Convexity in projection matrices: Projection to a calibration problem

Convexity, as a fundamental property of sets and functions defined on convex sets, plays an important role in many mathematical and applied disciplines, including extremal and optimal-control problems. We prove the set of all feasible projection matrices in a general class of matrix models for stage-structured population dynamics to be convex and the dominant eigenvalue (λ₁) of any projection 2 × 2 matrix to be either a convex, or a concave function on a simplex of the matrix first-row entries (i.e., stage-specific reproduction rates). The latter is also conjectured for the general n × n case. Though looking far from practical needs of matrix population models, this mathematical result has appeared to be quite useful in solving a practical problem to calibrate the projection matrix, i.e., to estimate all the stage-specific vital rates, from empirical data. The data from monitoring of individual life histories of marked plants on permanent sample plots during successive years enable direct calculation of the stage-specific survival and ontogenetic transition rates, but the rates of reproduction do remain uncertain as far as the parent plants can hardly be determined for the (not yet marked!) recruitment.     

Predation affects the susceptibility of hard clam Meretrix lusoria to Hg-stressed birnavirus

Predator–prey interaction in aquatic ecosystem is one of the simplest drivers affecting the species population dynamics. Predation controls are recognized as important aspects of ecosystem husbandry and management. In this paper we investigated how predation control cause an increase in host growth in the abundance of hard clam (Meretrix lusoria) populations subject to mercury (Hg)-stressed birnavirus. Here we linked predator–prey relationships with a bioenergetic matrix population model (MPM) associated with a susceptible–infectious–mortality (SIM) model based on a host–pathogen–predator framework to quantify the predator effects on population dynamics of disease in hard clam populations. Our results indicated that relative high predation rates could promote the hard clam abundances in relation to predators that selectively captured the infected hard clam, by which the disease transmission was suppressed. The results also demonstrated that predator-induced modifications in host behavior could have potential negative or positive effects on host growth depending on relative species density and resource dynamics. The most immediate implication of this study for the management of aquatic ecosystem is that, beyond the potential for causing a growth in abundance, predation might provoke greater predictability in aquatic ecosystem species populations and thereby increase the safety of ecosystem production from stochastic environmental events.     

Hazards, spatial transmission and timing of outbreaks in epidemic metapopulations

Highly infectious, immunizing pathogens can cause violent local outbreaks that are followed by the agent’s extinction as it runs out of susceptible hosts. For these pathogens, regional persistence can only be secured through spatial transmission and geographically asynchronous epidemics. In this paper we develop a hazard model for the waiting time between epidemics. We use the model, first, to discuss the predictability in timing of epidemics, and, second, to estimate the strength of spatial transmission. Based on the hazard model, we conclude that highly epidemic pathogens can at times be predictable in the sense that the waiting-time distribution between outbreaks is probabilistically bounded; The greater the spatial transmission the more periodic the outbreak dynamics. When we analyze the historical records of measles outbreaks in England and Wales between 1944 and 1965, we find the waiting-time between epidemics to depend inversely on community size. This is because large communities are much more tightly coupled to the regional metapopulation. The model further help identify the most important areas for spatial transmission. We conclude that the data on absence of these pathogens is the key to understanding spatial spread.     

A Comprehensive Approach to Identifying Monitoring Priorities of Small Landbirds on Military Installations

Military installations provide important native habitat for songbirds, including many species that have experienced population declines in recent decades. As part of the Land Condition Trend Analysis (LCTA) program to monitor animal populations on military lands, we surveyed small (<250 g) breeding landbirds on 60 permanent plots on the Fort Riley Military Installation in northeastern Kansas from 1991 to 2002. During this period, species richness averaged 39.0 species (SE 0.9)/year and mean species richness per plot ranged from 3.6 species (SE=0.2)/plot (1999) to 7.5 species (SE=0.3)/plot (1992). Turnover (the appearance and disappearance of species on all plots from one year to the next) ranged from 5 species (2000–2001) to 16 species (1992–1993) and was driven primarily by turnover of woodland species. We developed an index of relative difference (C) to evaluate relative trends of local populations and found that 25 species declined, 15 species increased, and 7 did not change. Based on migration assemblages, more resident species (6 of 10) and more short-distant migrants (9 of 12) decreased than long-distance migrants (10 vs. 11). Our analysis of major vegetation communities on plots showed few changes in the quantity of habitats (grassland vs. woodlands) during the study. Our results indicate that Fort Riley provides important habitats for many landbirds, particularly those that require grasslands for breeding. Several species exhibited local declines when compared to the regional Breeding Bird Survey routes. We offer an approach that evaluates population changes of small landbirds and provides objective inputs for conservation directives. These can be adopted easily for use on military installations (that use LCTA), parks, and wildlife refuges that have data from annual breeding bird surveys.     

Elevated CO2 reduces the response of Sitobion avenae (Homoptera: Aphididae) to alarm pheromone

The aphid alarm pheromone (E)-β-farnesene (EβF) is an efficient signal that warns aphids of attack by natural enemies. In this field study, eight open-top chambers (OTCs) located in Beijing, China (40°11′N, 116°24′E) with spring wheat Triticum aestivum were used to examine the response of the grain aphid Sitobion avenae to CO₂ (ambient vs. double ambient) and EβF (applied zero, two, or five times each day). We experimentally tested the hypotheses that, depending on frequency of EβF release, elevated CO₂ reduces the response (in terms of population density) of S. avenae to EβF, and that lower activity of acetylcholinesterase (AChE) in S. avenae may be involved in its reduced sensitivity to EβF under elevated CO₂. Numbers of S. avenae declined with increased frequency of EβF application under ambient CO₂ but were unaffected by EβF application under elevated CO₂. Additionally, the mean relative growth rate (MRGR) and the dry material and amino acid content of S. avenae increased with elevated CO₂ but declined when with EβF application. Activities of superoxide dismutase and catalase were higher in S. avenae under elevated vs. ambient CO₂. Under elevated CO₂, however, AChE activity remained low when S. avenae was exposed to the lower EβF frequency, while the highest AChE activity occurred in aphids exposed to the higher EβF frequency. These results indicate that aphids become insensitive to EβF under elevated CO₂, perhaps because of decreased AChE activity.     

Testing the effectiveness of capture mark recapture population estimation techniques using a computer simulation with known population size

Estimation of small mammal population sizes is important for monitoring ecosystem condition and for conservation. Here, we test the accuracy of standard methods of population size estimation using Capture-Mark-Recapture (CMR) on a simulated population of agents. The use of a computer simulation allows complete control of population sizes and behaviors, thereby avoiding assumptions that may be violated in real populations. We find that the recommended protocol for CMR sampling, using uniformly distributed traps, consistently overestimates population sizes by as much as 100% when studies are conducted over only two trapping periods. More than 20 trapping periods are required before this method, or that of placing traps randomly, gives an accurate estimation of population size (i.e., within a 95% confidence limit of the actual value). Non-random sampling, by placing traps on runways used by small mammals, produces the most accurate, and least variable, estimates of population. However, we show that around 10 trapping periods are still required to produce an accurate population estimate using this method. Given that most real populations do not comply with the ‘ideal’ assumptions made by CMR, we suggest that population estimates based on CMR may be fundamentally flawed, and recommend that protocols for CMR population estimation methods may need revising.     

Comparing the impacts of mitigation and non-mitigation on mountain pine beetle populations

Mountain pine beetles, Dendroctonus ponderosae (Hopkins) attack and can ultimately kill individuals and groups of pine trees, specifically lodgepole pine (Pinus contorta Dougl. ex. Loud var. latifolia Engl.). In British Columbia, beetle attack has increased from 164 000 ha in 1999 to over 13 million ha in 2008. Mitigation efforts can play a key role in addressing the impact beetle infestations can have on the forested landscape. In this research, the impact of mitigation on a mountain pine beetle infestation is examined within a network of 28 research plots where sanitation harvesting was completed (10 mitigated plots) and not completed (18 unmitigated plots). Three forest stand level modelling scenarios which predict the number of attacked trees, based on current infestation within the plots, were utilized to compare the differences between mitigated and non-mitigated plots. In the first scenario in the non-mitigated plots, 125 trees were infested after 10 years, while in the mitigated plots no trees were infested in the same time period. The second scenario indicates the level of mitigation required to suppress beetle infestations where the proportion of mitigated trees was calculated for each plot by counting the residual attack and the number of mitigated trees. The average mitigation rate over all plots of 43% (range 0–100%) is not sufficient to provide control. In the non-mitigated plots, the average population expansion rate was 5 (range of 0–18) which requires a detection accuracy of 74% to reliably detect infestation. The third scenario estimated the length of time required for ongoing detection, monitoring, and mitigation to bring an infestation under control. If mitigation efforts were maintained at the current rate of 43%, the beetle population would not be adequately controlled. However, when aided by continued detection and monitoring of attacked trees, mitigation rates greater than 50% are sufficient to control infestations, especially with persistent implementation, aided by continued detection and monitoring of infested trees.     

Modeling effects of toxin exposure in fish on long-term population size, with an application to selenium toxicity in bluegill (Lepomis macrochirus)

A primary goal in ecotoxicology is the prediction of population-level effects of contaminant exposure based on individual-level response. Assessment of toxicity at the population level has predominately focused on the population growth rate (PGR), but the PGR may not be a relevant toxicological endpoint for populations at equilibrium. Equilibrium population size may be a more meaningful endpoint than the PGR because a population with smaller equilibrium size is more susceptible to the negative effects of environmental variability. We address the individual-to-population extrapolation problem with modeling utilizing classical mathematical theory. We developed and analyzed a general model applicable to many freshwater fish species, that includes density-dependent juvenile survival and additional juvenile mortality due to toxicity exposure, and we quantified effect on equilibrium population size as a means of assessing toxicity. Individual-level effects are typically greater than population-level effects until the individual effect is large, due to compensatory density-dependent relationships. These effects are sensitive to the recruitment potential of a population, in particular the low-density first-year survival rate S_b. Assuming high S_b could result in underestimating effects of population-level toxicity. The equilibrium size depends directly on S_b, the reproductive potential, the toxin concentration at which mean mortality is 50% (LC₅₀), and the rate at which individual mortality increases with increasing toxin concentration. More experimental data are needed to decrease the uncertainty in estimating these parameters. We then used existing data for selenium toxicity in bluegill sunfish to parameterize a simulation version of the model as an example to assess the effects of environmental stochasticity on toxicity response. Effects of environmental variability resulted in simulated extinctions at much lower toxin concentrations than predicted deterministically.     

北京山区典型流域不同海拔椴树种群的空间点格局分析

采用点格局分析法对不同海拔的椴树（Tilia miqueliana Maxim.）种群进行分布格局及其种间关系进行了研究。结果表明：整体上群落内以中龄树个体数为最多,小树次之,成年树个体最少。随着海拔的增加可以看出：小树（d≤5 cm）随着海拔的增加而减少,中树（5 cm20 cm）的规律不明显;椴树种群的空间分布格局与空间尺度（25 m内）有密切关系,在较小的空间尺度上倾向于非随机分布,具有明显的空间相关性;在〉15 m或25m的某临界尺度时却倾向于随机分布,同时空间关联变得微弱。随着海拔的增加,各物种聚集分布的尺度有逐渐减小的趋势。种间关系随着海拔的增加,物种间的正相关尺度有增加的趋势。