Análisis mediante modelos de multiestados del impacto de la viruela aviar sobre una población de Verdecillos (Serinus serinus): la importancia de estimar las tasas de recaptura

Disease is one of the evolutionary forces shaping populations. Recent studies have shown that epidemics like avian pox, malaria, or mycoplasmosis have affected passerine population dynamics, being responsible for the decline of some populations or disproportionately killing males and larger individuals and thus selecting for specific morphotypes. However, few studies have estimated the effects of an epidemic by following individual birds using the capture–recapture approach. Because avian pox can be diagnosed by direct examination of the birds, we are here able to analyze, using multistate models, the development and consequences of an avian pox epidemic affecting in 1996, a population of Serins (Serinus serinus) in northeastern Spain. The epidemics lasted from June to the end of November of 1996, with a maximum apparent prevalence rate > 30% in October. However, recapture rate of sick birds was very high (0.81, range 0.37–0.93) compared to that of healthy birds (0.21, range 0.02–0.32), which highly inflated apparent prevalence rate. This was additionally supported by the low predicted transition from the state of being uninfected to the state of being infected (0.03, SE 0.03). Once infected, Serin avian pox was very virulent with (15–day) survival rate of infected birds being of only 0.46 (SE 0.17) compared to that of healthy ones (0.87, SE 0.03). Probability of recovery from disease, provided that the bird survived the first two weeks, however, was very high (0.65, SE 0.25). The use of these estimates together with a simple model, allowed us to predict an asymptotic increase to prevalence of about 4% by the end of the outbreak period, followed by a sharp decline, with the only remaining infestations being infected birds that had not yet recovered. This is in contrast to the apparent prevalence of pox and stresses the need to estimate recapture rates when estimating population dynamics parameters.Las enfermedades infecciosas son una de las fuerzas evolutivas que modulan a las poblaciones animales. Estudios recientes han puesto de manifiesto como epidemias como la viruela aviar, la malaria o la mycoplasmosis afectan a la dinámica de las poblaciones de passeriformes, siendo responsables de dramáticas reducciones en el tamaño de algunas poblaciones, o de la muerte desproporcionada de machos o de los individuos de mayor tamaño, seleccionando de ese modo en favor de determinados morfotipos. Sin embargo, pocos estudios han estimado los efectos de una epidemia mediante el seguimiento de los distintos individuos utilizando las técnicas de captura–recaptura. Debido al hecho de que la viruela aviar puede ser diagnosticada mediante el examen directo de los individuos, hemos podido analizar, utilizando modelos de multiestado, el desarrollo y consecuencias de una epidemia de viruela aviar que afectó en 1996, a una población de Verdecillos en el nordeste de España. La epidemia afectó a los Verdecillos desde junio hasta finales de noviembre, con una prevalencia aparente máxima de > 30% en octubre. Sin embargo, la tasa de recaptura de los individuos enfermos fue muy alta (0,81, rango 0,37–0,93), comparada con la de los individuos sanos (0,21, rango 0,02–0,32), lo cual exageraba en gran medida la tasa de prevalencia aparente. Este resultado estaba adicionalmente apoyado por la baja tasa estimada de transición del estado de no infectado al estado de infectado (0,03, SE 0,03). Una vez un Verdecillo quedaba infectado, la viruela aviar resultó muy virulenta, siendo la tasa de supervivencia (a 15 días) de los individuos enfermos de tan solo 0,46 (SE 0,17), comparada con la de los individuos no infectados (0,87, SE 0,03). La probabilidad de recuperación de la enfermedad, siempre y cuando el individuo hubiera sobrevivido las dos primeras semanas, fue sin embargo, muy alta (0,65, SE 0,25). Estos valores fueron utilizados para construir un modelo que permitió predecir el valor real de prevalencia de la enfermedad. Según el modelo, el porcentaje de individuos infectados después del brote debió incrementarse de forma asintótica hasta el 4%, manteniéndose en ese valor, hasta que se produjo una abrupta reducción en el número de individuos infectados al final de la epidemia, siendo estos los individuos que todavía no se habían recuperado de la enfermedad. Estos valores contrastan con los valores aparentes de prevalencia de la viruela y enfatiza la necesidad de estimar la tasa de recaptura cuando se realizan estimaciones de los distintos parámetros de dinámica de poblaciones

Aplicación de la modelación integrada bayesiana y de los métodos Monte Carlo basados en cadenas de Markov para la conservación de una especie recolectada

When endeavoring to make informed decisions, conservation biologists must frequently contend with disparate sources of data and competing hypotheses about the likely impacts of proposed decisions on the resource status. Frequently, statistical analyses, modeling (e.g., for population projection) and optimization or simulation are conducted as separate exercises. For example, a population model might be constructed, whose parameters are then estimated from data (e.g., ringing studies, population surveys). This model might then be used to predict future population states, from current population estimates, under a particular management regime. Finally, the parameterized model might also be used to evaluate alternative candidate management decisions, via simulation, optimization, or both. This approach, while effective, does not take full advantage of the integration of data and model components for prediction and updating; we propose a hierarchical Bayesian context for this integration. In the case of American black ducks (Anas rubripes), managers are simultaneously faced with trying to extract a sustainable harvest from the species, while maintaining individual stocks above acceptable thresholds. The problem is complicated by spatial heterogeneity in the growth rates and carrying capacity of black ducks stocks, movement between stocks, regional differences in the intensity of harvest pressure, and heterogeneity in the degree of competition from a close congener, mallards (Anas platyrynchos) among stocks. We have constructed a population life cycle model that takes these components into account and simultaneously performs parameter estimation and population prediction in a Bayesian framework. Ringing data are used to develop posterior predictive distributions for harvest mortality rates, given as input decisions about harvest regulations. Population surveys of black ducks and mallards are used to obtain stock–specific estimates of population size for both species, for inputs into the population life–cycle model. These estimates are combined with the posterior distributions for harvest mortality, to obtain posterior predictive distributions of future population status for candidate sets of regional harvest regulations, under alternative biological hypotheses for black duck population dynamics. These distributions might then be used for both the exploration of optimal harvest policies and for sequential updating of model posteriors, via comparison of predictive distributions to future survey estimates of stock–specific abundance. Our approach illustrates advantages of MCMC for integrating disparate data sources into a common predictive framework, for use in conservation decision making.En el momento de tomar decisiones bien fundamentadas, es habitual que los biólogos conservacionistas deban enfrentarse a fuentes de datos dispares e hipótesis alternativas acerca de los impactos probables que tendrán las decisiones propuestas en el estado del recurso. A menudo, tanto los análisis estadísticos, como la modelación (para la proyección poblacional, por ejemplo) y la optimización o simulación, se llevan a cabo como ejercicios independientes. Así, es posible que se construya un modelo poblacional, cuyos parámetros se estimen a partir de datos (como estudios de anillamiento y estudios poblacionales). Posteriormente, cabe la posibilidad de que este mismo modelo se emplee para predecir situaciones demográficas futuras a partir de las estimaciones de población actuales, utilizando para ello un sistema de gestión determinado. Por último, el modelo parametrizado también puede emplearse para evaluar posibles decisiones de gestión alternativas, a través de la simulación, la optimización, o ambos procedimientos. Si bien este enfoque resulta eficaz, no aprovecha al máximo la integración de datos y los componentes de los modelos para la predicción y actualización. En este estudio proponemos un contexto bayesiano jerárquico que permite efectuar dicha integración. En el caso del ánade sombrío americano (Anas rubripes), los gestores deben enfrentarse a la labor de intentar extraer una recolección sostenible de la especie, al tiempo que mantienen los stocks de individuos por encima de umbrales aceptables. El problema se ve agravado por la heterogeneidad espacial que presentan las tasas de crecimiento y la carga cinegética de los stocks de ánades sombríos, el movimiento entre los stocks, las diferencias regionales en la intensidad de la presión recolectora y la heterogeneidad en el grado de competencia por parte de un congénere cercano —el ánade real (Anas platyrynchos)— entre los stocks. Hemos formulado un modelo del ciclo vital de la población que toma en consideración estos componentes, al tiempo que permite llevar a cabo una estimación de los parámetros y una predicción de la población en un marco bayesiano. Los datos de anillamiento se emplean para desarrollar distribuciones predictivas posteriores para las tasas de mortalidad durante la recolección, expresadas como decisiones de entrada acerca de la normativa sobre recolecciones. Los estudios poblacionales del ánade sombrío y del ánade real se emplean para obtener estimaciones sobre el tamaño poblacional específicas de los stocks de ambas especies, que se emplearán como entradas para el modelo del ciclo vital de la población. Dichas estimaciones se combinan con las distribuciones posteriores para la mortalidad durante la recolección, con el propósito de obtener distribuciones predictivas posteriores de la situación demográfica futura para posibles conjuntos de normativas regionales acerca de la recolección, de acuerdo con hipótesis biológicas alternativas relativas a la dinámica poblacional del ánade sombrío. En una fase posterior, tales distribuciones pueden utilizarse tanto para la investigación de políticas óptimas en materia de recolección, como para la actualización secuencial de distribuciones posteriores del modelo mediante la comparación de distribuciones predictivas para estimaciones en estudios futuros acerca de la abundancia poblacional presente de forma específica en los stocks. Nuestro enfoque ilustra las ventajas que presentan las técnicas de Montecarlo basadas encadenas de Markov (MCMC) para integrar fuentes de datos dispares en un marco predictivo común, con vistas a su utilización en la toma de decisiones sobre conservación

The quantitative study of marked individuals in ecology, evolution and conservation biology: a foreword to the EURING 2003 Conference

Few fields in modern ecology have developed as fast as the analysis of marked individuals in the study of wild animal populations (Seber & Schwarz, 2002). This is the topic of EURING Conferences, which from 1986 have been the premier forum for advances in capture–recapture methodology. In this sense, EURING Conferences still maintain the flavour that originally inspired scientific meetings: to disseminate the very last findings, ideas and results on the field. Traditionally, EURING Conferences have been published in the form of Proceedings, which because of their relevant content, become a required reading to anyone interested in the capture–recapture methodology. EURING 2003 was held in Radolfzell (Germany), hosted by the Max Planck Research Centre for Ornithology, and the Proceedings appear as a special issue of Animal Biodiversity and Conservation. The full title of the 2003 meeting was "The quantitative study of marked individuals in ecology, evolution and conservation biology", which stands for one of the main aims of the meeting: to establish the capture-recapture approach as one of the standard methodologies in studies within these fields. One of the shared views is that capture–recapture methodologies have reached a considerable maturity, but the need still exists to spread their use as a "standard" methodology. The nice review paper by Lebreton et al. (1993) in Trends in Ecology and Evolution is still applicable, in that general ecologists and evolutionary biologists still resist their general use. The same applies to conservation biology, where the analysis of marked individuals may also be a key tool in its development. We hope, with the spread of 2003 Proceedings, to help to fill this gap. The Proceedings follow the same general structure as the Conference. We organised the EURING meeting in 10 technical sessions, covering what we considered as fastest growing areas in the field. We appointed for each session, two chairs, which were charged with selecting 4–7 talks on the topic of their session. Each session additionally included a plenary conference intended to summarise or to provide a general but synthetic flavour of the topic. As a novelty in EURING conferences, we asked session chairs to include at least one talk dealing with study species other than birds. This is the result of a heated but fruitful discussion at EURING 2000 in Point Reyes, and fits with the general aim to spread the capture–recapture methodology beyond zoological groups: although EURING as an organization, deals with birds, and conferences have traditionally focused on this group, the capture–recapture approach is becoming a standard way to address biologically relevant questions on populations and individuals (Schwarz, 2002), for any zoological group. This volume, contains several nice examples of taxa other than birds. As far as possible, we selected chairs so that each session was delineated with a good balance between the biological and the statistician emphasis. This balance has in fact characterised EURING conferences, which in addition to the workshop atmosphere always present, has lead to very fruitful exchanges. Session chairs were also asked to act as editors for the papers within their session. All the papers were hence subjected to peer review, as in any other issue of Animal Biodiversity and Conservation, and presentation of the paper in the Conference did not assure publication in the Proceedings. This has lead to an even higher quality of the papers presented at the Conference. Editors were additionally asked to write a short summary on their session. Given that these summaries also present the views of the Editors on the different topics presented, we have preferred each introduction to appear as a short paper in the front of each one of the sessions, so that it can be cited as a regular paper. The Proceedings start with the Honour Speaker Talk by James Nichols (Nichols, 2004). This talk is traditionally the last one in the Conference, but we think that it nicely summarises how and why capture–recapture has developed to its current healthy state. The talk is in fact a tribute to David Anderson, to whom, as Nichols says, all of us are more or less in debt. Hence, we have preferred to move the Honour Talk to the front position of the Proceedings, and we would like this to be our humble tribute to David. At the end of the Proceedings appear a few papers which were presented in poster format, and a paper summarising several of the main topics presented at the traditional short course on capture–recapture, this time organized by the unflagging Evan Cooch. We would like to thank all the people who helped in one way or another to the successful completion of the EURING Conference and the Proceedings. We thank to the Session Chairs, their dedication and enthusiasm in organizing the sessions and also in editing the different papers. All their names appear in the front page of the Proceedings as credits. We thank Wolfgang Fiedler for the local organization of the event: a very difficult and exhausting task that is not always properly recognized. Jean Clobert, although unfortunately unable to attend the Conference, supported us with ideas and friendship meanwhile preparing the scientific program. Evan Cooch maintained the always successful web page (which probably will also become a classic in EURING conferences…), and organized the traditional course on capture–recapture. Charles Francis very efficiently organized the poster session and acted as editor for the papers sent for publication. Finally we thank the Ministerio de Ciencia y Tecnología for financial support to the publication of this special issue of Animal Biodiversity and Conservation (B.O.S. 2002–12283–E) and to the Natural History Museum of Barcelona for their support

Population dynamics and monitoring applied to decision–making

Research in wildlife conservation and management often affects decisions made by managers. Improving understanding through applied research is key to advancing the ability to manage birds and other organisms efficiently. Indeed, many papers from EURING 2003 and previous EURING meetings describe research on problems of pressing management concern. In this session, we focus on a subset of studies in which modeling and statistical estimation is explicitly connected to management decision-making. In these decision–centric studies, data are gathered and models are constructed with the explicit intention of using the resulting information to inform decisions about conservation. Whereas ecological models often produce information of value to decision makers, decision models explicitly include two additional features. First, management options are modeled via decision variables that link to system attributes that are directly responsive to management actions, such as harvest and habitat management. Second, certain outcomes are assigned value, via an objective or utility function. Both of these features involve factors beyond the usual consideration of ecological modeling; the first implies the presence of one or more "decision makers", and the second characterizes the societal preferences of each possible outcome resulting from a prospective decision. Our plenary paper, by Tim Haas (Haas, 2004), ventures the furthest into the realm of human behavior and societal processes by modeling the political context for conservation of the endangered cheetah (Acinonyx jubatus) in Africa. Haas shows that scientific information (e.g., population monitoring and population viability analyses) reaches decision makers through multiple pathways, each of which can modify or reinterpret the information signal. A predictive understanding of the country’s political as well as ecological processes is essential. Hass uses a system of interacting ecological and political influence diagrams to capture the stochastic, temporal processes of managing cheetah population in Kenya. The model predicts likely management decisions made by various actors within these countries, (e.g., the President, the Environmental Protection Agency, and rural residents) and the resulting probability of cheetah extinction following these decisions. By approaching the problem in both its political and ecological contexts one avoids consideration of decisions that, while beneficial from a purely conservation point of view, are unlikely to be implemented because of conflicting political objectives. Haas’s analysis demonstrates both the promise and challenges of this type of modeling, and he offers suggestions for overcoming inherent technical difficulties such as model calibration. The second paper, by Simon Hoyle and Mark Maunder (Hoyle & Maunder, 2004), uses a Bayesian approach to model population dynamics and the effects of commercial fishing bycatch for the eastern Pacific Ocean spotted dolphin (Stenella attenuata). Their paper provides a good example of why Bayesian analysis is particularly suited to many management problems. Namely, because it allows the integration of disparate pieces of monitoring data in the simultaneous estimation of population parameters; allows for incorporation of expert judgment and data from other systems and species; and provides for explicit consideration of uncertainty in decision–making. Alternative management scenarios can then be explored via forward simulations. In the third paper, Chris Fonnesbeck and Mike Conroy (Fonnesbeck & Conroy, 2004) present an integrated approach for estimating parameters and predicting abundance of American black duck (Anas rubripes) populations. They also employ a Bayesian approach and overcome some of the computational challenges by using Markov chain–Monte Carlo methods. Ring–recovery and harvest data are used to estimate fall age ratios under alternative reproductive models. These in turn are used to predict abundance of black ducks in each of 3 breeding areas. Finally, calibration of model parameters is obtained by comparing predicted with observed abundance. Although not currently implemented, the authors discuss how a Bayesian approach can be integrated into decision–making procedures using conditional modeling and application of reinforcement or machine learning. The next paper, by Martin Drechler and Franz Wätzold (Drechler & Wätzold, 2004), considers the problem of optimally allocating a conservation budget over time to maximize the survival probability of an endangered species. This must be done in the presence of uncertainty both about the biological system (e.g., probability of extinction under alternative plans), as well as about the availability of future funding. On the one hand, it would be undesirable to imprudently spend money now that might be needed for future conservation effort, when funds may be limited. On the other hand, failure to take action (and thus spend funds) sooner might lead to a higher probability of extinction. Provided estimates of uncertainty in funding, a model for trend in funding, and a model relating funding levels to viability, stochastic dynamic programming can be used to solve for an optimal amount of expenditure during any budget period. The final paper, by Clint Moore and Bill Kendall (Moore & Kendall, 2004), examines the costs incurred when uncalibrated indices to abundance are used in lieu of unbiased abundance estimates to make management decisions. Indices are often used instead of abundance estimates in the belief that the latter are too difficult and expensive. Moore and Kendall analyzed the impacts of using indices when making silvicultural decisions for the joint benefit of two bird populations, an endangered woodpecker and a shrub–nesting neotropical migrant. They computed the expected cost of uncertainty in the relationship between the monitoring index and population size, in currency units of the composite objective for both species. The authors found that substantial degradation of decision value can occur, depending on how uncertain the relationship between the index and true abundance. The results have important implications for managers, who may endeavor to cut costs by using index–based methods, while in the process incur these hidden costs of loss of decision utility. The five papers summarized above provide a good sampling of applications and methodological approaches, but are not a comprehensive coverage of the topic. For useful introductions to decision theory and methods, we suggest that readers consult Lindley (1985) or Clemen & Reilly (2001). A more detailed coverage of optimal decision–making, decision–making under uncertainty, and adaptive resource management is provided in Williams et al. (2002: chapters 21–25)

Early respiratory viral infections in infants with cystic fibrosis

This article is made available for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.Background Viral infections contribute to morbidity in cystic fibrosis (CF), but the impact of respiratory viruses on the development of airway disease is poorly understood. Methods Infants with CF identified by newborn screening were enrolled prior to 4 months of age to participate in a prospective observational study at 4 centers. Clinical data were collected at clinic visits and weekly phone calls. Multiplex PCR assays were performed on nasopharyngeal swabs to detect respiratory viruses during routine visits and when symptomatic. Participants underwent bronchoscopy with bronchoalveolar lavage (BAL) and a subset underwent pulmonary function testing. We present findings through 8.5 months of life. Results Seventy infants were enrolled, mean age 3.1 ± 0.8 months. Rhinovirus was the most prevalent virus (66%), followed by parainfluenza (19%), and coronavirus (16%). Participants had a median of 1.5 viral positive swabs (range 0–10). Past viral infection was associated with elevated neutrophil concentrations and bacterial isolates in BAL fluid, including recovery of classic CF bacterial pathogens. When antibiotics were prescribed for respiratory-related indications, viruses were identified in 52% of those instances. Conclusions Early viral infections were associated with greater neutrophilic inflammation and bacterial pathogens. Early viral infections appear to contribute to initiation of lower airway inflammation in infants with CF. Antibiotics were commonly prescribed in the setting of a viral infection. Future investigations examining longitudinal relationships between viral infections, airway microbiome, and antibiotic use will allow us to elucidate the interplay between these factors in young children with CF

Achievement goals, self-handicapping, and performance: A 2 × 2 achievement goal perspective

Elliot and colleagues (2006) examined the effects of experimentally induced achievement goals, proposed by the trichotomous model, on self-handicapping and performance in physical education. Our study replicated and extended the work of Elliot et al. by experimentally promoting all four goals proposed by the 262 model (Elliot & McGregor, 2001), measuring the participants’ own situational achievement goals, using a relatively novel task, and testing the participants in a group setting. We used a randomized experimental design with four conditions that aimed to induce one of the four goals advanced by the 262 model. The participants (n¼138) were undergraduates who engaged in a dart-throwing task. The results pertaining to self-handicapping partly replicated Elliot and colleagues’ findings by showing that experimentally promoted performance-avoidance goals resulted in less practice. In contrast, the promotion of mastery-avoidance goals did not result in less practice compared with either of the approach goals. Dart-throwing performance did not differ among the four goal conditions. Personal achievement goals did not moderate the effects of experimentally induced goals on selfhandicapping and performance. The extent to which mastery-avoidance goals are maladaptive is discussed, as well as the interplay between personal and experimentally induced goals

The Mid-IR Contribution Of Dust Enshrouded Stars In Six Nearby Galaxies

We measure the integrated contributions of dusty AGB stars and other luminous red mid-IR sources to the mid-IR luminosities of 6 galaxies (M81, NGC 2403, NGC 300, M33 and the Magellanic Clouds). We find the dusty AGB stars whose mid-IR fluxes are dominated by dust rather than photospheric emission contribute from 0.6% (M81) to 5.6% (SMC) of the 3.6 micron flux and 1.0% (M81) to 10.1% (SMC) of the 4.5 micron flux. We find a trend of decreasing AGB contribution with increasing galaxy metallicity, luminosity and mass and decreasing SSFR. However, these galaxy properties are strongly correlated in our sample and the simplest explanation of the trend is galaxy metallicity. Bright, red sources other than dusty AGB stars represent a smaller fraction of the luminosity, ~1.2% at 3.6 microns, however their dust is likely cooler and their contributions are likely larger at longer wavelengths. Excluding the SMC, the contribution from these red sources correlates with the specific star formation rate as we would expect for massive stars. In total, after correcting for dust emission at other wavelengths, the dust around AGB stars radiates 0.1-0.8% of the bolometric luminosities of the galaxies. Thus, hot dust emission from AGB and other luminous dusty stars represent a small fraction of the total luminosities of the galaxies but a significant fraction of their mid-IR emissions.Comment: 9 pages, 6 figures, published in ApJ. For a brief video explaining the key results of this paper, see http://www.youtube.com/user/OSUAstronom

Violent quenching : Molecular Gas Blown to 1000 km s -1 during a Major Merger

Accepted for publication in ApJ LettersWe present Atacama Large Millimeter/submillimeter Array observations of a massive () compact ( pc) merger remnant at z = 0.66 that is driving a 1000 km s -1 outflow of cool gas, with no observational trace of an active galactic nucleus (AGN). We resolve molecular gas on scales of approximately 1-2 kpc, and our main finding is the discovery of a wing of blueshifted CO J(2 → 1) emission out to-1000 km s -1 relative to the stars. We argue that this is the molecular component of a multiphase outflow, expelled from the central starburst within the past 5 Myr through stellar feedback, although we cannot rule out previous AGN activity as a launching mechanism. If the latter is true, then this is an example of a relic multiphase AGN outflow. We estimate a molecular mass outflow rate of approximately 300 M o yr -1, or about one third of the 10 Myr-Averaged star formation rate. This system epitomizes the multiphase "blowout" episode following a dissipational major merger-a process that has violently quenched central star formation and supermassive black hole growth.Peer reviewedFinal Accepted Versio

Monte Carlo energy and variance minimization techniques for optimizing many-body wave functions

We investigate Monte Carlo energy and variance minimization techniques for optimizing many-body wave functions. Several variants of the basic techniques are studied, including limiting the variations in the weighting factors which arise in correlated sampling estimations of the energy and its variance. We investigate the numerical stability of the techniques and identify two reasons why variance minimization exhibits superior numerical stability to energy minimization. The characteristics of each method are studied using a non-interacting 64-electron model of crystalline silicon. While our main interest is in solid state systems, the issues investigated are relevant to Monte Carlo studies of atoms, molecules and solids. We identify a robust and efficient variance minimization scheme for optimizing wave functions for large systems.Comment: 14 pages, including 7 figures. To appear in Phys. Rev. B. For related publications see http://www.tcm.phy.cam.ac.uk/Publications/many_body.htm

An analytical model for the accretion of dark matter subhalos

An analytical model is developed for the mass function of cold dark matter subhalos at the time of accretion and for the distribution of their accretion times. Our model is based on the model of Zhao et al. (2009) for the median assembly histories of dark matter halos, combined with a simple log-normal distribution to describe the scatter in the main-branch mass at a given time for halos of the same final mass. Our model is simple, and can be used to predict the un-evolved subhalo mass function, the mass function of subhalos accreted at a given time, the accretion-time distribution of subhalos of a given initial mass, and the frequency of major mergers as a function of time. We test our model using high-resolution cosmological $N$-body simulations, and find that our model predictions match the simulation results remarkably well. Finally, we discuss the implications of our model for the evolution of subhalos in their hosts and for the construction of a self-consistent model to link galaxies and dark matter halos at different cosmic times.Comment: 14 pages, 10 figures (caption for figure 10 fixed). Accepted for publication in Ap