolved defense against parasitism to reject cuckoo eggs that look unlike their own and some cuckoos have evolved egg mimicry to counter this defense. Egg phenotype indeed plays a key role for both the cuckoo and its hosts to successfully reproduce. It has been argued that cuckoos should parasitize host nests where egg phenotype matches because this makes parasitism more successful. Details of the cuckoo’s parasitic behavior, however, largely remains unknown if they really parasitize hosts depending on “egg matching”. In this paper, we model a time sequence of parasitic events in which a cuckoo finds host nests and decides to parasitize them or not in the presence of egg polymorphism. We evaluate which strategy is optimal: (1) opportunistic parasitism where cuckoos parasitize hosts irrespective of the phenotype, or (2) non-opportunistic parasitism where cuckoos parasitize hosts where egg phenotype matches. The analysis showed that either of the two strategies can be optimal. Factors not considered in the model, e.g., ecological and evolutionary changes both in the cuckoo and the host side, are discussed to explain apparent contrasts observed in some cuckoo–host interactions.

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., The common cuckoo lays its eggs in nests of a variety of species and their eggs mimic the ones of their hosts. Here, the authors show that blue egg colouration in the common cuckoo is maternally inherited, originated in Asia and then expanded to Europe.

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.

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.

The Japanese rock ptarmigan Lagopus muta japonica breeds only in limited alpine areas at high elevations (> 2,500 m a.s.l.) in Japan. The estimated population size is about 2,000 birds and their breeding distribution is subdivided into several local areas, in each of which they may be at risk of local extinction. We estimated age-specific demographic parameters of the core population breeding on Mt. Norikura in Gifu and Nagano prefecture in Japan. We also estimated population viability using deterministic and stochastic population models. Age-specific fertility (the number of female offspring that survived to the next breeding season per female) was 0.417 ± 0.086, 0.490 ± 0.080, 0.513 ± 0.153, 0.435 ± 0.078, 0.562 ± 0.139, 0.580 ± 0.122 (mean ± SE) for ages 1-6+, respectively. The annual survival rate was 0.739 ± 0.047, 0.624 ± 0.064, 0.513 ± 0.087, 0.732 ± 0.151, 0.447 ± 0.220, 0.486 ± 0.089. The population growth rate, evaluated by use of a deterministic projection-matrix model, predicted a stable popul...

The evolutionary equilibrium hypothesis was proposed to explain variation in egg rejection rates among individual hosts (intra- and interspecific) of avian brood parasites. Hosts may sometimes mistakenly reject own eggs when they are not parasitized (i.e. make recognition errors). Such errors would incur fitness costs and could counter the evolution of host defences driven by costs of parasitism (i.e. creating equilibrium between acceptors and rejecters within particular host populations). In the present study, we report the disappearance of host eggs from nonparasitized nests in populations of seven actual and potential hosts of the common cuckoo Cuculus canorus. Based on these data, we calculate the magnitude of the balancing parasitism rate provided that all eggs lost are a result of recognition errors. Importantly, because eggs are known to disappear from nests for reasons other than erroneous host rejection, our data represent the maximum estimates of such costs. Nonetheless, the disappearance of eggs was a rare event and therefore incurred low costs compared to the high costs of parasitism. Hence, costs as a result of recognition errors are probably of minor importance with respect to opposing selective pressure for the evolution of egg rejection in these hosts. We cannot exclude the possibility that low or intermediate egg rejection rates in some host populations may be caused by spatiotemporal variation in the occurrence of parasitism and gene flow, creating a variable influence of opposing costs as a result of recognition errors and the costs of parasitism. WL was funded by the National Natural Science Foundation of China (Nos. 31071938, 31272328, and 31472013). BGS and FF were funded by the Research Council of Norway (218144). CY was funded by the National Natural Science Foundation of China (Nos. 31101464 and 31260514) and New Century Excellent Talents in University (NCET-13-0761). CM was funded by the Hungarian National Science Fund (OTKA, No. 83217).

In avian brood parasitism, egg phenotype plays a key role for both host and parasite reproduction. Several parrotbill species of the genus Paradoxornis are parasitized by the common cuckoo Cuculus canorus, and clear polymorphism in egg phenotype is observed. In this article, we develop a population genetics model in order to identify the key parameters that control the maintenance of egg polymorphism. The model analyses show that egg polymorphism can be maintained either statically as an equilibrium or dynamically with frequency oscillations depending on the sensitivity of the host against unlike eggs and how the parasite targets host nests with specific egg phenotypes. On the basis of the model, we discuss egg polymorphism observed in parrotbills and other host species parasitized by the cuckoo. We suggest the possibility that frequencies of egg phenotypes oscillate and we appeal for monitoring of cuckoo–host interactions over a large spatiotemporal scale.

Evolutionary adaptations are required by common cuckoos Cuculus canorus to match host eggs. Hosts may discriminate against alien eggs; hence, accurate matching of the parasite egg to the hosts' is essential. Egg shape is the least-studied component of egg mimicry, and it may also have other functions: an optimal egg shape is necessary for effective incubation. For this reason, cuckoo eggs may show a wide range of variations in shape to a set of host species. Here, we compare cuckoo and host eggs by using egg shape parameters in two distant areas: from the nests of great reed warblers Acrocephalus arundinaceus, robins Erithacus rubecula and marsh warblers Acrocephalus palustris in Hungary, and oriental reed warblers Acrocephalus orientalis, bull-headed shrikes Lanius bucephalus and black-faced buntings Emberiza spodocephala from Japan. Our results suggest the lack of evolutionary adaptation of different cuckoo gentes to their corresponding hosts in terms of egg shape. However, our analyses revealed that cuckoo eggs showed a geographical difference in egg shape.

Isolation by time occurs when different populations of a single species reproduce at different times and thereby reduce the probability of interbreeding, potentially causing divergent adaptation to timing of reproduction, eventually resulting in ecological species separated by timing of reproduction. We analysed extensive data on timing of reproduction by different host races of the common cuckoo Cuculus canorus that is an obligate brood parasite laying eggs in the nests of many different species of passerine birds. Because different hosts breed at different times, specific host races of cuckoos have adapted to specific hosts by laying eggs when nests of these hosts are available, and such divergence may be further exaggerated by differences in timing of breeding among host races with similar habitat requirements. Host species accounted for a quarter of the variance in timing of breeding by the cuckoo. Common cuckoos reproduced at a similar, but narrower subset of dates as did possible hosts, showing that only a fraction of hosts with specific breeding dates were parasitized. Common cuckoo eggs laid in the 'right' kind of nests, phenotypically matching the eggs of the host, were laid later during the season than cuckoo eggs laid in the 'wrong' kind of nests where the eggs did not mimic those of the host. Pairs of sympatric cuckoo host races differed more in timing of breeding than pairs of allopatric host races, and pairs of cuckoo host races with similar breeding habitat differed more in breeding date than pairs of cuckoo host races with dissimilar habitat, as expected from reproductive character displacement. These findings are consistent with cuckoo host races being isolated by timing of breeding and habitat.

Artificial release of marked adult Diaphorina citri, the insect vector of citrus greening disease, was performed in July 2007 (10,000 adults released, experiment 1) and October 2008 (1,000 adults released, experiment 2) to determine the association of the dispersal pattern with disease invasion risk. During the experimental periods, in experiment 1, the mean dispersal distances from the release point were 5–6 m and in experiment 2 they were 6–12 m. Further examination of the relationship between dispersal distance and season is needed. The number of released D. citri declined with increasing distance from the release point and did not change markedly with time. The center of distribution moved little during the experimental period. These results suggest that the adult D. citri barely moved once they had colonized a host plant within a few days after their release. Our results also suggest that the released D. citri moved with the wind. The diffusion coefficient was estimated at 7.23 from experiment 1, but random diffusion might be a poor descriptor of the dispersal of adult D. citri.

Avian brood parasites greatly reduce the reproductive success of their hosts. Empirical studies have demonstrated that some hosts have evolved defenses against parasitism like an ability to recognize and reject parasitic eggs that are dissimilar to their own eggs. Detailed mechanisms of how hosts recognize parasitism still remain unknown, but recent studies have shown that the host’s recognition, in many cases, is based on discordance of the eggs in a clutch, and that hosts are more error-prone when the nest is multiply parasitized, i.e., hosts tend to accept more multiple parasitism than single parasitism. In an area in Hungary, the great reed warbler Acrocephalus arundinaceus, one of the main hosts of the common cuckoo Cuculus canorus, is heavily parasitized and the parasitism rate has been kept at quite a high level for decades. Previous mathematical models suggest that such a high parasitism rate can be maintained because the focal host population behaves as a sink where few hosts can reproduce but immigration from outside replenishes the loss of host reproduction in the sink population. Here, we explore the consequences of the increased host tolerance towards multiple parasitism which has been overlooked in the previous studies using a simple model. Our model analysis shows that the increased host tolerance can dramatically contribute to both the parasite abundance and the parasitism rate being kept at a high level. We suggest that such a host behavior, combined with host immigration, can be an important factor responsible for the observed severe parasitism.

The common cuckoo Cuculus canorus parasitism greatly reduces the reproductive success of its hosts and imposes strong selection pressure for hosts to evolve defences against parasitism, such as the ability to recognize and reject dissimilar parasitic eggs, which, in turn, selects for better egg mimicry by the cuckoo. In the co-evolutionary interaction, however, it remains unknown how the cuckoo successfully expanded its range of host usage and how they developed egg mimicry. Most previous studies were conducted in areas where a very few number of host species (i.e. one or two at most) are sympatric with the cuckoo. Several host species, however, breed sympatric with the cuckoo and have been parasitized in the study site in Nagano, central Japan. Such a multiple-hosts system will provide valuable insights for understanding the cuckoo–hosts interactions in the past. In the present study, we report quantitative profiles of eggs based on spectrometer reflectance for four major host species and the corresponding cuckoo gentes. The hosts include the oriental reed warbler (Acrocephalus orientalis), bull-headed shrike (Lanius bucephalus), azure-winged magpie (Cyanopica cyana), and black-faced bunting (Emberiza spodocephala). We show that (1) egg morphs of each host and corresponding cuckoo gens can be categorized by two chromatic components of reflectance spectra and (2) there is a significant difference in a particular chroma component between hosts and the cuckoo. We suggest that the cuckoo parasitism in central Japan originated from parasitism on the black-faced bunting. © 2009 The Linnean Society of London, Biological Journal of the Linnean Society, 2009, 98, 291–300.

Pine wilt disease is caused by the pinewood nematode Bursaphelenchus xylophilus, which is vectored by the Japanese pine sawyer beetle Monochamus alternatus. Due to their mutualistic relationship, according to which the nematode weakens and makes trees available for beetle reproduction and the beetle in turn carries and transmits the nematode to healthy pine trees, this disease has resulted in severe damage to pine trees in Japan in recent decades. Previous studies have worked on modeling of population dynamics of the vector beetle and the pine tree to explore spatial expansion of the disease using an integro-difference equation with a dispersal kernel that describes beetle mobility over space. In this paper, I revisit these previous models but retaining individuality: by considering mechanistic interactions at the individual level it is shown that the Allee effect, an increasing per-capita growth rate as population abundance increases, can arise in the beetle dynamics because of the necessity for beetles to contact pine trees at least twice to reproduce successfully. The incubation period after which a tree contacted by a first beetle becomes ready for beetle oviposition by later beetles is crucial for the emergence of this Allee effect. It is also shown, however, that the strength of this Allee effect depends strongly on biological mechanistic properties, especially on beetle mobility. Realistic individual-based modeling highlights the importance of how spatial scales are dealt with in mathematical models. The link between mechanistic individual-based modeling and conventional analytical approaches is also discussed.

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, here 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.

The coevolutionary interaction between cuckoos and their hosts has been studied for a long time, but to date some puzzles still remain unsolved. Whether cuckoos parasitize their hosts by laying eggs randomly or matching the egg morphs of their hosts is one of the mysteries of the cuckoo problem. Scientists tend to believe that cuckoos lay eggs matching the appearance of host eggs due to selection caused by the ability of the hosts to recognize their own eggs. In this paper, we first review previous empirical studies to test this mystery and found no studies have provided direct evidence of cuckoos choosing to parasitize host nests where egg color and pattern match. We then present examples of unmatched cuckoo eggs in host nests and key life history traits of cuckoos, e.g. secretive behavior and rapid egg-laying and link them to cuckoo egg laying behavior. Finally we develop a conceptual model to demonstrate the egg laying behaviour of cuckoos and propose an empirical test that can provide direct evidence of the egg-laying properties of female cuckoos. We speculate that the degree of egg matching between cuckoo eggs and those of the host as detected by humans is caused by the ability of the hosts to recognize their own eggs, rather than the selection of matching host eggs by cuckoos. The case of Common Cuckoos (Cuculus canorus) and their parrotbill hosts (Paradoxornis alphonsianus), where it has been shown that both have evolved polymorphic eggs (mainly blue and white), was used to develop a conceptual model to demonstrate why cuckoos should utilize parrotbill hosts by laying eggs randomly rather than laying eggs matching the appearance of host eggs. In conclusion, we found no evidence for the hypothesis that cuckoos lay eggs based on own egg color matching that of the parrotbill-cuckoo system. We argue theoretically that laying eggs matching those of the hosts in this system violates a key trait of the life history of cuckoos and therefore should be maladaptive.

We investigate the speed of invasion waves for a single species generated by stochastic short- and/or long-distance colonizations in a time-continuous cellular automaton (CA) model on a two-dimensional homogenous landscape. By simulating the CA models, we demonstrate that stochasticity can dramatically increase the speed of invasion compared to the corresponding deterministic CA model or the corresponding one-dimensional stochastic CA model. To explain this phenomenon, we first develop a mathematical model for the invasion involving only short-distance colonization (i.e., colonization only occurs from the eight adjacent cells), and present several approximation methods for solving the model. Our analyses show that the increased wave speed in the stochastic model is due to irregularity in the shape of the wavefront. Further extension of this model to include long-distance colonization demonstrates that stochasticity influences speeds to even greater extents in this case. Using dimension analysis, we deduced a semi-empirical formula for the speed as a function of three parameters intrinsic to short- and long-distance colonization, which agrees well with simulation results. Based on these results, we discuss how important stochasticity in colonization and spatial dimensionality are in the acceleration of invasion speed.

We used metapopulation dynamics to develop a mathematical simulation model for brood parasites and their hosts in order to investigate the validity of the "spatial habitat structure hypothesis," which states that a low level of parasite egg rejection in host populations is due to the immigration of acceptor individuals from nonparasitized populations. In our model, we varied dispersal rate and the relative carrying capacity of host individuals in parasitized and unparasitized patches. When both the relative carrying capacity in the parasite-free patch and the dispersal rate increase, the nonparasitized patch will provide more acceptor individuals to the parasite-prone patch. As the relative carrying capacity in the parasite-free patch increases, the equilibrium frequency of rejecters both in the parasite-prone and in the parasite-free patch decreases toward zero for intermediate levels of the dispersal rate. Although the rejecter strategy is more adaptive than the acceptor strategy in the parasite-prone patch, large numbers of acceptors are produced in the parasite-free patch dispersing to the parasitized patch. As the number of individuals in the parasite-free patch increases, parasitism rate can be maintained stable at a high equilibrium level in the parasite-prone patch. Copyright 2006.

It has been suggested that parasitic interactions in general result in co-evolutionary arms races where parasites and hosts evolve adaptive behaviours and traits to maximize their fitness in a conflicting manner. Avian brood parasitism provides an ideal system for the study of such co-evolutionary interactions. In this paper I show and discuss possible consequences of the co-evolutionary arms race inherent in avian brood parasitism, especially focusing on egg appearance, a key factor for the reproduction of both hosts and parasites. In such an arms race, hosts evolve the ability to recognize and hence to reject dissimilar parasitic eggs, while parasites counter host defences by more closely mimicking their eggs. Egg mimicry by parasites might then be de-stabilized by hosts changing the appearance of their eggs, thus exposing the mimics. The evolutionary trajectory of the arms race varies depending on the specific detailed mode of interaction between parasite and host individuals. Mathematical mod...

Recent field studies have demonstrated that many bird species practice intra-specific brood parasitism. They lay eggs in the nests of other individuals of the same species, let the foster parents rear their offspring and avoid the cost of parental care. It has been shown that many birds, including starlings, swallows and geese, practice intra-specific brood parasitism in various forms. Intra-specific brood parasitism can be viewed in terms of optimal resource allocation: how many eggs should be put in the nests of other individuals under the risk of being parasitized by others. The situation here is a “game”, because the fitness of a parasitic individual depends on how other individuals behave (how many individuals practice parasitism and to what extent). The ecology of intra-specific brood parasitism has been investigated extensively by field ornithologists recently and it is full of material for modeling population/evolutionary biology. In this paper, I present a simple individual-based model to challenge the resource allocation problem in intra-specific brood parasitism. Previous theoretical studies of intra-specific brood parasitism have been based on ESS or quantitative genetics models, where a population is implicitly assumed to be homogeneous and the distribution form of the trait being studied (the allocation rate or the number of eggs laid parasitically) is inherently monomorphic. This paper aims to explore the evolution of intra-specific brood parasitism without these restrictions. In the model, an individual is assigned a strategy, an allocation ratio of eggs that are laid parasitically in the nests of other individuals, and the strategy is inherited by offspring either asexually or sexually. Based on the simulation analysis, the evolution of the allocation rate (the extent of intra-specific brood parasitism) is discussed. The extension of this model to a tractable analytical model is also discussed.

To address how habitat destruction and hierarchical competition among species affect the spatio-temporal dynamics of a multi-species community, we present a compartment model in which multiple species undergo dispersal and competitive interactions in a patchy habitat arranged in a two-dimensional lattice. We assume that disturbances are periodically imposed on some parts of the lattice in a block, followed by a period free of disturbance. For convenience, species are ranked in order of competitive ability. We further assume that the intrinsic growth rate of species i, e i , and the dispersal ability, D i , increase in decreasing order of rank. Our model can analytically determine the exact number of surviving species when disturbance is absent. In the presence of disturbance, we numerically examine how spatio-temporal changes in environmental heterogeneity affect species coexistence and extinction, for the case in which the value of e i /D i monotonically increases or decreases with rank. The results demonstrate that (1) when the interspecific competition is smaller than the intraspecific competition, we can provide predictions on the prospective order of species to be driven extinct and the order of potential species to revive with increasing extents of disturbance; (2) when the interspecific competition is stronger than intraspecific competition, a small difference in the disturbance level can lead to drastic changes in the species composition, their densities and the order of species extinction. In addition, comparison with other similar models reveals that differences in species interaction in local population dynamics critically affect the disturbance-mediated species diversity.

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.

In haremic angelfishes where protogynous (female to male) sex change is favored, females have been reported to adopt several tactics for earlier sex change on the basis of a trade-off between reproduction and growth, or survivorship. A recent field study on Centropyge ferrugatus revealed that females reduce spawning frequency in competition with similar-sized neighbors for social dominance. To evaluate the optimal spawning strategy taken by haremic fishes, we developed an evolutionarily stable strategy model that focuses on their life history and social structure based on field data of C. ferrugatus. The results of the analysis predict that the spawning frequency will be low when the mortality rate of females is high compared with males, the harem size is large, and there is a moderate degree of social control. Our model further predicts conditions under which females completely stop spawning, as if they have become bachelors. Thus, the regulated spawning frequency may be taken as a strategy to optimize the reproductive success of an individual in response to the available choices for sex change, social control, and environmental conditions. Social control would also play an important role in sex change in many other haremic species. Copyright 2002.

The spatio-temporal dynamics of three competitive species is considered. Mathematically, the community is described by a system of partial differential equations of Lotka-Volterra type. The properties of the system are investigated both numerically and analytically. We show that for finite initial conditions the dynamics of the system is typically reduced to a succession of travelling diffusive waves, some of which demonstrate rather an unusual behaviour. Particularly, a locally unstable equilibrium can become stable in the wake of a diffusive front. After propagation of the waves, the domain is invaded by irregular spatiotemporal population oscillations that can be classified as spatio-temporal chaos.

Pine wilt disease is caused by the introduced pinewood nematode, Bursaphelenchus xylophilus, for which the vector is the pine sawyer beetle, Monochamus alternatus. Native Japanese pines, black pine (Pinus thunbergii) and red pine (P. densiflora), are extremely sensitive to the nematode's infection, and the parasite has been expanding nationwide in the last few decades, despite intensive control efforts. To understand the parasite's range expansion in Japan, we modeled the dynamics of the pines and the beetle that disperses the nematode, using an integro-difference equation in a one-dimensional space. Based on field data collected in Japan, we investigated the dependence of the parasite's rate of range expansion on the eradication rate of the beetle, the initial pine density, and the beetle dispersal ability. Our model predicts several results. (1) The Allee Effect operates on beetle reproduction, and consequently the parasite cannot invade a pine stand, once the beetle density decreases below a threshold. (2) The distribution of the dispersal distance of the beetles critically affects the expansion rate of the disease. As the fraction of the beetles that travel over long distance increases from zero, the range expansion accelerates sharply. (3) However, too frequent long-range dispersal results in a failure of the parasite invasion due to the Allee Effect, suggesting the importance of correctly assessing the beetle's mobility to predict the speed of range expansion of the parasite. (4) As the eradication rate is increased, the range expansion speed decreases gradually at first and suddenly drops to zero at a specific value of the eradication rate.

An epidemic of pine wilt disease has been spreading in wide areas of Japan for nearly a century. The disease is caused by the pinewood nematode, Bursaphelenchus xylophilus, with the pine sawyer, Monochamus alternates, as vector. The spread of disease is facilitated by an obligatory mutualism between the nematode and the pine sawyer: the pine sawyer helps the nematode transmit to a new host tree, while the nematode supplies the pine sawyer with newly killed trees on which to lay eggs. We present a mathematical model to describe the host-vector interaction between pines and pine sawyers carrying nematodes, on the basis of detailed data on the population dynamics of pine sawyers and the incidence of pine wilt disease at a study site located on the northwest coast of Japan. We used the model to simulate the dynamics of the disease and predict how the epidemic could be controlled by eradication of the pine sawyer. The main results are as follows: (1) There is a minimum pine density below which the disease always fails in invasion. However, even if the pine density exceeds this minimum, the disease fails in invasion due to the Allee effect when the density of pine sawyers is very low. (2) The minimum pine density increases disproportionately with increase in the eradication rate. (3) The probability that a healthy tree will escape from infection until the epidemic dies out decreases sharply with increase in the initial pine density or the initial density of pine sawyers.

In brood parasitism, interactions between a parasite and its host lead to a co-evolutionary process called an arms race, in which evolutionary progress on one side provokes a further response on the other side. The host evolves defensive means to reduce the impact of parasitism, while the parasite evolves means to counter the host's defence. To gain insights into the co-evolutionary process of the arms race, a model is developed and analysed, in which the host's defence and the parasite's counterdefence are assumed to be genetically determined. First, the effect of parasite counterdefence on host defence is analysed. I show that parasite counterdefence can critically affect the establishment of host defence, giving rise to three situations in the equilibrium state: The host shows (1) no defence, (2) an intermediate level of defence or (3) perfect defence. Based on these results, the evolution of parasite counterdefence is considered in connection with host defence. It is suggested that the parasite can evolve counterdefence to a certain degree, but once it has established counterdefence beyond this, the host gives up its defence against parasitism provided the defence entails some cost to perform. Dynamic aspects of selection pressure are crucial for these results. Based on these results, I propose a hypothetical evolutionary sequence in the arms race, along which interactions between the host and parasite proceed.

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. © Springer Verlag. The final publication is available at https://link.springer.com/article/10.1007%2Fs10071-013-0615-1. This is the authors' manuscript to the article.

Avian brood parasites impose strong selection on their hosts leading to the evolution of antiparasite defenses like egg recognition and rejection. Discordance and template-based cognitive mechanisms may form the base for egg recognition by hosts. For discordance, hosts recognize eggs that constitute the minority in a clutch as alien, whereas in template-based recognition, hosts recognize eggs as alien when they do not match a template that can be innate or learnt. Template-based recognition by learning can be compromised in host species with polymorphic egg color like Paradoxornis parrotbills, hosts of the common cuckoo Cuculus canorus, because a male that learns an egg color in his first breeding attempt can subsequently mate with females having different colors and therefore reject his own eggs. We present a simple conceptual model to understand how an asymmetry in sex roles of care for eggs and egg polymorphism influence the evolution of egg recognition by hosts. We derive host reproductive success in the presence of variation in egg phenotype for both host and parasite. Our model shows that male recognition by learning is disadvantageous unless the host has monomorphic eggs. We suggest that interclutch variation in egg phenotype is the key to understanding the evolution of egg recognition and the sex involved. Key words: avian brood parasitism, discordance, egg polymorphism, egg recognition, learning and imprinting, template-based. This article has been accepted for publication in [Behavioral Ecology] Published by Oxford University Press.

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. © 2010 Yang et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Cuckoo parasitism in Nagano Prefecture in Japan has shown dramatic changes in the parasitism rate, host usage by the cuckoo, and defensive behavior of hosts during the past 60 yr. To gain insights into these phenomena, we model the population dynamics of a cuckoo-host association together with the population genetics of a rejecter gene in the host population. Analysis shows that both the dynamical change in the host-parasite association and the establishment of the host's counteradaptation crucially depend on the product of two factors, the carrying capacity of the host and cuckoo's searching efficiency. When the product is less than a critical value, the host population cannot evolve a counteradaptation even if parasitized by the cuckoo. Hence, the lack of counteradaptation does not necessarily imply that the host population only recently has become parasitized. As the product becomes larger, the rejection behavior will be eventually established at higher levels in the host population In this case, the spreading of rejection behavior is very fast, which suggests that the cuckoo-host association reaches an equilibrium state within a relatively short period. These results make possible new interpretations of several circumstances reported about cuckoo-host associations.

Avian brood parasitism reduces the reproductive success of hosts and is therefore expected to select for host defenses against parasitism, such as an ability to reject parasitic eggs. Field studies have shown that some hosts recognize and reject parasitism, whereas others do not, and the degree of the defense varies from population to population. One long-standing debate concentrates on the differences in the distribution of host defenses observed in hosts parasitized by the brown-headed cowbird and the common cuckoo. The cowbird's hosts show either few or nearly perfect defenses, whereas the cuckoo's hosts have defenses varying from none to complete, with most falling in between the two extremes. To explore the mechanisms underlying this pattern, I constructed a mathematical model in which host defense is assumed to be genetically determined and analyzed how the host defense is established under parasitic pressure. The model shows that differences in the defense-level distribution can be attributed to the difference in the parasite's breeding strategy, generalized or specialized: hosts parasitized by generalists show perfect, none, or intermediate levels of the defense depending on the host abundances, whereas hosts parasitized by specialists always exhibit either none or intermediate levels of the defense if the parasite lacks counter defenses such as egg mimicry. This result provides a testable explanation for the existence of accepter species of the brown-headed cowbird, which might reconcile the previously conflicting hypotheses.

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.

Range expansions of invading species in homogeneous environments have been extensively studied since the pioneering work of Fisher 1937 and Skellam 1951 [1, 4, 5, 7, 8, 10]. Here we focus on range expansion of a species in a two-dimensional heterogeneous environment that is generated by segmenting an original favorable habitat into a regularly striped or criss-cross pattern as shown in Fig. 18.1: (a) Striped fragmentation — an environment is segmented into belts in such a way that favorable and unfavorable habitats with widths l 1 and l 2 respectively, are arranged alternately [6]. (b) Criss-cross fragmentation — an environment is segmented in both horizontal and vertical axes in such a way that square-shaped favorable habitats with a side l 1 are regularly distributed to leave the criss-cross unfavorable belt with width l 2 in the background.

In a space environment such as Space Shuttle or Space Station, animal experiments with aquatic species in a closed system pose a crucial problem in maintaining their water quality for a long term. In nature, ammonia as an animal wastes is converted by nitrifying bacteria to nitrite or nitrate compounds, which usually become nitrogen sources for plants. Thus an application of the biological reactor with such bacteria attached on some filters has been suggested and experimentally studied for efficient waste managements of ammonia. Although some successful results were reported (Kozu et al. 1995, Nagaoka et al. 1998, Nakamura et al. 1997, 1998) in the space applications, purely empirical approaches have so far been taken to develop a biological filter having a stable nitrifying activity. In this study, we constructed a mathematical model to deal with the dynamics of the ammonia nitrifying processes in a biological reactor. The model describes population dynamics of the ammonia-oxidizing bacteria and the nitrite-oxidizing bacteria cultivated on the same filter. We estimated parameters involved in the model using the experimental data. The result shows that these estimated parameters could be applied to general cases and that the two bacteria are in a symbiotic relationship; they can better perform when both coexist, as has been empirically recognized. Based on the model analysis, we discuss how to prepare a high performance biological filter.

In haremic angelfishes where protogynous (female to male) sex change is favored, females have been reported to adopt several tactics for earlier sex change on the basis of a trade-off between reproduction and growth, or survivorship. A recent field study on Centropyge ferrugatus revealed that females reduce spawning frequency in competition with similar-sized neighbors for social dominance. To evaluate the optimal spawning strategy taken by haremic fishes, we developed an evolutionarily stable strategy model that focuses on their life history and social structure based on field data of C. ferrugatus. The results of the analysis predict that the spawning frequency will be low when the mortality rate of females is high compared with males, the harem size is large, and there is a moderate degree of social control. Our model further predicts conditions under which females completely stop spawning, as if they have become bachelors. Thus, the regulated spawning frequency may be taken as a strategy to optimize the reproductive success of an individual in response to the available choices for sex change, social control, and environmental conditions. Social control would also play an important role in sex change in many other haremic species. Copyright 2002.