Diversity Waves in Collapse-Driven Population Dynamics

Populations of species in ecosystems are often constrained by availability of resources within their environment. In effect this means that a growth of one population, needs to be balanced by comparable reduction in populations of others. In neutral models of biodiversity all populations are assumed to change incrementally due to stochastic births and deaths of individuals. Here we propose and model another redistribution mechanism driven by abrupt and severe reduction in size of the population of a single species freeing up resources for the remaining ones. This mechanism may be relevant e.g. for communities of bacteria, with strain-specific collapses caused e.g. by invading bacteriophages, or for other ecosystems where infectious diseases play an important role. The emergent dynamics of our system is characterized by cyclic ‘‘diversity waves’’ triggered by collapses of globally dominating populations. The population diversity peaks at the beginning of each wave and exponentially decreases afterwards. Species abundances have bimodal time-aggregated distribution with the lower peak formed by populations of recently collapsed or newly introduced species while the upper peak - species that has not yet collapsed in the current wave. In most waves both upper and lower peaks are composed of several smaller peaks. This self-organized hierarchical peak structure has a long-term memory transmitted across several waves. It gives rise to a scale-free tail of the time-aggregated population distribution with a universal exponent of 1.7. We show that diversity wave dynamics is robust with respect to variations in the rules of our model such as diffusion between multiple environments, species-specific growth and extinction rates, and bet-hedging strategies.     

The effects of the size and shape of landscape features on the formation of traveling waves in cyclic populations

Recent field data indicate that in a number of cyclic populations, the cycles are organized spatially with the form of a periodic traveling wave. One way in which this type of wave is generated is when dispersing individuals encounter landscape features that impede movement in certain directions. In this article, we investigate the dependence of such periodic waves on ecological parameters and on the form of the landscape feature. Using a standard predator-prey model as a prototype for a cyclic population, we calculate the speed and amplitude of waves generated by a large landscape feature. This enables us to determine parameters for which the waves are stable; in other cases, they evolve into irregular oscillations. We then undertake for the first time a detailed study of the effects of the size and shape of a landscape feature on the waves that it generates. We show that size rather than shape is the key wave-forming property, with smaller obstacles generating waves with longer wavelength and waves from larger landscape features dominating those from smaller ones. Our results suggest that periodic traveling waves may be much more common than has previously been assumed in real ecological systems, and they enable quantitative predictions on the properties of these waves for particular cases.     

The size distribution of conspecific populations: the peoples of New Guinea

The size distribution of the language populations in New Guinea, which represent over 15% of the world's languages, is analysed using models analogous to the resource division models of species abundance distribution in ecological communities. A model distribution of resource segments reflecting population size is created by repeated selection of an existing resource segment and its division into two. We found that any dependency of the selection probability on the size of the segment generated negatively skewed abundance distributions after log transformation. Asymmetric segment division further exacerbated the negative skewness. Size-independent selection produced lognormal abundance distributions, irrespective of the segment division method. Size-dependent selection and asymmetric division were deemed reasonable assumptions since large language populations are more likely to generate isolates, which develop into new populations, than small ones, and these isolates are likely to be small relative to the progenitor population. A negatively skewed distribution of the log-transformed population sizes was therefore expected. However, the observed distributions were lognormal, scale invariant for areas containing between 100 and over 1000 language populations. The dynamics of language differentiation, as reflected by the models, may therefore be unimportant relative to the effect of variable growth rates among populations. All lognormal distributions from resource division models had a higher variance than the observed one, where half of the 1053 populations had between 350 and 3000 individuals. The possible mechanisms maintaining such a low variance around a modal population size of 1000 are discussed.     

Population mixing and the adaptive divergence of quantitative traits in discrete populations: a theoretical framework for empirical tests

Empirical tests for the importance of population mixing in constraining adaptive divergence have not been well grounded in theory for quantitative traits in spatially discrete populations. We develop quantitative-genetic models to examine the equilibrium difference between two populations that are experiencing different selective regimes and exchanging individuals. These models demonstrate that adaptive divergence is negatively correlated with the rate of population mixing (m, most strongly so when m is low), positively correlated with the difference in phenotypic optima between populations, and positively correlated with the amount of additive genetic variance (G, most strongly so when G is low). The approach to equilibrium is quite rapid (fewer than 50 generations for two populations to evolve 90% of the distance to equilibrium) when either heritability or mixing are not too low (h2 > 0.2 or m > 0.05). The theory can be used to aid empirical tests that: (1) compare observed divergence to that predicted using estimates of population mixing, additive genetic variance/covariance, and selection; (2) test for a negative correlation between population mixing and adaptive divergence across multiple independent population pairs; and (3) experimentally manipulate the rate of mixing. Application of the first two of these approaches to data from two well-studied natural systems suggests that population mixing has constrained adaptive divergence for color patterns in Lake Erie water snakes (Nerodia sipedon), but not for trophic traits in sympatric pairs of benthic and limnetic stickleback (Gasterosteus aculeatus). The theoretical framework we outline should provide an improved basis for future empirical tests of the role of population mixing in adaptive divergence.     

Predicting population trends from size distributions: a direct test in a tropical tree community

ABSTRACT Forest ecologists often evaluate how well the species composition of saplings in the understory matches that of the canopy: absence of juveniles suggests that a tree species is suffering population decline. Here we offer a theoretical and empirical test of this assertion using data from a 50-ha census plot in Panama. Theory indicates that higher rates of population change, lambda, lead to more steeply declining size distributions (more juveniles relative to adults). But other parameters also affect the size distribution: lower growth rate of juveniles and lower survival at any size pro duce more steeply declining size distributions as well. Empirical evaluation of 216 tree populations showed that juvenile growth was the strongest predictor of size distribution, in the direction predicted by theory. Size distribution did correlate with population growth, but weakly and only in understory species, not canopy seecies. Size distribution did not correlate with the growth rate of larger individuals nor with survival. Results suggest that static in formation on the size distribution is not a good predictor of future population trends, while demographic information is. Fast-growing species will have fewer juveniles in the understory than slow growing species, even when population growth is equal.     

Current versus historical population sizes in vertebrate species with high gene flow: a comparison based on mitochondrial DNA lineages and inbreeding theory for neutral mutations

Using inbreeding theory as applied to neutral alleles inherited maternally, we generate expected probability distributions of times to identity by descent for random pairs of mitochondrial genotypes within a population or within an entire species characterized by high gene flow. For comparisons with these expectations, empirical distributions of times to most recent common ancestry were calculated (by conventional mtDNA clock calibrations) from mtDNA haplotype distances observed within each of three vertebrate species--American eels, hardhead catfish, and redwinged blackbirds. These species were chosen for analysis because census population size in each is currently large and because both genetic and life-history data are consistent with the postulate that historical gene flow within these species has been high. The observed molecular distances among mtDNA lineages were two to three orders of magnitude lower than predicted from census sizes of breeding females, suggesting that rate of mtDNA evolution is decelerated in these species and/or that long-term effective population size is vastly smaller than present-day population size. Several considerations point to the latter possibility as most likely. The genetic structure of any species is greatly influenced by historical demography; even for species that are currently abundant, mtDNA gene lineages appear to have been channeled through fairly small numbers of ancestors.      

Genetic relationship of Chinese ethnic populations revealed by mtDNA sequence diversity

The origin and demographic history of the ethnic populations of China have not been clearly resolved. In this study, we examined the hypervariable segment I sequences (HVSI) of the mitochondrial DNA control region in 372 individuals from nine Chinese populations and one northern Thai population. A relatively high percentage of individuals was found to share sequences with those from other populations of the same ethnogenesis. In general, the populations of southern or Pai-Yuei tribal origin showed high haplotype diversity and nucleotide diversity compared with the populations of northern or Di-Qiang tribal origin. Mismatch distributions from these populations showed concordant features. All except the northern groups Nu, Lisu, Tibetan, and Mongolian showed typical signatures of ancient population expansions in the mismatch distributions and neutrality tests. Episodes of extreme size reduction in the past are one of the likely explanations for the absence of evidence of expansion in northern populations. Small sample sizes as well as samples from isolated subpopulations contributed to the bumpy mismatch distributions observed. Phylogenetic analysis and haplotype sharing among populations suggest that current mtDNA variation in these ethnic populations could reveal their ethnohistory to some extent, but in general, linguistic and geographic classifications of the populations did not agree well with classification by mtDNA variation.     

A single theory explains two empirical laws applicable to plant populations

Two empirical laws, formulated independently, are known to be well satisfied in even-aged plant monocultures. One relates yield to plant density in different plant populations, and the other relates cumulative plant mass to cumulative plant number from the largest individual within a population. In this paper, we construct a mathematical model of plant growth under asymmetric competition between individuals in a population, where large individuals grow larger than small individuals because they pre-empt resources, especially light. The model categorizes influences on the growth of a plant into those from individuals larger than itself, and those from all individuals in the population. We derive the two laws from our model. Thus, individual growth, determined by asymmetric interaction between individuals in a population, can explain the two different laws relating to plant populations.     

Population structure of the echinoid Heterocentrotus mammillatus (L.) along the littoral zone of south-eastern Sinai

The population structure of the slate-pencil sea urchin Heterocentrotus mammillatus was studied along the southeastern coast of the Sinai peninsula. Evenly-distributed size classes were observed in populations occupying the forereef, while populations of this species from the reef slope and the back reef contained smaller proportions of small and medium-sized individuals. During the five years of study, growth rates and abundances of each size group were found to be stable. Analysis of size frequency distributions show that recruitment of H. mammillatus at the study area was regular and mortality rates were low during the second to fifth year of life and increasing later. This was supported by aging of dead individuals and observations indicating that large individuals were more susceptible to predation than smaller ones.     

Cooperative growth regulation in coral-dwelling fishes

Dominant individuals often grow faster than subordinates because they gain a greater share of important resources. However, dominants should also strategically adjust their growth rates, relative to the size of subordinates, if this improves their reproductive success. Here, we show that individuals in breeding pairs of the coral-dwelling fish Gobiodon histrio regulate their growth to reduce the size difference between partners. In pairs where one individual was larger than the other, the smaller individual increased its growth rate and the larger individual decreased its growth rate, compared to individuals in size-matched pairs. The reproductive success of breeding pairs is limited by the size of the smallest individual in the pair. Therefore, it appears that the larger individual trades-off its own growth against that of the smaller individual, thereby improving the reproductive success of both individuals in the pair. This demonstrates a remarkable ability of individuals to strategically adjust their body size to suit the local social environment, and reveals a novel mechanism for size-assortative mating.     

A test of the reproductive economy hypothesis in plants: more offspring per capita come from large (not small) parents in Avena barbata

Under crowded conditions, plant populations typically exhibit L-shaped distributions of size. Many plants remain small and suppressed in such populations, and more offspring are propagated into the next generation from the many smaller plants than from the few large plants. The hypothesis of “reproductive economy” advances that this creates natural selection favouring the ability to reproduce while still small over the ability to become large. We develop a simple model using exponential distributions of size within morphs that differ in their growth potential and size threshold for reproduction. Our model shows that selection consistently favours the morph with greater potential to become large, even if that potential comes at the cost of a larger size threshold for reproduction. We also tested the reproductive economy hypothesis using 4 years of field data at two sites in California, USA from an experiment with the annual grass Avena barbata. Despite strongly skewed size distributions, the genotypes giving larger size always increased in frequency between parents and offspring while those of the smallest size class decreased. Directional selection gradients were also always positive and significant, indicating that natural selection indeed favours the few larger plants over their more numerous smaller neighbours. Neither our empirical nor theoretical findings support the reproductive economy hypothesis. Instead, we argue that selection for large size is a manifestation of underlying selection to acquire resources, resolving any perceived paradox of a preponderance of small individuals under selection for large size.     

Wealth as a source of density dependence in human population growth

In modern industrialized countries, human birth rates have been declining persistently for decades. In many cases they have now fallen below the replacement threshold. However, unlike in natural populations where population growth is constrained by limited resources, birth rates in modern industrialized countries are negatively correlated with resource availability. Here, declining birth rates in human populations are shown to be a manifestation of density‐dependent population growth brought on by socioeconomic development. This is demonstrated by combining empirical power law relations between population size, gross domestic product (GDP) per capita, and fertility in a simple theoretical model describing population dynamics in developed countries. For a closed population, the model exhibits growth to a globally stable equilibrium population size, for both national and city populations. A version of the model that is open with respect to immigration and the influence of foreign technology and capital exhibits a good fit to long‐term time series data on population size, GDP per capita, and birth rates for the United States, France and Japan.     

Bottlenecks, drift and differentiation: the fragmented population structureof the saltmarsh beetle Pogonus chalceus

We investigated the distribution of genetic variation within and between 10 fragmented populations of the saltmarsh beetle Pogonus chalceus in the region of Flanders (Belgium) representing all extant populations of the species in that region by using allozyme and microsatellite markers. Beetle population size and habitat area failed to explain a significant part of the genetic variability. Microsatellite allelic diversity was sensitive to population size differences but not to saltmarsh area estimates. Heterozygosities of both marker types and allozyme allelic diversity on the other hand showed no significant correlation to population size and saltmarsh area. There was also no correlation between geographical and genetic distances among populations. Evidence was found for past bottlenecks in some of the smallest populations. Maximum likelihood methods using the coalescent approach revealed that the proportion of common ancestors was also high in those small populations. 35% of our studied individuals, especially in the largest populations showed a relative wing size smaller than 70%. Moreover, only six out of the 10 studied populations showed a few individuals with functional flight musculature. In conclusion, the overall pattern of distribution of genetic variation and the low flight capacity did not support an equilibrium model of population structure in P. chalceus, but mainly suggested a lack of regional equilibrium with both drift and gene flow influences.     

Variation in the population dynamics of the intertidal pulmonate gastropod Salinator solida Martens (Gastropoda: Amphibolidae) at Towra Point,NSW, Australia

This paper describes variation in the population dynamics of the intertidal pulmonate gastropod solida among mangrove and saltmarsh habitats at Towra Point, NSW, Australia over a two-year period. In general, this paper describes the degree to which the density of the populations fluctuated and the size structure of the populations varied among heights on shore. The density of individuals in the upper mangrove forest was most variable through time and their population size structure was dominated by smaller individuals. The density of populations in the Sarcocornia high on the shore fluctuated least through time and were dominated by large individuals. Those populations found on the mid-shore in the Sarcocornia had population characteristics intermediate to those populations in the upper mangrove forest and the Sarcocornia high on the shore. Analysis of size frequency data indicated that the growth rates of individuals and their annual mortality decreased with increasing height on shore.     

Unimodal Tree Size Distributions Possibly Result from Relatively Strong Conservatism in Intermediate Size Classes

Tree size distributions have long been of interest to ecologists and foresters because they reflect fundamental demographic processes. Previous studies have assumed that size distributions are often associated with population trends or with the degree of shade tolerance. We tested these associations for 31 tree species in a 20 ha plot in a Dinghushan south subtropical forest in China. These species varied widely in growth form and shade-tolerance. We used 2005 and 2010 census data from that plot. We found that 23 species had reversed J shaped size distributions, and eight species had unimodal size distributions in 2005. On average, modal species had lower recruitment rates than reversed J species, while showing no significant difference in mortality rates, per capita population growth rates or shade-tolerance. We compared the observed size distributions with the equilibrium distributions projected from observed size-dependent growth and mortality. We found that observed distributions generally had the same shape as predicted equilibrium distributions in both unimodal and reversed J species, but there were statistically significant, important quantitative differences between observed and projected equilibrium size distributions in most species, suggesting that these populations are not at equilibrium and that this forest is changing over time. Almost all modal species had U-shaped size-dependent mortality and/or growth functions, with turning points of both mortality and growth at intermediate size classes close to the peak in the size distribution. These results show that modal size distributions do not necessarily indicate either population decline or shade-intolerance. Instead, the modal species in our study were characterized by a life history strategy of relatively strong conservatism in an intermediate size class, leading to very low growth and mortality in that size class, and thus to a peak in the size distribution at intermediate sizes.     

Explaining leptokurtic movement distributions: intrapopulation variation in boldness and exploration

Leptokurtic distributions of movement distances observed in field-release studies, in which some individuals move long distances while most remain at or near their release point, are a common feature of mobile animals. However, because leptokurtosis is predicted to be transient in homogeneous populations, persistent leptokurtosis suggests a population heterogeneity. We found evidence for a heterogeneity that may generate persistent leptokurtosis. We tested individuals of the Trinidad killifish Rivulus hartii for boldness in a tank test and released them back into their native stream. Boldness in the tank test predicted distance moved in the field releases, even after effects of size and sex were removed. Further, data from a 19-mo mark-recapture study showed that individual growth correlated positively with movement in a predator-threatened river zone where the Rivulus population is spatially fragmented and dispersal is likely to be a hazardous activity. In contrast, no such correlation existed in a predator-absent zone where the population is unfragmented. These results show that a behavioral trait, not discernible from body size or sex, contributes to dispersal and that a component of fitness of surviving "dispersers" is elevated above that of "stayers," a fundamental assumption or prediction of many models of the evolution of dispersal through hazardous habitat.     

Invasion Waves in Populations with Excitable Dynamics

Whilst the most obvious mechanism for a biological invasion is the occupation of a new territory as a result of direct ingress by individuals of the invading population, a more subtle “invasion” may occur without significant motion of invading individuals if the population dynamics in a predator prey scenario has an “excitable” character. Here, “excitable” means that a local equilibrium state, either of coexistence of predator and prey, or of prey only, may, when disturbed by a small perturbation, switch to a new, essentially invaded state. In an invasion of this type little spatial movement of individuals occurs, but a wave of rapid change of population level nevertheless travels through the invaded territory. In this article we summarise and review recent modelling research which shows that the macroscopic features of these invasion waves depend strongly on the detailed spatial dynamics of the predator–prey relationship; the models assume simple (linear) diffusion and pursuit-evasion, represented by (non-linear) cross-diffusion, as examples. In the context of plankton population dynamics, such waves may be produced by sudden injections of nutrient and consequent rapid increase in plankton populations, brought about, for example, by the upwelling caused by a passing atmospheric low pressure system.     

Facilitation and competition interact with seed dormancy to affect population dynamics in annual plants

Seed dormancy increases population size via bet-hedging and by limiting negative interactions (e.g., competition) among individuals. On the other hand, individuals also interact positively (e.g., facilitation), and in some systems, facilitation among juveniles precedes competition among adults in the same generation. Nevertheless, studies of the benefits of seed dormancy typically ignore facilitation. Using a population growth model, we ask how the facilitation–competition balance interacts with seed dormancy rate to affect population dynamics in constant and variable environments. Facilitation increases the growth rate and equilibrium size (in both constant and variable environments) and reduces the extinction rate of populations (in a variable environment), and a higher rate of seed dormancy allows populations with facilitation to reach larger sizes. However, the combined benefits of facilitation and a high dormancy rate only occur in large populations. In small populations, weak facilitation does not affect the growth rate, but does induce a weak demographic Allee effect (where population growth decreases with decreasing population size). Our results suggest that facilitation within populations can interact with bet-hedging traits (such as dormancy) or other traits that mediate density to affect population dynamics. Further, by ensuring survival but limiting reproduction, ontogenetic switches from facilitation to competition may enable populations to persist but limit their maximum size in variable environments. Such intrinsic regulation of populations could then contribute to the maintenance of similar species within communities.     

Population variation and individual maximum size in two leech populations: energy extraction from cannibalism or niche widening?

The theory of cannibal dynamics predicts a link between population dynamics and individual life history. In particular, increased individual growth has, in both modeling and empirical studies, been shown to result from a destabilization of population dynamics. We used data from a long-term study of the dynamics of two leech (Erpobdella octoculata) populations to test the hypothesis that maximum size should be higher in a cycling population; one of the study populations exhibited a delayed feedback cycle while the other population showed no sign of cyclicity. A hump-shaped relationship between individual mass of 1-year-old leeches and offspring density the previous year was present in both populations. As predicted from the theory, the maximum mass of individuals was much larger in the fluctuating population. In contrast to predictions, the higher growth rate was not related to energy extraction from cannibalism. Instead, the higher individual mass is suggested to be due to increased availability of resources due to a niche widening with increased individual body mass. The larger individual mass in the fluctuating population was related to a stronger correlation between the densities of 1-year-old individuals and 2-year-old individuals the following year in this population. Although cannibalism was the major mechanism regulating population dynamics, its importance was negligible in terms of providing cannibalizing individuals with energy subsequently increasing their fecundity. Instead, the study identifies a need for theoretical and empirical studies on the largely unstudied interplay between ontogenetic niche shifts and cannibalistic population dynamics.     

Estimation of Successful Breeding Pairs for Wolves in the Northern Rocky Mountains,USA

Abstract: Under the Endangered Species Act, documenting recovery and federally mandated population levels of wolves (Canis lupus) in the Northern Rocky Mountains (NRM) requires monitoring wolf packs that successfully recruit young. United States Fish and Wildlife Service regulations define successful breeding pairs as packs estimated to contain an adult male and female, accompanied by ≥2 pups on 31 December of a given year. Monitoring successful breeding pairs will become more difficult following proposed delisting of NRM wolves; alternatives to historically intensive methods, appropriate to the different ecological and regulatory context following delisting, are required. Because pack size is easier to monitor than pack composition, we estimated probability a pack would contain a successful breeding pair based on its size for wolf populations inhabiting 6 areas in the NRM. We also evaluated the extent to which differences in demography of wolves and levels of human-caused mortality among the areas influenced the probability of packs of different sizes would contain successful breeding pairs. Probability curves differed among analysis areas, depending primarily on levels of human-caused mortality, secondarily on annual population growth rate, and little on annual population density. Probabilities that packs contained successful breeding pairs were more uniformly distributed across pack sizes in areas with low levels of human mortality and stable populations. Large packs in areas with high levels of human-caused mortality and high annual growth rates had relatively high probabilities of containing breeding pairs whereas those for small packs were relatively low. Our approach can be used by managers to estimate number of successful breeding pairs in a population where number of packs and their sizes are known. Following delisting of NRM wolves, human-caused mortality is likely to increase, resulting in more small packs with low probabilities of containing breeding pairs. Differing contributions of packs to wolf population growth based on their size suggests monitoring successful breeding pairs will provide more accurate insights into population dynamics of wolves than will monitoring number of packs or individuals only.