Monogenean body size,but not reproduction,increases with infracommunity density

Body size reveals a plethora of life-history, ecological, and evolutionary information about a species. It plays a critical role in success or failure during competitive, reproductive, or predator–prey interactions. Typically, there is a negative relationship between body size and population density in natural populations and communities. I analysed this relationship within and among multiple populations of two prominent monogenean parasites (>90% prevalence) on Lepomis macrochirus in three lakes in New Jersey (USA), using multiple regression models. To elucidate the causes and benefits of this relationship, I also measured host body condition via a regression index, and reproductive output of the parasite community by measuring parasite eggs shed from the host. The relationship between body size and density of infrapopulations (parasites of a single species on a single host) was positive, and the strength of this relationship for both species depended on which lake they occupied, indicating the potential for Allee effects. This relationship persists at the infracommunity level, where there was a similar positive relationship between a community weighted mean body size and density. However, this relationship did not result in greater reproductive success as measured by infracommunity egg production per individual per 24 h or egg size. The cause of this relationship also remains elusive; it was not explained by host condition or age. The results suggest that there is either no reproductive advantage to this increase in body size or the advantage conferred was not related to these measured fitness components. These findings indicate that researchers should be cautious using body size as a proxy for fitness or reproduction, while also raising further questions about the nature of the relationship between parasites on a host and that between those parasites and the host.     

Intra‐specific body size variation in Polistes paper wasps as a response to social parasite pressure

1. Like avian brood parasites, obligate insect social parasites exploit the parental care of a host species to rear their brood, causing an evident loss of host reproductive success. This fitness cost imposes selective pressure on the host to reduce the parasite effect. A possible outcome of an evolutionary arms race is the selection of host morphological counter‐adaptations to resist parasite attacks. 2. We studied host–parasite pairs of Polistes wasps in which the fighting equipment of the parasite's body allows it to enter the host colony. 3. We searched for host morphological traits related to fighting ability that could be considered counter‐adaptations. As a host–parasite co‐evolutionary arms race can only occur where the two lineages co‐exist, we compared morphological traits of hosts belonging to populations with or without parasite pressure. We report that host foundresses belonging to populations under strong parasite pressure have a larger body size than those belonging to populations without parasite pressure. 4. Behavioural experiments carried out to test if an increase in host body size is useful to oppose parasite usurpation show that large body size foundresses exhibit a greater ability of nest defence.     

Do threatened hosts have fewer parasites? A comparative study in primates

1. Parasites and infectious diseases have become a major concern in conservation biology, in part because they can trigger or accelerate species or population declines. Focusing on primates as a well-studied host clade, we tested whether the species richness and prevalence of parasites differed between threatened and non-threatened host species. 2. We collated data on 386 species of parasites (including viruses, bacteria, protozoa, helminths and arthropods) reported to infect wild populations of 36 threatened and 81 non-threatened primate species. Analyses controlled for uneven sampling effort and host phylogeny. 3. Results showed that total parasite species richness was lower among threatened primates, supporting the prediction that small, isolated host populations harbour fewer parasite species. This trend was consistent across three major parasite groups found in primates (helminths, protozoa and viruses). Counter to our predictions, patterns of parasite species richness were independent of parasite transmission mode and the degree of host specificity. 4. We also examined the prevalence of selected parasite genera among primate sister-taxa that differed in their ranked threat categories, but found no significant differences in prevalence between threatened and non-threatened hosts. 5. This study is the first to demonstrate differences in parasite richness relative to host threat status. Results indicate that human activities and host characteristics that increase the extinction risk of wild animal species may lead simultaneously to the loss of parasites. Lower average parasite richness in threatened host taxa also points to the need for a better understanding of the cascading effects of host biodiversity loss for affiliated parasite species.     

Specificity and host predictability: a comparative analysis among monogenean parasites of fish

1. This article compares generalist (parasite species found on two or more host species) and specialist (found on only one host species) monogenean parasite species of fish. The reduction of the host range – that is an increase in host specificity – may correspond with a better adaptation of the parasite to a more predictable host environment. A more predictable environment may allow the parasite species to develop specific adaptations.
2. We assume that the more predictable host environment can be evaluated by host body size, since numerous life-traits, such as longevity, are positively correlated with size.
3. We found that specialist parasites parasitize larger hosts species than generalist parasites. We also found a good relationship between host body size and parasite body size for specialist parasite species.
4. An adaptation to the mechanical problems encountered in the host's gill chamber may lead to an increase in parasite body size. The infection of a larger part of the host population in order to decrease the chances of local extinction due to fluctuations of host abundance may be another adaptive mechanism.
5. We found a negative correlation between parasite body size and prevalence for generalist parasite species. This relationship disappeared when using the comparative method controlling for phylogeny, which proved that it was a phylogenetic effect.     

The influence of a parasite community on the dynamics of a host population: a longitudinal study on willow ptarmigan and their parasites

Despite the fact that most host populations are infected by a community of different parasite species, the majority of empirical studies have focused on the interaction between the host and a single parasite species. Here, we explore the hypothesis that host population dynamics are affected both by single parasite species and by the whole parasite community. We monitored population density and breeding productivity of two populations of willow ptarmigan ( Lagopus lagopus ) in northern Norway for 8 and 11 years, respectively, and sampled eukaryotic endoparasites. We found that increasing abundances of the cestode Hymenolepis microps was associated with increased breeding mortality and reduced annual growth rate of the host population in both areas, and reduced host body mass and body condition in the area where such data were available. In one of the areas, the abundance of the nematode Trichostrongylus tenuis was associated with reductions in host body mass, body condition and breeding mortality and the filaroid nematode Splendidofilaria papillocerca was negatively related to host population growth rates. The parasite community was also negatively related to host fitness parameters, suggesting an additional community effect on host body mass and breeding mortality, although none of the parasites had a significant impact on their own. The prevalence of parasites with very different taxonomical origins tended to covary within years, suggesting that variability in the parasite community was not random, but governed by changes in host susceptibility or environmental conditions that affected exposure to parasites in general. Other variables including climate, plant production and rodent densities were not associated with the recorded demographic changes in the host population.     

The dynamics of preferential host switching: Host phylogeny as a key predictor of parasite distribution*

Parasites often jump to and become established in a new host species. There is much evidence that the probability of such host shifts decreases with increasing phylogenetic distance between donor and recipient hosts, but the consequences of such preferential host switching remain little explored. We develop a computational model to investigate the dynamics of parasite host shifts in the presence of this phylogenetic distance effect. In this model, a clade of parasites evolves on an evolving clade of host species where parasites can cospeciate with their hosts, switch to new hosts, speciate within hosts or become extinct. Our model predicts that host phylogenies are major determinants of parasite distributions across trees. In particular, we predict that trees consisting of few large clades of host species and those with fast species turnover should harbor more parasites than trees with many small clades and those that diversify more slowly. Within trees, large clades are predicted to exhibit a higher fraction of infected species than small clades. We discuss our results in the light of recent cophylogenetic studies in a wide range of host–parasite systems.     

Parasite prevalence and the size of host populations: an experimental test

Although important in epidemiological theory, the relationship between the size of host populations and the prevalence of parasites has not been investigated empirically. Commonly used models suggest no relationship, but this prediction is sensitive to assumptions about parasite transmission. In laboratory populations, I manipulated the size of Tribolium castaneum flour beetle populations and measured the prevalence and distribution of a parasitic mite, Acarophenax tribolii. I found that parasite prevalence did not vary for a wide range of host population sizes. However, prevalence was lower in populations with less than 40 hosts. This effect cannot be attributed to changes in host population density because host density was held constant among treatments. The reduction in prevalence of small populations below a threshold that I observed is predicted by the extinction debt model, but it is not expected from models of host-parasite interactions that assume density-dependent transmission. The distribution of parasites, measured using Lloyd's patchiness index, was not affected by host population size. The mean crowding of parasites, however, was negatively related with host density. Finally, the prevalence of parasites in large populations did not differ from that found in sets of smaller patches as long as the smaller populations in aggregate were equivalent in size to the large population.     

Host densities as determinants of abundance in parasite communities

Several epidemiological models predict a positive relationship between host population density and abundance of directly transmitted macroparasites. Here, we generalize these, and test the prediction by a comparative study. We used data on communities of gastrointestinal strongylid nematodes from 19 mammalian species, representing examination of 6670 individual hosts. We studied both the average abundance of all strongylid nematodes within a host species, and the two components of abundance, prevalence and intensity. The effects of host body weight, diet, fecundity and age at maturity and parasite body size were controlled for directly, and the phylogenetically independent contrast method was used to control for confounding factors more generally. Host population density and average parasite abundance were strongly positively correlated within mammalian taxa, and across all species when the effects of host body weight were controlled for. Controlling for other variables did not change this. Even when looking at single parasite species occurring in several host species, abundance was highest in the host species with the highest population density. Prevalence and intensity showed similar patterns. These patterns provide the first macroecological evidence consistent with the prediction that transmission rates depend on host population density in natural parasite communities.     

Comparative tests of parasite species richness in primates

Some hosts harbor diverse parasite communities, whereas others are relatively parasite free. Many factors have been proposed to account for patterns of parasite species richness, but few studies have investigated competing hypotheses among multiple parasite communities in the same host clade. We used a comparative data set of 941 host-parasite combinations, representing 101 anthropoid primate species and 231 parasite taxa, to test the relative importance of four sets of variables that have been proposed as determinants of parasite community diversity in primates: host body mass and life history, social contact and population density, diet, and habitat diversity. We defined parasites broadly to include not only parasitic helminths and arthropods but also viruses, bacteria, fungi, and protozoa, and we controlled for effects of uneven sampling effort on per-host measures of parasite diversity. In nonphylogenetic tests, body mass was correlated with total parasite diversity and the diversity of helminths and viruses. When phylogeny was taken into account, however, body mass became nonsignificant. Host population density, a key determinant of parasite spread in many epidemiological models, was associated consistently with total parasite species richness and the diversity of helminths, protozoa, and viruses tested separately. Geographic range size and day range length explained significant variation in the diversity of viruses.     

Parasitization of bats by bat flies (Streblidae) in fragmented habitats

Parasites represent a large fraction of the world's biodiversity. They control host population sizes and contribute to ecosystem functioning. However, surveys on species diversity rarely include parasitic species. Bats often present traits favoring parasite diversity, such as large home ranges, long life spans, and large colonies. The most conspicuous bat parasites are the highly host-specific, blood-sucking bat flies (Diptera: Streblidae, Nycteribiidae). Recent studies have found a direct effect of habitat alteration on the abundance of bat species. We expected, therefore, that changes in the host community in response to anthropogenic habitat modification will also result in changes in the associated parasite community. We captured bats in three different habitats in Central Panama between 2013 and 2015. We recorded information on prevalence and intensity of bat fly parasitization of the seven most commonly captured bat species. Prevalence and intensity were both significantly influenced by roost type, abundance, and host sex and age. We found that habitat variables and matrix type significantly influenced the prevalence and intensity of parasitization, while the direction of the responses was host species- and parasite species-specific. In general, roosting conditions and behavior of host bats appear to be fundamental in explaining changes in prevalence and intensity of parasitization between different habitat types, as bat flies are bound to the roost during their reproductive cycle. Habitat alterations affect next to the host community composition also the availability of possible roost structures as well as microclimatic conditions, which all three reflect in parasitization.     

Priority effects within coinfected hosts can drive unexpected population‐scale patterns of parasite prevalence

Organisms are frequently coinfected by multiple parasite strains and species, and interactions between parasites within hosts are known to influence parasite prevalence and diversity, as well as epidemic timing. Importantly, interactions between coinfecting parasites can be affected by the order in which they infect hosts (i.e. within‐host priority effects). In this study, we use a single‐host, two‐pathogen, SI model with environmental transmission to explore how within‐host priority effects scale up to alter host population‐scale infection patterns. Specifically, we ask how parasite prevalence changes in the presence of different types of priority effects. We consider two scenarios without priority effects and four scenarios with priority effects where there is either an advantage or a disadvantage to being the first to infect in a coinfected host. Models without priority effects always predict negative relationships between the prevalences of both parasites. In contrast, models with priority effects can yield unimodal prevalence relationships where the prevalence of a focal parasite is minimized or maximized at intermediate prevalences of a coinfecting parasite. The mechanism behind this pattern is that as the prevalence of the coinfecting parasite increases, most infections of the focal parasite change from occurring as solo infections, to first arrival coinfections, to second arrival coinfections. The corresponding changes in parasite fitness as the focal parasite moves from one infection class to another then map to changes in focal parasite prevalence. Further, we found that even when parasites interact negatively within a host, they still can have positive prevalence relationships at the population scale. These results suggest that within‐host priority effects can change host population‐scale infection patterns in systematic (and initially counterintuitive) ways, and that taking them into account may improve disease forecasting in coinfected populations.     

What determines species richness of parasitic organisms? A meta‐analysis across animal,plant and fungal hosts

Although a small set of external factors account for much of the spatial variation in plant and animal diversity, the search continues for general drivers of variation in parasite species richness among host species. Qualitative reviews of existing evidence suggest idiosyncrasies and inconsistent predictive power for all proposed determinants of parasite richness. Here, we provide the first quantitative synthesis of the evidence using a meta‐analysis of 62 original studies testing the relationship between parasite richness across animal, plant and fungal hosts, and each of its four most widely used presumed predictors: host body size, host geographical range size, host population density, and latitude. We uncover three universal predictors of parasite richness across host species, namely host body size, geographical range size and population density, applicable regardless of the taxa considered and independently of most aspects of study design. A proper match in the primary studies between the focal predictor and both the spatial scale of study and the level at which parasite species richness was quantified (i.e. within host populations or tallied across a host species' entire range) also affected the magnitude of effect sizes. By contrast, except for a couple of indicative trends in subsets of the full dataset, there was no strong evidence for an effect of latitude on parasite species richness; where found, this effect ran counter to the general latitude gradient in diversity, with parasite species richness tending to be higher further from the equator. Finally, the meta‐analysis also revealed a negative relationship between the magnitude of effect sizes and the year of publication of original studies (i.e. a time‐lag bias). This temporal bias may be due to the increasing use of phylogenetic correction in comparative analyses of parasite richness over time, as this correction yields more conservative effect sizes. Overall, these findings point to common underlying processes of parasite diversification fundamentally different from those controlling the diversity of free‐living organisms.     

The evolution of parasite virulence and transmission rate in a spatially structured population

If the transmission occurs through local contact of the individuals in a spatially structured population, the evolutionarily stable (ESS) traits of parasite might be quite different from what the classical theory with complete mixing predicts. In this paper, we theoretically study the ESS virulence and transmission rate of a parasite in a lattice-structured host population, in which the host can send progeny only to its neighboring vacant site, and the transmission occurs only in between the infected and the susceptible in the nearest-neighbor sites. Infected host is assumed to be infertile. The analysis based on the pair approximation and the Monte Carlo simulation reveal that the ESS transmission rate and virulence in a lattice-structured population are greatly reduced from those in completely mixing population. Unlike completely mixing populations, the spread of parasite can drive the host to extinction, because the local density of the susceptible next to the infected can remain high even when the global density of host becomes very low. This demographic viscosity and group selection between self-organized spatial clusters of host individuals then leads to an intermediate ESS transmission rate even if there is no tradeoff between transmission rate and virulence. The ESS transmission rate is below the region of parasite-driven extinction by a finite amount for moderately large reproductive rate of host; whereas, the evolution of transmission rate leads to the fade out of parasite for small reproductive rate, and the extinction of host for very large reproductive rate.     

Bat fly species richness in Neotropical bats: correlations with host ecology and host brain

Patterns of ectoparasite species richness in mammals have been investigated in various terrestrial mammalian taxa such as primates, ungulates and carnivores. Several ecological or life traits of hosts are expected to explain much of the variability in species richness of parasites. In the present comparative analysis we investigate some determinants of parasite richness in bats, a large and understudied group of flying mammals, and their obligate blood-sucking ectoparasite, streblid bat flies (Diptera). We investigate the effects of host body size, geographical range, group size and roosting ecology on the species richness of bat flies in tropical areas of Venezuela and Peru, where both host and parasite diversities are high. We use the data from a major sampling effort on 138 bat species from nine families. We also investigate potential correlation between bat fly species richness and brain size (corrected for body size) in these tropical bats. We expect a relationship if there is a potential energetic trade-off between costly large brains and parasite-mediated impacts. We show that body size and roosting in cavities are positively correlated with bat fly species richness. No effects of bat range size and group size were observed. Our results also suggest an association between body mass-independent brain size and bat fly species richness. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

A meta‐analysis of ant social parasitism: host characteristics of different parasitism types and a test of Emery’s rule

Abstract 1. In ant social parasitism, the process by which parasite–host systems evolved and the types of invasion mechanisms parasites use are being debated. Emery’s rule, for example, states that social parasites are the closest relatives to their hosts. The present study uses previously published data to test whether Emery’s rule applies equally to all parasitism types (i.e. xenobiosis, temporary, dulosis, and inquilinism). In addition, this study also investigates other links between parasite–host relatedness and host biology, which has implications for understanding the invasion mechanisms used by certain parasites. 2. We find that xenobiotic parasites typically use distantly‐related host species that are of at least medium colony size. Temporary parasites often have multiple host species that are very closely related to the parasite and hosts with medium‐size colonies. Dulotic parasites frequently have multiple host species that are slightly less related and of any size. Lastly, inquiline parasites tend to have a single, very closely related, host species with medium‐size colonies. 3. Parasites tend to be more closely related to host species if they have a single host species or when the host has a large colony size. In contrast, parasites with multiple host species or hosts of small colony size tend to be less related to their hosts. 4. This study is the first to examine trends in ant social parasitism across all known parasite species. Our meta‐analysis shows that Emery’s rule applies to inquilinism and temporary parasitism, but not to dulosis and xenobiosis. Our results also suggest that both parasitism type and parasite–host relatedness predict the number of hosts and host colony size. It may be that a chemical mimicry mechanism allows invasion of large host colonies, but requires close relatedness of parasite and host, and concentration on a single host species.     

Oh sister,where art thou? Spatial population structure and the evolution of an altruistic defence trait

The evolution of parasite virulence and host defences is affected by population structure. This effect has been confirmed in studies focusing on large spatial scales, whereas the importance of local structure is not well understood. Slavemaking ants are social parasites that exploit workers of another species to rear their offspring. Enslaved workers of the host species Temnothorax longispinosus have been found to exhibit an effective post‐enslavement defence behaviour: enslaved workers were observed killing a large proportion of the parasites’ offspring. As enslaved workers do not reproduce, they gain no direct fitness benefit from this ‘rebellion’ behaviour. However, there may be an indirect benefit: neighbouring host nests that are related to ‘rebel’ nests can benefit from a reduced raiding pressure, as a result of the reduction in parasite nest size due to the enslaved workers’ killing behaviour. We use a simple mathematical model to examine whether the small‐scale population structure of the host species could explain the evolution of this potentially altruistic defence trait against slavemaking ants. We find that this is the case if enslaved host workers are related to nearby host nests. In a population genetic study, we confirm that enslaved workers are, indeed, more closely related to host nests within the raiding range of their resident slavemaker nest, than to host nests outside the raiding range. This small‐scale population structure seems to be a result of polydomy (e.g. the occupation of several nests in close proximity by a single colony) and could have enabled the evolution of ‘rebellion’ by kin selection.     

Evolutionary associations between host traits and parasite load: insights from Lake Tanganyika cichlids

Parasite diversity and abundance (parasite load) vary greatly among host species. However, the influence of host traits on variation in parasitism remains poorly understood. Comparative studies of parasite load have largely examined measures of parasite species richness and are predominantly based on records obtained from published data. Consequently, little is known about the relationships between host traits and other aspects of parasite load, such as parasite abundance, prevalence and aggregation. Meanwhile, understanding of parasite species richness may be clouded by limitations associated with data collation from multiple independent sources. We conducted a field study of Lake Tanganyika cichlid fishes and their helminth parasites. Using a Bayesian phylogenetic comparative framework, we tested evolutionary associations between five key host traits (body size, gut length, diet breadth, habitat complexity and number of sympatric hosts) predicted to influence parasitism, together with multiple measures of parasite load. We find that the number of host species that a particular host may encounter due to its habitat preferences emerges as a factor of general importance for parasite diversity, abundance and prevalence, but not parasite aggregation. In contrast, body size and gut size are positively related to aspects of parasite load within, but not between species. The influence of host phylogeny varies considerably among measures of parasite load, with the greatest influence exerted on parasite diversity. These results reveal that both host morphology and biotic interactions are key determinants of host–parasite associations and that consideration of multiple aspects of parasite load is required to fully understand patterns in parasitism.     

Biotic and abiotic effects on endoparasites infecting Dipodomys and Perognathus species

Between 1989 and 1998, 3,504 rodents of the genera Dipodomys and Perognathus were collected from 4 permanent collecting sites on the University of New Mexico's Long Term Ecological Research station, located on the Sevilleta National Wildlife Refuge (SNWR), Socorro County. New Mexico. All animals were killed and examined for endoparasites (acanthocephalans, cestodes, coccidia, and nematodes). The present report focuses on 3 endoparasite groups, cestodes, coccidia, and nematodes. Specific analyses address how prevalence changes were related to abiotic factors such as habitat, season, or precipitation, and how prevalence of each parasite species in each host species differed in relation to host age, host sex, host reproductive status, host body mass, host density, parasite-parasite interactions, and host specificity. A logistic regression was used to determine which host characters and which abiotic factors are correlated with a parasite infection. Significant variables for at least half of the parasites include season, site, and winter precipitation. However, no parasite prevalences were correlated, and significant variables were not identical between parasites, indicating that each parasite species varied independently and that no generalizations can be drawn. The parasite prevalences in these rodents on the SNWR vary in independent and complex ways.     

Small and large wetland fragments are equally suited breeding sites for a ground-nesting passerine

Large habitat fragments are generally thought to host more species and to offer more diverse and/or better quality habitats than small fragments. However, the importance of small fragments for population dynamics in general and for reproductive performance in particular is highly controversial. Using an information-theoretic approach, we examined reproductive performance and probability of local recruitment of color-banded reed buntings Emberiza schoeniclus in relation to the size of 18 wetland fragments in northeastern Switzerland over 4 years. We also investigated if reproductive performance and recruitment probability were density-dependent. None of the four measures of reproductive performance (laying date, nest failure probability, fledgling production per territory, fledgling condition) nor recruitment probability were found to be related to wetland fragment size. In terms of fledgling production, however, fragment size interacted with year, indicating that small fragments were better reproductive grounds in some years than large fragments. Reproductive performance and recruitment probability were not density-dependent. Our results suggest that small fragments are equally suited as breeding grounds for the reed bunting as large fragments and should therefore be managed to provide a habitat for this and other specialists occurring in the same habitat. Moreover, large fragments may represent sinks in specific years because a substantial percentage of all breeding pairs in our study area breed in large fragments, and reproductive failure in these fragments due to the regularly occurring floods may have a much stronger impact on regional population dynamics than comparable events in small fragments. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

The parasite capacity of the host population

The estimation of parasitic pressure on the host populations is frequently required in parasitological investigations. The empirical values of prevalence of infection are used for this, however the latter one as an estimation of parasitic pressure on the host population is insufficient. For example, the same prevalence of infection can be insignificant for the population with high reproductive potential and excessive for the population with the low reproductive potential. Therefore the development of methods of an estimation of the parasitic pressure on the population, which take into account the features the host population, is necessary. Appropriate parameters are to be independent on view of the researcher, have a clear biological sense and be based on easily available characteristics. The methods of estimation of parasitic pressure on the host at the organism level are based on various individual viability parameters: longevity, resistance to difficult environment etc. The natural development of this approach for population level is the analysis of viability parameters of groups, namely, the changing of extinction probability of host population under the influence of parasites. Obviously, some critical values of prevalence of infection should exist; above theme the host population dies out. Therefore the heaviest prevalence of infection, at which the probability of host population size decreases during the some period is less than probability of that increases or preserves, can serve as an indicator of permissible parasitic pressure on the host population. For its designation the term "parasite capacity of the host population" is proposed. The real parasitic pressure on the host population should be estimated on the comparison with its parasite capacity. Parasite capacity of the host population is the heaviest possible prevalence of infection, at which, with the generation number T approaching infinity, there exists at least one initial population size ni(0) for which the probability of size decrease through T generations is less than the probability of its increase. [formula: see text] The estimation of the probabilities of host population size changes is necessary for the parasite capacity determination. The classical methods for the estimation of extinction probability of population are unsuitable in this case, as these methods require the knowledge of population growth rates and their variances for all possible population sizes. Thus, the development methods of estimate of extinction probability of population, based on the using of available parameters (sex ratio, fecundity, mortality, prevalence of infection PI) is necessary. The population size change can be considered as the Markov process. The probabilities of all changes of population size for a generation in this case are described by a matrix of transition probabilities of Markov process (pi) with dimensions Nmax x Nmax (maximum population size). The probabilities of all possible size changes for T generations can be calculated as pi T. Analyzing the behaviour matrix of transition at various prevalence of infection, it is possible to determine the parasite capacity of the host population. In constructing of the matrix of transition probabilities, should to be taken into account the features the host population and the influence of parasites on its reproductive potential. The set of the possible population size at a generation corresponds to each initial population size. The transition probabilities for the possible population sizes at a generation can be approximated to the binomial distribution. The possible population sizes at a generation nj(t + 1) can be calculated as sums of the number of survived parents N1 and posterities N2; their probabilities--as P(N1) x P(N2). The probabilities of equal sums N1 + N2 and nj(t + 1) > or = Nmax are added. The number of survived parents N1 may range from 0 to (1-PI) x ni(t). The survival probabilities can be estimated for each N1 as [formula: see text] The number of survived posterities N2 may range from 0 to N2max (the maximum number of posterities). N2max is [formula: see text] and the survival probabilities for each N2, is defined as [formula: see text] where [formula: see text], ni(t) is the initial population size (including of males and infected specimens of host), PI is the prevalence of infection, Q1 is the survival probabilities of parents, Pfemales is the frequency of females in the host population, K is the number of posterities per a female, and Q2 is the survival probabilities of posterities. When constructing matrix of transition probabilities of Markov process (pi), the procedure outlined above should be repeated for all possible initial population size. Matrix of transition probabilities for T generations is defined as pi T. This matrix (pi T) embodies all possible transition probabilities from the initial population sizes to the final population sizes and contains a wealth of information by itself. From the practical point of view, however, the plots of the probability of population size decrease are more suitable for analysis. They can be received by summing the probabilities within of lines of matrix from 0 to ni--1 (ni--the population size, which corresponds to the line of the matrix). Offered parameter has the number of advantages. Firstly, it is independent on a view of researcher. Secondly, it has a clear biological sense--this is a limit of prevalence, which is safe for host population. Thirdly, only available parameters are used in the calculation of parasite capacity: population size, sex ratio, fecundity, mortality. Lastly, with the availability of modern computers calculations do not make large labour. Drawbacks of this parameter: 1. The assumption that prevalence of infection, mortality, fecundity and sex ratio are constant in time (the situations are possible when the variability of this parameters can not be neglected); 2. The term "maximum population size" has no clear biological sense; 3. Objective restrictions exist for applications of this mathematical approach for populations with size, which exceeds 1000 specimens (huge quantity of computing operations--order Nmax 3*(T-1), work with very low probabilities). The further evolution of the proposed approach will allow to transfer from the probabilities of size changes of individual populations to be probabilities of size changes of population systems under the influence of parasites. This approach can be used at the epidemiology and in the conservation biology.