Population persistence time under intermittent control in stochastic environments

If there exists a critical population size above which environmental degradation becomes serious, the population should be suppressed or reduced upon reaching that level. Since population size control is accompanied by costs, a reduction in control frequency may be preferable from an economic viewpoint. Although this can be realized by decreasing the population size drastically in each control, such management may result in increased population extinction probability according to environmental stochasticity. The effects of population management on both mean population persistence time and management cost were analyzed theoretically using a diffusion process. The model showed the functional forms of both mean persistence time and control frequency explicitly; these decreased with an increasing number of individuals removed from the population in each control operation. Based on the analysis, indices representing management costs are proposed. Mean persistence time is generally an increasing function of the cost indices. Nevertheless, if the cost of each control increases with the number of individuals removed, even the most conservative management practice (continuous control) may not be overly expensive.     

Spatial network structure and amphibian persistence in stochastic environments

In the past few years, the framework of complex networks has provided new insight into the organization and function of biological systems. However, in spite of its potential, spatial ecology has not yet fully incorporated tools and concepts from network theory. In the present study, we identify a large spatial network of temporary ponds, which are used as breeding sites by several amphibian species. We investigate how the structural properties of the spatial network change as a function of the amphibian dispersal distance and the hydric conditions. Our measures of network topology suggest that the observed spatial structure of ponds is robust to drought (compared with similar random structures), allowing the movement of amphibians to and between flooded ponds, and hence, increasing the probability of reproduction even in dry seasons.     

Species persistence decreases with habitat fragmentation: an analysis in periodic stochastic environments

This paper presents a study of a nonlinear reaction–diffusion population model in fragmented environments. The model is set on , with periodic heterogeneous coefficients obtained using stochastic processes. Using a criterion of species persistence based on the notion of principal eigenvalue of an elliptic operator, we provided a precise numerical analysis of the interactions between habitat fragmentation and species persistence. The obtained results clearly indicated that species persistence strongly tends to decrease with habitat fragmentation. Moreover, comparing two stochastic models of landscape pattern generation, we observed that in addition to local fragmentation, a more global effect of the position of the habitat patches also influenced species persistence.      

Persistence,extinction, and critical patch number for island populations

Sufficient conditions are derived for persistence and extinction of a population inhabiting several islands. Discrete reaction-diffusion population models are analyzed which describe growth and diffusion of a population on a group of islands or a patch environment. A critical patch number is defined as the number of islands below which the population goes extinct on that group of islands. It is shown that population persistence on one island leads to population persistence for the entire archipelago. Both single-species and multi-species models are discussed.     

A theory of stochastic harvesting in stochastic environments

We investigate how model populations respond to stochastic harvesting in a stochastic environment. In particular, we show that the effects of variable harvesting on the variance in population density and yield depend critically on the autocorrelation of environmental noise and on whether the endogenous dynamics of the population display over- or undercompensation to density. These factors interact in complicated ways; harvesting shifts the slope of the renewal function, and the net effect of this shift will depend on the sign and magnitude of the other influences. For example, when environmental noise exhibits a positive autocorrelation, the relative importance of a variable harvest to the variance in density increases with overcompensation but decreases with undercompensation. For a fixed harvesting level, an increasing level of autocorrelation in environmental noise will decrease the relative variation in population density when overcompensation would otherwise occur. These and other intricate interactions have important ramifications for the interpretation of time series data when no prior knowledge of demographic or environmental details exists. These effects are important whenever the harvesting rate is sufficiently high or variable, conditions likely to occur in many systems, whether the harvesting is caused by commercial exploitation or by any other strong agent of density-independent mortality.     

On the definition and the computation of the type-reproduction number T for structured populations in heterogeneous environments

In the context of mathematical epidemiology, the type-reproduction number (TRN) for a specific host type is interpreted as the average number of secondary cases of that type produced by the primary cases of the same host type during the entire course of infection. Here, it must be noted that T takes into account not only the secondary cases directly transmitted from the specific host but also the cases indirectly transmitted by way of other types, who were infected from the primary cases of the specific host with no intermediate cases of the target host. Roberts and Heesterbeek (Proc R Soc Lond B 270:1359–1364, 2003) have shown that T is a useful measure when a particular single host type is targeted in the disease control effort in a community with various types of host, based on the fact that the sign relation sign(R ₀ ? 1) = sign(T ? 1) holds between the basic reproduction number R ₀ and T. In fact, T can be seen as an extension of R ₀ in a sense that the threshold condition of the total population growth can be formulated by the reproduction process of the target type only. However, the original formulation is limited to populations with discrete state space in constant environments. In this paper, based on a new perspective of R ₀ in heterogeneous environments (Inaba in J Math Biol 2011), we give a general definition of the TRN for continuously structured populations in heterogeneous environments and show some examples of its computation and applications.     

Bacterial persistence: a model of survival in changing environments

The persistence phenotype is an epigenetic trait exhibited by a subpopulation of bacteria, characterized by slow growth coupled with an ability to survive antibiotic treatment. The phenotype is acquired via a spontaneous, reversible switch between normal and persister cells. These observations suggest that clonal bacterial populations may use persister cells, whose slow division rate under growth conditions leads to lower population fitness, as an "insurance policy" against antibiotic encounters. We present a model of Escherichia coli persistence, and using experimentally derived parameters for both wild type and a mutant strain (hipQ) with markedly different switching rates, we show how fitness loss due to slow persister growth pays off as a risk-reducing strategy. We demonstrate that wild-type persistence is suited for environments in which antibiotic stress is a rare event. The optimal rate of switching between normal and persister cells is found to depend strongly on the frequency of environmental changes and only weakly on the selective pressures of any given environment. In contrast to typical examples of adaptations to features of a single environment, persistence appears to constitute an adaptation that is tuned to the distribution of environmental change.     

Conserving extirpated sites: using habitat quality to manage unoccupied patches for metapopulation persistence

Conservation of metapopulations requires managing extirpated sites, particularly with current threats of increased fragmentation and displacement from global warming. Determining the habitat requirements of threatened species and how they relate to defining characteristics of occupied and unoccupied sites is key to managing suitable habitat in extirpated patches. Due to habitat destruction and degradation, the endangered Ohlone tiger beetle (Cicindela ohlone) is found in only five sites of a once more extensive metapopulation in Santa Cruz County, California. To determine the role of habitat quality in classifying sites, I measured vegetation and ground cover as well as plant and soil composition in sites in which C. ohlone are present, extirpated, and absent. I used conditional inference trees to determine what habitat factors significantly predicted the different sites types. I also analyzed habitat characteristics within present sites to determine factors that predicted egg-laying habitat. As isolation has been shown to be an important driver of metapopulation patch extirpation, I tested the spatial autocorrelation of C. ohlone occupancy to determine if extirpated patches were significantly isolated. Habitat characteristics successfully differentiated nearly 90 % of extirpated plots, which were not isolated from occupied sites. Sites in which C. ohlone are currently present were classified as having at least 10 % cover of bare ground, high forb cover, low litter cover and depth, and high soil bulk density, characteristics that extirpated sites lacked. I illustrate how the defining characteristics could be used to manage habitat in extirpated and absents sites for potential recolonization or translocation, which is vital for metapopulation persistence.     

Invasion speeds for structured populations in fluctuating environments

We live in a time where climate models predict future increases in environmental variability and biological invasions are becoming increasingly frequent. A key to developing effective responses to biological invasions in increasingly variable environments will be estimates of their rates of spatial spread and the associated uncertainty of these estimates. Using stochastic, stage-structured, integrodifference equation models, we show analytically that invasion speeds are asymptotically normally distributed with a variance that decreases in time. We apply our methods to a simple juvenile–adult model with stochastic variation in reproduction and an illustrative example with published data for the perennial herb, Calathea ovandensis. These examples buttressed by additional analysis reveal that increased variability in vital rates simultaneously slow down invasions yet generate greater uncertainty about rates of spatial spread. Moreover, while temporal autocorrelations in vital rates inflate variability in invasion speeds, the effect of these autocorrelations on the average invasion speed can be positive or negative depending on life history traits and how well vital rates “remember” the past.     

Persistence in fluctuating environments for interacting structured populations

Individuals within any species exhibit differences in size, developmental state, or spatial location. These differences coupled with environmental fluctuations in demographic rates can have subtle effects on population persistence and species coexistence. To understand these effects, we provide a general theory for coexistence of structured, interacting species living in a stochastic environment. The theory is applicable to nonlinear, multi species matrix models with stochastically varying parameters. The theory relies on long-term growth rates of species corresponding to the dominant Lyapunov exponents of random matrix products. Our coexistence criterion requires that a convex combination of these long-term growth rates is positive with probability one whenever one or more species are at low density. When this condition holds, the community is stochastically persistent: the fraction of time that a species density goes below \(\delta >0\) approaches zero as \(\delta \) approaches zero. Applications to predator-prey interactions in an autocorrelated environment, a stochastic LPA model, and spatial lottery models are provided. These applications demonstrate that positive autocorrelations in temporal fluctuations can disrupt predator-prey coexistence, fluctuations in log-fecundity can facilitate persistence in structured populations, and long-lived, relatively sedentary competing populations are likely to coexist in spatially and temporally heterogenous environments.     

Horn growth in male pronghornsAntilocapra americana: selection for precocialmaturation in stochastic environments

PronghornsAntilocapra americana (Ord, 1818), the sole member of a family unique to North America, grow rapidly and reproduce at an early age. Recent studies have found male pronghorns can grow large horns by 2 to 3 yrs of age. This pattern contrasts with many other ungulates, and it has profound implications for life history strategies. We examine 5 hypotheses that might explain precocial horn growth: (1) sampling bias, (2) nutrition, (3) phylogenetic inertia, (4) reproductive benefits conveyed by rapid horn growth alone, and (5) rapid horn growth as part of a suite of characteristics acquired due to precocial maturation. Hypotheses 1, 2 and 3 do not imply any natural selection, whereas hypotheses 4 and 5 do. We reject hypotheses 1, 2 and 4, and we cannot evaluate hypothesis 3. We conclude that hypothesis 5 most likely explains precocial maturation in male pronghorns, and mortality related to frequent, severe weather events may drive this pattern. We suggest several experiments to further examine relationships between age, size, and horn growth.     

Allee effects in stochastic populations

The Allee effect, or inverse density dependence at low population sizes, could seriously impact preservation and management of biological populations. The mounting evidence for widespread Allee effects has lately inspired theoretical studies of how Allee effects alter population dynamics. However, the recent mathematical models of Allee effects have been missing another important force prevalent at low population sizes: stochasticity. In this paper, the combination of Allee effects and stochasticity is studied using diffusion processes, a type of general stochastic population model that accommodates both demographic and environmental stochastic fluctuations. Including an Allee effect in a conventional deterministic population model typically produces an unstable equilibrium at a low population size, a critical population level below which extinction is certain. In a stochastic version of such a model, the probability of reaching a lower size a before reaching an upper size b , when considered as a function of initial population size, has an inflection point at the underlying deterministic unstable equilibrium. The inflection point represents a threshold in the probabilistic prospects for the population and is independent of the type of stochastic fluctuations in the model. In particular, models containing demographic noise alone (absent Allee effects) do not display this threshold behavior, even though demographic noise is considered an "extinction vortex". The results in this paper provide a new understanding of the interplay of stochastic and deterministic forces in ecological populations.     

Some stochastic models for plasmid copy number

Some stochastic models for the copy number of plasmids in a cell line are studied. When considering the behavior of copy number in the whole cell line, the theory of multitype branching processes is appropriate. Attention is paid to the cure rate in the cell line, and the asymptotic fractions of cells containing a given number of plasmids. These quantities are used to compare the models numerically.     

Biodiversity and persistence of ecological communities in variable environments

Recent analyses of climate data indicate that the intensity and frequency of different weather extremes have increased. Such increased environmental variability may lead to increased species extinction rates and hence have important consequences for the long-term persistence of ecological communities. Here we use model communities in order to investigate the relationship between species richness and community persistence in a fluctuating environment. We model two scenarios: (1) correlated species responses to environmental fluctuations and (2) uncorrelated (independent) species responses. We quantify the risk and extent of species extinctions using the so-called community viability analysis. It is shown that species-rich communities are more sensitive to environmental stochasticity than species-poor communities. Specifically, per species risk of extinction is higher in species-rich communities than in species-poor ones. Moreover, for a given species richness, communities with uncorrelated species responses to environmental variation run a considerable higher risk of losing a fixed proportion of species compared with communities with correlated species responses. We discuss the compatibility of these results with the ecological insurance hypothesis.     

Propagule pressure and persistence in experimental populations

Average inoculum size and number of introductions are known to have positive effects on population persistence. However, whether these factors affect persistence independently or interact is unknown. We conducted a two-factor experiment in which 112 populations of parthenogenetic Daphnia magna were maintained for 41 days to study effects of inoculum size and introduction frequency on: (i) population growth, (ii) population persistence and (iii) time-to-extinction. We found that the interaction of inoculum size and introduction frequency-the immigration rate-affected all three dependent variables, while population growth was additionally affected by introduction frequency. We conclude that for this system the most important aspect of propagule pressure is immigration rate, with relatively minor additional effects of introduction frequency and negligible effects of inoculum size.