The Lotka-Volterra predator-prey model with foraging-predation risk trade-offs

This article studies the effects of adaptive changes in predator and/or prey activities on the Lotka-Volterra predator-prey population dynamics. The model assumes the classical foraging-predation risk trade-offs: increased activity increases population growth rate, but it also increases mortality rate. The model considers three scenarios: prey only are adaptive, predators only are adaptive, and both species are adaptive. Under all these scenarios, the neutral stability of the classical Lotka-Volterra model is partially lost because the amplitude of maximum oscillation in species numbers is bounded, and the bound is independent of the initial population numbers. Moreover, if both prey and predators behave adaptively, the neutral stability can be completely lost, and a globally stable equilibrium would appear. This is because prey and/or predator switching leads to a piecewise constant prey (predator) isocline with a vertical (horizontal) part that limits the amplitude of oscillations in prey and predator numbers, exactly as suggested by Rosenzweig and MacArthur in their seminal work on graphical stability analysis of predator-prey systems. Prey and predator activities in a long-term run are calculated explicitly. This article shows that predictions based on short-term behavioral experiments may not correspond to long-term predictions when population dynamics are considered.     

羊尿对典型草原不同生活型草地植物生长特性的影响

连续2a研究了施尿量(4,2,1L/m2和0 L/m2)和施尿期(营养期和生殖期)对典型草原多年生密丛型禾本科植物长芒草(Stipa bungeana)、多年生轴根型菊科植物茵陈蒿(Artemisia capillaries)和多年生半灌木豆科植物胡枝子(Lespedeza davurica)生长特性的影响.结果表明,不同植物对畜尿沉积的响应不同,并受施尿量和施尿时期的作用.畜尿对草地植物具短期(4周内)灼烧作用,灼烧主要发生于尿斑中心;畜尿对长芒草生长具长期正效应(4周后),对茵陈蒿和胡枝子生长具持续负效应,此效应持续至少2a且随施尿量降低而降低.一般尿斑中心(4 L/m2)所有植物伤害,尿斑中心至边缘圈植物局部器官(嫩枝叶)伤害(2～4 L/m2),尿斑外渗区域(1～2 L/m2)所有植物无显著伤害.高施尿量(2～4 L/m2)下,长芒草具较高的年均分蘖数和地上生物量,而胡枝子和茵陈蒿与之相反.尿斑处3种植物具较高的分蘖(枝)死亡率和死物质率.茵陈蒿对各时期施尿均反应敏感,胡枝子和长芒草对生殖期施尿更敏感.尿斑处禾草枯黄期延迟,返青期提前.     

The average lifetime of a population in a varying environment

I derive an approximate formula relating the average time to extinction of a population in a varying environment to its initial size, its equilibrium size (if it is self-regulated), its innate capacity for natural increase, and the impact upon it of environmental variation. The greater the impact of environmental variation, the more slowly a population's prospective lifetime increases with increase in its equilibrium size. The lifetimes of populations greatly influenced by environmental variation are more sensitive to the relative amplitude of fluctuation in their numbers than to their equilibrium size. Since species tend to avoid competitive displacement by specializing, rendering themselves more sensitive to environmental change, and since populations are no more likely to risk extinction in one environment than in another, the degree to which a community's populations fluctuate will be unrelated to environmental stability.     

Mass invariance of population nitrogen flux by terrestrial mammalian herbivores: an extension of the energetic equivalence rule

According to the energetic equivalence rule, energy use by a population is independent of average adult body mass. Energy use can be equated with carbon flux, and it has been suggested that population fluxes of other materials, such as nitrogen and phosphorus, might also be independent of body mass. We compiled data on individual nitrogen deposition rates (via faeces and urine) and average population densities of 26 species of mammalian herbivores to test the hypothesis of elemental equivalence for nitrogen. We found that the mass scaling of individual nitrogen flux was opposite to that of population density for the species in our dataset. By computing the product of individual nitrogen flux and average population density for each species in our dataset, we found that population-level nitrogen flux was independent of species mass, averaging c. 3.22 g N ha⁻¹ day⁻¹. Results from this analysis can be used to understand the influence of mammalian herbivore communities on nitrogen cycling in terrestrial ecosystems.     

Effects of vole fluctuations on the population dynamics of the barn owl <Emphasis Type="Italic">Tyto alba</Emphasis>

Many predator species feed on prey that fluctuates in abundance from year to year. Birds of prey can face large fluctuations in food abundance i.e. small mammals, especially voles. These annual changes in prey abundance strongly affect the reproductive success and mortality of the individual predators and thus can be expected to influence their population dynamics and persistence. The barn owl, for example, shows large fluctuations in breeding success that correlate with the dynamics in voles, their main prey species. Analysis of the impact of fluctuations in vole abundance (their amplitude, peaks and lows, cycle length and regularity) with a simple predator prey model parameterized with literature data indicates population persistence is especially affected by years with low vole abundance. In these years the population can decline to low owl numbers such that the ensuing peak vole years cannot be exploited. This result is independent of the length and regularity of vole fluctuations. The relevance of this result for conservation of the barn owl and other birds of prey that show a numerical response to fluctuating prey species is discussed.     

Diversity in soil fungi as influenced by DDT

the application of 1 and 2 ppm DDT to soil did not result in any consistent trends in fungal numbers through a 14 week period. However the amplitude of population fluctuations was markedly suppressed in treated soils during the early weeks of treatment.A study of the effect of DDT on the population structure of the genusPenicillium indicated that it undergoes a reduction of diversity with treatment that persists at least through a 9 week survey period.     

An acarine predator-prey population infesting roses

When Phytoseiulus persimilis was reared with Tetranychus urticae, infesting roses propagated in a greenhouse at controlled daily temperatures of 24°C (12 hrs) and 18°C (12 hrs), prey numbers fluctuated with peaks of increasing amplitude. Differential dispersal of prey and predator species was one factor contributing to the inability of the natural enemy to control the pest population.     

Morphometric analysis of the translocation of lumenal membrane between cytoplasm and cell surface of transitional epithelial cells during the expansion-contraction cycles of mammalian urinary bladder

The flow of membrane between the cytoplasm and the lumenal surface during the expansion-contraction cycle of urinary bladder was estimated by stereological examination of electron micrographs of urothelial cells from guinea pigs, gerbils, hamsters, rabbits, and rats. The quantitative data obtained allowed an approximation of the surface area, volume, and numbers of lumenal membranelike vesicles and infoldings per unit volume of cytoplasm. Depending upon the species, approximately 85 to approximately 94% of the membrane surface area translocated into and out of the cytoplasm was in the form of discoidal vesicles. The remainder was accounted for by infoldings of the lumenal plasma membrane. The density of vesicles involved in transfer of membrane was quite similar in all the species examined, except guinea pigs which yielded lower values. In contrast, the densities of the total cytoplasmic pools of discoidal vesicles potentially available for translocation varied greatly among the different species. In general, species of animals with a highly concentrated urine had a greater density of discoidal vesicles than species with a less concentrated urine. This correlation may indicate an authentic relationship between lumenal membranes and the tonicity of urine, such as increased membrane recycling or turnover with increasingly hypertonic urine; or it may signify the existence of some other, more obscure relationship.     

Weather-induced changes in moth activity bias measurement of long-term population dynamics from light trap samples

Interpretation of light trap catches of moths is complicated by daily variation in weather that alters flight activity and numbers caught. Light trap efficiency is also modified by wind and fog, and daily weather may effect absolute abundance (numbers actually present). However, actograph experiments and other sampling methods suggest that changes in daily activity are large by comparison to changes in absolute abundance. Daily variation in weather (other than wind and fog) is therefore a form of sampling error in absolute abundance estimates. We investigated the extent of this sampling bias in 26 years of population dynamics from 133 moth species. In a subset of 20 noctuid and geometrid species, daily numbers caught were positively correlated with temperature in 14 species, and negatively correlated with rainfall in 11 species. The strength of correlations varied between species, making it difficult to standardize catches to constant conditions. We overcame this by establishing how weather variation changed with time and duration of the flight period. Species flying later in the summer and for shorter periods experienced more variable temperatures, making sampling error greater for these species. Of the 133 moth species, those with shorter flight periods had greater population variability and more showed significant temporal density dependence. However, these effects were weak, which is encouraging because it suggests that population analyses of light trap data largely reflect factors other than sampling error.     

Staphylococci in Competition: II. Effect of Total Numbers and Proportion of Staphylococci in Mixed Cultures on Growth in Artificial Culture Medium

In studies carried on in bacteriological media with selected cultures, definite repressive effects were noted on the growth of the Staphylococcus population by a mixture of saprophytic, psychrophilic bacterial species. This repressive effect became more pronounced as the relative proportion of the bacterial population which was staphylococcal became smaller. A varied saprophytic bacterial flora of some numbers apparently would offer definite protection to foods through repression of staphylococcal growth and by rendering the food inedible before the rise of appreciable numbers of staphylococci. It would appear that at the optimal temperature for staphylococcal growth, staphylococci could multiply rapidly in the mixed population due to the comparative shortness of the generation time of this species and because of the lengthened lag phase of the saprophytic bacterial species at this elevated temperature, especially when only cultures having psychrophilic characteristics were present. This temperature is substantially above that encountered in practical experience. With the passage of time, the staphylococcal population was completely overgrown by the saprohytes present. This effect might be eliminated in the presence of psychrophilic and mesophilic, saprophytic species. The repressive effect of competition by saprophytic, psychrophilic organisms is extremely effective up to room temperature on the staphylococcal population. Even when significant staphylococcal populations were achieved in the artificial media, such tremendous numbers of saprophytes were obtained either earlier or at the same time so that a frozen food containing this population would be organoleptically unacceptable due to the degradative action of enzymes from the saprophytic psychrophile population.     

Quantitative estimation of population numbers of shrews (mammalia,insectivora) after wintering

Autumn-winter mortality in shrews (Sorex araneus, S. caecutiens, S. minutus) was estimated on the basis of long-term (12 years) live-trapping on the permanent transect lines in Tver oblast. Relative as well as absolute population numbers were estimated. Lesser shrew (S. minutus) has permanently low population numbers. Fall in this species made 40.1%, and it was scattered through this term. Common shrew (Sorex araneus) lose 89.3% of population and in masked shrew (S. caecutiens) those lost was 73.6%. The most lost was found in autumn and winter fall was as least as 38,2% and 30.4% in the latter two species. The mortality is positively dependent on population density in preceding summer and with severity of winter.     

InvA protein is a Nudix hydrolase required for infection by pathogenic Leptospira in cell lines and animals

Leptospirosis caused by pathogenic species of the genus Leptospira is a re-emerging zoonotic disease, which affects a wide variety of host species and is transmitted by contaminated water. The genomes of several pathogenic Leptospira species contain a gene named invA, which contains a Nudix domain. However, the function of this gene has never been characterized. Here, we demonstrated that the invA gene was highly conserved in protein sequence and present in all tested pathogenic Leptospira species. The recombinant InvA protein of pathogenic L. interrogans strain Lai hydrolyzed several specific dinucleoside oligophosphate substrates, reflecting the enzymatic activity of Nudix in Leptospira species. Pathogenic leptospires did not express this protein in media but temporarily expressed it at early stages (within 60 min) of infection of macrophages and nephric epithelial cells. Comparing with the wild type, the invA-deficient mutant displayed much lower infectivity and a significantly reduced survival rate in macrophages and nephric epithelial cells. Moreover, the invA-deficient leptospires presented an attenuated virulence in hamsters, caused mild histopathological damage, and were transmitted in lower numbers in the urine, compared with the wild-type strain. The invA revertant, made by complementing the invA-deficient mutant with the invA gene, reacquired virulence similar to the wild type in vitro and in vivo. The LD(50) in hamsters was 1000-fold higher for the invA-deficient mutant than for the invA revertant and wild type. These results demonstrate that the InvA protein is a Nudix hydrolase, and the invA gene is essential for virulence in pathogenic Leptospira species.     

Benthic invertebrates as indicators of organic pollution in the Western Baltic Sea

The quantitative distribution of some important benthic invertebrates in a shallow inshore area of Kiel Bay (Western Baltic Sea) is described. This region is partly polluted by domestic sewage from the municipality of Kiel. Three groups of species are distinguished with reference to their densities and other population parameters in the different subareas: Progressive species of the 1st and 2nd order indicate a high and moderate to slight degree of pollution respectively by high population numbers. Regressive species are adverse indicators, absent or occurring in exceptionally low numbers in affected areas. In many cases the examination must be concentrated on sand bottom, because a series of species normally dwelling on aufwuchs build up dense populations in sand, if it is organically enriched. The polychaetes Capitella capitata, Nereis diversicolor and Polydora ligni are regarded as progressive species of the 1st order. The amphipods Corophium insidiosum and Gammarus salinus, the mussel Mytilus edulis, the polychaete Pygospio elegans, the snail Hydrobia ulvae, and some other invertebrates belong to the group of indicators for slight organic pollution. The main regressive species are the amphipod Bathyporeia sarsi and the mite Copidognathus fabriciusi.     

Long-term decline in numbers of cyclic voles in boreal Sweden: analysis and presentation of hypotheses

Cyclic vole populations, defined as showing fairly regular 3–4 yr density fluctuations but with variable amplitudes, were monitored in boreal Sweden in spring and fall 1971–2002, starting in fall 1971. Voles were snap-trapped on permanent sampling plots at the landscape level within a 100 by 100 km study area north of Umeå. The predominating species trapped were Clethrionomys glareolus, C. rufocanus and Microtus agrestis. In addition to the 3–4 yr cycles, there was a long-term decrease in numbers and amplitude of the fluctuations, which was especially conspicuous in C. rufocanus. In this latter species there was a persistent decline of both spring and fall densities, apparently bringing the population close to extinction in the area. However, the decline of spring densities from the 1970s to the 1980s and onwards was also evident in C. glareolous and M. agrestis. The declines in numbers and amplitude were largely linked to an increased frequency and/or accentuation of winter declines, which more or less neutralized or even overrode the density increase during the reproductive season in the previous summer, especially so in the second year of the cycles. Thereby the gradual two-large-step build-up of high spring densities, very much founding the base for the very large peak densities and amplitudes in the 1970s, was successively replaced by a one-smaller-step build-up of more modest spring densities, leading to lower peak densities and amplitudes in the 1980s, 1990s and early 2000s. Understanding the causes of the increased frequency and/or severeness of winter declines appears critical to understanding the observed long-term changes in numbers. However, the underlying causes of the increase of winter declines and the decrease of densities and amplitudes are unknown, but some hypotheses are presented and discussed here. Also, some implications from the decreased vole abundance for reproduction and densities of predators on the voles, and on predators’ alternative prey species, are briefly discussed.     

Localised control of an introduced predator: creating problems for the future?

Introduced mammalian predators have had significant impacts on many native prey species. Although control of such predators for conservation management is becoming increasingly commonplace, it is often undertaken at a relatively small scale in relation to the overall predator population. Processes such as immigration mean that it remains difficult to determine the effectiveness of control measures. We investigated the impacts of feral ferret Mustela furo removal on the entire feral ferret population on Rathlin Island, UK. Removal of ferrets prior to breeding led to a substantial increase in the post-dispersal population through the enhanced survival of juveniles. Despite increased numbers, overwinter survival remained high, potentially aided by the reduced territoriality shown by this feral species compared to wild carnivores. The response of this ferret population to control is a further illustration of the complex ecological processes and outcomes arising from the anthropogenic disruption of wildlife populations. It highlights how partial or localised management may prove ineffective, and at worst might exacerbate the problems that management was designed to avert.     

Random effects in population models with hereditary effects

This paper discusses the influence of environmental noise on the dynamics of single species population models with hereditary effects. A detailed analysis is carried out for the logistic equation with discrete delay in the resource limitation term (Hutchinson's equation). When the system undergoes Hopf bifurcation, we find the stationary probability density distribution for the amplitude of the periodic solution by means of an averaged Fokker-Planck equation. Finally, we estimate the persistence time of the species when the population density has a lower bound beyond which it goes extinct.     

Understanding the population dynamics of a rare, polyvoltine butterfly

Understanding the effects of endogenous and exogenous factors on population dynamics is essential for assessing the viability of populations, setting recovery goals for endangered species, and evaluating management options. Invertebrates are particularly difficult to monitor and few long-term datasets are available for these species. Additionally, limited resources make it necessary to perform monitoring as efficiently as possible. Here, I use the bivoltine Karner blue butterfly Lycaeides melissa samuelis to demonstrate how analyzing the effects of density-dependent factors and weather on separate life stages can be utilized to understand monitoring data, assess populations and identify critical life-history parameters. My first step was to compare the use of peak numbers as an index of population size with estimates obtained from a more data intensive methodology. Peak numbers proved to be an effective index, and so I utilized this index to analyze 10 and 13 years of monitoring data at two Karner blue butterfly sites in New York, USA. I modeled the effects of weather and density dependence on two distinct population growth rates ( λ ) per year. Analysis with Akaike's Information Criteria indicated that both sites were primarily influenced by density dependence during the summer period and by weather conditions during the winter period. Large population declines occurred in the winter period and were a result of the previous year's dry summer and cool spring weather. I conclude that recovery goals for this endangered species should include a second brood-carrying capacity, mean winter growth rate and multiple sites with independent populations. This study represents a rare, long-term study on the population dynamics of a polyvoltine species. Understanding the population dynamics of polyvoltine species, such as the Karner blue butterfly, will assist in the conservation of many invertebrate and small mammal species.     

Some clouds have a silver lining: paradoxes of anthropogenic perturbations from study cases on long-lived social birds

In recent centuries and above all over the last few decades, human activities have generated perturbations (from mild to very severe or catastrophes) that, when added to those of natural origin, constitute a global threat to biodiversity. Predicting the effects of anthropogenic perturbations on species and communities is a great scientific challenge given the complexity of ecosystems and the need for detailed population data from both before and after the perturbations. Here we present three cases of well-documented anthropogenic severe perturbations (different forms of habitat loss and deterioration influencing fertility and survival) that have affected three species of birds (a raptor, a scavenger and a waterbird) for which we possess long-term population time series. We tested whether the perturbations caused serious population decline or whether the study species were resilient, that is, its population dynamics were relatively unaffected. Two of the species did decline, although to a relatively small extent with no shift to a state of lower population numbers. Subsequently, these populations recovered rapidly and numbers reached similar levels to before the perturbations. Strikingly, in the third species a strong breakpoint took place towards greater population sizes, probably due to the colonization of new areas by recruits that were queuing at the destroyed habitat. Even though it is difficult to draw patterns of resilience from only three cases, the study species were all long-lived, social species with excellent dispersal and colonization abilities, capable of skipping reproduction and undergoing a phase of significant long-term population increase. The search for such patterns is crucial for optimizing the limited resources allocated to conservation and for predicting the future impact of planned anthropogenic activities on ecosystems.     

Ultraviolet properties of Australian mammal urine

The exploitation of predator signals by potential prey is well researched, but relatively little is known about how predators exploit chemical cues (either deliberate signals or waste by-products) produced by their prey. In Finland, the urine of some small rodents (Microtus spp. and Clethrionomys spp.) is reflective in the ultraviolet range of wavelengths, and diurnal raptors with ultraviolet vision use these urine marks to track their rodent prey. This study examines the potential for such a phenomenon in Australian systems by studying the ultraviolet properties of urine from 13 native and introduced mammal species that are variously preyed upon by raptors. Urine from all 13 species displayed various levels of ultraviolet absorbance in their urine and fluorescence in the ultraviolet range. However, no signs of ultraviolet hyper-reflectance were detected, suggesting that the urine of European voles have unique ultraviolet properties. Ultraviolet-sensitive predators in Australia may be able to distinguish between species based on variation in the ultraviolet absorbance of their urine, but ultraviolet properties did not differ between prey and non-prey species, nor marsupial and placental groups. Moreover, because many natural surfaces are ultraviolet absorbing, it is unlikely that raptors could rely upon the ultraviolet properties of urine to target key prey species.     

On the Volterra-Lotka principle

The supplantation of one of two closely similar competing species by the other (Volterra-Lotka principle) is studied as an example, according to Volterra's general theory of population dynamics, of the decay of a biological association of an odd number 2n+1 of species into one with an even number 2n. The three-species association (n=1) is worked out in detail, with a demonstration of how a Volterra predator-prey cycle gets gradually deformed—when a slightly superior predator is introduced—into another new-predator-prey cycle, spelling a steady eclipse of the original predator. Whenn is made large, the close competitors being embedded in an association of many other species, a statistical treatment of the supplantation process can be given through the author's statistical-mechanical theory of Volterra's dynamics. The result is a probability law, changing systematically as time goes on, for the chance that the successful competitor's population has any given amplitude; explicitly time-dependent measures of mean amplitude and mean frequency of oscillation of all populations can then be worked out. Throughout, the simplifying assumption is made that the competitors differ only as regards intrinsic rate of self-growth. Two things are accomplished by viewing the competition as a decay of 2n+1 into 2n: the competitors are not abstracted from the rest of the biological world, and their population variations are always oscillatory (with long-term rises and falls of amplitude); this is in contrast to the original Volterra-Lotka analysis in which purely static, and therefore ecologically unrealistic, population levels of but two species eventuate.