The evolution of complex life cycles when parasite mortality is size- or time-dependent

doi:10.1016/j.jtbi.2008.02.025

Journal of Theoretical Biology

Volume 253, Issue 1, 7 July 2008, Pages 202-214

https://doi.org/10.1016/j.jtbi.2008.02.025 Get rights and content

Abstract

In complex cycles, helminth larvae in their intermediate hosts typically grow to a fixed size. We define this cessation of growth before transmission to the next host as growth arrest at larval maturity (GALM). Where the larval parasite controls its own growth in the intermediate host, in order that growth eventually arrests, some form of size- or time-dependent increase in its death rate must apply. In contrast, the switch from growth to sexual reproduction in the definitive host can be regulated by constant (time-independent) mortality as in standard life history theory. We here develop a step-wise model for the evolution of complex helminth life cycles through trophic transmission, based on the approach of Parker et al. [2003a. Evolution of complex life cycles in helminth parasites. Nature London 425, 480–484], but which includes size- or time-dependent increase in mortality rate. We assume that the growing larval parasite has two components to its death rate: (i) a constant, size- or time-independent component, and (ii) a component that increases with size or time in the intermediate host. When growth stops at larval maturity, there is a discontinuous change in mortality to a constant (time-independent) rate. This model generates the same optimal size for the parasite larva at GALM in the intermediate host whether the evolutionary approach to the complex life cycle is by adding a new host above the original definitive host (upward incorporation), or below the original definitive host (downward incorporation). We discuss some unexplored problems for cases where complex life cycles evolve through trophic transmission.

Introduction

Parker et al. (2003a) modelled the evolution of complex life cycles of helminth parasites through the incorporation of a new host by a series of successive steps, starting from a one-host (direct) cycle, leading to a two-host (indirect) cycle. The models were devised primarily for parasites that are transmitted in the food of their host (trophic transmission), e.g. when a predator consumes prey containing helminth larvae. In a two-host cycle, the first (intermediate) host supports the growth of larval stages, and in the second (definitive) host the parasite attains sexual maturity and releases propagules (Bush et al., 2001).

Cestodes, nematodes, and acanthocephalans typically transfer between hosts by trophic transmission and (with rare exceptions) do not have a phase of asexual reproduction. Here, a larval parasite in an intermediate host transfers to the definitive host at the size that the larva has achieved when the definitive host eats the intermediate host. Our models are devised for such cycles (termed Type I cycles by Parker et al., 2003a). In contrast, Iwasa and Wada (2006) have modelled cases where the larva leaves the intermediate host and becomes free-living before infecting the definitive host, and where the critical size for larval transmission must be reached in the intermediate host before successful infection of the definitive host can occur. Such life cycles are usually also characterised by a stage of asexual reproduction in the intermediate host, and are typical of trematodes (termed Type II cycles by Parker et al., 2003a).

In this paper and its companion (Parker et al., in prep.), we extend the logic of Parker et al. (2003a) for Type I cycles by using the more realistic assumption that parasite mortality in the intermediate host increases with the growth of the parasite(s). This allows us to define the size and/or time at which a parasite should stop growing (growth arrest) in an intermediate host. Helminths may show various forms of growth or reproductive arrest, some of which may be determined by environmental cues (e.g. see Viney, 2002). Here, we are concerned with growth arrest of larvae with complex life cycles that typically reach a mature size and structure (bauplan) in their intermediate host, after which growth stops. This we define as growth arrest at larval maturity (GALM).

We assume that the parasite's death rate changes at GALM, since it then switches from active growth (often accompanied by migration through the host tissues) to a state of quiescence. This change in a parasite's size-dependent death rate after reaching GALM is important because cessation of growth in an intermediate host is often accompanied either by encapsulation by the host, or encystment by the parasite, both of which are likely to affect larval mortality rate.

In the present paper, we model this change, and derive an equation defining the optimal size or age for a parasite at GALM in its intermediate host. A companion paper (Parker et al., in prep.) extends the same logic to investigate the differences between hosts in which larvae grow (intermediate hosts), and those hosts in which larvae do not grow (paratenic hosts). There, we examine the biological implications of this strategic life history divergence in terms of the potential death and growth rates achievable by larvae in their hosts.

Section snippets

The model

Parker et al. (2003a) emphasised and analysed the three main possibilities for the incorporation of new hosts into helminth life cycles with trophic transmission, the history of which was reviewed by Dogiel (1964; see also Smith Trail, 1980; Combes, 1991; Choisy et al., 2003; and the excellent monograph of Poulin, 2007). These are: (i) the cycle extends by adding an intermediate host (downward incorporation); (ii) the cycle extends by adding a new host higher up the food chain, which then

Analysis: steps in evolution

We next analyse the evolutionary conditions governing growth in an intermediate host, first for downward incorporation of an intermediate host, and then for upward incorporation of a replacement definitive host. In both, we take i as a prey species eaten by predator species j. Thus in downward incorporation, we start with host j as the definitive host, and examine the addition of a new (intermediate) host i. In contrast, for upward incorporation, we start with host i as the original definitive

Optimal size/age at GALM: the equation for $W_{d}^{}$ or, equivalently, $t_{d}^{}$

We examine Eq. (14), which determines $W_{d}^{*}$ . Factoring out the common terms like $A e^{p_{j} g_{i} t_{d} / g_{j}}$ , we get $n_{i} + (p_{j} g_{i} n_{i} / g_{j} + d / d t_{d} (n_{i} (t_{d}, t_{d}, g_{i})) - n_{i} d p_{i}^{d} / d t_{d} / p_{i}^{d}) / p_{i}^{d} = 0 .$

This equation, using Eq. (A.5) and eliminating n_i, reduces to $p_{ni}^{(1)} (t_{d}^{*}) - p_{ni}^{(2)} (t_{d}^{*}) = p_{j} g_{i} / g_{j} - (d p_{ni}^{(2)} / d t_{d}) / (p_{ni}^{(2)} (t_{d}^{*}) + p_{ij}) .$

Eq. (18) allows calculation of $t_{d}^{*}$ and $W_{d}^{*}$ , and relies only on the assumptions that birth rate is proportional to body mass, W, and that $p_{ni}^{(2)} (t_{d}^{*})$ is constant with respect to t. Note that Eq. (18) is expressed in terms

Discussion

The present paper develops the concepts of Parker et al. (2003a) on the evolution of complex helminth life cycles by including size- or time-dependent mortality, while retaining the same evolutionary steps. Here we discuss these advances, and expand ideas on the evolution of complex cycles.

Acknowledgements

We are indebted to the Natural Environment Research Council for supporting this work (Grant GR3/12774), and we thank two anonymous reviewers for their help in improving the manuscript.

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Cited by (27)

Complex life-cycles in trophically transmitted helminths: Do the benefits of increased growth and transmission outweigh generalism and complexity costs?
2022, Current Research in Parasitology and Vector-Borne Diseases
Citation Excerpt :
Downward incorporation of small prey hosts, besides decreasing propagule mortality, may also shield parasites from abiotic conditions, e.g. through host mechanisms to maintain homeostasis, like thermoregulation (Molnár et al., 2013). Then again, small hosts have short life expectancies that could be further shortened by growing worms (Ball et al., 2008). Transmission rates between successive hosts likely vary with life-cycle length.
Why do so many parasitic worms have complex life-cycles? A complex life-cycle has at least two hypothesized costs: (i) worms with longer life-cycles, i.e. more successive hosts, must be generalists at the species level, which might reduce lifetime survival or growth, and (ii) each required host transition adds to the risk that a worm will fail to complete its life-cycle. Comparing hundreds of trophically transmitted acanthocephalan, cestode, and nematode species with different life-cycles suggests these costs are weaker than expected. Helminths with longer cycles exhibit higher species-level generalism without impaired lifetime growth. Further, risk in complex life-cycles is mitigated by increasing establishment rates in each successive host. Two benefits of longer cycles are transmission and production. Longer cycles normally include smaller (and thus more abundant) first hosts that are likely to consume parasite propagules, as well as bigger (and longer-lived) definitive hosts, in which adult worms grow to larger and presumably more fecund reproductive sizes. Additional factors, like host immunity or dispersal, may also play a role, but are harder to address. Given the ubiquity of complex life-cycles, the benefits of incorporating or retaining hosts in a cycle must often exceed the costs.
Developmental inflexibility of larval tapeworms in response to resource variation
2010, International Journal for Parasitology
The timing of habitat switching in organisms with complex life cycles is an important life history characteristic that is often influenced by the larval growth environment. Under starvation, longer developmental times are frequently observed, probably as a consequence of developmental thresholds, but prolonged ontogeny sometimes also occurs under good conditions, as organisms may take advantage of the large potential gains in body size. I investigated whether variation in growth conditions affects the larval development time of a complex life cycle tapeworm (Schistocephalus solidus) in its copepod first host. Moreover, I reviewed patterns of developmental plasticity in larval tapeworms to assess the generality of my findings. Copepod starvation weakly retarded parasite growth but did not affect development. Worms grew bigger in larger copepods, but they developed at a similar rate in large and small hosts. Thus, S. solidus does not delay ontogeny under good conditions nor does it fail to reach a developmental threshold under poor conditions. Although unusual in comparison to free-living organisms, such inflexibility is common in tapeworms. Plasticity, namely prolonged ontogeny, has been mainly observed at high infection intensities. For S. solidus, there were large cross-environment genetic correlations for development, suggesting there may be genetic constraints on the evolution of developmental plasticity.
Living in intermediate hosts: evolutionary adaptations in larval helminths
2010, Trends in Parasitology
Citation Excerpt :
The intermediate host has a major role in, and poses special problems for, life history evolution [4], and these are only just being revealed. Strategies to locate, enter, establish, and persist in the intermediate host aid larval survival until transmission to the next host; however, growth generates risks that must be balanced against the potential for future growth in successive hosts [5,6]. Transmission is well known to be partially under parasite control through host manipulation [7], yet the underlying evolutionary rules are only now becoming evident [8,9].
In the complex life cycles of helminths, life in intermediate hosts poses special problems not covered by standard life history strategy theory. While under selection to reduce mortality and to increase growth, there is the additional problem of transmission between hosts. This review attempts to harmonise classical knowledge of the overall life cycle patterns with recent evolutionary theory as to how larval helminths exploit intermediate host tissues and avoid the gut to maximise fitness in terms of growth and mortality. It also considers the evolutionary rules by which trophically transmitted larvae are expected to increase their transmission rates to the next host.
Why do larval helminths avoid the gut of intermediate hosts?
2009, Journal of Theoretical Biology
In complex life cycles, larval helminths typically migrate from the gut to exploit the tissues of their intermediate hosts. Yet the definitive host's gut is overwhelmingly the most favoured site for adult helminths to release eggs. Vertebrate nematodes with one-host cycles commonly migrate to a site in the host away from the gut before returning to the gut for reproduction; those with complex cycles occupy sites exclusively in the intermediate host's tissues or body spaces, and may or may not show tissue migration before (typically) returning to the gut in the definitive host. We develop models to explain the patterns of exploitation of different host sites, and in particular why larval helminths avoid the intermediate host's gut, and adult helminths favour it. Our models include the survival costs of migration between sites, and maximise fitness (=expected lifetime number of eggs produced by a given helminth propagule) in seeking the optimal strategy (host gut versus host tissue exploitation) under different growth, mortality, transmission and reproductive rates in the gut and tissues (i.e. sites away from the gut). We consider the relative merits of the gut and tissues, and conclude that (i) growth rates are likely to be higher in the tissues, (ii) mortality rates possibly higher in the gut (despite the immunological inertness of the gut lumen), and (iii) that there are very high benefits to egg release in the gut. The models show that these growth and mortality relativities would account for the common life history pattern of avoidance of the intermediate host's gut because the tissues offer a higher growth rate/mortality rate ratio (discounted by the costs of migration), and make a number of testable predictions. Though nematode larvae in paratenic hosts usually migrate to the tissues, unlike larvae in intermediates, they sometimes remain in the gut, which is predicted since in paratenics mortality rate and migration costs alone determine the site to be exploited.
To grow or not to grow? Intermediate and paratenic hosts as helminth life cycle strategies
2009, Journal of Theoretical Biology
Larval helminths in intermediate hosts often stop growing long before their growth is limited by host resources, and do not grow at all in paratenic hosts. We develop our model [Ball, M.A., Parker, G.A., Chubb, J.C., 2008. The evolution of complex life cycles when parasite mortality is size- or time-dependent. J. Theor. Biol. 253, 202–214] for optimal growth arrest at larval maturity (GALM) in trophically transmitted helminths. This model assumes that on entering an intermediate host, larval death rate initially has both time- (or size-) dependent and time-constant components, the former increasing as the larva grows. At GALM, mortality changes to a new and constant rate in which the size-dependent component is proportional to that immediately before GALM. Mortality then remains constant until death or transmission to the definitive host. We analyse linear increasing and accelerating forms for time-dependent mortality to deduce why there is sometimes growth (intermediate hosts) and sometimes no growth (paratenic hosts). Calling i the intermediate or paratenic host, and j the definitive host, conditions favouring paratenicity are: (i) high values in host i for size at establishment, size-related mortality, expected intensity, (ii) low values in host i for size-independent mortality rate, potential growth rate, transmission rate to j, and ratio of death rate in j/growth rate in j. Opposite conditions favour growth in the (intermediate) host, either to GALM or until death without GALM. We offer circumstantial evidence from the literature supporting some of these predictions. In certain conditions, two of the three possible growth strategies (no growth; growth to an optimal size then growth arrest (GALM); unlimited growth until larval death) can exist as local optima. The effect of the discontinuity in death rate after GALM is complex and depends on mortality and growth parameters in the two hosts, and on the mortality functions before and after GALM.
Chapter 5 Ecological Immunology of a Tapeworms' Interaction with its Two Consecutive Hosts
2009, Advances in Parasitology
Host–parasite interactions in parasites with complex life cycles have recently gained much interest. Here, we take an evolutionary ecologist's perspective and analyse the immunological interaction of such a parasite, the model tapeworm Schistocephalus solidus, with its two intermediate hosts, a cyclopoid copepod and the three‐spined stickleback. We will be focussing especially on the parallel links between the different phases during an infection in the different hosts; the immunological interactions between host(s) and parasite; and their impact on parasite establishment, growth, host manipulation and parasite virulence in the next host in the cycle. We propose to extend the ‘extended phenotype’ concept and not only include the ultimate but also the proximate, physiological causes. In particular, parasite‐induced host manipulation is suggested to be caused by the interactions of the parasite with the hosts' immune systems.

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Journal of Theoretical Biology

Abstract

Introduction

Section snippets

The model

Analysis: steps in evolution

Optimal size/age at GALM: the equation for $W_{d}^{}$ or, equivalently, $t_{d}^{}$

Discussion

Acknowledgements

References (25)

The evolution of trophic transmission

Parasit. Today

The evolution of host resistance: tolerance and control as distinct strategies

J. Theor. Biol.

“Adaptive” changes in the behaviour of parasitized animals: a critical review

Int. J. Parasit.

Nematode Parasites of Vertebrates their Development and Transmission

Infections of the three-spined stickleback, Gasterosteus aculeatus L., with the plerocercoid larvae of Schistocephalus solidus (Müller, 1776), with special reference to pathological effects

Parasitology

Evolution of trophic transmission in parasites: the need to reach a mating place?

J. Evol. Biol.

Parasitism: The Diversity and Ecology of Animal Parasites

Evolution of trophic transmission in parasites: why add intermediate hosts?

Am. Nat.

Evolution of parasite life cycles

Coevolution of macroparasites and their hosts

General Parasitology

Optimal timing of first reproduction in parasitic nematodes

J. Evol. Biol.

Cited by (27)

Complex life-cycles in trophically transmitted helminths: Do the benefits of increased growth and transmission outweigh generalism and complexity costs?

Developmental inflexibility of larval tapeworms in response to resource variation

Living in intermediate hosts: evolutionary adaptations in larval helminths

Why do larval helminths avoid the gut of intermediate hosts?

To grow or not to grow? Intermediate and paratenic hosts as helminth life cycle strategies

Chapter 5 Ecological Immunology of a Tapeworms' Interaction with its Two Consecutive Hosts

The evolution of complex life cycles when parasite mortality is size- or time-dependent

Abstract

Introduction

Section snippets

The model

Analysis: steps in evolution

Optimal size/age at GALM: the equation for Wd* or, equivalently, td*

Discussion

Acknowledgements

Parasit. Today

J. Theor. Biol.

Int. J. Parasit.

Nematode Parasites of Vertebrates their Development and Transmission

Infections of the three-spined stickleback, Gasterosteus aculeatus L., with the plerocercoid larvae of Schistocephalus solidus (Müller, 1776), with special reference to pathological effects

Parasitology

Evolution of trophic transmission in parasites: the need to reach a mating place?

J. Evol. Biol.

Parasitism: The Diversity and Ecology of Animal Parasites

Evolution of trophic transmission in parasites: why add intermediate hosts?

Am. Nat.

Evolution of parasite life cycles

Coevolution of macroparasites and their hosts

General Parasitology

Optimal timing of first reproduction in parasitic nematodes

J. Evol. Biol.

Optimal size/age at GALM: the equation for $W_{d}^{}$ or, equivalently, $t_{d}^{}$