Fugo Takasu

Modeling the Population Dynamics of a Cuckoo-Host Association and the Evolution of Host Defenses

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 hosts counteradaptation crucially depend on the product of two factors, the carrying capacity of the host and cuckoos 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.

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.

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

Abstract 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 THE SPREAD OF PINE WILT DISEASE CAUSED BY NEMATODES WITH PINE SAWYERS AS VECTOR

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.

Why Do All Host Species Not Show Defense against Avian Brood Parasitism: Evolutionary Lag or Equilibrium?

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 cowbirds hosts show either few or nearly perfect defenses, whereas the cuckoos 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 parasites 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.

Modeling the Expansion of an Introduced Tree Disease

Pine wilt disease is caused by the introduced pinewood nematode, Bursaphelenchusxylophilus, 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 nematodes infection, and the parasite has been expanding nationwide in the last few decades, despite intensive control efforts. To understand the parasites 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 parasites 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 beetles 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.

Modelling the arms race in avian brood parasitism

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 hosts defence. To gain insights into the co-evolutionary process of the arms race, a model is developed and analysed, in which the hosts defence and the parasites 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.

How does stochasticity in colonization accelerate the speed of invasion in a cellular automaton model

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.

Survival and anti-parasite defense in a host metapopulation under heavy brood parasitism: a source-sink dynamic model

The obligate brood parasite common cuckoo Cuculus canorus, widespread in Eurasia, occasionally reaches a high parasitism rate (over 20%), which usually exists only for a short period of time and in cases of new parasitism. Recent results from Hungary proved that a remarkably high parasitism rate (50–66%) can also be maintained constantly for several decades. In this paradoxical situation the reproductive success of the strongly exploited host population is lower than would be necessary for self-reproduction. We developed a model for a hypothetical host–brood parasite system that demonstrated that immigration of naive individuals from a highly reproductive (‘source’) host population might explain the survival of the highly parasitized (‘sink’) population. Our results also showed the possibility of maintaining the high parasitism rate and the imperfection of the host’s counter-adaptation against the brood parasite over a longer period. Gene flow was necessary to maintain both the acceptor genes and the non-mimetic cuckoo eggs in heavy parasitism. When the immigration rate was low (1–2%), an early expansion of the mimetic cuckoos was followed by a spread of anti-parasite defense, and consequently, the parasitism rate stabilized at a lower, but still relatively high level of about 45–60%.