Diseases and parasites play a major role in most ecosystem dynamics; yet, they have received relatively little attention in ecological modelling [1–3]. Traditionally, ecologists have mostly considered disease outbreaks as disturbances rather than as an integral part of the ecosystem dynamics . However, there is mounting evidence that diseases and parasites play a vital role in the stability and dynamics of most ecosystems [5–9].
In this paper we will consider the effects of a disease that specifically infects juvenile individuals and subsequently prevents the infected individual from producing offspring. The work is inspired by the interaction between the tape worm Ligula intestinalis and its cyprinid fish host species roach (Rutilis rutilis). The parasite has a complex life cycle, involving three host species. The final host species of the parasite are fish eating birds, such as cormorant (Phalacrocorax carbo), grey herron (Ardea cinerea), and great crested grebe (Podiceps cristatus) . In this final host the parasite completes its sexual cycle and produces eggs, which are shed to the water via the faeces of the birds. The larvae of the parasite are eaten by copepods, which in turn are a primary food source for the juvenile fish. After a fish is infected, the parasite settles and grows in the host gut system and may obtain a staggering weight of up to half the host weight . Surprisingly, the physical condition of such a fish-parasite combination can be not noticeably different from uninfected individuals . However, the consequences for the infected fish are severe, as the parasites supress gonad development and consequently prevent the individual from maturing. Even infection with a single parasite can act to sterilize the infected fish . Furthermore, the parasite might induce behavioural changes, such as directing the infected fish to move to the littoral zone, where it can be caught more easily by the fish eating birds and thus complete the parasite life cycle [13,14].
Also the consequences of the parasite infection on the host population dynamics can be extensive. A well-documented case are the recurrent Ligula parasite outbreaks in the roach population of lake Slapton Ley [11,15,16]. The roach population in this lake shows a tendency to build-up a so-called stunted population. In this population state, small juvenile individuals are very numerous. This causes exploitation competition amongst juveniles to be so fierce, that individual growth rate substantially slows down, effectively preventing juveniles from reaching the size necessary for maturation [16,17].
In this stunted population situation, the Ligula parasite can cause a large epidemic, reaching a prevalence of more than 70% of all juveniles being infected . This in turn seems to act to relieve the stuntedness in the juvenile population, causing a reduction in the juvenile population size, with a subsequent acceleration in juvenile growth and maturation, accompanied by a strong reduction of the parasite prevalence. However, hereafter, the stuntedness in the host population slowly rebuilds, after which a second epidemic of the parasite can occur. In the case of the Slapton Ley dataset, such recurrent epidemics were recorded three times, spanning a total period of 31 years .
In this paper we will study a mathematical model to investigate the interplay between ecological population dynamics of a potentially stunted population and a disease. Furthermore, we will study the interaction between the disease and a natural predator of the host. In the Ligula–Roach system there are several predators on Roach, including Northern Pike (Esox Lucius) and European Perch (Perca fluvitilis). Often, such predator species are of commercial or recreational interest for fisherman, and stunting of the prey species can greatly affect predator numbers or predator quality. Here, we will study the potential indirect influence of a prey disease on the predator species. For the ecological baseline, we will use a model that we have introduced before for the dynamics of a structured prey population and a predator that attacks adult prey [18,19]. In this model a stunted juvenile prey population can build up due to a maturation bottleneck, and it has a parameter region of bistability between a stunted and non-stunted equilibrium state . To this system we will add a disease that specifically infects juvenile individuals, and that acts to sterilize these individuals and prevents maturation. In this way we can study the indirect interaction between a predator and a disease, that both attack the same host species, but each targeting a different host life stage. For mathematical simplicity, we model a disease that spreads through direct contact. This differs from the parasite infection in the Ligula-Roach system, where the parasite has to pass through two additional host stages. Our simplified model would roughly correspond to a constancy assumption in the copepod and bird populations. Furthermore, we do not explicitly account for individual parasite load, but instead we only distinguish between infected and uninfected individuals.
Our main objective in this paper is to study the effects of a disease that infects and sterilizes juvenile individuals on the population dynamics of its host species. In particular, we will focus on a system where the host population is in a stunted population state, which is strongly dominated by juvenile individuals and where individual growth rate and maturation are strongly reduced. We will map the dynamic consequences of introducing such a disease in a stunted host population state. It will turn out that these consequences strongly depend on the ability of infected juveniles to compete with uninfected conspecifics. We will discuss the biological implications of our results.