Instability and complex dynamic behaviour in population models with long time delays

Some of the properties of the delay-differential equation $\text{dX(t)}\text{dt}\text{= R(X(t ? τ)) ? D(X(t))}$, where R and D represent the rates of recruitment to, and death from, an adult population of size X, with maturation period τ are examined. The biological constraints upon these recruitment and death functions are specified, and they are used to establish results on stability, boundedness, and persistent fluctuations of limit cycle type. The relationship between models based on delay-differential and difference equations is then explored, and it is shown how well-established results on period-doubling and chaotic behaviour in the latter can yield insight into the qualitative dynamics of the former. Using numerical studies of two population models with differing forms of recruitment function, we show how, by making use of our results, it is possible to simplify the analysis of delay-differential equation population models.     

Continued use of soft‐metal bands on gulls in North America reduces the value of recovery data

Use of soft‐metal (aluminum alloy) bands on gulls (Laridae) is known to result in high rates of band loss and, as a result, hard‐metal (monel, incoloy, or stainless steel) bands are superior for most studies. However, the U.S. Bird Banding Laboratory (BBL) and the Canadian Wildlife Service Bird Banding Office continue to issue soft bands for use on gulls, and the BBL does not make specific recommendations about use of hard bands so many banders continue to use soft bands. For wholly marine species of gulls banded in North America since 1996, ～20% have been banded with soft bands; the proportion of soft bands used on partially freshwater gulls was ～70% up to 2009, but has since fallen to 40%. Using hierarchical Bayesian models in program MARK, we analyzed recovery data for three gull species and found that estimates of annual survival rates derived from soft bands (0.68–0.81) were lower than those derived from hard bands (0.85–0.96). Comparison of survival rates of Herring Gulls (Larus argentatus) in the Great Lakes basin and on the Atlantic coast provided no evidence that soft bands last longer in freshwater than saltwater. Band loss compromises many types of studies, including those assessing the possible effects of climate change. We recommend that use of soft bands on gulls be discontinued, and that banders be required to use hard bands on these species in the future. The same consideration applies to other long‐lived species, including some waterfowl and all albatrosses, pelicans, cormorants, shearwaters, petrels, terns, shorebirds, and alcids. Use of hard bands should be based on expectations about a species’ longevity and evidence of band wear, rather than on whether or not it occurs in saltwater.     

The geological setting of the earliest life forms

Summary Life on Earth may have begun about 4×10⁹ years (4 Ga) ago. Plate tectonics probably operated in the early Archaean, with rapid spreading at mid-ocean ridges, a komatiitic (magnesium-rich) oceanic crust, active volcanic arcs and the development of extensional basins on continental crust. Shallow water environments would have been more restricted and probably shorter-lived than in later geological times; however, extensive shallow seas existed in the later phases of the development of extensional basins. Bacterial communities-presumably photosynthetic-have probably existed in such shallow-water settings and probably at shallow depths in the oceans for at least 3.5 Ga. Because the mid-ocean ridges were probably subaqueous, hydrothermal systems would have been very vigorous and would have offered suitable habitats for early chemo-autotrophic bacterial communities. Early life forms probably also occupied vesicles in lavas, pumice and volcanic breccias, and pores in soft sediments, living in the constant flux of fluid flushing through permeable strata. Other, similar habitats would have existed in volcanic island arcs and in extensional basins.     

Departures from neutrality induced by niche and relative fitness differences

Breaking the core assumption of ecological equivalence in Hubbell’s “neutral theory of biodiversity” requires a theory of species differences. In one framework for characterizing differences between competing species, non-neutral interactions are said to involve both niche differences, which promote stable coexistence, and relative fitness differences, which promote competitive exclusion. We include both in a stochastic community model in order to determine if relative fitness differences compensate for changes in community structure and dynamics induced by niche differences, possibly explaining neutral theory’s apparent success. We show that species abundance distributions are sensitive to both niche and relative fitness differences, but that certain combinations of differences result in abundance distributions that are indistinguishable from the neutral case. In contrast, the distribution of species’ lifetimes, or the time between speciation and extinction, differs under all combinations of niche and relative fitness differences. The results from our model experiment are inconsistent with the hypothesis of “emergent neutrality” and support instead a hypothesis that relative fitness differences counteract effects of niche differences on distributions of abundance. However, an even more developed theory of interspecific variation appears necessary to explain the diversity and structure of non-neutral communities.