CALCULATING LIMITS TO THE ALLOWABLE HUMAN-CAUSED MORTALITY OF CETACEANS AND PINNIPEDS

A simulation method was developed for identifying populations with levels of human-caused mortality that could lead to depletion, taking into account the uncertainty of available information. A mortality limit (termed the Potential Biological Removal, PBR , under the U. S. Marine Mammal Protection Act) was calculated as the product of a minimum population estimate ( N _MIN), one-half of the maximum net productivity rate ( R _MAX), and a recovery factor ( F _R). Mortality limits were evaluated based on whether at least 95% of the simulated populations met two criteria: (1) that populations starting at the maximum net productivity level ( MNPL ) stayed there or above after 20 yr, and (2) that populations starting at 30% of carrying-capacity ( K ) recovered to at least MNPL after 100 yr. Simulations of populations that experienced mortality equal to the PBR indicated that using approximately the 20th percentile (the lower 60% log-normal confidence limit) of the abundance estimate for N _MIN met the criteria for both cetaceans (assuming R _MAX= 0.04) and pinnipeds (assuming R _MAX= 0.12). Additional simulations that included plausible levels of bias in the available information indicated that using a value of 0.5 for F _R would meet both criteria during these "bias trials." It is concluded that any marine mammal population with an estimate of human-caused mortality that is greater than its PBR has a level of mortality that could lead to the depletion of the population. The simulation methods were also used to show how mortality limits could be calculated to meet conservation goals other than the U. S. goal of maintaining populations above MNPL .     

DYNAMIC RESPONSE ANALYSIS. III. A CONSISTENCY FILTER AND APPLICATION TO FOUR NORTHERN ELEPHANT SEAL COLONIES

Dynamic response analysis, a technique for determining stock size relative to the maximum net productivity level (MNPL), was applied to northern elephant seal populations from the South Farallon Islands, Año Nuevo Island, San Nicolas Island and San Miguel Island. Pup counts were used as indices of population size. The application of dynamic response analysis presented here involved some methodological innovations. We present a moving interval method which involves calculating separate dynamic response analyses for intervals of various lengths ranging from four counts to the total number available for the colony. The sign of the second order polynomial regression coefficient computed from a particular interval was used to indicate the colony's apparent status (relative to its MNPL, += above MNPL, - = below MNPL) on that interval. Consistency in the sign of the second order coefficient, as the interval was moved along the trajectory, was used to determine the minimum reliable interval size. Each colony exhibited growth similar to that of a population below its MNPL. These results are consistent with recent natural history observations at San Nicolas, San Miguel and the South Farallon islands. Natural history observations at Año Nuevo Island suggest that the colony there is now at equilibrium. Thus, if our results from dynamic response analysis of the Ano Nuevo colony are correct, it appears that the MNPL may be close to the carrying capacity for these animals.     

Spatial-temporal population dynamics across species range: from centre to margin

Understanding the boundaries of species' ranges and the variations in population dynamics from the centre to margin of a species' range is critical. This study simulated spatial-temporal patterns of birth and death rates and migration across a species' range in different seasons. Our results demonstrated the importance of dispersal and migration in altering birth and death rates, balancing source and sink habitats, and governing expansion or contraction of species' ranges in changing environments. We also showed that the multiple equilibria of metapopulations across a species' range could be easily broken following climatic changes or physical disturbances either local or regional. Although we refer to our models as describing the population dynamics across whole species' range, they should also apply to small-scale habitats (metapopulations) in which species abundance follows a humped pattern or to any ecosystem or landscape where strong central-marginal (C-M) environmental gradients exist. Conservation of both central and marginal populations would therefore be equally important considerations in making management decisions.     

Effects of host social hierarchy on disease persistence

The effects of social hierarchy on population dynamics and epidemiology are examined through a model which contains a number of fundamental features of hierarchical systems, but is simple enough to allow analytical insight. In order to allow for differences in birth rates, contact rates and movement rates among different sets of individuals the population is first divided into subgroups representing levels in the hierarchy. Movement, representing dominance challenges, is allowed between any two levels, giving a completely connected network. The model includes hierarchical effects by introducing a set of dominance parameters which affect birth rates in each social level and movement rates between social levels, dependent upon their rank. Although natural hierarchies vary greatly in form, the skewing of contact patterns, introduced here through non-uniform dominance parameters, has marked effects on the spread of disease. A simple homogeneous mixing differential equation model of a disease with SI dynamics in a population subject to simple birth and death process is presented and it is shown that the hierarchical model tends to this as certain parameter regions are approached. Outside of these parameter regions correlations within the system give rise to deviations from the simple theory. A Gaussian moment closure scheme is developed which extends the homogeneous model in order to take account of correlations arising from the hierarchical structure, and it is shown that the results are in reasonable agreement with simulations across a range of parameters. This approach helps to elucidate the origin of hierarchical effects and shows that it may be straightforward to relate the correlations in the model to measurable quantities which could be used to determine the importance of hierarchical corrections. Overall, hierarchical effects decrease the levels of disease present in a given population compared to a homogeneous unstructured model, but show higher levels of disease than structured models with no hierarchy. The separation between these three models is greatest when the rate of dominance challenges is low, reducing mixing, and when the disease prevalence is low. This suggests that these effects will often need to be considered in models being used to examine the impact of control strategies where the low disease prevalence behaviour of a model is critical.     

MAXIMUM NET PRODUCTIVITY LEVEL ESTIMATION FOR THE NORTHERN FUR SEAL (CALLORHINUS URSINUS) POPULATION OF ST. PAUL ISLAND, ALASKA

The goal of this study was to assess the maximum net productivity level for the northern fur seal ( Callorhinus ursinus ) population of St. Paul Island, Alaska. Definitive determination of this level is not possible due to uncertainty in life table parameters and density-dependent changes in those parameters. To account for such uncertainty, repetitive numerical simulations were used to generate frequency distributions of estimates for the maximum net productivity level and related population parameters. This approach systematically varied simulation input parameters, ran a separate simulation with each input parameter combination, and validated the simulations on the basis of comparison with historical observations. Results from validated simulations were compiled in frequency distributions to provide a measure of confidence for MNPL estimates. The distributions confirm that this population is probably well below its maximum net productivity level. Because they reflect the uncertainty in our understanding of northern fur seal population dynamics, these distributions are a more realistic basis for management than single point estimates.     

Dynamics of mutualist populations that are demographically open

1. Few theoretical studies have examined the impact of immigration and emigration on mutualist population dynamics, but a recent empirical study (A.R. Thompson Oecologia, 143, 61-69) on mutualistic fish and shrimp showed that immigration can prevent population collapse, and that intraspecific competition for a mutualistic partner can curb population expansion. To understand in a theoretical context the implications of these results, and to assess their generality, we present a two-species model that accounts explicitly for immigration and emigration, as well as distinguishing the impacts of mutualism on birth rates, death rates and habitat acquisition. 2. The model confirms that immigration can stabilize mutualistic populations, and predicts that high immigration, along with enhanced reproduction and/or reduced mortality through mutualism, can cause population sizes to increase until habitat availability curbs further expansion. 3. We explore in detail the effects of different forms of habitat limitation on mutualistic populations. Habitat availability commonly limits the density of both populations if mutualists acquire shelter independently. If a mutualist depends on a partner for habitat, densities of that mutualist are capped by the amount of space provided by that partner. The density of the shelter-provider is limited by the environment. 4. If a mutualism solely augments reproduction, and most locally produced individuals leave the focal patch, then the mutualism will have a minimal effect on local dynamics. If the mutualism operates by reducing rates of death or enhancing habitat availability, and there is at least some immigration, then mutualism will affect local dynamics. This finding may be particularly relevant in marine systems, where there is high variability (among species and locations) in the extent to which progeny disperse from natal locations. 5. Overall, our results demonstrate that the consequences of immigration and emigration for the dynamics of mutualists depend strongly on which demographic rate is influenced by mutualism. 6. By relating our model to a variety of terrestrial and aquatic systems, we provide a general framework to guide future empirical studies of the dynamics of mutualistic populations.     

On the dynamic persistence of cooperation: how lower individual fitness induces higher survivability

We study a model in which cooperation and defection coexist in a dynamical steady state. In our model, subpopulations of cooperators and defectors inhabit sites on a lattice. The interactions among the individuals at a site, in the form of a prisoner's dilemma (PD) game, determine their fitnesses. The chosen PD payoff allows cooperators, but not defectors, to maintain a homogeneous population. Individuals mutate between types and migrate to neighboring sites with low probabilities. We consider both density-dependent and density-independent versions of the model. The persistence of cooperation in this model can be explained in terms of the life cycle of a population at a site. This life cycle starts when one cooperator establishes a population. Then defectors invade and eventually take over, resulting finally in the death of the population. During this life cycle, single cooperators migrate to empty neighboring sites to found new cooperator populations. The system can reach a steady state where cooperation prevails if the global "birth" rate of populations is equal to their global "death" rate. The dynamic persistence of cooperation ranges over a large section of the model's parameter space. We compare these dynamics to those from other models for the persistence of altruism and to predator-prey models.     

The dynamics of hierarchical age-structured populations

An age-structured population is considered in which the birth and death rates of an individual of age a is a function of the density of individuals older and/or younger than a. An existence/uniqueness theorem is proved for the McKendrick equation that governs the dynamics of the age distribution function. This proof shows how a decoupled ordinary differential equation for the total population size can be derived. This result makes a study of the population's asymptotic dynamics (indeed, often its global asymptotic dynamics) mathematically tractable. Several applications to models for intra-specific competition and predation are given.     

Macroecology meets macroevolution: evolutionary niche dynamics in the seaweed Halimeda

Aim Because of their broad distribution in geographical and ecological dimensions, seaweeds (marine macroalgae) offer great potential as models for marine biogeographical inquiry and exploration of the interface between macroecology and macroevolution. This study aims to characterize evolutionary niche dynamics in the common green seaweed genus Halimeda, use the observed insights to gain understanding of the biogeographical history of the genus and predict habitats that can be targeted for the discovery of species of special biogeographical interest. Location Tropical and subtropical coastal waters. Methods The evolutionary history of the genus is characterized using molecular phylogenetics and relaxed molecular clock analysis. Niche modelling is carried out with maximum entropy techniques and uses macroecological data derived from global satellite imagery. Evolutionary niche dynamics are inferred through application of ancestral character state estimation. Results A nearly comprehensive molecular phylogeny of the genus was inferred from a six‐locus dataset. Macroecological niche models showed that species distribution ranges are considerably smaller than their potential ranges. We show strong phylogenetic signal in various macroecological niche features. Main conclusions The evolution of Halimeda is characterized by conservatism for tropical, nutrient‐depleted habitats, yet one section of the genus managed to invade colder habitats multiple times independently. Niche models indicate that the restricted geographical ranges of Halimeda species are not due to habitat unsuitability, strengthening the case for dispersal limitation. Niche models identified hotspots of habitat suitability of Caribbean species in the eastern Pacific Ocean. We propose that these hotspots be targeted for discovery of new species separated from their Caribbean siblings since the Pliocene rise of the Central American Isthmus.     

Population dynamics and production of five crustacean zooplankters in a subtropical reservoir during years of contrasting turbidity

SUMMARY 1. The temporal dynamics and demography of Meta-diaptomus meridianus (Van Douwe), Lovenula excellens Kiefer. Daphnia gibba Methuen, D. barbata Weltner and Moina brachiata Jurine were studied for 2 years in a small bay of Lake le Roux (Orange River, South Africa). Total zooplankton biomass and population density were 1.4–3 times higher during the less turbid conditions of 1982/83 (Secchi depth transparency around 35 cm) than they were at around 25 cm Secchi depth during 1981/82, when D. barbata was absent.
2. On average, instantaneous birth rates, rates of population change and death rates varied only slightly between years. Birth and death rates were considerably higher above 15°C than below 15°C. These rates correlated with one another and with zooplankton abundance both inter- and intra-specifically suggesting that competitive interactions were important in population regulation. Mortality rates varied more strongly and consistently in a density-dependent direction than did birth rates. In addition to depressed fecundity, the inferred survival of young was poor and population growth low, possibly because food shortage caused high post-natal mortality.
3. Estimates of annual production derived from finite birth rate values varied consistently with annual differences in biomass, and amounted to between 6 and 10 g m⁻² y⁻¹ dry wt. Annual P/B values varied from around 20 for the daphnids to 55 for the copepods and 75 for Moina. Apart from the latter, whose annual P/B ratio virtually doubled from 45 to 75 following reductions in turbidity, annual differences in P/B ratio were slight.     

The effect of seasonal harvesting on stage-structured population models

In most models of population dynamics, increases in population due to birth are assumed to be time-independent, but many species reproduce only during a single period of the year. We propose an exploited single-species model with stage structure for the dynamics in a fish population for which births occur in a single pulse once per time period. Since birth pulse populations are often characterized with a discrete time dynamical system determined by its Poincaré map, we explore the consequences of harvest timing to equilibrium population sizes under seasonal dependence and obtain threshold conditions for their stability, and show that the timing of harvesting has a strong impact on the persistence of the fish population, on the volume of mature fish stock and on the maximum annual-sustainable yield. Moreover, our results imply that the population can sustain much higher harvest rates if the mature fish is removed as early in the season (after the birth pulse) as possible. Further, the effects of harvesting effort and harvest timing on the dynamical complexity are also investigated. Bifurcation diagrams are constructed with the birth rate (or harvesting effort or harvest timing) as the bifurcation parameter, and these are observed to display rich structure, including chaotic bands with periodic windows, pitch-fork and tangent bifurcations, non-unique dynamics (meaning that several attractors coexist) and attractor crisis. This suggests that birth pulse, in effect, provides a natural period or cyclicity that makes the dynamical behavior more complex.This work is supported by National Natural Science Foundation of China (10171106)     

The spatial structure of populations

1. Studies of the spatio-temporal dynamics and structure of populations have identified many categories of population type. However, recognized categories intergrade, making it difficult to assign empirical population systems to single categories.
2. We suggest that most population categories can be arranged along two axes that combine per capita birth (B), death (D), emigration (E) and immigration (I) rates. The 'Compensation Axis' describes the source-sink component of population structure, with source populations exporting individuals (B > D, E > I) and sinks and pseudosinks consuming individuals (B < D, E < I). The 'Mobility Axis' describes the involvement of a local population in regional (I + E) rather than local (B + D) processes, running from separate populations, through metapopulations, to patchy populations.
3. Each sample area within a spatially structured population system can potentially be assigned to a position along each of these axes, with individual sample areas weighted by local population size. The positions of these sample areas and their relative weightings allow the relative importance of different types of process to be judged. A worked exampled is provided, using the butterfly Hesperia comma . This approach shifts the emphasis from pattern (categories that real population systems do not fit) onto process.
4. In many systems, continuous variation in habitat quality and demographic parameters make clear distinctions between 'habitat' and 'non-habitat' difficult to sustain. In such cases, we advocate the use of a spatial grid system, with effects of patch size and isolation combined into a single, weighted distance function (neighbourhood).
5. The relative importance of different processes depends on the spatial scale at which the system is observed. This again emphasizes the value of a process-based approach.     

Flexible parametric modeling of survival from age at death data: A mixed linear regression framework

Many long-lived vertebrate species are under threat in the Anthropocene, but their conservation is hampered by a lack of demographic information to assess population long-term viability. When longitudinal studies (e.g., Capture-Mark-Recapture design) are not feasible, the only available data may be cross-sectional, for example, stranding for marine mammals. Survival analysis deals with age at death (i.e., time to event) data and allows to estimate survivorship and hazard rates assuming that the cross-sectional sample is representative. Accommodating a bathtub-shaped hazard, as expected in wild populations, was historically difficult and required specific models. We identified a simple linear regression model with individual frailty that can fit a bathtub-shaped hazard, take into account covariates, allow goodness-of-fit assessments and give accurate estimates of survivorship in realistic settings. We first conducted a Monte Carlo study and simulated age at death data to assess the accuracy of estimates with respect to sample size. Secondly, we applied this framework on a handful of case studies from published studies on marine mammals, a group with many threatened and data-deficient species. We found that our framework is flexible and accurate to estimate survivorship with a sample size of 300 . This approach is promising for obtaining important demographic information on data-poor species.     

Monogamy in marine fishes

The formation of long-term pair bonds in marine fish has elicited much empirical study. However, the evolutionary mechanisms involved remain contested and previous theoretical frameworks developed to explain monogamy in birds and mammals are not applicable to many cases of monogamy in marine fish. In this review, we summarise all reported occurrences of social monogamy in marine fish, which has so far been observed in 18 fish families. We test quantitatively the role of ecological and behavioural traits previously suggested to be important for the evolution of monogamy and show that monogamous species occur primarily in the tropics and are associated with coral reef environments in which territory defence and site attachment is facilitated. However, there is little evidence that obligately monogamous species are smaller in body size than species that can adopt a polygynous mating system. We review the evidence pertaining to six hypotheses suggested for the evolution of monogamous pair bonds: (1) biparental care, (2) habitat limitation, (3) low population density/low mate availability/low mobility, (4) increased reproductive efficiency, (5) territory defence, and (6) net benefit of single mate sequestration. We outline predictions and associated empirical tests that can distinguish between these hypotheses, and assess how generally each hypothesis explains monogamy within and between breeding periods for species with different types of territories (i.e. feeding only or feeding and breeding). Hypotheses (1) and (2) have limited applicability to marine fishes, while hypotheses (3)-(5) have little empirical support beyond the species for which they were designed. However, the role of paternal care in promoting monogamous pair bonds is not explicit in these hypotheses, yet paternal care has been reported in more than 70 monogamous marine fish. We show that paternal care may act to increase the likelihood of monogamy in combination with each of the proposed hypotheses through decreased benefits to males from searching for additional mates or increased advantages to females from sequestering a single high-quality mate. Among species defending breeding and feeding territories, the benefits, both within and between reproductive periods, of sequestering a single high-quality mate (hypothesis 6) appear to be the best explanation for socially monogamous pairs. For species without parental care (i.e. holding only feeding territories), territory defence (hypothesis 5) in combination with the benefits of guarding a large mate (hypothesis 6) could potentially explain most instances of monogamy. Empirical studies of marine fishes over the past two decades are therefore slowly changing the view of monogamy from a mating system imposed upon species by environmental constraints to one with direct benefits to both sexes.     

种群统计随机性和环境随机性对种群绝灭的影响

影响种群绝灭的随机干扰可分为种群统计随机性、环境随机性和随机灾害三大类。在相对稳定的环境条件下和相对较短的时间内,以前两类随机干扰对种群绝灭的影响为生态学家关注的焦点。但是,由于自然种群动态及其影响因子的复杂特征,进一步深入研究随机干扰对种群绝灭的作用在理论上和实践上都必须发展新的技术手段。本文回顾了种群统计随机性与环境随机性的概念起源与发展,系统阐述了其分析方法。归纳了两类随机性在种群绝灭研究中的应用范围、作用方式和特点的异同和区别方法。各类随机作用与种群动态之间关系的理论研究与对种群绝灭机理的实践研究紧密相关。根据理论模型模拟和自然种群实际分析两方面的研究现状,作者提出了进一步深入研究随机作用与种群非线性动态方法的策略。指出了随机干扰影响种群绝灭过程的研究的方向：更多的研究将从单纯的定性分析随机干扰对种群动力学简单性质的作用,转向结合特定的种群非线性动态特征和各类随机力作用特点具体分析绝灭极端动态的成因,以期做出精确的预测。     

Diffusion analysis and stationary distribution of the two-species lottery competition model

The lottery model is a stochastic population model in which juveniles compete for space. Examples include sedentary organisms such as trees in a forest and members of marine benthic communities. The behavior of this model appears to be characteristic of that found in other sorts of stochastic competition models. In a community with two species, it was previously demonstrated that coexistence of the species is possible if adult death rates are small and environmental variation is large. Environmental variation is incorporated by assuming that the birth rates and death rates are random variables. Complicated conditions for coexistence and competitive exclusion have been derived elsewhere. In this paper, simple and easily interpreted conditions are found by using the technique of diffusion approximation. Formulae are given for the stationary distribution and means and variances of population fluctuations. The shape of the stationary distribution allows the stability of the coexistence to be evaluated.     

Extinction times and moment closure in the stochastic logistic process

We investigate the statistics of extinction times for an isolated population, with an initially modest number M of individuals, whose dynamics are controlled by a stochastic logistic process (SLP). The coefficient of variation in the extinction time V is found to have a maximum value when the death and birth rates are close in value. For large habitat size K we find that Vmax is of order K1/4 / M1/2, which is much larger than unity so long as M is small compared to K1/2. We also present a study of the SLP using the moment closure approximation (MCA), and discuss the successes and failures of this method. Regarding the former, the MCA yields a steady-state distribution for the population when the death rate is low. Although not correct for the SLP model, the first three moments of this distribution coincide with those calculated exactly for an adjusted SLP in which extinction is forbidden. These exact calculations also pinpoint the breakdown of the MCA as the death rate is increased.     

Host mating system and the prevalence of disease in a plant population

A modified susceptible-infected-recovered (SIR) host-pathogen model is used to determine the influence of plant mating system on the outcome of a host-pathogen interaction. Unlike previous models describing how interactions between mating system and pathogen infection affect individual fitness, this model considers the potential consequences of varying mating systems on the prevalence of resistance alleles and disease within the population. If a single allele for disease resistance is sufficient to confer complete resistance in an individual and if both homozygote and heterozygote resistant individuals have the same mean birth and death rates, then, for any parameter set, the selfing rate does not affect the proportions of resistant, susceptible or infected individuals at equilibrium. If homozygote and heterozygote individual birth rates differ, however, the mating system can make a difference in these proportions. In that case, depending on other parameters, increased selfing can either increase or decrease the rate of infection in the population. Results from this model also predict higher frequencies of resistance alleles in predominantly selfing compared to predominantly outcrossing populations for most model conditions. In populations that have higher selfing rates, the resistance alleles are concentrated in homozygotes, whereas in more outcrossing populations, there are more resistant heterozygotes.     

Evaluation of methodology for detection of genetic bottlenecks: inferences from temporally replicated lake trout populations

Statistical methods have been proposed to detect recent bottlenecks on the basis of genetic characterizations of natural populations. In the absence of direct estimates of contemporary or historical population numbers, we tested the indirect M-ratio method based on microsatellite motif size frequency profiles using three historical and three contemporary Great Lakes populations of Salvelinus namaysuch for which severe reductions in population numbers are documented. Simulations employing plausible ranges of empirical population parameter values were used to explore bottleneck likelihood surfaces. We show that single values of the M-ratio are not sufficient to unambiguously infer a bottleneck without knowledge of mutation rates and effective population size (i.e., 4Ne mu or [symbol: see text]). Inferences of the degree of population bottleneck would be best supported if analyses were conducted across plausible ranges of [symbol: see text] and by qualitative comparisons among population samples.