Journal of Plankton Research Vol.13 no.l pp.119-129, 1991
Infection of the diatom Asterionella by a chytrid. II. Effects of lighton survival and epidemic development of the parasite
Kees Bruning
Department of Aquatic Ecology, University of Amsterdam, Kruislaan 320, 1098SM, Amsterdam, The Netherlands
Abstract. A model is formulated to investigate the ability of chytrid parasites to survive or becomeepidemic within populations of their algal hosts The model is used for an analysis of the effects oflight on the occurrence of Rfuzophydium planktontcum Canter emend., a chytnd parasite of thefreshwater diatom Astenonella formosa Hass., using the information on the growth parameters ofhost and parasite presented in the first part of this article (/. Plankton Res., 13, 103-117). Accordingto the model, conditions for survival of the parasite are optimal when the host grows at saturatinglight conditions. Under limiting light conditions, Rhizophydium needs higher host densities in orderto maintain itself. The parasite is not able to survive prolonged periods of severe light limitation ofthe host Epidemic development, however, turned out to be facilitated by a moderate light limitationof the host. Both light saturation and severe light limitation hamper epidemic development, but inthe first case, epidemic development is still possible at sufficiently high host densities.
Introduction
Chytrid fungi have been observed growing on a large number of phytoplanktonspecies. Not all of these chytrids are necessarily parasites, and sometimes only alow percentage of the algae is infected. Nevertheless, several authors report asubstantial impact of chytrid infection upon the algal host populations (e.g.Canter and Lund, 1948; Reynolds, 1973; Youngman etal., 1976; Muller and vonSengbusch, 1983; van Donk and Ringelberg, 1983; Sommer, 1987).
The interaction between algae and their fungal parasites is a rather poorlyinvestigated topic as compared to phytoplankton-nutrient or phytoplankton-herbivore interactions. This may be caused partly by the apparent absence of atheoretical framework that can be used for the analysis of field observations orfor the design of experiments. Although an impressive amount of literatureexists that deals with the population dynamics of parasite-host interactions ingeneral, and a wide range of models has been developed to deal with specificassociations, these do not seem to be applicable to situations where algalpopulations are parasitized by a chytrid fungus. Most conventional epidemio-logical models (e.g. Bailey, 1975) assume the host population to be constantduring the course of an epidemic (Anderson and May, 1979), which may be arealistic assumption for human populations, but not when generation times ofhost and parasite are of comparable magnitude. In other cases, the modelscontain inappropriate concepts, like the area of discovery, which determines thenumber of hosts a parasite is able to infect during its lifetime (Hassell and May,1973). The chytrid infective stage infects only one host. Host mortality issometimes formulated as a function of the number of parasites per host(Anderson and May, 1978), but again this does not apply to the chytrid-algaassociation: mortality is independent of parasite burden, since every infectedalga will die. As a contribution to the development of a theoretical basis for
further investigations, a model is presented that can be used to analyse theeffects of external conditions upon the occurrence of chytrid fungi withinphytoplankton populations.
Model
The specific growth rate of the parasite
Rhizophydium planktonicum is a chytrid fungus that lives parasitically upon onlyone host, the diatom Asterwnella formosa (Canter and Jaworski, 1978). Ascompared to other parasitic organisms, Rhizophydium displays a relativelysimple life cycle. Algae are infected by free-swimming flagellate zoospores. Arhizoidal system is developed within the host cell, but the encysted zoosporeremains on the outside of the host and enlarges into a spherical or ovalsporangium in which 1-30 new zoospores are produced asexually. All zoosporesare released simultaneously. As in most chytrids, each zoospore produces onlyone sporangium (Sparrow, 1960). Infection results inevitably in the death of thehost cell. Rhizophydium belongs to a category of chytrids from which no restingstages are known (Canter, 1969).
The specific growth rate of Rhizophydium depends on parameters that arerelated to the production of zoospores (the number of zoospores per maturesporangium and the development time of a sporangium) and to the infection ofthe host cells (the host cell concentration, the efficiency of the mechanism(s)used to find a host and the infective lifetime of the zoospores). In addition, thespecific growth rate is influenced by the age distribution of the parasite. Themodel is based on the simplifying assumption that the parasite has reached astable age distribution, which implies that conditions that influence birth rateand death rate of the parasite have been unchanged for some time (Pielou,1969). Since the infection rate depends on the host density, this assumption ofconstant conditions includes the assumption of a constant host cell concen-tration.
At a stable age distribution, the relationship between birth rate, death rateand specific growth rate of a population is represented by the well-known Lotkaequation (Lotka, 1925):
Um,e-'l'"dt= 1 (1)
In this equation, age-specific death is formulated as /„ the proportion ofsurvivors at time t of a cohort of individuals all born simultaneously at r = 0. Theage specific birth rate m, is the number of offspring produced per unit of time perindividual of age t. The specific growth rate of the parasite population isrepresented by ftp. A summary of the notation used is given in the Appendix.
From a cohort of z0 zoospores the number of surviving parasites at time t isZQI,. When v represents the number of offspring per unit time, it follows from thedefinition of m, that
The zoospore production rate v can be expressed as a function of the growthparameters of the parasite.
Consider a cohort of z0 free-swimming zoospores, all produced at t = 0. Theyare supposed to be homogeneously mixed with an uninfected host population.The chance of an encounter between a zoospore and a host cell, and thus therate at which the concentration of free zoospores declines, is proportional to thezoospore concentration z and the host cell concentration h
dzldt = -ihz (4)
The proportionality constant i in this equation has been called the infectivityconstant (Bruning, 1991). This parameter is a measure of the efficiency of themechanism(s) that enable the zoospores to find and infect a host cell. It will beassumed that the infectivity constant does not change during the infectivelifetime of a zoospore.
The number of zoospores that at time t still did not succeed in finding a host,z,, is described by the solution of equation (4)
z, = z0 e-* (5)
The time span between an infection and the release of the new generation ofzoospores at sporulation is equal to the development time of a sporangium d. So,when losses of sporangia due to processes other than sporulation are zero, therate at which zoospore-containing sporangia are lost at time t is equal to the rateat which the zoospores infected host cells at time t — d. Multiplication of thisrate by n, the number of zoospores released per sporangium, yields the zoosporeproduction rate v
v, = -n (dz/dt)t_d (6)
Since the assumption of constant conditions implies that i and h are constants, itfollows from equation (4) that
The first zoospores are produced one sporangial development time d after thefirst infection. So v, = 0 when t < d. Zoospores that fail in finding a host willlose their infectiveness sooner or later. After this infective lifetime q, no newinfections will arise, and one sporangial development time later no newzoospores are produced. So v, = 0 when t > (d + q). Substitution of equation(9) with these boundary conditions in equation (3) yields
f* e~m n i h «"*"-* dt = 1 (10)d
When this integral is solved, the following relationship between the specificgrowth rate of the parasite, the host cell density and the parasite's growthparameters is found:
[n i h e'^/Qip + ih)] x [1 - e-*Co+*>] = l (11)
Since this equation cannot be solved analytically for fip, the value of fip must beestimated by means of a numerical approximation technique.
The specific growth rate of the parasite reaches a theoretical maximum valuefiPmax at infinite host concentration. This value depends only upon the zoosporeproduction parameters n and d, and not upon the infection parameters i or q,since at an infinite host concentration every zoospore will infect a host cellimmediately after its release from the sporangium. An expression for thismaximum growth rate was derived by Bruning (1991):
W W = (In n)/d (12)
The same expression is obtained when h = °° is substituted in equation (11).
Threshold values of the host density
Since the parasite's specific growth rate depends on the host density, there mustbe a certain threshold value of the host density, below which the parasite isunable to maintain itself. Likewise, the development of an epidemic requires aminimum host density. These threshold values can be used as criteria for theability of the parasite to survive or become epidemic within the host population.When conditions become favourable for survival or epidemic development ofthe parasite, this must be reflected by decreasing values of the correspondingthreshold host densities.
The threshold host density for survival of the parasite
Survival of the parasite within the host population requires at least a host densityat which the parasite reaches a zero growth rate. With this condition: fip = 0,equation (11) can be solved analytically for h, and an equation for the thresholdhost density for survival of the parasite hs can be obtained
At this threshold, exactly one zoospore out of the n that are produced persporangium is able to infect a host cell within the infective lifetime q.
The threshold host density for epidemic development
When a host cell becomes infected, its ability to reproduce is lost. The followingderivation of the threshold host density for the development of an epidemicapplies to a population in which the fraction of infected host cells (theprevalence of infection) is so low that the presence of infected, not reproducingalgae does not reduce the specific growth rate of the host populationsignificantly. When ftp and fih represent the specific growth rate of the parasiteand the uninfected host respectively, changes in the host density h and theparasite density p are given by
dhldt = hfih (14)
dpldt = p fip (15)
The supposed stable age distribution of the parasite population implies that thenumber of attached sporangia s is a constant fraction of the entire parasitepopulation, so equation (15) can be replaced by
dsldt = s ftp (16)
Because of the assumptions of a low prevalence of infection and a homogeneousmixing of free zoospores and host cells, multiple-infected host cells will be rare,and the prevalence of infection / can be approximated by
/ = slh (17)
The rate of change of the prevalence dfldt will then be
dfldt = [(/i dsldt) - (s dhJdt)]lh2 (18)
which, using equations (14) and (16), reduces to
dfldt = / {jip - fih) (19)
The development of an epidemic requires that the prevalence of infectionincreases. Equation (19) shows that the prevalence starts to increase, and thusan epidemic starts to develop, when the specific growth rate of the parasiteexceeds the specific growth rate of the uninfected host. Since the parasite'sspecific growth rate depends on the host density, there is a threshold value of thehost density, he, below which the development of an epidemic is impossible. Atthe host density he, the specific growth rates of host and parasite are equal andthe prevalence of infection is constant. So, when the parasite's growth
parameters are known, the threshold host density for epidemic development canbe calculated by substitution of ftp = fih in equation (11)
[n i + ihe)] x [1 - e-90«*+«*•)] = (20)
Since this equation cannot be solved analytically for he, the value of he must beestimated by means of a numerical approximation technique.
Results
Influence of light on the growth parameters of host and parasite
The influence of light upon the growth parameters of host and parasite at 6°C(Bruning, 1991) is summarized in Figure 1 in terms of relative parameter valuesplotted against light intensity.
The infective lifetime of the zoospores was not found to be influenced by thelight intensity. The zoospore production per sporangium was substantiallyreduced at low light conditions, but the development time of the sporangia wasonly slightly affected. Light-limited host cells were less susceptible to infectionwith zoospores; at light intensities below ~2 u,Em~2 s"1 the infectivity constantwas zero. Light intensities above the saturation level for algal growth did notinfluence any of the parasite's growth parameters.
Threshold host densities
The growth parameters of host and parasite were measured in cultures adapted
100 r
10light intensity <
100
Fig. 1. The effects of light on the specific growth rate of Asterionella (p.), and on the growthparameters of Rhizophydium: the infective lifetime of the zoospores (<j), the development time ofthe sporangia (d), the zoospore content of the mature sporangia (n) and the infectivity constant (i).Parameters are plotted as % of maximum value.
to a 15:9 h light:dark cycle. The infectivity constant / was determined during thelight phase since the infectivity constant is zero in darkness. In order to correctfor the stagnant infection during the dark phase, the actually discontinuousinfection was simulated by a continuous process with a weighted mean value ofthe infectivity constant: i* = 15/24 /.
The influence of light upon the threshold host densities for survival andepidemic development of the parasite is shown in Figure 2. The thresholds,calculated from the growth parameters of host and parasite measured at sixdifferent light intensities, are plotted as functions of the light intensity and asfunctions of the relative light-limited growth rate of the host. The latterrepresentation facilitates comparison with threshold plots that are obtainedunder different conditions. The relative algal growth rate (jih//xhmax) is ameasure of the degree of growth limitation of the host.
The plot surface is schematically divided into three regions by curves based onregressions described in Bruning (1991). In the upper region, the parasite canbecome epidemic since algal densities exceed he values. In the middle region, thedevelopment of an epidemic is impossible, but the parasite population willincrease since the host densities are high enough to support a positive growthrate of Rhizophydium. In the lower region, the parasite displays negative growthrates, and will ultimately become extinct. The curves have an asymptote at alight intensity of ~2 u,Em~2 s"1 and a relative algal growth rate of 0.137. Heresurvival as well as epidemic development of the parasite becomes impossiblesince the infectivity constant is zero at lower light levels.
1OOOQ 1000Q
100
light (nErrr2s-1)1000 00 05 10
relative growth rate Astenonella
Fig. 2. Threshold host densities for survival (filled symbols) and epidemic development (opensymbols) of the parasite, plotted against the light intensity (left) and against the relative light limitedgrowth rate of the host (right)
The threshold host density for epidemic development displays a finite value atlight saturation. Thus, even at optimal growth conditions for Asterionella, theparasite is able to reach a higher growth rate and become epidemic at sufficientlyhigh host densities. The same conclusion, based upon calculation of the fungalgrowth rate at infinite host concentration, was already drawn by Bruning (1991).
Curve and calculated values of the threshold host density for epidemicdevelopment indicate a minimum value when the host is moderately lightlimited. At lower light conditions, epidemic development becomes hampered bythe decreased infectivity constant and zoospore production of the parasite; athigher light intensities, the increased growth rate of the host demands a higherhost density before an epidemic can develop. Apparently, a moderate lightlimitation of the host favours the development of an epidemic. At appropriatehost densities, changes in light conditions may induce a Rhizophydium epidemicwithin an Asterionella population.
This conclusion should not be interpreted as if light limitation favours growthof the parasite. On the contrary, light-limited host cells are less readily infectedand on these cells the parasite produces less zoospores at a lower rate. Lightlimitation reduces the growth rate of both host and parasite but, at a moderatelight limitation, an epidemic can start at a lower host density because the algalgrowth rate is reduced to a greater extent than the fungal growth rate.
Influence of light on survival of the parasite
The results of the model indicate a markedly different effect of light uponsurvival of the parasite. Minimum threshold values, and thus optimal conditionsfor survival, are found at saturating light levels. Light limitation of the host is anunfavourable condition for survival of the parasite. The reason is that survivalthresholds do not depend on the growth rate of the host (equation 13). In thiscase, the positive effects of light upon fungal growth are not counteracted bychanges in the growth rate of the host.
Under natural conditions, the parasite may be faced regularly with theproblem of maintaining an inoculum of sufficient size during periods of low hostdensity, since annual cycles of Asterionella populations commonly contain longperiods of low algal density (e.g. Lund, 1949; van Donk, 1983), and the parasiteis not able to survive these periods by means of resting stages (Canter, 1969).The development of an epidemic during an Asterionella bloom period maydepend on the parasite's ability to sustain a population of sufficient size in thepreceding period of low host densities.
Model assumptions
The model is based on various simplifying assumptions: that (i) the parasitepopulation has reached a stable age distribution; (ii) the zoospores have aconstant infectivity during their infective lifetime; and (iii) the infection level is
low at the time when a threshold host density is reached. The impact of possibledeviations from these assumptions is unknown at this stage and needs furtherinvestigation, but some qualitative inferences can be made. As long as thesedeviations exert comparable effects at the different light conditions, thequalitative conclusions from the model results remain unchanged, although theactual levels of the threshold curves might change.
The simplification of a low infection level means that it is assumed that thepresence of the parasite starts with a relatively small fungal inoculum. Whenautochthonous sources of infection are involved—mixing of infected anduninfected populations, for instance, or release of zoospores from accumulatedresting stages—a relatively high prevalence of infection may occur at the firstappearance of the parasite. In this case, the threshold host density for epidemicdevelopment is lower than the value calculated with the model, since the growthrate of the host population is substantially reduced by the presence of infected,not reproducing host cells and, as a consequence, the parasite's growth rate willexceed the growth rate of the host at a lower host density.
Threshold values of heavily infected populations are also relevant in thecontext of the stability of infected populations. The decreasing threshold forepidemic development when the host becomes more and more infected suggestsan aspect of irreversibility in the development of chytrid epidemics. Thequestion is complicated, however, since a high prevalence of infection may havea drawback on the parasite's growth rate as well. At high prevalences, anincreasing proportion of the host cells become multiple infected, and Rhizo-phydium sporangia produce fewer zoospores upon multiple-infected hosts.
The effect of turbulence
Deviations from the model results may also be expected at conditions other thanthose applied during the experiments. These conditions were: temperature 6°C,discontinuous illumination (15 h light, 9 h dark) with a constant light intensityin the light phase, and no turbulence (Bruning, 1991). The influence oftemperature is presently under investigation.
Turbulent mixing may lead to an increased chance of an encounter betweenzoospores and host cells, and thus to an increased infectivity constant, and tolower values of the threshold host densities. The effects of turbulence depend onthe mechanism of the infection-reduction at low light intensity (Canter andJaworski, 1980, 1981; Bruning, 1991). As a first approximation, it may beassumed that the increase of the contact rate does not depend on the lightconditions. This will be the case when the reduced infectivity constant is causedby a reduced effectivity of host-recognition mechanisms after contact is madewith the host. From equations (13) and (20) it can be seen that infectivityconstant and threshold host density are inversely proportional. As a con-sequence, an encounter rate enhanced by turbulent entrainment will lead to aproportional descent of the threshold curves. This implies that the qualitativeconclusions from the model results apply to conditions both with and without
turbulence, although the threshold values are probably lower when turbulentmixing is involved, as will be the case in the natural environment.
However, other possible mechanisms of the infectivity-reduction at low lightlevels may lead to more complex turbulence effects. When reduced zoosporeswimming speeds play a role, turbulence effects depend on light conditions,since the influence of turbulence on contact rates is more pronounced in slow-moving particles (Rothschild and Osborn, 1988). Also when depressed excretionof attractive substances by the host contributes to the reduced infectivity, theeffects of turbulence may become light dependent, and the shape of thethreshold curves may change.
Some indication about the extent of overestimation in the threshold valuesmay be obtained from field observations. Lund (1957) estimated a minimumhost density of ~10 cells ml"1 for the development of fungal epidemics inAsterionella populations in lakes of the English Lake District. However, theselow threshold values may equally well be caused by factors other than lightlimitation. Any external factor that reduces the growth rate of the host withoutaffecting the growth rate of the parasite will depress the threshold host densityfor epidemic development below the calculated minimum value of roughly 100cells ml"1 for light-limited algae.
Acknowledgements
I thank Prof. Dr J.Ringelberg and Prof. Dr N.Daan for their useful commentson the manuscript. I am also grateful to Prof. Dr O.Diekmann and DrR.Lingeman, who checked the population dynamics and mathematical aspects.This investigation was supported by the foundation for Fundamental BiologicalResearch (BION), which is subsidized by The Netherlands Organization for theAdvancement of Pure Research (ZWO).
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Received on February 21, 1990, accepted September 14, 1990
Appendix
Symbols and description of the population parameters
d development time of the sporangia.h host cell concentration.he threshold host density for the development of an epidemic.hs threshold host density for survival of the parasite./ proportion of the host cells infected (prevalence of infection).i infectivity constant, a measure for the efficiency of the host-finding
mechanism(s)./, proportion of parasites still alive at age t.m, age-specific birth rate of the parasite.fi.h specific growth rate of the uninfected host.fj.p specific growth rate of the parasite.PPmtx specific growth rate of the parasite at infinite host concentration.n number of zoospores per mature sporangium.p concentration of total parasite population.q infective lifetime of a zoospore.s concentration of attached sporangia,v zoospore production rate.z concentration of free zoospores.
