Mathematical model of invasion of mysids (Mysidacea) into the Naroch Lake system

We present a mathematical model of the invasion of mysid into the Naroch Lake system. The model is parameterized with the use of field observation data. We show that the mysid invasion can lead to an increase in the time-averaged fish population size, and to a decrease in the time-averaged rotifer population size.     

Dietary shifts in a stressed fish assemblage: Consequences of a bivalve invasion in the San Francisco Estuary

We compared dietary patterns within a temperate estuarine fish assemblage (Suisun Marsh, CA, U.S.A.) during a period of high mysid shrimp abundance and after a major decline in mysid abundance caused by the invasion of the overbite clam Potamocorbula amurensis. Prior to the invasion, high dietary overlap, high stomach fullness, and low niche breadth occurred among the fishes in spring when mysid populations were high. Dietary overlaps decreased and niche breadth increased for all species but the endemic splittail Pogonichthys macrolepidotus in fall when mysid populations were low. Eight native species exhibited lower overall collective overlaps and fuller stomachs than five alien species, suggesting more efficient resource partitioning. After mysid abundance declined, only alien striped bass Morone saxatilis preyed upon mysids in greater than trace amounts. An alien mysid became an important prey for small striped bass, but striped bass also switched to piscivory at a smaller size than when mysids were abundant. Eight of 13 species exhibited significant declines in abundance during the study period, which were concordant with the original importance of mysids in their diets. Our results suggest that altered lower food web dynamics in the San Francisco Estuary caused by the invasion of the overbite clam changed fish diets and have contributed to declines in fish abundance.     

The changing ecosystem of a shallow, brackish lake, Hickling Broad, Norfolk, U.K. I. Trophic relationships with special reference to the role of Neomysis integer

• 1 Hickling Broad, a shallow, brackish lake in England, changed from dominance by submerged aquatic plants to dominance by phytoplankton in the 1970s. These changes were ascribed to the effects of guanotrophicatioh by black-headed gulls, and increased salinity which together resulted in fish kills caused by a toxic alga, Prymnesium parvum. A mysid, Neomysis integer, was believed to be important in switching the system to plankton dominance through its presumed selective feeding on Cladocera and increasing population size as fish predation decreased.
• 2 Studies on laboratory predation rates of the mysid on Cladocera and on the population dynamics, predation rates and diet of the mysid and the populations of the major zooplankter, Eurytemora affinis in the Broad in the 1980s, have shown that the former explanations were incomplete. The mysid could have markedly reduced the cladoceran community, for it has potentially high predation rates, but Cladocera were probably lost through salinization. Neomysis feeds efficiently on Eurytentora affinis, but the latter reproduces rapidly and its populations are unlikely to be controlled by mysid predation. Nauplii and small copepodites are selectively taken. Alternative and probably major food sources for the mysid are periphyton and benthic algae and detritus.
• 3 Roach and bream readily take the mysid but the present fish stock in the Broad is very low and can now exert minimal pressure on the mysid population. An invertebrate predator on the mysid, Palaemometes varians, is also unlikely to have major effects. The former model of the operation of the Broad's ecosystem needs reconsideration in view of the findings.

     

Seasonal shifts in the life cycle of the ponto-caspian invader <Emphasis Type="Italic">Limnomysis benedeni</Emphasis> (Crustacea: Mysida): a physiological adaptation?

The mysid Limnomysis benedeni, one of the most important ponto-caspian invaders, was found in Lake Constance (southern Germany) in 2006. As part of larger studies to evaluate the effects of L. benedeni on the ecosystem, we studied its life-cycle strategies over an entire seasonal cycle in intervals of 3–5 weeks, addressing factors (predation, temperature) which we expected to be most important triggers of the observed changes. The size class distribution and the reproductive pattern indicated that the life cycle of L. benedeni changes seasonally. During winter (November to March), the mysid invested energy in growth and delayed reproduction until April, when the population was dominated by adults. In summer (June to September), the adults reproduced at a smaller body size and the population was disproportionately dominated by juveniles. In a mesocosm experiment that excluded fish predators, the mysids followed the same seasonal patterns of growth and energy investment as in the field population, but the size class distribution differed. Even in summer, the population in the mesocosm was dominated by adults. Stomach analyses of fish showed that L. benedeni is preyed upon by juvenile Perca fluviatilis, which fed size selectively on larger mysids. In conclusion, our results suggest predation was the reason for the dominance of juveniles and the observed size class distribution in summer. In contrast, the smaller adults in summer were most likely a physiological adaptation, perhaps evolved to avoid predation or as a reaction on metabolic losses at higher temperatures.     

Spatial dynamics of invasion: the geometry of introduced species

Many exotic species combine low probability of establishment at each introduction with rapid population growth once introduction does succeed. To analyse this phenomenon, we note that invaders often cluster spatially when rare, and consequently an introduced exotic's population dynamics should depend on locally structured interactions. Ecological theory for spatially structured invasion relies on deterministic approximations, and determinism does not address the observed uncertainty of the exotic-introduction process. We take a new approach to the population dynamics of invasion and, by extension, to the general question of invasibility in any spatial ecology. We apply the physical theory for nucleation of spatial systems to a lattice-based model of competition between plant species, a resident and an invader, and the analysis reaches conclusions that differ qualitatively from the standard ecological theories. Nucleation theory distinguishes between dynamics of single- and multi-cluster invasion. Low introduction rates and small system size produce single-cluster dynamics, where success or failure of introduction is inherently stochastic. Single-cluster invasion occurs only if the cluster reaches a critical size, typically preceded by a number of failed attempts. For this case, we identify the functional form of the probability distribution of time elapsing until invasion succeeds. Although multi-cluster invasion for sufficiently large systems exhibits spatial averaging and almost-deterministic dynamics of the global densities, an analytical approximation from nucleation theory, known as Avrami's law, describes our simulation results far better than standard ecological approximations.     

Inbreeding depression is purged in the invasive insect Harmonia axyridis

Bottlenecks in population size reduce genetic diversity and increase inbreeding, which can lead to inbreeding depression. It is thus puzzling how introduced species, which typically pass through bottlenecks, become such successful invaders. However, under certain theoretical conditions, bottlenecks of intermediate size can actually purge the alleles that cause inbreeding depression. Although this process has been confirmed in model laboratory systems, it has yet to be observed in natural invasive populations. We evaluate whether such purging could facilitate biological invasions by using the world-wide invasion of the ladybird (or ladybug) Harmonia axyridis. We first show that invasive populations endured a bottleneck of intermediate intensity. We then demonstrate that replicate introduced populations experience almost none of the inbreeding depression suffered by native populations. Thus, rather than posing a barrier to invasion as often assumed, bottlenecks, by purging deleterious alleles, can enable the evolution of invaders that maintain high fitness even when inbred.     

Mathematical modeling of evolution of horizontally transferred genes

We describe a stochastic birth-and-death model of evolution of horizontally transferred genes in microbial populations. The model is a generalization of the stochastic model described by Berg and Kurland and includes five parameters: the rate of mutational inactivation, selection coefficient, invasion rate (i.e., rate of arrival of a novel sequence from outside of the recipient population), within-population horizontal transmission ("infection") rate, and population size. The model of Berg and Kurland included four parameters, namely, mutational inactivation, selection coefficient, population size, and "infection." However, the effect of "infection" was disregarded in the interpretation of the results, and the overall conclusion was that horizontally acquired sequences can be fixed in a population only when they confer a substantial selective advantage onto the recipient and therefore are subject to strong positive selection. Analysis of the present model in different domains of parameter values shows that, as long as the rate of within-population horizontal transmission is comparable to the mutational inactivation rate and there is even a low rate of invasion, horizontally acquired sequences can be fixed in the population or at least persist for a long time in a substantial fraction of individuals in the population even when they are neutral or slightly deleterious. The available biological data strongly suggest that intense within-population and even between-populations gene flows are realistic for at least some prokaryotic species and environments. Therefore, our modeling results are compatible with the notion of a pivotal role of horizontal gene transfer in the evolution of prokaryotes.     

MASS-MORTALITY LAYERS OF FOSSIL STICKLEBACK FISH: CATASTROPHIC KILLS OF POLYMORPHIC SCHOOLS

Stickleback fish (Gasterosteus doryssus) from late middle-Miocene lacustrine deposits of the Truckee Formation in west-central Nevada are abundant and well preserved. They occasionally occur in unusually high densities on single annual laminations (varves) in “mass-mortality layers.” We demonstrate that stickleback mass-mortality layers consist of members of schools and may be used as population samples. Comparison of stickleback mass-mortality samples to time-averaged samples, which accumulated over hundreds or thousands of years in the same deposit, indicates that, for some purposes, the time-averaged samples are acceptable surrogates for instantaneous population samples from the G. doryssus lineage. Mass-mortality and time-averaged samples are similar for variation of pelvic structure and dorsal-spine number, but associations between states of different characters may be weaker in mass-mortality samples than in time-averaged samples. Thus, character variances in time-averaged samples of G. doryssus are comparable to those of living populations, but character correlations are suspect. Character variances and correlations in time-averaged fossil samples must be evaluated on a case-by-case basis and interpreted with caution.     

Mating preference in the invasion of growth enhanced fish

Fish with a transgene for growth hormone grow faster than the wild type and may have an advantage in sexual selection due to their larger size and earlier maturation. The cost in these genetically modified organisms (GMOs) is a lower viability of their offspring. The Trojan gene effect is a hypothesis that predicts that the release of such fish in nature can lead to an invasion by GMOs but ultimately decrease population size to extinction. We modelled GMO invasion with Mendelian inheritance of two alleles in one locus and the resulting mating and population dynamics of wild, GMO and hybrid genotypes. Invasion was attempted over a range of initial densities, representing scenarios from accidental escape to large-scale deliberate introduction of the transgenic genotype. Our results show that invasion strongly depends on hybrid fitness, requiring only a low initial density when GMOs and hybrids are preferred in mating. Preference against hybrids results in an invasion threshold, above which mating between GMOs are sufficiently frequent for invasion to take place. GMO invasion may decrease population size, but contrary to earlier studies on the Trojan gene effect, extinctions do not occur. This is due to the lower viability of GMOs being balanced by the decreased number of competitors reducing the effects of density dependence. The results emphasize the importance of initial density, hybrid fitness and density dependence when considering invasion through hybridization.     

Reduced population size can induce quick evolution of inbreeding depression in the invasive ladybird <Emphasis Type="Italic">Harmonia axyridis</Emphasis>

Understanding biological invasion is currently one of the main scientific challenges for ecologists. The introduction process is crucial for the success of an invasion, especially when it involves a demographic bottleneck. A small introduced population is expected to face a higher risk of extinction before the first stage of invasion is complete if inbreeding depression, caused by the expression of deleterious alleles, is important. Changes in mating regimes or in population size can induce the evolution of deleterious allele frequencies, either by selection or by drift, possibly resulting in the purging or the fixation of such alleles within the population. The harlequin ladybird Harmonia axyridis became invasive on several continents following a scenario including at least one event of demographic bottleneck. Although native populations suffered from severe inbreeding depression, it was greatly reduced in invasive ones suggesting that deleterious alleles were purged during the invasion process. In this study, we performed an experiment designed to manipulate the effective population size of H. axyridis across successive generations to mimic contrasting introduction events. We used the measurement of two fitness-related phenotypic traits in order to test (1) if inbreeding depression can evolve at the time-scale of an invasion; and (2) if the changes in inbreeding depression following a bottleneck in laboratory conditions are compatible with the purging of deleterious alleles observed in this species. We found that two generations of very low population size are enough to induce a substantial change in inbreeding depression. Although the genetic changes mostly consisted in fixation of deleterious alleles, purging did also occur, sometimes simultaneously with fixation.     

The possibility of predator avoidance by Lake Michigan zooplankton

Low densities of Diaptomus ashlandi, Diacyclops thomasi, and Daphnia galeata mendotae were measured at depths where Mysis relicta formed nighttime aggregations. Calculations suggest that mysid predation can not account for the rarity of prey animals at these depths, which further suggests that the prey avoided the mysids. Unlike D. galeata mendotae, Daphnia pulicaria was common in mysid aggregations. The somewhat larger size of D. pulicaria may reduce its vulnerability to mysid predation, and consequently may explain the vertical distribution differences between the two congeners. Vertical distributions of Limnocalanus macrurus and copepod nauplii showed no obvious relationships to the mysid distributions. These were the only two taxa with distributions that were correlated with chlorophyll a concentrations. All crustacean taxa were rare in the epilimnion at night when sonar recorded a dense fish school.     

Life histories ofNeomysis integer,and its copepod prey,Eurytemora affinis,in a eutrophic and brackish shallow lake

Data was collected on the population structure and fecundity of the mysidNeomysis integer and the calanoid copepodEurytemora affinis in Hickling Broad, a shallow and eutrophic brackish lake, over a two-year period 1988/89. Standing biomass and production rate estimates were made using estimates of size-specific dry weights and development times obtained from laboratory measurements, field observations and information found in the literature. Both mysid and copepod are capable of a rapid response to favourable conditions and have high rates of birth, growth and production.E. affinis reproduces throughout the year with an estimated annual (May 1988–May 1989) production of 20 g dry wt m⁻². Copepod standing biomass was less in 1989 compared with 1988 owing to an overall reduction in copepod body-size and a reduction of size at maturity. There was a suggestion from the data that this was caused by predation from a greater number of large (>9 mm body-length) mysids in 1989 compared with 1988.N. integer is highly seasonal in its growth with distinct peaks of recruitment in May and July. Annual (May 1988–May 1989) production of the mysid was estimated as 5.8 g dry wt m⁻². AlthoughE. affinis is the only available prey ofN. integer in the lake, the mysid population appears independent of changes in that of the copepod and probably avoids negative predator-prey feedback mechanisms owing to an ability to feed on epiphytic algae.     

Evolution of age-dependent sex-reversal under adaptive dynamics

We investigate the evolution of the age (or size) at sex-reversal in a model of sequential hermaphroditism, by means of the function-valued adaptive dynamics. The trait is the probability law of the age at sex-reversal considered as a random variable. Our analysis starts with the ecological model which was first introduced and analyzed by Calsina and Ripoll (Math Biosci 208(2), 393–418, 2007). The structure of the population is extended to a genotype class and a new model for an invading/mutant population is introduced. The invasion fitness functional is derived from the ecological setting, and it turns out to be controlled by a formula of Shaw–Mohler type. The problem of finding evolutionarily stable strategies is solved by means of infinite-dimensional linear optimization. We have found that these strategies correspond to sex-reversal at a single particular age (or size) even if the set of feasible strategies is considerably broader and allows for a probabilistic sex-reversal. Several examples, including in addition the population-dynamical stability, are illustrated. For a special case, we can show that an unbeatable size at sex-reversal must be larger than 69.3% of the expected size at death.     

Global diversity of mysids (Crustacea-Mysida) in freshwater

In this article we present a biogeographical assessment of species diversity within the Mysida (Crustacea: Malacostraca: Peracarida) from inland waters. Inland species represent 6.7% (72 species) of mysid diversity. These species represent three of the four families within the Mysida (Lepidomysidae, Stygiomysidae, and Mysidae) and are concentrated in the Palaearctic and Neotropical regions. The inland mysid species distributional patterns can be explained by four main groups representing different freshwater invasion routes: (1) Subterranean Tethyan relicts (24 spp.); (2) Autochthonous Ponto-Caspian endemics (20 spp.); (3) Mysis spp. ‘Glacial Relicts’ (8 spp.); and (4) Euryhaline estuarine species (20 spp.). The center of inland mysid species diversity is the Ponto-Caspian region, containing 24 species, a large portion of which are the results of a radiation in the genus Paramysis. Electronic Supplementary Material The online version of this article (doi:) contains supplementary material, which is available to authorized users. Guest editors: E. V. Balian, C. Lévêque, H. Segers and K. Martens Freshwater Animal Diversity Assessment     

A branching process for the early spread of a transposable element in a diploid population

Transposable elements (TEs) face significant challenges upon transfer into a new host population, invariably beginning their invasion with only a single element. The fate of this element is a product of its internal properties, the population dynamics of the host species, and genetic drift. We present a continuous-time multi-type branching process to model the early stages of TE spread. The model incorporates seasonal population size changes and is applicable to diploid hosts for prevalences up to 10%. We reproduce standard results of TE population dynamics and show that population growth may have a greater influence on reducing TE loss probability than a transpositional burst. These results are applied to the planned use of a TE to drive an antimalarial gene into an Anopheles gambiae population. The model favors a transgenic release immediately following the dry season when the An. gambiae population begins to grow. Increasing the number of transgenic hosts released has the greatest influence on reducing the probability of TE loss. Following release, the rate at which the TE increases its proportion in the population is most sensitive to its replicative transposition rate. The model recommends a replicative transposition rate greater than 0.1 per TE per generation to satisfy public health goals.     

A fully coupled, mechanistic model for infectious disease dynamics in a metapopulation: movement and epidemic duration

The drive to understand the invasion, spread and fade out of infectious disease in structured populations has produced a variety of mathematical models for pathogen dynamics in metapopulations. Very rarely are these models fully coupled, by which we mean that the spread of an infection within a subpopulation affects the transmission between subpopulations and vice versa. It is also rare that these models are accessible to biologists, in the sense that all parameters have a clear biological meaning and the biological assumptions are explained. Here we present an accessible model that is fully coupled without being an individual-based model. We use the model to show that the duration of an epidemic has a highly non-linear relationship with the movement rate between subpopulations, with a peak in epidemic duration appearing at small movement rates and a global maximum at large movement rates. Intuitively, the first peak is due to asynchrony in the dynamics of infection between subpopulations; we confirm this intuition and also show the peak coincides with successful invasion of the infection into most subpopulations. The global maximum at relatively large movement rates occurs because then the infectious agent perceives the metapopulation as if it is a single well-mixed population wherein the effective population size is greater than the critical community size.     

The highs and lows of dispersal: how connectivity and initial population size jointly shape establishment dynamics in discrete landscapes

Identifying the main factors driving introduced populations to establishment is a major challenge of invasion biology. Due to their small initial size, introduced populations are most vulnerable to extinction because of demographic stochasticity or Allee effects. While an increase in initial population size is known to increase establishment success, much remains to be understood regarding its interplay with connectivity in spatially structured environments. In order to better understand how demographic mechanisms interact at such spatial scale, we developed a stochastic model of population dynamics in discrete space to investigate the effect of connectivity and initial population size on establishment. The predictions derived from the model were then tested using experimental introductions of an insect parasitoid (Trichogramma chilonis) in spatially structured laboratory microcosms. Both theoretical and experimental results demonstrated that the connectivity of the introduction site had 1) a deleterious effect in the first generation when the introduced population was small and 2) a beneficial impact brought about by metapopulation effects in the subsequent generations. Interestingly, populations displayed a weakly pushed invasion pattern promoting early establishment, which was mainly underpinned by dispersal stochasticity and the discrete nature of the landscape. These results shed light on the critical influence of landscape connectivity on establishment dynamics.     

Allee Effects, Propagule Pressure and the Probability of Establishment: Risk Analysis for Biological Invasions

Colonization is of longstanding interest in theoretical ecology and biogeography, and in the management of weeds and other invasive species, including insect pests and emerging infectious diseases. Due to accelerating invasion rates and widespread economic costs and environmental damages caused by invasive species, colonization theory has lately become a matter of considerable interest. Here we review the concept of propagule pressure to inquire if colonization theory might provide quantitative tools for risk assessment of biological invasions. By formalizing the concept of propagule pressure in terms of stochastic differential equation models of population growth, we seek a synthesis of invasion biology and theoretical population biology. We focus on two components of propagule pressure that affect the chance of invasion: (1) the number of individuals initially introduced, and (2) the rate of subsequent immigration. We also examine how Allee effects, which are expected to be common in newly introduced populations, may inhibit establishment of introduced propagules. We find that the establishment curve (i.e., the chance of invasion as a function of initial population size), can take a variety of shapes depending on immigration rate, carrying capacity, and the severity of Allee effects. Additionally, Allee effects can cause the stationary distribution of population sizes to be bimodal, which we suggest is a possible explanation for time lags commonly observed between the detection of an introduced population and widespread invasion of the landscape.     

Evolutionarily stable consumer home range size in relation to resource demography and consumer spatial organization

There is a large variation in home range size within species, yet few models relate that variation to demographic and life-history traits. We derive an approximate deterministic population dynamics model keeping track of spatial structure, via spatial moment equations, from an individual-based spatial consumer-resource model; where space-use of consumers resembles that of central place foragers. Using invasion analyses, we investigate how the evolutionarily stable home range size of the consumer depends on a number of ecological and behavioral traits of both the resource and the consumer. We show that any trait variation leading to a decreased overall resource production or an increased spatial segregation between consumer and resource acts to increase consumer home range size. In this way, we extend theoretical predictions on optimal territory size to a larger range of ecological scenarios where home ranges overlap and population dynamics feedbacks are possible. Consideration of spatial traits such as dispersal distances also generates new results: (1) consumer home range size decreases with increased resource dispersal distance, and (2) when consumer agonistic behavior is weak, more philopatric consumers have larger home ranges. Finally, our results emphasize the role of the spatial correlation between consumer and resource distributions in determining home range size, and suggest resource dispersion is less important.     

Invasion of an intermediate predator: the dynamics of fish populations in the mathematical model of a trophic chain (as applied to the Syamozero lake)

We present a mathematical model of the dynamics of a spatially heterogeneous predator-prey population system. A prototype of the model system is the Syamozero lake fish community. We study the impact of the invader, an intermediate predator, on the dynamics of the fish community. We show that the invasion can lead to the appearance of chaotic oscillations in the population density. We show also that different dynamical regimes resulting from the invasion, i.e., stationary, non-chaotic oscillatory and chaotic ones, can coexist. The "choice" of a specific regime therewith depends on the initial invader density. Our analysis of solutions of the mathematical models shows that the successful invasion of the alien species takes place solely in the absence of the competition between the invaders and the native species.