A simple time-delay model of laboratory insect populations which postulates a ‘humped’ relationship between future adult recruitment and current adult population gives good quantitative agreement with Nicholson's classic blowfly data and explains the appearance of narrow ‘discrete’ generations in cycling populations
A wide variety of organisms inhabit streams, rivers, and estuaries where they are continually subjected to downstream drift. It is well known that when this is the only transport process, extinction is inevitable (the ''drift paradox''). Using a series of analytical and numerical models, representing a range of hydrodynamic scenarios, we demonstrate that the action of diffusive dispersal can permit persistence in an advective environment. The mechanism underlying this phenomenon is that diffusive dispersal can allow a proportion of the population to reproduce close to their natal location. For well-and poorly mixed non-tidal systems we establish approximate analytic conditions for diffusionmediated persistence both throughout the water column and in a benthic boundary layer. Although tidal forcing results in residual landward flow near the base of the water column, we find that this has little effect on persistence, which is respectably approximated by our analytic results. We apply these analytic results to four hydrodynamically disparate systems: a stream (Broadstone Stream [UK]), a river (Christiana Creek [USA]), a shallow estuary (Ythan [UK]) and a deep fast-flowing estuary (Saco River [USA]). Using parameters derived from published studies we examine the persistence of a number of real and hypothetical organisms in these systems and identify those for which diffusively mediated persistence is a realistic possibility. We note that such persistence is only likely when advection is low or horizontal dispersal is high.
Ecological theory predicts that stable populations should yield to large-amplitude cycles in richer environments1±3. This does not occur in nature. The zooplankton Daphnia and its algal prey in lakes throughout the world illustrate the problem4±6. Experiments show that this system its the theory's assumptions7±9, yet it is not destabilized by enrichment 6. We have tested and rejected four of ive proposed explanations 10. Here, we investigate the fifth mechanism: inedible algae in nutrient-rich lakes suppress cycles by reducing nutrients available to edible algae. We found three novel results in nutrient-rich microcosms from which inedible algae were excluded. First, as predicted by theory, some Daphniaedible algal systems now display large-amplitude predator-prey cycles. Second, in the same environment, other populations are stable, showing only small-amplitude demographic cycles. Stability is induced when Daphnia diverts energy from the immediate production of young. Third, the system exhibits coexisting attractors -a stable equilibrium and large-amplitude cycle. We describe a mechanism that flips the system between these two states
(1) We develop a mathematically rigorous approach to modelling the effects of age structure, in which the life-history of a species is divided into age classes of arbitrary duration and attention is focused on the sub-populations of the various classes. (2) By assuming that all individuals in a particular age class have the same birth and death rates (which may be time-and density-dependent), we reduce the normal integro-differential equations describing an age-structured population with overlapping generations to a set of coupled ordinary delay-differential equations which are readily integrated numerically. (3) We illustrate the use of the formalism in the construction and analysis of two models of laboratory insect populations: a detailed model of Nicholson's blowflies and a 'strategic' model of larval competition intended to refine the design of experiments in progress on the dynamics of the Indian meal-moth Plodia interpunctella (Hiibner). (4) The model of Nicholson's blowflies is dynamically identical to a model previously derived heuristically. We have fitted the parameters using a more comprehensive range of data, and have illustrated explicitly the passage of large, quasi-cyclic fluctuations through the age structure. (5) We use the larval competition model to distinguish the effects of 'uniform competition' (all larvae competing) and 'cohort competition' (larvae of a given age competing). The former can produce quasi-cycles of a type characteristic of delayed regulation, while the latter causes quasi-cycles consisting of 'bursts' of population propagating through the age structure. (6) We also use the larval competition model to demonstrate that apparently minor changes in the description of adult survival can induce dramatic alterations in model behaviour. This supports our emphasis on rigour in the formulation of the model, so as to distinguish genuinely interesting dynamics from mathematical artifacts. INTRODUCTION Age structure effects are widely believed to be of crucial importance in determining the stability properties of many natural populations, but are almost equally widely neglected in theoretical studies. The reasons for this neglect appear to lie in the technical deficiencies of the various methods presently used to formulate age-structure models. The continuous time description due to Sharpe & Lotka (1911) and von Foerster (1959), while both elegant and rigorous, presents mathematical difficulties severe enough to deter all but the most intrepid and dextrous analyst. The Leslie matrix approach, although less technically demanding,
1. Emergence and inland dispersal of adult stoneflies (Plecoptera) and caddisflies (Trichoptera) from Broadstone Stream, an acidic and iron‐rich stream in southern England, were studied over 10 months in 1996–1997. Fifteen pyramidal emergence traps were placed randomly in a 200‐m stretch. Three Malaise traps were placed above the stream and six more on each side (one wooded, one open) along a transect at distances of 1, 15, 30, 45, 60 and 75 m from the channel. 2. More than 16 000 stoneflies, belonging to 11 species, and just under 400 caddisflies (22 species) were caught. Four dominant stoneflies (Leuctra fusca, Leuctra nigra, Leuctra hippopus and Nemurella pictetii) accounted for 96% and 95% of the catches in the emergence and Malaise traps, respectively. Two caddisflies (Plectrocnemia conspersa and Potamophylax cingulatus) accounted for 63% of the catch in the Malaise traps. Few caddisflies were taken in emergence traps. 3. The emergence periods of L. fusca, L. nigra and L. hippopus were well‐defined and unimodal, whereas that of N. pictetii was prolonged and erratic. Overall, more females (1285) emerged than males (740). 4. Female stoneflies and caddisflies were in the majority in the Malaise traps above the stream. On land, significantly more females than males of L. fusca, L. nigra and P. cingulatus were caught. The sex ratio of the remaining species did not deviate significantly from 1:1. 5. The three Malaise traps placed above the stream caught most of the stoneflies though there was also dispersal away from the channel, the numbers caught declining with distance. Exponential models explained between 67% and 99% of the variation in numbers of individuals with distance from the channel in the four common stoneflies. Half the individuals went less than 11–16 m from the stream, while 90% travelled less than 51 m. Significantly more L. nigra and N. pictetii were caught in the woodland than on the open side, whereas L. hippopus showed no overall preference for either side.
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