MODELLING PARASITE POPULATIONS

Even though parasites constitute a large proportion of the species on the planet, ecologists have only rather belatedly become interested in parasite populations. Parasite-host interactions are a subset of general two trophic level interactions, where energy and essential nutrients move from one population to another. The donor population (the host) is the lower trophic level, the recipient population (the parasite) is the upper trophic level. Parasites in general are all at the same trophic level, although some parasites have their own parasites (hyperparasites).

Parasite ecology can be considered in the context of two quite different methodologies. Synecology deals with groups of organisms of different species that live together, so is concerned with communities. Autecology is concerned with the study of an individual species, so is concerned with populations.

Parasites often have complex life cycles, frequently involving more than one host, this can present difficulties in defining what is meant by a population and parasite ecologists have adopted an hierarchical approach.

In autecology:

• Infra-population: all parasites of a single species in one host individual.
• Meta-population: all of the infra-populations of a single species of parasite within all of the hosts in an ecosystem.
• Supra-population: all of the parasites of a single species in all stages of development in all of its hosts in an ecosystem.

In synecology the equivalents are:

• Infra-community: all of the parasites (all species) in a single host.
• Component community: all of the parasites (all species) in a single host species in an ecosystem.
• Compound community: all of the parasites (all species) in all of the hosts (all species) in an ecosystem.

Surveys of parasites in hosts can generate vast amounts of data: species lists, prevalence data (number of hosts infected), intensity data (average number of parasites per host), correlations with host age, sex etc. In trying to make sense of these data, the first thing is to see if there is any pattern in the data. Having discerned a pattern in the data you can then try and determine the mechanism or mechanisms responsible for generating that pattern and finally how the pattern changes or evolves over time.

The Frequency Distribution of Metapopulations in Space

Or how parasites are distributed between different hosts in a population. There are three possibilities, random, regular (under dispersed) or clumped (over dispersed). If parasites are randomly dispersed, when you sample hosts you would find that the number of parasites per host follows a Poisson distribution. If the parasites were evenly distributed amongst their hosts, the number per host would follow a normal distribution. Finally if the parasites were clumped, sampling would give a negative binomial distribution (skewed). Most parasites show this last type of distribution and are over dispersed.

What this means is that you get more hosts than expected by chance with none or only a few parasites, but also more hosts with a lot of parasites. So most of the parasite population is present in relatively few hosts (70% of the parasite burden is typically found in 15% of the hosts). Parasites are not evenly distributed throughout the host population, and you get some 'wormy' individuals, that is individuals who are much more heavily infected than others. In control campaigns if you could identify those individuals that are heavily infected, you could target your chemotherapy more efficiently.

The factors that generate an over dispersed population of parasites in hosts can be divided into two sorts, density independent factors (ie do not depend on parasite numbers) and density dependent factors (ie depend on parasite numbers).

Density independent factors include:

1. Genetic variation in the hosts, some hosts are more susceptible to infection than others.
2. Host behaviour, this may effect the degree of exposure of different individuals to infection.
3. Heterogenous environment, parasite transmission may be restricted to foci.

Density dependent factors are:

1. Host immune response, the intensity of which can depend on parasite density.
2. Competition, both homospecific and heterospecific for nutrients and/or space can result in crowding effects, which affect growth rates and fecundity. Crowding effects have been noted in nematodes, digeneans, cestodes and acanthocephalans. A general observation is that worms from high-density infections are smaller and produce fewer eggs than worms from low density infections.
3. The level at which parasites start to kill their hosts. The importance of lethal levels in determining parasite population structure has been hotly debated, as has the importance of parasites in regulating host populations.

The age prevalence curve for malaria in man is low for the first 3 months of life, peaks sharply at about 4 years, then declines in adulthood. Transplacentally acquired immunity keeps infection low for the first 3 months of life, individuals are then highly susceptible and prevalence peaks. Immunity is slowly acquired and after several years exposure, prevalence falls. This acquired immunity is lost in about 6 months in the absence of continuous challenge (eg when person  moves to non malarious region, acquired immunity to malaria is also reduced in pregnancy.

The age prevalence curve for schistosomiasis in man shows very low levels below 5 years old then rises to a peak at 20, before falling away again. Small children are not exposed to infection. There is a build up through childhood to peak in late adolescence, as this is a time of peak water contact. The decline in prevalence after 20 may be attributed to:

1. Slow death of adult worms acquired in childhood.
2. Slow development of acquired resistance.
3. Reduced water contact.

Or a combination of all three.

The ultimate aim of parasite ecologists is to produce a model that can be used to predict parasite population behaviour over time. Such models could give warnings of epidemic situations and be used to evaluate the likely efficacy of control measures and predict the results of man made changes to the environment brought about by such things as building dams or cutting down forests. Failure of the model to predict the real situation can lead to the discovery of important factors in the life cycle that were previously unsuspected (e.g. the presence of a reservoir host). The new information can then be incorporated into the model. But it must be remembered that models attempt to resemble reality, but do not necessarily duplicate it.

When constructing a model you must decide what parameters to use and in parasitology it is usual to use parasite number or density (parasites/host). But you could also use the proportion of hosts infected or work in terms of energy consumption. Two different approaches have been taken for parasite population models, descriptive models and theoretical models.

Descriptive models, fitting the data to an equation, the more data you have, the better the fit. The distribution of parasites in their hosts is over dispersed and can be quite accurately modelled by the negative binomial distribution. If you know the mean number of parasites/host and the variance, the negative binomial equation will predict fairly accurately the number of hosts with 0,1,2,3,4, etc parasites. The weakness of a descriptive model is that it tells you nothing about why the population behaves as it does and the parameters of the equation have no intrinsic biological meaning.

An extension of descriptive models are the empirical models used by the Ministry of Agriculture to predict outbreaks of parasitic disease. The formula used to predict Nematodirus outbreaks (a nematode parasite of sheep and cows) is:

Disease Index = 0.5 (94 - T₁ - T₂)

Where T₁ and T₂ are the average earth temperatures recorded at two meterological stations in March of that year. Another formula has been widely used for predicting Fasciola outbreaks:

Index = n (R - P + 5)

• n = number of rainy days
• R = rainfall (in inches)
• P = potential transpiration

These formulae can give surprisingly good predictions in an average year. Where they fall down is when you get a non-average year, when there is excessive cold or heat or above average rainfall. What these relatively simple formulae do is reflect what the most significant environmental factor is in an average year. For Nematodirus this is the temperature in spring, which influences the rate of development of the infective larvae. In Fasciola the key factor is adequate moisture for the snail host.

The process of model building can be divided into a number of steps.

• The problem is stated and presented as a diagram.
• The mechanisms that control flux between the different components are identified.
• The model is translated into a series of simultaneous equations.
• The behaviour of the model is compared with the biological data.

Starting with a simple model to predict the level of snail infection for a given rate of egg production in schistosomiasis.

RE --> Egg ---- P₁ ---- Sporocyst --> RS

• RE = rate of egg production.
• RS = rate of snail infection.
• P₁ = probability of an egg successfully infecting a snail.

RS = (RE) P₁

P₁, the probability of successful infection could be broken down into:

• P_H = probability of egg hatching.
• P_L = probability of a miracidium finding a snail.
• P_P = probability of a miracidium penetrating a snail.
• P_D = probability of the parasite establishing in a snail.

P₁ = (P_H) (P_L) (P_P) (P_E)

So we are trying to identify the different factors regulating snail infection. To make a dynamic model, host dynamics would have to be added (birth, death, immigration and emigration rates).

The schistosome model could then be expanded to include the vertebrate host. Values for the different rates and probabilities are then derived from field studies or laboratory experiments.

When the model has been finally constructed, it can be run through several generations to see how the population evolves. Such models can be used to try and predict the outcome of control measures. Schistosome life cycle models for example predict that increase in hygiene has little effect on the level of the disease. This is because there is always an excess production of miracidia and one infected individual can infect a lot of snails. In general the models predict that combinations of control methods are most effective at reducing worm burdens and this forms the theoretical basis for integrated control, where you attack all points of the life cycle.

Models have also been developed to try and assess the cost effectiveness of different control methods. This is important where there may be a limited health budget. On a cost/person basis chemotherapy is usually cheapest. Control programmes involving environmental modification such as draining swamps and clean water schemes involve very high initial capital expenditure and continuing maintenance costs.

Cost benefit i.e. the increase in productivity as a result of treatment or return on investment. Estimates of the financial returns from parasite control campaigns range from 1:2 to 1:100.

One thing that models of parasite populations predict is that as control programmes reduce average worm burden, there is a critical point (the break point) at which the parasite population suddenly goes to extinction. Similarly if there is a slow build up of parasites by immigration, when the parasite level reaches this critical point you suddenly get an epidemic. So there is a critical population size, below which spontaneous transmission cannot be sustained. The frequency of contact between host and parasite becomes too low. What this means is that control campaigns do not have to eliminate every last parasite, when the parasite population is reduced to below the critical level the parasite will spontaneously disappear.