Influence of infection rate and migration on extinction of disease in spatial epidemics

Extinction of disease can be explained by the patterns of epidemic spreading, yet the underlying causes of extinction are far from being well understood. To reveal a mechanism of disease extinction, a cellular automata model with both birth, death rate and migration is presented. We find that, in single patch, when the infection rate is small or large enough, the disease will disappear for a long time. When the invasion form is in the coexistence of stable spiral and turbulent wave state, the disease will persist. Also, we find that the migration has dual effects on the epidemic spreading. On one hand, in the extinction region of single patch, if the migration rate is large enough, there is a phase transition from the disease free to endemic state in two patches. On the other hand, migration will induce extinction in the regime, which can ensure the persistence of the disease in single patch, due to emergence of anti-phase synchrony. The results obtained well reveal the effect of infection rate and migration on the extinction of the disease, which enriches the finding in the filed of epidemiology and may provide some new ideas to control the disease in the real world.     

Habitat fragmentation and population extinction of birds

It has not been established that a major cause of extinction in birds or any other taxa is failure of metapopulation dynamics: the collapse of a network of ephemeral but discrete populations as movement between them becomes increasingly infrequent. The few data on who goes where and who mates with whom suggest that most species are structured as either a single large population or a small set of source populations and a larger set of sinks. The extinction of the latter is irrelevant to the persistence of the species. However, regional decline of a species in the face of habitat destruction and fragmentation can mimic a failure of metapopulation dynamics, because distinct aggregations of individuals will disappear much as they would if populations in an interacting network were eliminated one by one. Any species with highly restricted range is at great risk of extinction from spatially localized forces, such as cyclones or deforestation. Restricted range rather than inherent weakness is the main reason that so many island species have gone extinct or are endangered. Species with small populations in contact with much larger heterospecific ones with which they are interfertile are threatened with extinction by hybridization. Finally, the disappearance of a species from a site may be due to subtle habitat change, even if this observation seems superficially consistent with some general population theory, such as the dynamic equilibrium theory of island biogeography. Current theory is an inadequate substitute for intensive field studies as a means to address the conservation problems of individual species.     

Discrete-time growth-dispersal models with shifting species ranges

Many species are responding to global climate change by shifting their ranges poleward in latitude or upward in elevation. We analyze an integrodifference equation that combines growth, dispersal, and a constant-speed, climate-induced range shift and find that a shifting population can die out, even if the width of its range remains constant. We show how to determine the critical range-shift speed (for extinction) and study the effects of the growth rate and of the shape and scale of the dispersal kernel on persistence.     

Sexual selection and the risk of extinction in birds

The relationship between sexual selection and extinction risk has rarely been investigated. This is unfortunate because extinction plays a key role in determining the patterns of species richness seen in extant clades, which form the basis of comparative studies into the role that sexual selection may play in promoting speciation. We investigate the extent to which the perceived risk of extinction relates to four different estimates of sexual selection in 1030 species of birds. We find no evidence that the number of threatened species is distributed unevenly according to a social mating system, and neither of our two measures of pre-mating sexual selection (sexual dimorphism and dichromatism) was related to extinction risk, after controlling for phylogenetic inertia. However, threatened species apparently experience more intense post-mating sexual selection, measured as testis size, than non-threatened species. These results persisted after including body size as a covariate in the analysis, and became even stronger after controlling for clutch size (two known correlates of extinction risk). Sexual selection may therefore be a double-edged process-promoting speciation on one hand but promoting extinction on the other. Furthermore, we suggest that it is post-mating sexual selection, in particular, that is responsible for the negative effect of sexual selection on clade size. Why this might be is unclear, but the mean population fitness of species with high intensities of post-mating sexual selection may be especially low if costs associated with multiple mating are high or if the selection load imposed by post-mating selection is higher relative to that of pre-mating sexual selection.     

Chaotic dynamics may determine the effect of inter-patch migration on metapopulation survival

A simple, strategic model of a system of habitat fragments connected by conservation corridors is presented. The intrinsic dynamics of the population on each fragment are stochastic. In addition, at each generation there is a probability of a catastrophic event occurring which affects all the habitat fragments by greatly reducing the size of the population on each. Global extinction is considered to occur when all the populations simultaneously fall below a threshold value. If the intrinsic dynamics on each fragment are simple cycles or a stable equilibrium, then the addition of conservation corridors does not reduce the frequency of global extinction. This is because migration between fragments induces their populations to have values which are similar to each other. However, if the intrinsic population dynamics are chaotic then the probability of global extinction is greatly reduced by the introduction of conservation corridors. Although local extinction is likely, the chaos acts to oppose the synchronising effect of migration. Often a subset of the populations survive a catastrophe and can recolonize the other patches.     

Spontaneous and Ethyl Methanesulfonate-Induced Mutations Controlling Viability in DROSOPHILA MELANOGASTER. II. Homozygous Effect of Polygenic Mutations

Polygenic mutations affecting viability were accumulated on the second chromosome of Drosophila melanogaster by treating flies with EMS in successive generations. The treated chromosomes were later made homozygous and tested for their effects on viability by comparison of the frequency of such homozygotes with that of other genotypes in the same culture. The treated wild-type chromosomes were kept heterozygous in Pm/+ males by mating individual males in successive generations to Cy/Pm females. The number of generations of accumulation was 1 to 30 generations, depending on the concentration of EMS. A similar experiment for spontaneous polygenic mutations was also conducted by accumulating mutations for 40 generations. The lower limit of the spontaneous mutation rate of viability polygenes is estimated to be 0.06 per second chromosome per generation, which is about 12 times as high as the spontaneous recessive lethal mutation rate, 0.005. EMS-induced polygenic mutations increase linearly with the number of treated generations and with the concentration of EMS. The minimum mutation rate of viability polygenes is about 0.017 per 10(-4)m, which is only slightly larger than the lethal rate of 0.013 per 10(-4) m. The maximum estimate of the viability reduction of a single mutant is about 6 to 10 percent of the normal viability. The data are consistent with a constant average effect per mutant at all concentrations, but this is about three times as high as that for spontaneous mutants. It is obvious that one can obtain only a lower limit for the mutation rate, since some mutants may have effects so near to zero that they cannot be detected. The possibility of measuring something other than the lower limit is discussed. The ratio of the load due to detrimental mutants to that caused by lethals, the D/L ratio, is about 0.2 to 0.3 for EMS-induced mutants, as compared to about 0.5 for spontaneous mutants. This is to be expected if EMS treatment produces a large fraction of small deletions and other chromosome rearrangements which are more likely to be lethal.     

Direct evidence of an essential role for extended involution in the specification of a dorsal marginal mesoderm during Cynops gastrulation

It has been indicated that specification of the dorsal marginal mesoderm of the Cynops gastrula is established by vertical interactions with other layers, which occur during its extended involution. In the present study, when the prospective notochordal area of the early gastrula was almost completely removed together with the dorsal mesoderm-inducing endoderm and most of the bottle cells, the D-less gastrulas still formed the dorsal axis with a well-differentiated notochord; in half of them, where the involution occurred bi-laterally, twin axes were observed. On the other hand, when the wound of a D-less gastrula was repaired by transplanting the ventral marginal zone and ectoderm, the formation of the dorsal axis was inhibited if the involution of the lateral marginal zone was prevented by the transplanted piece. The present study suggests that: (i) cells having dorsal mesoderm-forming potency distribute farther laterally than the fate map; and (ii) the extended involution plays an essential role in the specification of the dorsal marginal mesoderm, especially in notochordal differentiation in normal Cynops embryogenesis.     

Extinction probabilities and times to extinction for populations of tsetse flies Glossina spp. (Diptera: Glossinidae) subjected to various control measures

A stochastic branching process was used to derive equations for the mean and variance of the probability of, and time to, extinction in tsetse populations. If the remnant population is a single inseminated female, the extinction probability increases linearly with adult mortality and is always certain if this mortality >3.5% per day even for zero pupal mortality. If the latter mortality is 4% per day, certain extinction is only avoided if adult mortality <1.5% per day. For remnant female populations >1, the extinction probability increases in a non-linear manner with adult mortality. Extinction is still certain for adult mortality >3.5% per day but, when the remnant population is >16, extinction is highly unlikely for adult mortality <2.5% per day if all females are inseminated. Extinction probability increases with increasing probability of sterile mating in much the same way as it does with increasing adult mortality. Extinction is assured if the probability of insemination can be reduced to 0.1. The required reduction decreases with increasing adult mortality. For adult mortality = 6-8% per day, the time to extinction increases only by one generation per order of magnitude increase in the starting population. Time to extinction is less sensitive to changes in the pupal than in the adult mortality. Reductions in the probability of insemination only become important when adult mortality is small; if the adult mortality is 8% per day, reducing the insemination probability from 1 to 0.1 only reduces the expected time to extinction by two generations. Conversely, increases in adult mortality produce important reductions in the required time even when the probability of insemination is 0.1. The practical, economic implication for the sterile insect technique is that the low-tech methods used to suppress tsetse populations should not be halted when the release of sterile males is initiated. The sterile insect technique should only be contemplated when it has been demonstrated that the low-tech methods have failed to effect eradication. The theory is shown to be in good accord with the observed results of tsetse control campaigns involving the use of odour-baited targets in Zimbabwe and the sterile insect technique on Unguja Island, Zanzibar.     

Genetic management of captive populations: the advantages of circular mating

We performed computer simulations to evaluate the effectiveness of circular mating as a genetic management option for captive populations. As a benchmark, we used the method proposed by Fernández and Caballero according to which parental contributions are set to produce minimum coancestry among the offspring and matings are performed so as to minimize mean pairwise coancestry (referred to as the Gc/mc method). In contrast to other methods, fitness does not vary with population size in the case of circular mating, and can be higher than under random mating. Whether circular mating is an effective method in conserving captive populations depends on the trade-off between different considerations. On the one hand, circular mating shows the highest allelic diversity and the lowest mean pairwise coancestry for all population sizes. It also shows a relatively higher efficiency of purging deleterious alleles. More importantly, circular mating can significantly increase the success probability of populations released to the wild relative to the Gc/mc method. On the other hand, circular mating has the drawback of showing high inbreeding rates and low fitness in early generations, which can result to an increase in the extinction probability of the captive populations. However, this increase is slight unless population size and litter size are both very low. Overall, if the slight increase in extinction probability can be tolerated then circular mating fulfils the primary goals of a captive breeding program, i.e., it maintains high levels of genetic diversity and increases the success probability of reintroduced populations.     

Fitness effects of new mutations in Chlamydomonas reinhardtii across two stress gradients

Most spontaneous mutations affecting fitness are likely to be deleterious, but the strength of selection acting on them might be impacted by environmental stress. Such stress‐dependent selection could expose hidden genetic variation, which in turn might increase the adaptive potential of stressed populations. On the other hand, this variation might represent a genetic load and thus lead to population extinction under stress. Previous studies to determine the link between stress and mutational effects on fitness, however, have produced inconsistent results. Here, we determined the net change in fitness in 29 genotypes of the green algae Chlamydomonas reinhardtii that accumulated mutations in the near absence of selection for approximately 1000 generations across two stress gradients, increasing NaCl and decreasing phosphate. We found mutational effects to be magnified under extremely stressful conditions, but such effects were specific both to the type of stress and to the genetic background. The detection of stress‐dependent fitness effects of mutations depended on accurately scaling relative fitness measures by generation times, thus offering an explanation for the inconsistencies among previous studies.     

On the Organization of Higher Chromosomes

OHTA and Kimura¹ have argued that only about 6% of the sequences in mammalian DNA can be under the intense selection that has characterized the evolutionary history of the cytochromes c, the globin chains and the histones. From the calculated mutation rate of fibrinopeptides A and B they show that if all genes are subjected to the same mutation rate 8.3 mutations would accumulate per genome per generation. Because 0,5 deleterious mutations per genome per generation is the maximum allowable in an equilibrium population², they conclude that the amount of DNA that codes for informational sequences such as the cytochromes, globins and histones must be no more than 0.5/8.3, or 6%. We are therefore left with the interesting observation that 94% of mammalian nuclear DNA serves a function not under strong selection. These authors make several assumptions, one of which is that the spontaneous mutation rate characteristic of a species is constant over all nucleotide sequences. I suggest here that this assumption is incorrect, for a variety of reasons and that by assuming that spontaneous mutation rates vary sequence by sequence, one can arrive at a plausible organizing principle for the structure of higher chromosomes.     

Now you See them, Now you don't! – Population Crashes of Established Introduced Species

Substantial populations of invasive non-indigenous species occasionally collapse dramatically. Although disease is often invoked, the causes are rarely studied experimentally and/or quantitatively, and some collapses remain quite mysterious. The widespread invasive snail Achatina fulica and pondweed Elodea canadensis appear to be characterized by rapid expansion followed by rapid decline. For the former species, disease may be the proximal cause of the collapse, while repeated collapse of the latter species is unexplained. Several other widely cited collapses of introduced species may simply be temporary lows during a more or less regular boom-and-bust cycle. However, on a restricted site (such as a small island), a boom-or-bust cycle may be impossible and recovery may never ensue; local extinction may even occur. In several instances, apparently spontaneous crashes were in fact probably caused by subsequently introduced competitors. Except for the few species in which spontaneous collapse has been repeatedly observed, the possibility of such an event is unwarranted as a potential rationale for a do-nothing approach to management. For such species, even if a crash ultimately occurs, the species may already have caused persistent ecological damage.     

The evolution of regeneration: adaptive or inherent?

If regeneration were adaptive, it would have arisen autonomously by natural selection from non-regenerative antecedents. Unless each episode coincidentally reinvented the same method of regeneration independently, one would expect the various lineages to differ basically from each other, which they do not. On the other hand, if regeneration were inherent to metazoan life, a derivative of embryogenesis, its various expressions should be as much like each other as they resemble the development of embryonic appendage buds, which they do. It follows that the uneven distribution of regeneration must have been due to its extinction here and there, not as a negative adaptation by natural selection but as a pleiotropic epiphenomenon linked to more useful adaptations with which it was incompatible. In vertebrate evolution, these adaptations have included the transition from aquatic to terrestrial habitats and the modification of poikilothermic to homeothermic metabolism. The former advance rendered the regeneration of weight-bearing limbs impractical; the latter favored rapid wound healing and scar formation which effectively precluded blastema formation. If the latent capacity for regeneration persists in non-regenerative appendages, as would seem to be the case, then the restoration of its overt expression should be possible if the mechanisms of its inhibition could be discovered and eventually rendered ineffectual.     

PERSPECTIVE: SPONTANEOUS DELETERIOUS MUTATION

Mildly deleterious mutation has been invoked as a leading explanation for a diverse array of observations in evolutionary genetics and molecular evolution and is thought to be a significant risk of extinction for small populations. However, much of the empirical evidence for the deleterious-mutation process derives from studies of Drosophila melanogaster, some of which have been called into question. We review a broad array of data that collectively support the hypothesis that deleterious mutations arise in flies at rate of about one per individual per generation, with the average mutation decreasing fitness by about only 2% in the heterozygous state. Empirical evidence from microbes, plants, and several other animal species provide further support for the idea that most mutations have only mildly deleterious effects on fitness, and several other species appear to have genomic mutation rates that are of the order of magnitude observed in Drosophila. However, there is mounting evidence that some organisms have genomic deleterious mutation rates that are substantially lower than one per individual per generation. These lower rates may be at least partially reconciled with the Drosophila data by taking into consideration the number of germline cell divisions per generation. To fully resolve the existing controversy over the properties of spontaneous mutations, a number of issues need to be clarified. These include the form of the distribution of mutational effects and the extent to which this is modified by the environmental and genetic background and the contribution of basic biological features such as generation length and genome size to interspecific differences in the genomic mutation rate. Once such information is available, it should be possible to make a refined statement about the long-term impact of mutation on the genetic integrity of human populations subject to relaxed selection resulting from modern medical procedures.     

Extinction processes in hot spots of avian biodiversity and the targeting of pre-emptive conservation action

Hot spots of endemism are regarded as important global sites for conservation as they are rich in threatened endemic species and currently experiencing extensive habitat loss. Targeting pre-emptive conservation action to sites that are currently relatively intact but which would be vulnerable to particular human activities if they occurred in the future is, however, also valuable but has received less attention. Here, we address this issue by using data on Endemic Bird Areas (EBAs). First, we identify the ecological factors that affect extinction risk in the face of particular human activities, and then use these insights to identify EBAs that should be priorities for pre-emptive conservation action. Threatened endemic species in EBAs are significantly more likely to be habitat specialists or relatively large-bodied than non-threatened species, when compared across avian families. Increasing habitat loss causes a significant increase in extinction risk among habitat specialists, but we found no evidence to suggest that the presence of alien species/human exploitation causes a significant increase in extinction risk among large-bodied species. This suggests that these particular human activities are contributing to high extinction risk among habitat specialists, but not among large-bodied species. Based on these analyses, we identify 39 EBAs containing 570 species (24% of the total in EBAs) that are not currently threatened with severe habitat loss, but would be ecologically vulnerable to future habitat loss should it occur. We show that these sites tend to be poorly represented in existing priority setting exercises involving hot spots, suggesting that vulnerability must be explicitly included within these exercises if such sites are to be adequately protected.     

Extinction times for a birth-death process with two phases

Many populations have a negative impact on their habitat or upon other species in the environment if their numbers become too large. For this reason they are often subjected to some form of control. One common control regime is the reduction regime: when the population reaches a certain threshold it is controlled (for example culled) until it falls below a lower predefined level. The natural model for such a controlled population is a birth-death process with two phases, the phase determining which of two distinct sets of birth and death rates governs the process. We present formulae for the probability of extinction and the expected time to extinction, and discuss several applications.     

On the time to extinction for a two-type version of Bartlett's epidemic model

We are interested in how the addition of type heterogeneities affects the long time behaviour of models for endemic diseases. We do this by analysing a two-type version of a model introduced by Bartlett under the restriction of proportionate mixing. This model is used to describe diseases for which individuals switch states according to susceptible-->infectious-->recovered and immune, where the immunity is life-long. We describe an approximation of the distribution of the time to extinction given that the process is started in the quasi-stationary distribution, and we analyse how the variance and the coefficient of variation of the number of infectious individuals depends on the degree of heterogeneity between the two types of individuals. These are then used to derive an approximation of the time to extinction. From this approximation we conclude that if we increase the difference in infectivity between the two types the expected time to extinction decreases, and if we instead increase the difference in susceptibility the effect on the expected time to extinction depends on which part of the parameter space we are in, and we can also obtain non-monotonic behaviour. These results are supported by simulations.