Conditions for coexistence of freshwater mussel species via partitioning of fish host resources
Introduction
Communities of freshwater mussels of the family Unionidae in many North American rivers support high diversities of similar species over long periods of time. For example, some rivers consistently support 20–40 freshwater mussel species (e.g., Strayer, 1980, Ahlstedt, 1986). These species are similar in terms of their use of food and habitat resources (Coker et al., 1921, Fuller, 1980, Strayer, 1981, Bronmark and Malmqvist, 1982, Hanson et al., 1988, Strayer, 1993). Virtually all North American freshwater mussel larvae (glochidia) are obligate parasites on fish for a period of weeks to months during recruitment (Fuller, 1974). Most mussel communities are thought to be limited at recruitment (Young and Williams, 1984, Haag and Warren, 1998), so populations may be regulated by the number of new post-glochidial recruits supplied to the site, rather than by interactions between adults (Grosberg and Levitan, 1992, Chesson, 1998). It is possible that mussel species compete for fish hosts (Bauer, 2001). Larvae of a particular mussel species can only develop successfully on a subset of the fish species in a river (Bauer and Vogel, 1987, Waller and Holland-Bartels, 1988). Most species are specialists, using one or a few host fish species, although some generalists may use a dozen hosts or more (Strayer et al., 2004). Ecologically similar species, such as these, are expected to compete for the resources that most limit population growth. Because it is unlikely that two species will be perfectly balanced in their abilities to use resources, the stronger competitor is expected to outcompete the weaker competitor and force its exclusion (Hardin, 1960).
Coexistence among freshwater mussels that overlap on fish hosts may be facilitated by the partitioning of fish host resources used during recruitment (Fuller, 1980). Resource partitioning promotes species coexistence because species differ from each other in at least one ecological characteristic that allows them to utilize different portions of the resource spectrum (Schoener, 1974). Early theoretical work by MacArthur and Levins (1967) and May (1974) showed that species in competition for a single, continuously-distributed resource could coexist only if their resource utilization differed by a limiting similarity. However, Abrams (1983) found that models with competition in different dimensions or with alternate utilization curves lead to alternate limits to similarity. In the case of multiple substitutable resources, such as species of fish hosts for mussels, a general condition for coexistence is that each competing species must remove at a higher rate the resource that contributes more to its own growth rate (Leon and Tumpson, 1975, Tilman, 1982, Abrams, 1987a, Abrams, 1987b). The importance of trade-offs in resource use among species has been emphasized recently as a mechanism promoting coexistence in plant communities (Silvertown, 2004). Resource partitioning during the glochidial stage may determine species coexistence for freshwater mussels. However, to date this hypothesis has not been addressed quantitatively.
In this paper, mathematical conditions for coexistence via resource partitioning of host fish were derived for two species of freshwater mussels. A model of resource utilization was developed for the mussel species, in which larval and adult stages were assumed to occupy different niches. Adults of each species were assumed to overlap with each other in terms of food and habitat use and larvae were assumed to overlap in their use of two species of fish hosts. Invasibility analysis was used to determine conditions for coexistence, and the effects of host contact success, carrying capacities (in this case, the maximum glochidial infestation rates per fish), and fish host densities on coexistence were examined. An understanding of the conditions for coexistence of freshwater mussel species may foster an explanation of the factors promoting the high mussel diversity found in some rivers, and may also guide ongoing conservation activities, such as mussel transplants and population augmentations (e.g., Ahlstedt, 1979, Cope and Waller, 1995, Biggins and Butler, 2000). Conservation activities and efforts are crucial because over seventy percent of North American freshwater mussel species are in decline, threatened, or extinct (Williams et al., 1992) and the fauna is undergoing extinctions in the “kilo-death” range (Nott et al., 1995).
Section snippets
A model of competition between two mussel species
The two competing mussel populations, i and j, are represented by difference equations with yearly time steps. Consider mussel population j. Its adult population size at the end of the breeding season of year t + 1, Nj (t + 1), can be represented by two terms, which are functions of the population size in the preceding year; survivors from the preceding year, and new recruits. For the case of two competing mussel species, the adult survivorship is a function of the densities of the two species;
Effects of fish host contact success on coexistence
To illustrate these conditions in terms of fish host contact success, it is assumed that life histories and maximum infestation loads are equivalent between the two mussel species (e.g., sifi = sjfj, Ki1 = Ki2 = Kj1 = Kj2) and densities of the two fish host species are equal (F1 = F2). In this case, Eqs. (9) and (10) reduce toandrespectively. The conditions given in Eqs. (11) and (12) are shown in Fig. 1 for cj1 = cj2 = 0.5. For this figure, the assumption is also made that the
Discussion
Modeled freshwater mussel species with similar life history characteristics that experience overlap on fish hosts could coexist with an interspecific trade-off in fish host contact success. This finding coincides with the conclusion of Leon and Tumpson (1975) and Tilman (1982) that in order for species using substitutable resources to coexist, each species must remove at a higher rate that resource which contributes more to its own growth rate. In cases where potential host infestation loads
Acknowledgments
We thank Jim Drake, Michael Huston, David Etnier, and Mark Kot for helpful reviews and we would like to thank Deborah Hart, Michael Neubert, Jeff Tyler, and Craig Barber for very useful discussions. This research was performed under an appointment to the Graduate Student Research Participation Program, administered by the Oak Ridge Institute for Science and Education under contract number DE-AC05-00OR22750 between the U.S. Department of Energy and Oak Ridge Associated Universities (B.R.).
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