Fitting probability models to population dynamics data

Methods for modeling population dynamics in probability using the generalized point process approach are developed. The life history of these populations is such that seasonal reproduction occurs during a short time. Several models are developed and analyzed. Data about two species: colonial spiders (Stegodyphus dumicola) and a migratory bird (wood thrush, Hylocichla mustelina) are used to estimate model parameters with appropriate log maximum likelihood functions. For the spiders, the model is fitted to provide evolutionary feasible colony size based on maximum likelihood estimates of fecundity and survival data. For the migratory bird species, a maximum likelihood estimates are derived for the fecundity and survival rates of young and adult birds and immigration rate. The presented approach allows computation of quantities of interest such as probability of extinction and average time to extinction.     

Use of fecundity measured directly throughout the breeding season to test a source-sink demographic model

Populations of landbirds (bird species that occupy terrestrial habitats for most of their life cycle) are declining throughout North America (north of Mexico) and Europe, yet little is known about how demography is driving this trend. A recent model of 5 geographically separated populations of Cerulean Warblers (Dendroica cerulea) that was based on within-season sampling of nest survival and fledgling success shows that all populations are sinks (annual reproduction is consistently less than annual adult mortality). I tested this indirect model by directly measuring fecundity (number of female fledglings/female) during the breeding season for 2 years in a Cerulean Warbler population occupying a mature forest in southwestern Michigan (U.S.A.) I determined territories of male birds on the basis of male plumage characters and phases of the nesting cycle (2007) and on uniquely color-banded males (2008). I transferred locations of identified males to topographic maps. I counted all fledglings in territories from May to July each year. The model I tested may apply only to single-brooded species; therefore, I searched the literature to estimate the percentage of single-brooded species in North America. The breeding season of Cerulean Warblers was short- nearly all nests were initiated from mid-May to late June. Nest predation and brood parasitism were primary and rare causes of nest failure, respectively. Significantly fewer Cerulean Warblers fledged from parasitized than from nonparasitized nests. Fledgling survival required to maintain the population size was well above previously published values for Neotropical migrants. Single-brooded species comprise 62% of North American breeding bird species for which the number of broods per year is known; I believe my results may apply to these species. The consistency between identification of populations as sources or sinks on the basis of either model estimates or direct measurements suggests that a demographic model relying on within-season sampling of fecundity is adequate to determine population status of single-brooded avian populations. In addition, on the basis of results of previous studies, annual adult survival rate of the Cerulean Warbler is typical of parulid warblers that are not declining. Thus, low fecundity, here determined with different quantitative methods, can drive status of landbird species with high-observed survival.     

Potential Misuse of Avian Density as a Conservation Metric

Abstract: Effective conservation metrics are needed to evaluate the success of management in a rapidly changing world. Reproductive rates and densities of breeding birds (as a surrogate for reproductive rate) have been used to indicate the quality of avian breeding habitat, but the underlying assumptions of these metrics rarely have been examined. When birds are attracted to breeding areas in part by the presence of conspecifics and when breeding in groups influences predation rates, the effectiveness of density and reproductive rate as indicators of habitat quality is reduced. It is beneficial to clearly distinguish between individual‐ and population‐level processes when evaluating habitat quality. We use the term reproductive rate to refer to both levels and further distinguish among levels by using the terms per capita fecundity (number of female offspring per female per year, individual level) and population growth rate (the product of density and per capita fecundity, population level). We predicted how density and reproductive rate interact over time under density‐independent and density‐dependent scenarios, assuming the ideal free distribution model of how birds settle in breeding habitats. We predicted population density of small populations would be correlated positively with both per capita fecundity and population growth rate due to the Allee effect. For populations in the density‐dependent growth phase, we predicted no relation between density and per capita fecundity (because individuals in all patches will equilibrate to the same success rate) and a positive relation between density and population growth rate. Several ecological theories collectively suggest that positive correlations between density and per capita fecundity would be difficult to detect. We constructed a decision tree to guide interpretation of positive, neutral, nonlinear, and negative relations between density and reproductive rates at individual and population levels.     

A survival-analysis-based simulation model for Russian wheat aphid population dynamics

A simulation model for Russian wheat aphid (RWA), Diuraphis noxia (Mordvilko), populations is built by integrating survival-analysis-based development and survivor functions and the same-shape reproduction distribution model in the framework of Leslie [Leslie, P.H., 1945. On the use of matrices in certain population mathematics. Biometrika 33, 183–212] matrix structure. Survival analysis is utilized to model both the development and survival of RWA populations, and the Cox (1972) proportional hazards model is fitted with the data sets from our laboratory observation of 1800 RWA individuals under 25 factorial combinations of five temperature regimes and five barley plant-growth stages. Rather than using simple age-specific survivor rates as in the traditional Leslie matrix, the survivor functions based on survival analysis describe age-specific, temperature and plant stage-dependent RWA survival probabilities. Similarly, a probability model from survival analysis to estimate the probability that an individual will reach mature adult stage is utilized to describe the development process; this makes the transition from nymphal stage to mature adult stage dependent on RWA age as well as temperature and plant-growth stage.Inspired by the same-shape distribution and rate-summation approach for modeling insect development, a similar approach for modeling insect reproduction under variable temperature is developed. This new same-shape reproduction distribution model incorporates individual variation in reproduction capability, as well as the effects of RWA age, temperature and plant-growth stage. Consequently, the same-shape reproduction distribution model replaces the simple age-specific fecundities in Leslie matrix model. To the best of our knowledge, this work is the first to introduce survival analysis to simulation modeling in entomology and ecology and also the first to integrate our newly developed same-shape reproduction distribution model into application.     

Dependence of the Endangered Black‐Capped Vireo on Sustained Cowbird Management

Conservation‐reliant species depend on active management, even after surpassing recovery goals, for protection from persistent threats. Required management may include control of another species, habitat maintenance, or artificial recruitment. Sometimes, it can be difficult to determine whether sustained management is required. We used nonspatial stochastic population projection matrix simulation and a spatially explicit population model to estimate the effects of parasitism by a brood parasite, the Brown‐headed Cowbird (Moluthrus ater), on a population of endangered Black‐capped Vireos (Vireo atricapilla). We simulated parasitism as a percentage of breeding vireo pairs experiencing decreased fecundity due to cowbirds. We estimated maximum sustainable parasitism (i.e., highest percentage of parasitized vireo breeding pairs for which population growth is ≥1) with the nonspatial model under multiple scenarios designed to assess sensitivity to assumptions about population growth rate, demographic effects of parasitism, and spatial distribution of parasitism. We then used the spatially explicit model to estimate cumulative probabilities of the population falling below the population recovery target of 1000 breeding pairs for a range of parasitism rates under multiple scenarios. We constructed our models from data on vireos collected on the Fort Hood Military Reservation, Texas (U.S.A.). Estimates of maximum sustainable parasitism rates ranged from 9–12% in scenarios with a low (6%) vireo population growth rate to 49–60% in scenarios with a high (24%) growth rate. Sustained parasitism above 45–85%, depending on the scenario, would likely result in the Fort Hood Vireo population dropping below its recovery goal within the next 25 years. These estimates suggest that vireos, although tolerant of low parasitism rates, are a conservation‐reliant species dependent on cowbird management. Dependencia de Vireo atricapilla, Especie en Peligro, hacia el Manejo Sostenido de Moluthurs ater     

Population Viability Analysis of the Florida Manatee (Trichechus manatus latirostris), 1976–1991

Recent development of age-determination techniques for Florida manatees (Trichechus manatus latirostris) has permitted derivation of age-specific data on reproduction and survival of a sample of 1212 carcasses obtained throughout Florida from 1976–1991. Population viability analysis using these data projects a slightly negative growth rate (−0.003) and an unacceptably low probability of persistence (0.44) over 1000 years. The main factors affecting population projections were adult survival and fecundity. A 10% increase in adult mortality would drive the population to extinction over a 1000-year time scale, whereas a 10% decrease in adult mortality would allow slow population growth. A 10% decrease in reproduction would also result in extinction. We conclude that management must focus on retaining and improving the conditions under which manatee demography operates. The major identified agent of mortality is boat-manatee collisions, and rapidly increasing numbers of humans and registered boats portend an increase in manatee mortality. Zoning of manatee-occupied waters for reductions in boating activity and speed is essential to safeguard the manatee population. If boating regulations being implemented by the state of Florida in each of 13 key coastal counties are completed, enforced, and effective, manatees and human recreation could coexist indefinitely. If regulation is unsuccessful, the Florida manatee population is likely to decline slowly toward extinction.     

Between discrete and continuous: consumer-resource dynamics with synchronized reproduction

In many consumer-resource systems the consumer population has synchronized reproduction at regular intervals (e.g., years) but consumes the resource and dies continuously, while the resource population grows continuously or has overlapping generations that are short relative to the time between consumer reproductive events. Such systems require "semi-discrete" models that have both discrete and continuous components. This paper defines and analyzes a canonical, semi-discrete model for a widespread class of consumer-resource interactions in which the consumer is a discrete breeder and the resource reproduction can be described continuously. The model is the analog of the Nicholson-Bailey and Lotka-Volterra models for discrete and continuous systems, respectively. It thereby develops the basis for understanding more realistic, and hence more complex, semi-discrete models. The model can display stable equilibria, consumer-resource cycles, and single-species-like overcompensation cycles. Cycles are induced by high maximum fecundity in the consumer. If the resource grows rapidly and the consumer has high maximum fecundity, the model reduces to a single-species discrete-time model of the consumer, which can exhibit overcompensation cycles. By contrast, such cycles in discrete consumer-resource models typically occur only in the resource once the consumer is extinct. Also unlike a common class of discrete models that do not display consumer-resource cycles with periods below four years, semi-discrete models can exhibit consumer-resource cycles with periods as short as two years.     

Pre-reproductive survival in a tropical bird and its implications for avian life histories

The factors that affect survival until reproduction are essential to understanding the organization of life histories within and among species. Theory predicts, for example, that survival until reproduction influences the optimum level of reproductive investment by parents, which might partly explain prolonged parental care in species with high first-year survival. Tests and refinements of life-history theory have been hampered, however, by a lack of field-based estimates of pre-reproductive survival, especially for tropical species, which have been the subject of many comparative analyses. Tropical species are predicted to have higher first-year survival and delayed reproduction compared to Northern Hemisphere species. We estimated survival until reproduction, age at first reproduction, and sources of variation in juvenile survival in a Neotropical passerine, the Western Slaty-Antshrike (Thamnophilus atrinucha), in central Panama. We observed that fledged antshrikes had 76% survival through the dependent period and 48% survival to the age of 1 year; survival rate was lowest during the first week after leaving the nest. Timing of fledging within the breeding season, fledgling mass, and age at dispersal influenced survival, while sex of offspring and year did not. Individuals did not breed until two years of age, and post-fledging pre-reproductive survival was 41% of annual adult survival. High survival until reproduction in antshrikes balanced their low annual productivity, resulting in a stable population. Survival during the post-fledging period of dependence and the first year of independence in the Western Slaty-Antshrike exceeded estimates for Northern Hemisphere species. This difference appears to be associated with the extended post-fledging parental care, delayed dispersal, low costs of dispersal, and the less seasonal environment of antshrikes.     

Floater mortality within settlement areas can explain the Allee effect in breeding populations

The Allee effect (the positive relationship between population growth rate and population size) is a constraint of some animal populations at low numbers, which increases their likelihood of extinction because of a decrease in reproduction and/or survival. We were able to demonstrate that the Allee effect can be the result of a mortality increase affecting floaters (i.e. dispersing individuals able to enter as breeders in the reproductive population when a breeding territory or a potential mate – owner of a suitable breeding territory – becomes available). Previously, potential mechanisms underlying Allee effects were always related to the breeding portion of a population only. In contrast, our understanding of or solutions to population declines due to the Allee effects can reside elsewhere, away from breeding territories.     

Effects of age and sex ratios on offspring recruitment rates in translocated black rhinoceros

Success of animal translocations depends on improving postrelease demographic rates toward establishment and subsequent growth of released populations. Short‐term metrics for evaluating translocation success and its drivers, like postrelease survival and fecundity, are unlikely to represent longer‐term outcomes. We used information theory to investigate 25 years of data on black rhinoceros (Diceros bicornis) translocations. We used the offspring recruitment rate (ORR) of translocated females—a metric integrating survival, fecundity, and offspring recruitment at sexual maturity—to detect determinants of success. Our unambiguously best model (AICω = 0.986) predicted that ORR increases with female age at release as a function of lower postrelease adult rhinoceros sex ratio (males:females). Delay of first postrelease reproduction and failure of some females to recruit any calves to sexual maturity most influenced the pattern of ORRs, and the leading causes of recruitment failure were postrelease female death (23% of all females) and failure to calve (24% of surviving females). We recommend translocating older females (≥6 years old) because they do not exhibit the reproductive delay and low ORRs of juveniles (<4 years old) or the higher rates of recruitment failure of juveniles and young adults (4–5.9 years old). Where translocation of juveniles is necessary, they should be released into female‐biased populations, where they have higher ORRs. Our study offers the unique advantage of a long‐term analysis across a large number of replicate populations—a science‐by‐management experiment as a proxy for a manipulative experiment, and a rare opportunity, particularly for a large, critically endangered taxon such as the black rhinoceros. Our findings differ from previous recommendations, reinforce the importance of long‐term data sets and comprehensive metrics of translocation success, and suggest attention be shifted from ecological to social constraints on population growth and species recovery, particularly when translocating species with polygynous breeding systems.     

Population level effects of reduced fecundity in the fish species perch (Perca fluviatilis) and the implications for environmental monitoring

A 40% reduction in relative gonad size in perch (Perca fluviatilis) has been observed over that past two decades at the Swedish national reference site Kvädöfjärden. This biomarker response could be interpreted as a reduction in fecundity and increased risk of local extinction. However, abundance estimates from the same area has not provided any evidence of a reduction in population size. In the present study, a matrix population model was developed to investigate if a reduction in fecundity can be expected to have long term effects on population viability for perch and to evaluate the probability to detect such effects through abundance estimates. The model was parameterized from 17 years of population data from Kvädöfjärden as well as from other studies on perch. The model included density dependence and environmental stochasticity. The results indicated that a reduction in fecundity that is in level with the observed reduction in relative gonad size in Kvädöfjärden will cause a substantial risk for local extinction. The risk that the population will fall below 20% of the carrying capacity within 50 years is 44% when the fecundity is reduced by 40%. However, due to variability in abundance measurements it will take some time before a reduction in gonad size leads to statistically significant effects on the population. If the fecundity is reduced by 40% successively over a 10-year period, the probability to detect this through abundance estimates within 10 years is less than 50%. The results of the present study clearly show that relevant biomarkers have an important role in environmental monitoring as early warning signals, preferably in combination with measurements at higher levels of biological organization.     

Population dynamics of Euterpina acutifrons (Copepoda: Harpacticoida) from North Inlet,South Carolina,with reference to Dimorphic Males

The population dynamics of Euterpina acutifrons (Dana), a pelagic, harpacticoid copepod, are summarized in a life table based on field data. Highest mortality occurred in the last naupliar stage (NVI) and the first copepodite stage (CI). Overall survival in the field was 0.06% from the first naupliar stage (NI) to adult (CVI). The net reproductive rate (R _o=55.590) and intrinsic rate of increase (I _m=0.28) were sufficiently high to maintain a population with such a low survival rate in nature. E. acutifrons was present and breeding in the field from April through December. Low temperatures limited breeding, which began when the temperature reached 16.5°C and ceased when it fell to 11°C. Optimum temperature for North Inlet E. acutifrons was 25°C, with a maximum laboratory survival of 15.3% and a generation time of 10.3 days. Generation time in the field (20°C) was 14 days. Temperature also affected the abundance of dimorphic males. Small males were always most abundant, but peaked during the coldest month; large males became equal in abundance only during the varmest months.Contribution No. 298 from the Belle W. Baruch Institute for Marine Biology and Coastal Research.     

Effect of butyl benzyl phthalate on life table-demography of two successive generations of cladoceran Moina macrocopa Straus

In this study, the acute toxicity of butyl benzyl phthalate (BBP) to freshwater cladoceran Moina macrocopa was tested, and its chronic effects on survival and reproduction of two successive generations of the cladoceran were studied using life-table demographic method. The results showed that the 48-hr LC50 of BBP for M. macrocopa was 3.69 mg l(-1). Compared to the blank controls, BBP at 125, 500, 1000 and 2000 microg l(-1) significantly shortened the life expectancy at birth, BBP at 125-2000 microg l(-1) decreased the net reproductive rate, and BBP at 500 and 1000 microg I(-1) shortened the generation time but increased the intrinsic rate of population increase of the parental M. macrocopa. BBP at 62.5,125, 500,1000 and 2000 microg l(-1) increased the intrinsic rate of population increase of the F1 generation. A significant dose-effect relationship existed between BBP concentration and life expectancy at birth, net reproductive rate as well as intrinsic rate of population increase of the parental M. macrocopa. The parental M. macrocopa were more sensitive in survival, development and reproduction to BBP than the F1 generation, but the reverse was also true in the population growth. Extending chronic toxicity tests to the second generation of M. macrocopa increased the cost-effectiveness of the assays.     

Bridging the generation gap in plants: pollination, parental fecundity, and offspring demography

Despite extensive study of pollination and plant reproduction on the one hand, and of plant demography on the other, we know remarkably little about links between seed production in successive generations, and hence about long-term population consequences of variation in pollination success. We bridged this "generation gap" in Ipomopsis aggregata, a long-lived semelparous wildflower that is pollinator limited, by adding varying densities of seeds to natural populations and following resulting plants through their entire life histories. To determine whether pollen limitation of seed production constrains rate of population growth in this species, we sowed seeds into replicated plots at a density that mimics typical pollination success and spacing of flowering plants in nature, and at twice that density to mimic full pollination. Per capita offspring survival, flower production, and contribution to population increase (lambda) did not decline with sowing density in this experiment, suggesting that typical I. aggregata populations freed from pollen limitation will grow over the short term. In a second experiment we addressed whether density dependence would eventually erase the growth benefits of full pollination, by sowing a 10-fold range of seed densities that falls within extremes estimated for the natural "seed rain" that reaches the soil surface. Per capita survival to flowering and age at flowering were again unaffected by sowing density, but offspring size, per capita flower production, and lambda declined with density. Such density dependence complicates efforts to predict population dynamics over the longer term, because it changes components of the life history (in this case fecundity) as a population grows. A complete understanding of how constraints on seed production affect long-term population growth will hinge on following offspring fates at least through flowering of the first offspring generation, and doing so for a realistic range of population densities.     

Growth and population dynamic model for the non-zooxanthellate temperate solitary coral Leptopsammia pruvoti (Scleractinia, Dendrophylliidae)

In corals where complex life history processes decoupling age from size (e.g., fragmentation, fusion, partial colony mortality) are rare or clearly detectable, individual age may be determined from size, and age-based growth and population dynamic models may be applied. One example is the solitary Mediterranean coral Leptopsammia pruvoti Lacaze-Duthiers 1897, whose population size and structure, and growth rates were determined at Calafuria (43°28′N and 10°20′E), Ligurian Sea, from December 2007 to June 2009. Growth rate decreased with increasing size. The growth curve derived from field measurements confirmed the one obtained by growth band analysis. The frequency of individuals decreased exponentially with age, indicating a steady state population. Turnover time was 2.3 years. Maximum life span was 13 years. Most reproductive output was from intermediate age classes (6 years), while older individuals (>7 years), although having higher fecundity, were rare and accounted for a minority of population reproductive output. In comparison with other solitary dendrophylliids, L. pruvoti life strategy was characterized by a reproduction with r-strategy correlates (high fecundity, short embryo incubation, small planula size, fast achievement of sexual maturity), and a rate of demographic renewal occurring halfway along the r–K continuum (intermediate turnover time and maximum longevity).     

Complex dynamics of the population with a simple age structure

The effects of the following modes of density-dependent control of population growth: density-dependent birth rate, adult survival rate, juvenile survival rate are compared based on the mathematical model of population dynamics. It is shown that the most efficient mechanisms limiting population size are decreasing with the growth of the adult population birth rate and/or the decreasing survival rate of the offspring with the increase in their number. However, these same mechanisms are responsible for oscillations of the population size and its chaotic change. The density-dependence of the adult survival rate is not efficient in constraining the population growth, but it can substantially limit the magnitude of oscillations of the population size.     

Use of Integrated Modeling to Enhance Estimates of Population Dynamics Obtained from Limited Data

Abstract:  Demographic data of rare and endangered species are often too sparse to estimate vital rates and population size with sufficient precision for understanding population growth and decline. Yet, the combination of different sources of demographic data into one statistical model holds promise. We applied Bayesian integrated population modeling to demographic data from a colony of the endangered greater horseshoe bats (Rhinolophus ferrumequinum) . Available data were the number of subadults and adults emerging from the colony roost at dusk, the number of newborns from 1991 to 2005, and recapture data of subadults and adults from 2004 and 2005. Survival rates did not differ between sexes, and demographic rates remained constant across time. The greater horseshoe bat is a long-lived species with high survival rates (first year: 0.49 [SD 0.06]; adults: 0.91 [SD 0.02]) and low fecundity (0.74 [SD 0.12]). The yearly average population growth was 4.4% (SD 0.1%) and there were 92 (SD 10) adults in the colony in year 2005. Had we analyzed each data set separately, we would not have been able to estimate fecundity, the estimates of survival would have been less precise, and the estimate of population growth biased. Our results demonstrate that integrated models are suitable for obtaining crucial demographic information from limited data.     

Why breed communally? Factors affecting fecundity in a communal breeding mammal: the banded mongoose (<Emphasis Type="Italic">Mungos mungo</Emphasis>)

Fecundity is an important component of fitness. In cooperatively breeding species, studies aimed at understanding the factors that affect fecundity have largely been restricted to species that exhibit high reproductive skew, where reproduction is monopolised by a few individuals. In such species, dominant suppression and inbreeding avoidance are the principal explanations for low fecundity in subordinate females. In this paper, we evaluate the relative effects of individual, social, and environmental factors on female fecundity in a low skew cooperative breeding mammal: the banded mongoose (Mungos mungo). Most females (80%) conceived in each breeding event, and most pregnant females (93%) carried their litter to term. The principal determinants of a females fecundity were intrinsic qualities, particularly age and body size. However, there was no evidence of dominant suppression of subordinate reproduction or inbreeding avoidance. Similarly, there was little indication that social or environmental factors influence fecundity. We suggest that in the banded mongoose, the apparent lack of costs to inbreeding, and the absence of dominant female suppression of reproduction in other females result in low reproductive skew. Indeed, in banded mongooses, like lions (Felis leo), multiple breeding may be a consequence of benefits to rearing young communally.Communicated by F. Trillmich     

A model for intraguild predation dynamics between immature stages

Dynamical models usually assume that predation occurs between mature stages and/or between mature and immature stages. In this work a stage-structured discrete time model is developed for a system where intraguild predation takes place only in the course of immature stages of predator and its prey. Therefore, the proposed mathematical setup demands functional relations linking predation in immature life stages with survival and fecundity in mature stages. The behavior of the model is examined in order to investigate the interplay among predator attack rate, its satiation of prey consumption and the success of intraguild predator invasion.     

Albatross populations in peril: a population trajectory for black-browed albatrosses at south Georgia.

Simulation modeling was used to reconstruct Black-browed Albatross (Diomedea melanophris) population trends. Close approximations to observed data were accomplished by annually varying survival rates, reproductive success, and probabilities of returning to breed given success in previous years. The temporal shift in annual values coincided with the start of longline fishing at South Georgia and potential changes in krill abundance. We used 23 years of demographic data from long-term studies of a breeding colony of this species at Bird Island, South Georgia, to validate our model. When we used annual parameter estimates for survival, reproductive success, and probabilities of returning to breed given success in previous years, our model trajectory closely followed the observed changes in breeding population size over time. Population growth rate was below replacement (lambda < 1) in most years and was most sensitive to changes in adult survival. This supports the recent IUCN uplisting of this species from "Vulnerable" to "Endangered." Comparison of pre-1988 and post-1988 demography (before and after the inception of a longline fishery in the breeding area) reveals a decrease in lambda from 0.963 to 0.910. A life table response experiment (LTRE) showed that this decline in lambda was caused mostly by declines in survival of adults. If 1988-1998 demographic rates are maintained, the model predicts a 98% chance of a population of fewer than 25 pairs within 78 years. For this population to recover to a status under which it could be "delisted," a 10% increase in survival of all age classes would be needed.