Insights into population ecology from long-term studies of red grouse Lagopus lagopus scoticus.

Long-term studies have been the backbone of population ecology. The red grouse Lagopus lagopus scoticus is one species that has contributed widely to this field since the 1950s. This paper reviews the trajectory and profound impact that these studies have had. Red grouse research has combined long-term studies of marked individuals with demographic studies over wide geographical areas and replicated individual- and population-level manipulations. A main focus has been on understanding the causes of population cycles in red grouse, and in particular the relative importance of intrinsic (behaviour) and extrinsic (climate, food limitation and parasite) mechanisms. Separate studies conducted in different regions initially proposed either the nematode parasite Trichostrongylus tenuis or changes in male aggressiveness in autumn as drivers of population cycles. More recent experiments suggest that parasites are not a necessary cause for cycles and have highlighted that behavioural and parasite-mediated mechanisms are interrelated. Long-term experiments show that parasites and aggressiveness interact. Two outstanding questions remain to be tested experimentally. First, what intrinsic mechanism causes temporal variation in patterns of male aggressiveness? The current favoured mechanism is related to patterns of kin structuring although there are alternative hypotheses. Second, how do the dual, interacting mechanisms, affect population dynamics? Red grouse studies have had an important impact on the field of population ecology, in particular through highlighting: (1) the impact of parasites on populations; (2) the role of intrinsic mechanisms in cyclic dynamics and (3) the need to consider multiple, interacting mechanisms.

Abundance of stable periodic behavior in a Red Grouse population model with delay: a consequence of homoclinicity.

Shrimp-shaped periodic regions embedded in chaotic regions in two-dimensional parameter spaces are of specific interest for physical and biological systems. We provide the first observation of these shrimp-shaped stability regions in a parameter space of a continuous time-delayed population model, obtained by taking the delays as bifurcation parameters. The parameter space organization is governed by the presence of infinitely many periodicity hubs, which trigger the spiraling organization of these shrimp-shaped periodic regions around them. We provide evidence that this spiraling organization in the parameter space is a consequence of the existence of homoclinic orbits in the phase space.

To age, to die: parity, evolutionary tracking and Cole's paradox.

The existence of semelparity or "big bang" reproduction (reproducing only once in a lifetime) and iteroparity (reproducing more than once in a lifetime) has led to many questions investigating the evolution or persistence of these strategies. Here we investigate semelparity and iteroparity for their evolutionary importance. A mathematical model is used to illustrate how a population's ability to evolve depends on this life-history trait, and how this rate of evolution impacts the individual. We find that the ability of a trait to evolve is greater toward a semelparous strategy and this expresses a fitness advantage. This leads to an optimality between survival, population tracking ability, and lifetime fecundity.

The evolution of stability in a competitive system.

The characteristics governing the dynamics of populations can evolve and this evolution can either be towards stability or chaos. Yet it is not obvious how or why such population characteristics can evolve through selection on individuals. In this paper we construct a mathematical model, inspired by experimental results, illustrating the dynamics of a population of competing Drosophila. We demonstrate how selection of life history characteristics and stability influence one another as a population interacts with its environment. We generalize this result and show that population stability can evolve as a consequence of selection on individuals.