Quantifying the relative importance of niches and neutrality for coexistence in a model microbial system

1.  Ecologists have identified two types of processes promoting species coexistence: stabilizing mechanisms (niche differentiation and related processes) that increase negative intraspecific interactions relative to negative interspecific interactions, and equalizing mechanisms (neutrality) that minimize the differences in species' demographic parameters. It has been theoretically and empirically shown that the two types of mechanisms can operate simultaneously; however, their relative importance remains unstudied although this is a key question in the synthesis of niche and neutral theories.
2.  We experimentally quantified the relative importance of niche and neutral mechanisms in promoting phenotypic diversity in a model microbial system involving different phenotypes of the bacterium Pseudomonas fluorescens . Initially isogenic populations of the bacterium can diversify into a series of major and minor classes of phenotypes that can be treated as analogues of species. We estimated the relative population growth rate when rare of 32 phenotypes from six replicate microcosms. Each phenotype was assessed in a re-assembled microcosm in which the relative densities of all phenotypes remained the same except for the focal one which was reduced in frequency. A growth rate advantage when rare was considered evidence of non-neutral processes.
3.  Approximately one-third of the phenotypes had a growth rate advantage when rare while the remaining two-thirds showed neutral or near-neutral dynamics. Furthermore, there was overall little evidence that productivity increased with phenotypic diversity.
4.  Our results suggest that niche and neutral processes may simultaneously contribute to the maintenance of biodiversity, with the latter playing a more important role in our system, and that the operation of niche mechanisms does not necessarily lead to a positive biodiversity effect on ecosystem properties.     

LONG-TERM EXPERIMENTAL EVOLUTION IN ESCHERICHIA COLI. VII. MECHANISMS MAINTAINING GENETIC VARIABILITY WITHIN POPULATIONS

Six replicate populations of the bacterium Escherichia coli were propagated for more than 10,000 generations in a defined environment. We sought to quantify the variation among clones within these populations with respect to their relative fitness, and to evaluate the roles of three distinct population genetic processes in maintaining this variation. On average, a pair of clones from the same population differed from one another in their relative fitness by approximately 4%. This within-population variation was small compared with the average fitness gain relative to the common ancestor, but it was statistically significant. According to one hypothesis, the variation in fitness is transient and reflects the ongoing substitution of beneficial alleles. We used Fisher's fundamental theorem to compare the observed rate of each population's change in mean fitness with the extent of variation for fitness within that population, but we failed to discern any correspondence between these quantities. A second hypothesis supposes that the variation in fitness is maintained by recurrent deleterious mutations that give rise to a mutation-selection balance. To test this hypothesis, we made use of the fact that two of the six replicate populations had evolved mutator phenotypes, which gave them a genomic mutation rate approximately 100-fold higher than that of the other populations. There was a marginally significant correlation between a population's mutation rate and the extent of its within-population variance for fitness, but this correlation was driven by only one population (whereas two of the populations had elevated mutation rates). Under a third hypothesis, this variation is maintained by frequency-dependent selection, whereby genotypes have an advantage when they are rare relative to when they are common. In all six populations, clones were more fit, on average, when they were rare than when they were common, although the magnitude of the advantage when rare was usually small (~1% in five populations and ~5% in the other). These three hypotheses are not mutually exclusive, but frequency-dependent selection appears to be the primary force maintaining the fitness variation within these experimental populations.     

A population dynamics model for annual plants subject to inbreeding depression

Summary We present a population dynamics model for annual plants subject to density dependent competition and a decline in mean individual fitness with inbreeding. An analysis of this model provides three distinct sets of parameter values that define the relative influence of inbreeding depression and density on population growth. First, a population with a relatively high finite rate of increase and a relatively small environmental carrying capacity can persist in spite of low levels of inbreeding depression. These types of population may occur during a bottleneck event that is caused by pure predation (or collecting) pressure rather than loss of habitat. Second, there can exist a minimum viable population size when the finite rate of increase is relatively low and the population is also affected by density: the growth or decline of the population will depend on the initial population size. Third, when the population is small enough to be simultaneously effected by density and by inbreeding depression, there can be no viable population.     

Effective population size of a population with stochastically varying size

For a Wright–Fisher model with mutation whose population size fluctuates stochastically from generation to generation, a heterozygosity effective population size is defined by means of the equilibrium average heterozygosity of the population. It is shown that this effective population size is equal to the harmonic mean of population size if and only if the stochastic changes of population size are uncorrelated. The effective population size is larger (resp. smaller) than the harmonic mean when the stochastic changes of population size are positively (resp. negatively) autocorrelated. These results and those obtained so far for other stochastic models with fluctuating population size suggest that the property that effective population sizes are always larger than the harmonic mean under the fluctuation of population size holds only for continuous time models such as diffusion and coalescent models, whereas effective population sizes can be equal to or smaller than the harmonic mean for discrete time models.     

Sulfur Isotope Fractionation during the Evolutionary Adaptation of a Sulfate-Reducing Bacterium

Dissimilatory sulfate reduction is a microbial catabolic pathway that preferentially processes less massive sulfur isotopes relative to their heavier counterparts. This sulfur isotope fractionation is recorded in ancient sedimentary rocks and generally is considered to reflect a phenotypic response to environmental variations rather than to evolutionary adaptation. Modern sulfate-reducing microorganisms isolated from similar environments can exhibit a wide range of sulfur isotope fractionations, suggesting that adaptive processes influence the sulfur isotope phenotype. To date, the relationship between evolutionary adaptation and isotopic phenotypes has not been explored. We addressed this by studying the covariation of fitness, sulfur isotope fractionation, and growth characteristics in Desulfovibrio vulgaris Hildenborough in a microbial evolution experiment. After 560 generations, the mean fitness of the evolved lineages relative to the starting isogenic population had increased by ∼17%. After 927 generations, the mean fitness relative to the initial ancestral population had increased by ∼20%. Growth rate in exponential phase increased during the course of the experiment, suggesting that this was a primary influence behind the fitness increases. Consistent changes were observed within different selection intervals between fractionation and fitness. Fitness changes were associated with changes in exponential growth rate but changes in fractionation were not. Instead, they appeared to be a response to changes in the parameters that govern growth rate: yield and cell-specific sulfate respiration rate. We hypothesize that cell-specific sulfate respiration rate, in particular, provides a bridge that allows physiological controls on fractionation to cross over to the adaptive realm.     

INFLUENCE OF ENVIRONMENTAL FACTORS AND POPULATION COMPOSITION ON THE TIMING OF CELL DIVISION IN THALASSIOSIRA FLUVIATILIS (BACILLARIOPHYCEAE) GROWN ON LIGHT/DARK CYCLES1

Cell division patterns in Thalassiosira fluviatilis grown in a cyclostat were analyzed as a function of temperature, photoperiod, nutrient limitation and average cell size of the population. Typical cell division patterns in populations doubling more than once per day had multiple peaks in division rate each day, with the lowest rates always being greater than zero. Division bursts occurred in both light and dark periods with relative intensities depending on growth conditions. Multiple peaks in division rate were also found, when population growth rates were reduced to less than one doubling per day by lowering temperature, nutrients, or photoperiod and the degree of division phasing was not enhanced. Temperature and nutrient limitation shifted the timing of the major division burst relative to the light/dark cycle. Average cell volume of the inoculum was found to be a significant determinant of the average population growth rate and the timing and magnitude of the peaks in division rate. The results are interpreted in the context of a cell cycle model in which generation times are “quantized” into values separated by a constant time interval.     

How does temporal variability affect predictions of weed population numbers?

1. Population models that are used to predict weed population dynamics or the impact of control measures on weed abundance typically ignore temporal variability in life-history parameters and control measures, and utilize mean arithmetic population growth rates to predict population abundance.
2. We demonstrate that the persistence of weeds in a stochastically varying environment depends on the geometric mean population growth rate being greater than zero, rather than the arithmetic mean population growth rate being greater than zero.
3. In a stochastically varying environment we show that temporal variability in fecundity, germination and survivorship will tend to decrease population size, relative to predictions based on arithmetic means. Conversely, variability in competitive effects and weed control will tend to increase population size, relative to predictions based on arithmetic mean values. The distinction between these two sets of parameters is that increases in the former will increase population growth rate, whereas increases in the latter will decrease it.
4. We argue that population models based on arithmetic mean population growth rates will tend to over-estimate population size. Numerical simulations indicate that this bias may be considerable.
5. Since short-term studies cannot, in general, estimate the geometric mean growth rate of a population we suggest several approaches for estimating the degree of bias in the predictions of models owing to the effects of variability. Accounting for such variability is necessary since current models for the dynamics of weed populations are based on arithmetic mean measures of population growth and hence likely to be biased.     

Distribution of nucleotide differences between two randomly chosen cistrons in a population of variable size

The distribution of the number of nucleotide differences between two randomly chosen cistrons in a finite population is studied here when the population size changes from generation to generation. When genetic variability is measured by heterozygosity (i.e., the probability that two cistrons are different), by the probability that two cistrons differ at two or more nucleotide sites, or by mean number of site differences between cistrons, it is seen that in a population going through a small bottleneck all of these measures decline rapidly but, as soon as population size becomes large, they start to increase owing to new mutations. The amount of reduction in these measures depends not only on the size of bottleneck but also on the rate of population growth. The implications of this study explaining the observed variations in the rates of amino acid substitutions during the evolutionary process are also discussed.     

Relative Fitness, Teleology, and the Adaptive Landscape

The metaphor of the adaptive landscape, introduced by Sewall Wright in 1932, has played, and continues to play, a central role in much evolutionary thought. I argue that the use of this metaphor is tied to a teleological view of the evolutionary process, in which natural selection directs evolution toward an improved future state. I argue further that the use of “relative fitnesses” standardized to an arbitrary value, which is closely connected with the metaphor of an adaptive landscape, produces a disconnect between the mean fitness of a population and any real property of that population. This allows for a vague and ill-defined improvement to occur under the influence of selection. Instead, I suggest that relative fitnesses should be standardized by the mean absolute fitness (expected population growth rate), so that they express the expected rate of increase in frequency, rather than number. Under this definition, the mean relative fitness of all populations is always 1.0, and never changes as long as the population continues to exist.     

Enhanced individual selection for selecting fast growing fish: the "PROSPER" method,with application on brown trout (Salmo trutta fario)

Growth rate is the main breeding goal of fish breeders, but individual selection has often shown poor responses in fish species. The PROSPER method was developed to overcome possible factors that may contribute to this low success, using (1) a variable base population and high number of breeders (Ne > 100), (2) selection within groups with low non-genetic effects and (3) repeated growth challenges. Using calculations, we show that individual selection within groups, with appropriate management of maternal effects, can be superior to mass selection as soon as the maternal effect ratio exceeds 0.15, when heritability is 0.25. Practically, brown trout were selected on length at the age of one year with the PROSPER method. The genetic gain was evaluated against an unselected control line. After four generations, the mean response per generation in length at one year was 6.2% of the control mean, while the mean correlated response in weight was 21.5% of the control mean per generation. At the 4th generation, selected fish also appeared to be leaner than control fish when compared at the same size, and the response on weight was maximal (≈130% of the control mean) between 386 and 470 days post fertilisation. This high response is promising, however, the key points of the method have to be investigated in more detail.     

Social selection in human populations: sufficient conditions for protection of deleterious alleles in a subdivided population

Population dynamics of wild type (A1) and the deleterious genes (A2) under social selection have been studied by considering a subdivided population where the i-th subpopulation consists of Ni individuals with relative size ci (= Ni/sigma i Ni, i = 1,2, ..., n). A social selection model is constructed by assuming that the fitness of an individual is determined by its own as well as the parental phenotypes and that the number of migrants (M) from the ith subpopulation is divided equally into other subpopulations including the ith subpopulation itself. It has been shown that the gene frequency change depends on the loss of fitness of an individual due to the trait (gamma), an affected parent in the ith subpopulation (beta i), the probability that the heterozygote develops the trait (h), and the migration rates mi (= M/Ni). For 0 less than h less than or equal to 1, a sufficient condition for protection of the deleterious allele from extinction also depends on all of these parameters. However, when mi much less than 1 for all i, the condition is beta i less than gamma/(1 - gamma) for some i, whereas when mi much greater than h[gamma + beta i(1 - gamma)] for all i it is given by sigma i ci beta i less than -gamma/(1 - gamma). When h = 0, that condition is given by sigma ici beta i less than - gamma/(1 - gamma). Analyses also show that, when the deleterious alleles in a population are rare, the relative fitnesses of A1A1, A1A2, and A2A2 are given approximately by 1, 1-hS, and 1 - S, respectively, where S is the harmonic mean of Si = gamma + beta i(1 - gamma). Thus, under mutation-selection balance, the equilibrium frequency of deleterious alleles in the entire population is given by alpha/hS for 0 less than h less than or equal to 1 and square root alpha/S for h = 0, where alpha is the irreversible mutation rate from A1 to A2 in each generation. Population dynamics of rare deleterious genes under social selection can readily be studied by considering a finite population size.     

French wasps in the New World: experimental biological control introductions reveal a demographic Allee effect

Many populations introduced into a novel environment fail to establish. One underlying process is the Allee effect, i.e., the difficulty of individuals to survive and reproduce when rare, and the consequently low or negative population growth. Although observations showing a positive relation between initial population size and establishment probability suggest that the Allee effect could be widespread in biological invasions, experimental tests are scarce. Here, we used a biological control program against Diuraphis noxia (Mordvilko) (Hemiptera: Aphididae) in the United States to manipulate initial population size of the introduced parasitoid Aphelinus asychis Walker (Hymenoptera: Aphelinidae) originating from France. For eight populations and three generations after introduction, we studied spatial distribution and spread, density, mate-finding, and population growth. Dispersal was lower in small populations during the first generation. Smaller initial population size nonetheless resulted in lower density during the three generations studied. The proportion of mated females and the population sex ratio were not affected by initial population size or population density. Net reproductive rate decreased with density within each generation, suggesting negative density-dependence. But for a given density, net reproductive rate was smaller in populations initiated with few individuals than in populations initiated with many individuals. Hence, our results demonstrate a demographic Allee effect. Mate-finding is excluded as an underlying mechanism, and other component Allee effects may have been overwhelmed by negative density-dependence in reproduction. Impact of generalist predators could provide one potential explanation for the relationship between initial population size and net reproductive rate. However, the continuing effect of initial population size on population growth suggests genetic processes may have been involved in the observed demographic Allee effect.     

Life history of a neotropical marsupial: Evaluating potential contributions of survival and reproduction to population growth rate

The relative effect of survival and reproductive rates to population growth rate is expected to be similar across species with similar life-histories. We employed a matrix population model and sensitivity and elasticity analysis to assess the absolute and relative importance of age-specific survival and fertility to population growth rate of Didelphis aurita (Didelphimorphia, Didelphidae) in a rural area of Rio de Janeiro, southeastern Brazil. The results were compared to expectations for mammals that mature early and have short generation time, such as D. aurita. Prospective analysis showed that changes in pouch young and juveniles survival would have large effects on population growth rate, relative to other vital rates, being the most critical time periods in the life cycle of D. aurita, whereas the effect of fertilities were always low. These findings do not fit to the observed pattern in mammals that mature early, where reproductive parameters have the largest relative influence on population growth rate. Although reproductive rates were characterized by a relatively small influence on population growth rate, they are still relevant because of their high variability and response to potential environmental disturbances. The first application of matrix population models to a neotropical rainforest marsupial provides information on marsupial demography and life-history strategy, increasing comprehension of this unknown group.     

Population responses of a conifer-dwelling aphid to seasonal changes in its host

Abstract.  1. Current evidence suggests that seasonal changes in spruce needle sap nutrients have a decisive influence on green spruce aphid ( Elatobium abietinum ) population density, but the mechanisms of population change, the roles of development rate, fertility and mortality, and the existence of density-dependent processes, are not clearly understood.
2. Experimental studies of aphid populations were conducted in controlled environments to estimate seasonal patterns in aphid mean relative growth rate, prenatal development, fertility, and mortality. Studies were also made of the effect of aphid crowding on vital rates.
3. Independent of the degree of aphid crowding, seasonal changes in the amino acid concentration of needle sap were tracked by aphid growth rate, fertility (and adult size), but not by rates of aphid mortality. The most pronounced change in vital rates, and the one most likely to drive seasonal population change, was in fertility. Prenatal development time actually became shorter in periods when nutrients were scarce, but the resulting adult aphids were smaller and less fertile than during periods of improved nutrition.
4. Density dependence of vital rates was only observed during mid-summer when nutrients were least available. Mortality, growth rate, and prenatal development were the most strongly density-dependent processes. In contrast, there was no evidence that fertility rates were likely to respond to crowding.
5. There were no important differences between populations reared on small, potted spruce trees and those on plantation trees aged 25 years. This gives confidence that demographic data from a variety of field and laboratory sources could be used to compile data appropriate for population models.     

Long-Term Experimental Evolution in Escherichia coli. VIII. Dynamics of a Balanced Polymorphism

We describe the short- and long-term dynamics of a phenotypic polymorphism that arose in a population of Escherichia coli while it was serially propagated for almost 20,000 generations in a glucose-limited minimal medium. The two types, designated L and S, differ conspicuously in the size of the colonies they form on agar plates as well as the size of their individual cells, and these differences are heritable. The S type reached a detectable frequency (>1%) at generation 6,000, and it remained above that frequency throughout the subsequent generations. In addition to morphological differences, L and S diverged in important ecological properties. With clones isolated at 18,000 generations, L has a maximal growth rate in fresh medium that is approximately 20% higher than that of S. However, experiments with conditioned media demonstrate that L and S secrete one or more metabolites that promote the growth of S but not of L. The death rate of L during stationary phase also increases when S is abundant, which suggests that S may either secrete a metabolite that is toxic to L or remove some factor that enables the survival of L. One-day competition experiments with the clones isolated at generation 18,000 show that their relative fitness is frequency dependent, with each type having an advantage when rare. When these two types are grown together for a period of several weeks, they converge on an equilibrium frequency that is consistent with the 1-d competition experiments. Over the entire 14,000-generation period of coexistence, however, the frequency of the S type fluctuated between approximately 10% and 85%. We offer several hypotheses that may explain the fluctuations in this balanced polymorphism, including the possibility of coevolution between the two types.     

Determinants of species rarity: population growth rates of species sharing the same habitat

Determining differences between common and rare species is commonly used to identify factors responsible for rarity. Existing studies, however, suffer from two important drawbacks. First, studies compare species that are closely related phylogenetically but occupy different habitats. Second, these studies concentrate on single life history traits, with unknown relevance for population growth rates. Complete life cycles of one rare and one common Cirsium species sharing the same habitat were compared. Population growth rate was slightly lower in the rare species, translating into a large difference in local extinction probability. Seed predation intensity did not differ between species. However, it can be demonstrated that in connection with the data on complete demography, seed predation is the key factor causing a lower population growth rate in the rare species. These results are the first estimation of factors responsible for commonness or rarity of plants in terms of population growth rate without confounding differences in ecology. They demonstrate that conclusions based on single traits may be misleading and that only a comparison based on a complete life cycle can provide unequivocal evidence for concluding which factors are really those responsible for species commonness or rarity.     

Response of population size to changing vital rates in random environments

Population size and population growth rate respond to changes in vital rates like survival and fertility. In deterministic environments change in population growth rate alone determines change in population size. In random environments, population size at any time t is a random variable so that change in population size obeys a probability distribution. We analytically show that, in a density-independent population, the proportional change in population size with respect to a small proportional change in a vital rate has an asymptotic normal distribution. Its mean grows linearly at a rate equal to the elasticity of the long-term stochastic growth rate λ _S while the standard deviation scales as $\sqrt t$ . Consequently, a vital rate with a larger elasticity of λ _S may produce a larger mean change in population size compared to one with a smaller elasticity of λ _S. But a given percentage change in population size may be more likely when the vital rate with smaller elasticity is perturbed. Hence, the response of population size to perturbation of a vital rate depends not only on the elasticity of the population growth rate but also on the variance in change in population size. Our results provide a formula to calculate the probability that population size changes by a given percentage that works well even for short time periods.     

A simple persistence condition for structured populations

The fundamental question in both basic and applied population biology of whether a species will increase in numbers is often investigated by finding the population growth rate as the largest eigenvalue of a deterministic matrix model. For a population classified only by age, and not stage or size, a simpler biologically interpretable condition can be used, namely whether R ₀, the mean number of offspring per newborn, is greater than one. However, for the many populations not easily described using only age classes, stage-structured models must be used for which there is currently no quantity like R ₀. We determine analogous quantities that must be greater than one for persistence of a general structured population model that have a similar useful biological interpretation. Our approach can be used immediately to determine the magnitude of changes and interactions that would either allow population persistence or would ensure control of an undesirable species.     

Hydrobiological consequences of the addition of phosphate precipitants to inlet water of lakes

Summary In three model reservoirs (LUND, 1975) a method reducing bluegreen algal blooms in lakes was studied. Iron or aluminium were added to inlet waters for chemically binding the inflowing phosphorus.The research program, started in 1975, includes intensive monitoring of many chemical and hydrobiological variables, the determination of water and mass balances and since 1977 measurements or primary production rates with¹⁴C. In this paper only the results found in 1977 are discussed. An attempt is made to describe quantitatively how growth rates and changes in biomass are interconnected and how phosphorus precipitation changes these variables.In all reservoirs a large discrepancy was observed between the actual rate of increase in the algal population and the relative production rate. The latter appeared to be higher by one order of magnitude. The relative death rate due to grazing can account for the large difference between these growth rates only when selective grazing of zooplankton on phytoplankton is assumed.It can be concluded that treatment of inlet water with AVR, an aluminium salt, is unsuccessful in reducing algal development. Treatment with ironsulphate may be successful, but a reduction of the relative growth rates was not observed. The effects of grazing of zooplankton andDreissena polymorpha need further investigation.     

Partitioning the effects of deterministic and stochastic processes on species extinction risk

Species populations are subjected to deterministic and stochastic processes, both of which contribute to their risk of extinction. However, current understanding of the relative contributions of these processes to species extinction risk is far from complete. Here, we address this knowledge gap by analyzing a suite of models representing species populations with negative intrinsic growth rates, to partition extinction risk according to deterministic processes and two broad classes of stochastic processes – demographic and environmental variance. Demographic variance refers to random variations in population abundance arising from random sampling of events given a particular set of intrinsic demographic rates, whereas environmental variance refers to random abundance variations arising from random changes in intrinsic demographic rates over time. When the intrinsic growth rate was not close to zero, we found that deterministic growth was the main driver of mean time to extinction, even when population size was small. This contradicts the intuition that demographic variance is always an important determinant of extinction risk for small populations. In contrast, when the intrinsic growth rate was close to zero, stochastic processes exerted substantial negative effects on the mean time to extinction. Demographic variance had a greater effect than environmental variance at low abundances, with the reverse occurring at higher abundances. In addition, we found that the combined effects of demographic and environmental variance were often substantially lower than the sum of their effects in isolation from each other. This sub-additivity indicates redundancy in the way the two stochastic processes increase extinction risk, and probably arises because both processes ultimately increase extinction risk by boosting variation in abundance over time.