Metapopulation moments: coupling, stochasticity and persistence

1.  Spatial heterogeneity has long been viewed as a reliable means of increasing persistence. Here, an analytical model is developed to consider the variation and, hence, the persistence of stochastic metapopulations. This model relies on a novel moment closure technique, which is equivalent to assuming log-normal distributions for the population sizes.
2.  Single-species models show the greatest persistence when the mixing between subpopulations is large, so spatial heterogeneity is of no benefit. This result is confirmed by stochastic simulation of the full metapopulation.
3.  In contrast, natural-enemy models exhibit the greatest persistence for intermediate levels of coupling. When the coupling is too low, there are insufficient rescue effects between the subpopulations to sustain the dynamics, whereas when the coupling is too high all spatial heterogeneity is lost.
4.  The difference in behaviour between the one- and two-species models can be attributed to the oscillatory nature of the natural-enemy system.     

Reproductive ecology and the persistence of an endangered plant

Amsinckia grandiflora (large-flowered fiddleneck)is an extremely rare California annual wildflower, known only from threepopulations. We conducted field and greenhouse experiments to compare the rareheterostyle with a cryptic self-incompatibility system (A.grandiflora) to a common, self-compatible, homostylous, sympatriccongener (A. tessellata). Inter-species comparisons ofadult plants suggested that in the greenhouse, A.grandiflora balances low floral seed set (seeds per flower) withincreased floral output (flowers/plant) and a greater number of flowers perinflorescence. Seed set from active self-, intra- and inter-morph pollinationswas high in A. grandiflora, indicating that the crypticself-incompatibility system does not prevent seed set in the species. In thefield, A. grandiflora floral output was only slightlygreater than for A. tessellata, and did not fully balance lowerfloral seed set. Amsinckia tessellata average seed weightwas lower than that of A. grandiflora, which, along with the lowernumber of flowers produced, indicated lower maternal investment per nutlet thanfor A. grandiflora. Under conditions of unlimited resources, itappears that A. grandiflora fitness is not intrinsicallylimited when compared to its weedy relative A. tessellata.The differences in nutlet output between A. grandiflora andA. tessellata under field conditions are more likely due todifferential responses to extrinsic factors such as competition and pollinatoravailability.     

The tortoise and the hare: ecology of angiosperm dominance and gymnosperm persistence

Gymnosperms, and conifers in particular, are sometimes very productive trees yet angiosperms dominate most temperate and tropical vegetation. Current explanations for angiosperm success emphasize the advantages of insect pollination and seed dispersal by animals for the colonization of isolated habitats. Differences between gymnosperm and angiosperm reproductive and vegetative growth rates have been largely ignored. Gymnosperms are all woody, perennial and usually have long reproductive cycles. Their leaves are not as fully vascularized as those of angiosperms and are more stereotyped in shape and size. Gymnosperm tracheids are generally more resistant to solute flow than angiosperm vessels. A consequence of the less efficient transport system is that maximum growth rates of gymnosperms are lower than maximum growth rates of angiosperms in well lit, well watered habitats. Gymnosperm seedlings may be particularly uncompetitive since their growth depends on a single cohort of relatively inefficient leaves. Later, some gymnosperms attain a higher productivity than co-occurring angiosperm trees by accumulating several cohorts of leaves with a higher total leaf area. These functional constraints on gymnosperm growth rates suggest that gymnosperms will be restricted to areas where growth of angiosperm competitors is reduced, for example, by cold or nutrient shortages. Biogeographic evidence supports this prediction since conifers are largely confined to high latitudes and elevations or nutrient-poor soils. Experimental studies show that competition in the regeneration niche (between conifer seedlings and angiosperm herbs and shrubs) is common and significantly affects conifer growth and survival, Fast-growing angiosperms, especially herbs and shrubs, may also change the frequency of disturbance regimes thereby excluding slower-growing gymnosperms. Shade-tolerant and early successional conifers share similar characteristics of slow initial growth and low plasticity to a change in resources. Shade-tolerant gymnosperms would be expected to occur only where forest openings are small or otherwise unsuitable for rapid filling by fast-growing angiosperm trees, lianas or shrubs. The limited evidence available suggests that shade-tolerant conifers are confined to forests with small gap sizes where large disturbances are very rare. The regeneration hypothesis for gymnosperm exclusion by angiosperms is consistent with several aspects of the fossil record such as the early disappearance of gymnosperms from early successional environments where competition with angiosperms would have been most severe. However there are unresolved difficulties in interpreting process from paleoecological pattern which prevent the testing of alternative hypotheses.     

Probabilistic measures of persistence and extinction in measles (meta)populations

Persistence and extinction are fundamental processes in ecological systems that are difficult to accurately measure due to stochasticity and incomplete observation. Moreover, these processes operate on multiple scales, from individual populations to metapopulations. Here, we examine an extensive new data set of measles case reports and associated demographics in pre‐vaccine era US cities, alongside a classic England & Wales data set. We first infer the per‐population quasi‐continuous distribution of log incidence. We then use stochastic, spatially implicit metapopulation models to explore the frequency of rescue events and apparent extinctions. We show that, unlike critical community size, the inferred distributions account for observational processes, allowing direct comparisons between metapopulations. The inferred distributions scale with population size. We use these scalings to estimate extinction boundary probabilities. We compare these predictions with measurements in individual populations and random aggregates of populations, highlighting the importance of medium‐sized populations in metapopulation persistence.     

Individuals,populations and the balance of nature: the question of persistence in ecology

Explaining the persistence of populations is an important quest in ecology, and is a modern manifestation of the balance of nature metaphor. Increasingly, however, ecologists see populations (and ecological systems generally) as not being in equilibrium or balance. The portrayal of ecological systems as “non-equilibrium” is seen as a strong alternative to deterministic or equilibrium ecology, but this approach fails to provide much theoretical or practical guidance, and warrants formalisation at a more fundamental level. This is available in adaptation theory, which allows population persistence to be explained as an epiphenomenon stemming from the maintenance, survival, movement and reproduction of individual organisms. These processes take place within a physicochemical and biotic environment that persists through structured annual cycles, but which is also spatiotemporally dynamic and subject to stochastic variation. The focus is thus shifted from the overproduction of offspring and the consequent density dependent population pressure thought to follow, to the adaptations and ecological circumstances that support those relatively few individuals that do survive.     

The ecology of conifer persistence in tropical rainforests: Podocarpus neriifolius in northern Thailand

Plant Ecology - A range of hypotheses seek to explain why conifers are infrequent in tropical rainforests. Here, we explore how the conifer, Podocarpus neriifolius, persists at low density in...     

Boundedness,persistence and stability for classes of forced difference equations arising in population ecology

Journal of Mathematical Biology - Boundedness, persistence and stability properties are considered for a class of nonlinear, possibly infinite-dimensional, forced difference equations which arise...     

Trophic ecology and persistence of invasive silver carp Hypophthalmichthys molitrix in an oligotrophic South African impoundment

The alien invasive silver carp Hypophthalmichthys molitrix established a self-sustaining feral population in an oligotrophic impoundment, Flag Boshielo Dam, in South Africa. The ability of this population to persist in a dam with low algal biomass (median annual suspended chlorophyll a = 0.08 µg l^?1), and limited access to rivers considered large enough for successful spawning, has implications for their invasive potential in other systems. Stomach content and stable isotope analysis were used to assess the trophic ecology of H. molitrix, which was then compared with indigenous Mozambique tilapia Oreochromis mossambicus, on a seasonal basis during 2011. Hypophthalmichthys molitrix are generalist filter feeders, with a diet consisting primarily of sediment, vegetative detritus, dinoflagellates and diatoms. The dominance of sediments in their stomachs suggests occasional benthic scavenging. However, H. molitrix occupied a higher trophic level (TL = 2.8) than expected, suggesting that this population subsidised their diet with an unidentified dietary constituent, characterised by enriched nitrogen values. Although the stomach contents indicated dietary overlap between H. molitrix and O. mossambicus, stable isotopes revealed fine-scale resource partitioning, despite both species occupying the same trophic level. Nonetheless, the persistence of this feral H. molitrix population in an oligotrophic impoundment highlights their phenotypic plasticity.     

On the use of measures of structure and diversity in applied diatom ecology

Water managers ask for simple ecological indices as a tool for measuring the effectiveness of their activities. Diversity indices are often used as such tools. The concept of diversity is closely related to the nature of species-abundance distributions. There is empirical and theoretical evidence that diatom-assemblages have a species-abundance distribution of log-series type. Then the most appropriate diversity index is the dominance,i.e. the relative abundance of the commonest species. The number of species in a sample of fixed size of the assemblage is a useful additional index. It appears from some examples that these indices have no consistent relationships with the degree of water pollution. This in contrast to the species composition of the assemblages. (Complete paper published in: HAKANSSON, H. and J.GERLOFF, Eds., (1982). Festschrift Niels Foged. Diatomaceae III. Beiheft zur Nova Hedwigia     

PhyloMeasures: a package for computing phylogenetic biodiversity measures and their statistical moments

We present PhyloMeasures, a new software package including both a C++ and R version, that provides very fast computation of popular phylogenetic diversity measures. PhyloMeasures introduces two major advances over existing methods. First, it uses efficient algorithms for calculating basic phylogenetic metrics (such as Faith's PD and the mean pairwise distance, MPD) and two‐sample measures (such as common branch length, CBL, and the unique fraction) that are designed to perform well even on very large trees. Second, it computes exact richness‐standardised versions of these measures (such as the widely used net relatedness index, NRI) by efficiently evaluating analytical expressions for the mean and variance of the basic measures, rather than by the slow and inexact randomization techniques that are the current standard. Together, these lead to massive improvements in performance compared to the current state of the art. For example, running on a standard laptop, PhyloMeasures functions can provide the NRI for 20 samples from a tree of 100 000 tips in about 1.5 s, compared to an estimated 37 d using standard resampling approaches. This will allow analyses on larger data sets than were previously possible.     

Paradoxical persistence through mixed-system dynamics: towards a unified perspective of reversal behaviours in evolutionary ecology

Counterintuitive dynamics of various biological phenomena occur when composite system dynamics differ qualitatively from that of their component systems. Such composite systems typically arise when modelling situations with time-varying biotic or abiotic conditions, and examples range from metapopulation dynamics to population genetic models. These biological, and related physical, phenomena can often be modelled as simple financial games, wherein capital is gained and lost through gambling. Such games have been developed and used as heuristic devices to elucidate the processes at work in generating seemingly paradoxical outcomes across a spectrum of disciplines, albeit in a field-specific, ad hoc fashion. Here, we propose that studying these simple games can provide a much deeper understanding of the fundamental principles governing paradoxical behaviours in models from a diversity of topics in evolution and ecology in which fluctuating environmental effects, whether deterministic or stochastic, are an essential aspect of the phenomenon of interest. Of particular note, we find that, for a broad class of models, the ecological concept of equilibrium reactivity provides an intuitive necessary condition that must be satisfied in order for environmental variability to promote population persistence. We contend that further investigations along these lines promise to unify aspects of the study of a range of topics, bringing questions from genetics, species persistence and coexistence and the evolution of bet-hedging strategies, under a common theoretical purview.     

Semi-linear stochastic models: Computation of moments and conditional moments

In this article we show how linearity with respect to the output of a stochastic dynamic model can be exploited in order to simplify the computation of moments or conditional moments. The results are presented for two examples, one of which includes delays. This feature is often encountered in biological models.     

Multiplicative genetic effects in scrapie disease susceptibility

Despite experimental evidence that scrapie is an infectious disease of sheep, variations of the occurrence of the natural disease suggest an influence of host genetic factors. It has been established that the genetic polymorphism of the prion protein (PrP) gene is correlated to the incidence of scrapie and to the survival time: five polymorphisms have been described by variations at amino-acid codons 136, 154 and 171. In this paper we study the effect on scrapie susceptibility of the pairing of the five allelic variants known to exist: we show that scrapie susceptibility is given by the produce of the elementary allelic factors. This first well-documented evidence of a multiplicative property of genetic risk factors could give hints on the underlying mechanisms of prion-induced neurodegenerative diseases.