First-order difference equations arise in many contexts in the biological, economic and social sciences. Such equations, even though simple and deterministic, can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations. There are consequently many fascinating problems, some concerned with delicate mathematical aspects of the fine structure of the trajectories, and some concerned with the practical implications and applications. This is an interpretive review of them.

Simple mathematical models with very complicated dynamics

Interactions between organisms are a major determinant of the distribution and abundance of species. Ecology textbooks (e.g., Ricklefs 1984, Krebs 1985, Begon et al. 1990) summarise these important interactions as intra- and interspecific competition for abiotic and biotic resources, predation, parasitism and mutualism. Conspicuously lacking from the list of key processes in most text books is the role that many organisms play in the creation, modification and maintenance of habitats. These activities do not involve direct trophic interactions between species, but they are nevertheless important and common. The ecological literature is rich in examples of habitat modification by organisms, some of which have been extensively studied (e.g. Thayer 1979, Naiman et al. 1988).

Organisms as ecosystem engineers

Cooperation is needed for evolution to construct new levels of organization. Genomes, cells, multicellular organisms, social insects, and human society are all based on cooperation. Cooperation means that selfish replicators forgo some of their reproductive potential to help one another. But natural selection implies competition and therefore opposes cooperation unless a specific mechanism is at work. Here I discuss five mechanisms for the evolution of cooperation: kin selection, direct reciprocity, indirect reciprocity, network reciprocity, and group selection. For each mechanism, a simple rule is derived that specifies whether natural selection can lead to cooperation.

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Five Rules for the Evolution of Cooperation

http://osenberglab.ecology.uga.edu/wp-content/uploads/2015/09/Charnov-1976-TPB.pdf

Optimal foraging, the marginal value theorem.

The metacommunity concept is an important way to think about linkages between different spatial scales in ecology. Here we review current understanding about this concept. We first investigate issues related to its definition as a set of local communities that are linked by dispersal of multiple potentially interacting species. We then identify four paradigms for metacommunities: the patch-dynamic view, the species-sorting view, the mass effects view and the neutral view, that each emphasizes different processes of potential importance in metacommunities. These have somewhat distinct intellectual histories and we discuss elements related to their potential future synthesis. We then use this framework to discuss why the concept is useful in modifying existing ecological thinking and illustrate this with a number of both theoretical and empirical examples. As ecologists strive to understand increasingly complex mechanisms and strive to work across multiple scales of spatio-temporal organization, concepts like the metacommunity can provide important insights that frequently contrast with those that would be obtained with more conventional approaches based on local communities alone.

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The metacommunity concept: a framework for multi-scale community ecology

Indirect effects such as apparent competition (in which two hosts that do not compete for resources interact via a shared natural enemy) are increasingly being shown to be prevalent in the structure and function of ecological assemblages. Here, we review the empirical and theoretical evidence for these enemy-mediated effects in host–parasitoid assemblages. We first address questions about the design of experiments to test for apparent competition. Second, we consider factors likely to affect the coexistence of host species that share a parasitoid and are involved in apparent competition. We show that parasitoid aggregation, and the switching effect that this can generate when hosts occur in separate patches, not only promotes persistence but is also strongly stabilizing. The broader consequences of these effects are discussed.

Parasitoid-mediated effects: Apparent competition and the persistence of host-parasitoid assemblages

The extent of within-patch dispersal by a tephritid fly and its four major parasitoids was examined over three field seasons. Hosts and parasitoids were marked using acrylic paint and observed as they oviposited into the flowerheads of marsh thistle, Cirsium palustre. The average recapture rate pooled across all species was 22%. The four parasitoids showed consistently greater rates of movement than the host in all three years. In nearly all comparisons, male dispersal was less than female dispersal. There was no evidence that parasitoids moved longer distances after visiting low quality rather than high quality patches. In the one season it was studied, no correlations between movement and insect size were observed. The relevance of these observations to host-parasitoid population dynamics is discussed.

Relative movement patterns of a tephritid fly and its parasitoid wasps

We describe analytical and simulation models of metapopulations consisting of local populations that obey a random walk between a reflecting upper boundary (population 'ceiling') and an absorbing lower boundary (local extinction). We present analytical results for the expected time to local extinction, expected size of local populations, and incidence of density dependence. The latter is defined as the frequency of hitting the ceiling per generation per population. With these models we examine the proposition that a metapopulation consisting of random walk local populations would persist without density dependence. Long-term persistence of a metapopulation is not possible without local populations occasionally becoming large and hence being affected by density dependence. But it is possible to construct examples in which a metapopulation persists for a long time with a low incidence of density dependence, in which cases local populations typically have very short expected lifetimes. We demonstrate that, paradoxically, a persisting metapopulation may consist of only 'sink' populations (negative average growth rate in the absence of migration). Contrary to some previous suggestions, increasing migration rate generally increases density dependence in persisting metapopulations.

Random walks in a metapopulation : how much density dependence is necessary for long-term persistence ?

. 1. The augmentative release of Trichogranznza species for the biological control of graminaceous stalkborers is reviewed.



2. Previous experiments indicate strong density dependence acting on the early larval stages of the sorghum stalkborer (Chilo partellus). These data are described by a simple model for density dependence, whose properties are briefly described.



3. The effects upon the total mortality of different levels of egg parasitism are discussed when combined with density dependent larval losses that vary from under- to over-compensating.

Density dependence and the augmentative release of egg parasitoids against graminaceous stalk borers

Two or more species cannot coexist on a single limiting resource in a constant environment unless each species can increase when rare. In this paper, we show, theoretically and empirically, how trade-offs in life history characters have the potential to mitigate the effects of interspecific competition and promote persistence in a host–multiparasitoid interaction. Theoretically, we show how niche partitioning between competing parasitoids can arise through differences in resource breadth and utilization. We demonstrate, empirically, how trade-offs between parasitoid larval competitive ability and wasp life history characters (adult wasp longevity and the ability to paralyze hosts) can be mediated. Differences, not only in the mean, but also in the variance of these life history traits can influence the outcome of competition, and we discuss how species life history trade-offs can promote species coexistence.

Michael P. Hassell

Papers

Parasitoid-mediated effects: Apparent competition and the persistence of host-parasitoid assemblages

Relative movement patterns of a tephritid fly and its parasitoid wasps

Random walks in a metapopulation : how much density dependence is necessary for long-term persistence ?

Density dependence and the augmentative release of egg parasitoids against graminaceous stalk borers

Ecological trade-offs, resource partitioning, and coexistence in a host–parasitoid assemblage