We generalize the one-dimensional population model of Anguige & Schmeiser [1] reflecting the cell-to-cell adhesion and volume filling and classify the resulting equation into the six types. Among these types, we fix one that yields a class of advection-diffusion equations of forward-backward-forward type and prove the existence of infinitely many global-in-time weak solutions to the initial-Dirichlet boundary value problem when the maximum value of an initial population density exceeds a certain threshold. Such solutions are extracted from the method of convex integration by Müller & Šverák [12]; they exhibit fine-scale density mixtures over a finite time interval, then become smooth and identical, and decay exponentially and uniformly to zero as time approaches infinity. TE check: Please check the reference citation in abstract.

Herbicide resistance jeopardizes the usefulness of valuable chemical tools and, therefore, weed management in many crop systems. Models must be developed to evaluate management tactics that prevent, delay, or reduce resistance. The complexity of biological processes involved in herbicide resistance also requires models to focus research and to integrate experiments. A population model was developed that improves upon previous attempts to predict herbicide resistance dynamics. The model incorporates plant population demographics with the Hardy-Weinberg concept for gene segregation. The model simulates the evolution, spread, and subsequent dynamics of resistance in the presence and absence of a herbicide. Analysis of model simulations identified two sets of biological processes as key factors in the evolution and dynamics of herbicide-resistant weed populations. These are processes that influence ecological fitness and gene flow. Several options are suggested as examples for the management of resistant weed populations.

We investigate the approximate controllability of a size- and space-structured population model, for which the control function acts on a subdomain and corresponds to the migration of individuals. We establish the main result via the unique continuation property of the adjoint system. The desired controller is the minimizer of an infinite-dimensional optimization problem.

A population model was constructed to simulate the development of imazamox-resistant jointed goatgrass (AEGCY) in imazamox-resistant (Clearfield™) wheat. The model computed changes in the surface and in the buried AEGCY seed banks for both resistant and susceptible biotypes. Simulations started with an initial density of 1,000 susceptible and zero resistant seeds/m2 in each seed bank. Simulation of continuous, no-till Clearfield wheat production resulted in rapid development of resistant AEGCY without hybridization with wheat and in extremely rapid resistance development with hybridization. In less than 10 yr, the resistant population was growing exponentially in both simulations. Adding a fallow year with tillage into the simulated rotation did not substantially slow down the appearance of resistance but did delay the rate of resistant population increase by several orders of magnitude over 10 yr. Alternating Clearfield and a nonresistant winter wheat in combination with fallowing prevented the establishment of a significant resistant AEGCY population and prevented the susceptible seed population from increasing exponentially. These projections suggest that imazamox-resistant wheat can be a tool for managing AEGCY populations especially if combined with rotations that include fallow and crops other than Clearfield winter wheat.

A general life cycle model was modified to demonstrate how agronomic practices and weed biology factors affect the rate of appearance of herbicide-resistant downy brome, jointed goatgrass, and wild oat in Pacific Northwest wheat cropping systems. The model suggests herbicide rotation strategies for cropping systems that include imidazolinone-resistant wheat as a weed management tool. Simulation of continuous annual imidazolinone-resistant winter wheat and imazamox herbicide use resulted in the resistant soil seed banks of downy brome, jointed goatgrass, and wild oat surpassing their susceptible soil seed banks in 5, 7, and 10 yr, respectively. Reducing the initial seed bank density of downy brome before beginning a rotation that includes imidazolinone-resistant winter wheat reduces the likelihood of selecting for herbicide-resistant biotypes. The best simulated management option for reducing the total jointed goatgrass soil seed bank in low-precipitation areas is an imidazolinone-resistant winter wheat–fallow rotation. Rotations that include winter and spring crops and rotations that include non–group 2 herbicides minimize herbicide resistance selection pressure and reduce the wild oat soil seed bank.

Trends in the populations of large herbivores in Niassa Reserve, Mozambique, have been monitored through biennial aerial surveys since 1998. The elephant Loxodonta africana population has been subjected to intensive illegal hunting since 2006. We used a simple population model to mimic the observed trends in the numbers of live and dead elephants to demonstrate the impact of poaching. The number of fresh or recent carcasses recorded was used in the model as an index of the annual mortality rate. A maximum likelihood analysis to compare population models revealed that the best fit to the survey estimates of both live elephants and old or very old carcasses was a model that started with 6,635 elephants in 1987. This number increased through births by 4.6% annually and decreased through deaths from natural and anthropogenic causes. In the best-fit model, the mean mortality rate in any year was 3.2 times the observed 1 + 2 carcass ratio (ratio for carcasses in age categories 1 and 2), and carcasses remained visible for a mean of 6 years. The model suggested that c. 900 elephants were poached during 2007–2010 and another c. 1,000 during 2011. Population estimates for live elephants and carcasses are now routine outcomes of aerial surveys conducted as part of the CITES programme for Monitoring the Illegal Killing of Elephants, and our method can be applied to any population with a time series of estimates for live and dead elephants.

Conservation managers and policy makers require models that can rank the impacts of multiple, interacting threats on biodiversity so that actions can be prioritized. An integrated modelling framework was used to predict the viability of plant populations for five species in southern California's Mediterranean-type ecosystem. The framework integrates forecasts of land-use change from an urban growth model with projections of future climatically-suitable habitat from climate and species distribution models, which are linked to a stochastic population model. The population model incorporates the effects of disturbance regimes and management actions on population viability. This framework: (1) ranks threats by their relative and cumulative impacts on population viability, such as land-use change, climate change, altered disturbance regimes or invasive species, and (2) ranks management responses in terms of their effectiveness for land protection, assisted dispersal, fire management and invasive species control. Too-frequent fire was often the top threat for the species studied, thus fire reduction was ranked the most important management option. Projected changes in suitable habitat as a result of climate change were generally large, but varied across species and climate scenarios; urban development could exacerbate loss of suitable habitat.

The use of population modelling has become an increasingly common tool in reintroduction planning and assessment. Although initial reintroduction success is often measured by quantifying post-release survival and reproduction, longer-term success is best assessed through measurements of population viability. Here we develop a population model capable of providing useful results for influencing management of a reintroduction programme for a long-lived and slow-reproducing primate, the western lowland gorilla Gorilla gorilla gorilla. We used post-release monitoring data from two reintroduced populations in the Batéké Plateau region of Congo and Gabon, complemented with published data on wild and captive populations, to develop a population model using Vortex. Sensitivity testing illustrated that the model was highly sensitive to changes in the input parameters for annual birth rates, the number of lethal equivalents, and for female annual mortality rates, especially for adults. The results of the population viability analysis suggested that the reintroduced gorilla populations have a reasonable chance of persistence (> 90% over 200 years) but illustrated that reinforcement of the populations could significantly improve probabilities of population persistence and retention of genetic diversity. Equally, catastrophic events could have significant negative impacts. Continued monitoring of the populations should allow refinement of the model, improving confidence in its predictions and its relevance to decision-making.

We consider a model of fixed size N = 2l in which there are l generations of daughter cells and a stem cell. In each generation i there are 2i−1 daughter cells. At each integral time unit the cells split so that the stem cell splits into a stem cell and generation 1 daughter cell and the generation i daughter cells become two cells of generation i+1. The last generation is removed from the population. A stem cell acquires first and second mutations at rates u1 and u2, and a daughter cell acquires first and second mutations at rates v1 and v2. We find the distribution for the time it takes to acquire two mutations as N goes to ∞ and the mutation rates go to 0. The mutation rates may tend to 0 at different speeds. We also find the distribution for the locations of the mutations. In particular, we determine whether or not the mutations occur on a stem cell and if not, at what generation in the daughter cells they occur. Several outcomes are possible, depending on how fast the rates go to 0. The model considered has been proposed by Komarova (2007) as a model for colon cancer.

A survey of the Sebungwe elephant Loxodonta africana population in Zimbabwe in 2006 revealed a large rise in the number of dead elephants. The estimated number of carcasses increased >16-fold from 1989 to 2006 and the carcass ratio (number of all elephant carcasses as a percentage of the number of all elephants) rose from 1.25 to 15.4%. The ratio for fresh or recent carcasses, which reflected the mortality rate during the survey year, increased from 0.19 to 1.70% during 1995-2006. Records of elephants killed before 1995 were supplemented with estimates of the numbers killed after 1995, with these estimates increasing exponentially, as did the observed number of fresh or recent carcasses. A maximum likelihood analysis to compare population models revealed that the best fit to the survey estimates of this closed population was a model that started with 9,500 elephants in 1979 and that each year increased at 4.02% and decreased by the number killed, with the number killed annually increasing at 23.5% per year after 1995. A rise in anthropogenic mortality, mostly due to poaching, caused the increase in carcass numbers observed after 1999. Since 1997 the mortality rate of elephants in the National Parks and Safari Areas in the Sebungwe has been positively correlated with the observed number of poachers’ camps. Anthropogenic mortality is now great enough to keep the elephant population approximately constant at 14,000-16,000 animals. The population number was also constant (at a lower level) during the 1980s, when elephants were culled and the sale of meat, hides and ivory covered the costs of elephant management but there have been no recent culls, partly because the ivory trade ban prevents tusks from culled elephants being sold to offset the costs of management. This study illustrates the value of a long-term data set collected with consistent techniques, and including data on other species and the environment collected at no extra cost under the financial umbrella of a charismatic species.

The historical regulation of African elephant Loxodonta africana populations could provide guidelines for management efforts and decisions in areas where elephant numbers are now increasing. However, there are few detailed records of the natural mortality processes of the past. Therefore, we modelled elephant population growth to evaluate possible effects of age-specific mortality. Model projections indicated that an annual mortality of 17.1% of juveniles or 10.5% of adults would be sufficient to prevent population growth. For age classes below or just at sexual maturity (i.e. 0-3, 4-7, 8-11) 37.5% annual mortality of one of these classes was required to achieve 0% population growth. These mortality levels are much higher than those reported in southern Africa today. Simulations of episodic mortality events (e.g. droughts) indicated that such events would need to occur every 16 years at a severity that would cause the mortality of all infants and weaned calves (0-7 years old), as well as 10% of adults and subadults (8-60 years old) to prevent long-term population growth. An 8-year frequency required the mortality of 84.7% of infants and weaned calves. Historically, it is possible that high drought mortality and frequency, and high predation levels, may have reduced population growth significantly but current mortality rates and frequencies are insufficient to constrain long-term average population growth at 0%. The natural limitation of existent elephant populations through mortality is therefore unlikely, indicating a need for active management of the increasing elephant populations in southern Africa.

Many population models which are far from stationarity can nevertheless be written in autoregressive format, perhaps with random coefficient. It is the thesis of this paper that procedures developed for stationary time series models are a useful guide to inferential results for population processes and may indeed be directly applicable. The illustrations concentrate on estimation of the matrix of mean vital rates in an age-structured population.

The process we consider is a binary splitting, where the probability of division, , depends on the population size, 2i. We show that Zn converges to ∞ almost surely on a set of positive probability. Zn/n converges in distribution to a proper limit, diverges almost surely on converges almost surely on and there are no constants cn such that Zn/cn converges in probability to a non-degenerate limit.

A continuous-time model of a multigrade system is developed, which includes Poisson arrivals, interaction between grades and a leaving process. It therefore constitutes a continuous-time analogue of Pollard's hierarchical population model with Poisson recruitment. An expression is found for the first and second moments of grade size at any time. A general formulation of the joint probability generating function of the numbers in each grade is given, and the limiting distribution of grade size is shown to be Poisson.

A simple birth-death model of particle fluctuations is studied where at each discrete time a birth and/or death may occur. We show that if the probability of a birth does not depend on the number of particles present and if births and deaths are independent, then the times between successive deaths are independent geometrically distributed random variables, which is false in the general case. Since the above properties of the times between successive neuron firings have been observed in nerve cells, the model proposed in [2] obtains added credence.