Evolutionary games and two species population dynamics

Competition between species has long been modeled by population dynamics based on total numbers of each species. Recently, the evolution of strategy frequencies has been used successfully for competition models between individuals. In this paper, we illustrate that these two views of competition are compatible. It is shown that the rate of intra and interspecific competitions between individuals largely determines the population dynamics. Competition models over a single common resource and predator-prey models are developed from this individual competition approach. In particular, the equilibrium strategies in a co-evolving predator-prey system are shown to be more stable than the predicted strategy cycling of standard evolutionary game theory.     

The life histories and population dynamics of two carabid species on a Dutch heathland

Summary We deal with the causes of the synchronously fluctuating numbers of subpopulations of the carabid species Calathus melanocephalus as compared with the asynchronously fluctuating numbers of subpopulations of the carabid Pterostichus versicolor. Both species continuously occupy a large heath area, Dwingelder Veld (1600 ha), in The Netherlands, and are studied there in the same localities with the same methods. Of the adults of C. melanocephalus, 90% do not cover more than 2 ha during the entire reproductive season, while 90% of adults of P. versicolor cover no more than 12 ha. In C. melanocephalus egg production in the field is usually similar to that under optimal feeding conditions in the laboratory, but in P. versicolor egg production seems to be much lower in the field. In the field 70–80% of the eggs most probably are killed by eelworms, followed by more than 90% mortality among the remaining larvae. Comparing mortality of developmental stages in laboratory experiments with that in field experiments in enclosures, it appears that mortality of larvae is not density-dependent, even when density in the experiments is much higher than it ever is in the field. Larval mortality mainly results from the poor ability of the larvae to find prey, even when in field experiments prey density is increased far above natural densities. We discuss why these poor prey-finding abilities are not improved by natural selection. In the spring breeder P. versicolor differences between localities both in abiotic factors, soil moisture and surface temperature, and biotic factors, reactions of prey species to abiotic factors, in spring and summer when the larvae are maturing contribute to the asynchronous fluctuations of numbers between subpopulations. In the autumn breeder C. melanocephalus possible differences in biotic factors between sites are outnumbered by the effects of winters with a higher or lower than normal amount of precipitation respectively. During a wet winter mortality among the larvae is much higher than during a dry winter. As these winter conditions are similar over large areas (many km²) the fluctuations of numbers between subpopulations are synchronous.Communication No. 443 of The Biological Station, Wijster     

A population balance model for fish population dynamics

A population balance model of fish population dynamics for batch systems was developed. A growth rate expression was introduced and coupled with the population balance. Solutions of the model provide predictions of such fish size distribution characteristics as average size, standard deviation and coefficient of variation. A growth diffusivity mechanism was found to be inapplicable to systems where a terminal size is reached. A study of the two parameter growth rate expression was conducted, illustrating that conditions conducive to high growth rates also resulted in broadening of size distributions. The model was compared to data found in the literature to demonstrate its predictive capabilities.     

A study of spatial distribution and population dynamics of two sympatric species of trichodorid nematodes

The spatial distribution and population dynamics of Trichodorus primitivus and Paratrichodorus pachydermus were studied at a Scottish nursery site in replicated plots. Each plot was split and half was fumigated with dichloropropene. The numbers of males, females and juveniles under Scots pine (Pinus sylvestris), grass/clover (Lolium perenne/Trifolium repens) and fallow in non-fumigated and fumigated subplots were recorded at 10 cm intervals to a depth of 50 cm every 4 months for 3 years. In the non-fumigated subplots the population densities of T. primitivus under each crop and the fallow soil were similar at the beginning and end of the experiment but P. pachydermus responded differentially, decreasing in fallow soils and increasing under pine. The ratios of adult: juvenile and male: female for the two species were not significantly affected by crop or sampling depth. T. primitivus was the more numerous species except under pine where P. pachydermus gradually became dominant during the study. Both species were present in all the depth samples but showed an aggregated distribution with different modal depths. The depth at which most P. pachydermus were found was shallower than for T. primitivus. Differences in the distribution and behaviour of the two species were found indicating how the two species could co-exist or succeed each other. Fumigation with dichloropropene decreased the trichodorid populations to < 1 per 200 g soil to a depth of 50 cm. The relative development of the populations under the different crops and fallow soil were similar to those in non-fumigated soils.     

Testing for reproductive interference in the population dynamics of two congeneric species of herbivorous mites

When phylogenetically close, two competing species may reproductively interfere, and thereby affect their population dynamics. We tested for reproductive interference (RI) between two congeneric haplo-diploid spider mites, Tetranychus evansi and Tetranychus urticae, by investigating their interspecific mating and their population dynamics when they competed on the same plants. They are both pests of tomato, but differ in the host plant defences that they suppress or induce. To reduce the effect of plant-mediated interaction, we used a mutant tomato plant lacking jasmonate-mediated anti-herbivore defences in the competition experiment. In addition, to manipulate the effect of RI, we introduced founder females already mated with conspecific males in mild RI treatments or founder, virgin females in strong RI treatments (in either case together with heterospecific and conspecific males). As females show first-male sperm precedence, RI should occur especially in the founder generation under strong RI treatments. We found that T. urticae outcompeted T. evansi in mild, but not in strong RI treatments. Thus, T. evansi interfered reproductively with T. urticae. This result was supported by crossing experiments showing frequent interspecific copulations, strong postmating reproductive isolation and a preference of T. evansi males to mate with T. urticae (instead of conspecific) females, whereas T. urticae males preferred conspecific females. We conclude that interspecific mating comes at a cost due to asymmetric mate preferences of males. Because RI by T. evansi can improve its competitiveness to T. urticae, we propose that RI partly explains why T. evansi became invasive in Europe where T. urticae is endemic.     

On detecting interactions between species in population dynamics

If we are to progress out of our current state of uncertainty about the role of interspecific competition in community structure, it is essential that we can distinguish competition from other types of population interaction, and from lack of interaction, in particular case studies. To make such distinctions, it is necessary to quantify the effect of species on each other. One way to do this is to calculate interaction coefficients, and another (only readily applicable in experimental systems) is to plot graphs of N against time and to contrast monocultures with mixed cultures. We show (1) that these methods often appear to give contradictory results, and (2) that the problems are most pronounced when one species has a low equilibrium population size in mixed culture. To resolve the question of whether an interspecific interaction is taking place (and if so, what kind of interaction), it is necessary to apply tests of significance which overcome the problems of serial correlation inherent in all long-term population experiments. We illustrate the use of such tests in the analysis of the results from an experimental Drosophiia system. In the past, this kind of test has generally not been applied, and this raises the question of whether some of the 'classic cases of competition' in the experimental literature were really competition at all.     

Indirect population interaction between two aphid species

We designed an experiment to test whether two species of aphid feeding on different species of host plant influence each others population dynamics via shared parasitoids (apparent competition) or other indirect processes. Pea aphid ( Acyrthosiphon pisum ) colonies declined faster towards mid-summer when there were nearby colonies of nettle aphid ( Microlophium carnosum ), though the significance of the difference ( P  = 0.06) was just short of the traditional 0.05 level. Observations suggested that parasitoids were not responsible for this difference, however, and that it was highly likely to be caused by aphid-specific predators.     

Influence of weather factors on population dynamics of two lagomorph species based on hunting bag records

Weather conditions can have a significant influence on short-term fluctuations of animal populations. In our study, which is based on time series of hunting bag records of up to 28?years from 26 counties of The Netherlands and Germany, we investigated the impact of different weather variables on annual counts of European rabbits (Oryctolagus cuniculus) and European hares (Lepus europaeus). Overall, the long-term dynamics of both species could be described by higher-order polynomials. On a smaller time scale, the number of European hares shot was lower in years with higher amounts of precipitation during late summer/autumn, and the number of European rabbits shot was lower in years with high precipitation in spring of the respective year. We suggest that rainy weather conditions might have lowered the survival of young rabbits in spring and might have generally facilitated the outbreak or spread of diseases in rabbits as well as in hares, specifically in autumn. In addition, the results showed a time-delayed, interactive effect between precipitation in spring and winter weather on European rabbit dynamics: rabbit numbers were limited by low temperatures of the prior winter season, but only when precipitation was high during spring of the previous year. The latter result might be explained by the lowering effects of rainy spring weather on the body condition of the animals, leading to higher sensitivity to harsh winter conditions. In conclusion, our study provides evidence for the impact of weather conditions on the population dynamics of both study species and particularly highlights complex interactions between the prevailing weather conditions during different seasons in the European rabbit.     

The population dynamics of two vertically transmitted infections

The transmission of Keystone virus in the mosquito Aedes atlanticus and of Rickettsia rickettsii in the tick Dermacentor andersoni is modeled and analyzed. Both of these infections can be transmitted vertically from an infective parent to newborn offspring as well as horizontally via direct or indirect contacts with infected individuals. The vertical transmission mechanism plays a major role in the maintenance of these infections and its effects are analyzed in detail. This same mechanism can act as a means for controlling the size of the infected host population and an analysis of this effect is also provided. The sensitivity of the threshold parameters and the endemic prevalence rates of the disease to variations in the basic infection transmission components are investigated. The transmission components that are considered include the ability to transmit the pathogen vertically as well as horizontally, the size of the host population, and survival probabilities of the hosts.     

Equilibrium solutions of age-specific population dynamics of several species

Summary A mathematical model describing the dynamics of a population consisting of several species is studied. The interactions in the population are assumed to be age-specific. Using an evolution equation approach, sufficient conditions for well-posedness in L ¹ of the dynamics and for existence as well as for stability of equilibrium solutions are given.     

Molecular identification and population dynamics of two species of Pemphigus (Homoptera: Pemphidae) on cabbage

The poplar petiole gall aphid, Pemphigus populitransversus Riley, has been one of the major pests on cruciferous vegetable in the Rio Grande Valley (LRGV) of Texas since the late 1940s. It normally migrates from poplar trees to cruciferous vegetables in the fall, and migrates back to the trees in early spring of the coming year. Some root‐feeding aphids were found on cruciferous vegetables in late spring and early summer in 1998 and the following years. Those aphids have been identified as Pemphigus obesinymphae Moran. This discovery completely changed the current knowledge about the root‐feeding aphids on cruciferous vegetables in the LRGV. Due to their small size, morphological and feeding similarities between P. populitransversus and P. obesinymphae, their identification and distinction are difficult. In this study, random amplification of polymorphic DNA (RAPD) and amplified fragment length polymorphism (AFLP) were used to distinguish these two species over a period of time when the two species occurred together, or separately, in cabbage fields. The two species occurred on cabbage at different times of the year, and overlapped from October to June. From May to October, both species migrated to their primary hosts. The apterous aphids found on cabbage in winter contained mainly P. obesinymphae, whereas in early spring more apterous P. populitransversus were recovered. The root‐feeding aphids would feed on cabbage plants as long as this host was available even during the hot, dry summer in the LRGV, although their populations were generally low. Both RAPD and AFLP techniques were efficient in discriminating the two species that showed obviously genetic variability. These molecular techniques confirmed the existence of the two aphid species in apterous samples collected from the soil in cabbage fields in the LRGV, and the results performed by RAPD were confirmed by AFLP. Furthermore, the results suggest that RAPD technique was a better choice despite its reproducibility problem, as it was less time‐consuming and required less technology, labor and expense than AFLP.     

Long-term population dynamics of two Carex curvula species in the Central Alps on native and alien soils

The demography of two closely related alpine sedges, Carex curvula subsp. curvula and Carex curvula subsp. rosae (=C. curvula and C. rosae) has been investigated on their typical sites in the Central Alps. Both species proliferate vegetatively and develop dense tussocks but they show different dominance behaviours in their respective grasslands. It was hypothesized that this may be caused by different growth abilities. The main aim of the study was to compare the vegetative growth of the species under field conditions, under competition-free conditions and under changed soil conditions. An attempt was also made to clarify whether vegetative growth is density dependent. Permanent plots were established in the respective grasslands of the two species and the ramet density was counted over 3 years. Groups of 10 and of 30 ramets of each species were grown in pots with typical and with alien substrate and their growth was observed for 5 years at the field site. The grassland populations of both species were very stable and the overall ramet growth rate (λ) was close to 1.0. Within the pots, both species reached a high ramet number. Only the group of 30 ramets of C. curvula on alien soil could not recover from the transplantation shock. Within the pots, C. rosae showed a greater ramet turnover and a higher increase in ramets than C. curvula. On their native substrate, both species had a significantly higher ramet increase than on the alien substrate. Ramet growth was found to be density dependent for both species, the increases recorded for the groups of 10 being significantly greater than for the groups of 30. Although C. curvula produced fewer ramets than C. rosae, the aboveground dry weight of the former was significantly higher. This may be decisive for its greater competitive success in closed grasslands. Received: 12 April 1997 / Accepted: 12 December 1997     

A model for aggregation-dispersion dynamics of a population

An important feature that distinguishes the movement of living systems from the random motion of inorganic material is a delicate balance between spreading and concentrating. This movement is based on the kind of interactions which a bacterial colony may establish during migration. Namely, the antagonistic effects of dispersal which take place preferentially down the population gradient and the tendency in grouping together. In this work a model is proposed which considers these effects. The phase plane analysis and the numerical calculations reveal the existence of stable sharp wave front solutions. The speed of the wave front is modulated by the compromise between the tendencies of spreading and aggregating. The results obtained were compared with experimental observations in cultures of Escherichia coli and Streptococcus faecalis. The agreement between both types of results supports the hypothesis on which the model was based.     

Recruitment dynamics of two low-density neotropical multiple-use tree species

In the present study, we describe the temporal and spatial variability in recruitment, growth, and mortality rates of seedlings and saplings of two low-density neotropical tree species, Dipteryx odorata and Copaifera reticulata in Eastern Amazonia, Brazil. As both species have important timber and non-timber uses, for each species we compare regeneration parameters among different management scenarios (sites used for timber logging, non-timber product extraction, and undisturbed forests). Results suggest that both species share similar natural regeneration characteristics. These include temporally and spatially asynchronous germination, existence of individuals that have more abundant and frequent fruit production than the average of the population and a positive influence of the mother tree crown on seedling and sapling density. The management activities analyzed did not influence the regeneration parameters of both species, which suggests that timber logging the way it was performed and current rates of D. odorata seed gathering and C. reticulata tapping at the study site are not sufficiently intense to threaten species population. However, some species characteristics, such as their reproductive strategies, light-demanding syndromes, low-dispersal ranges, and high-mortality rates of seedlings make both species vulnerable to exploitation.     

Stochastic population dynamics and life-history variation in marine fish species

Abstract We examined whether differences in life-history characteristics can explain interspecific variation in stochastic population dynamics in nine marine fish species living in the Barents Sea system. After observation errors in population estimates were accounted for, temporal variability in natural mortality rate, annual recruitment, and population growth rate was negatively related to generation time. Mean natural mortality rate, annual recruitment, and population growth rate were lower in long-lived species than in short-lived species. Thus, important species-specific characteristics of the population dynamics were related to the species position along the slow-fast continuum of life-history variation. These relationships were further associated with interspecific differences in ecology: species at the fast end were mainly pelagic, with short generation times and high natural mortality, annual recruitment, and population growth rates, and also showed high temporal variability in those demographic traits. In contrast, species at the slow end were long-lived, deepwater species with low rates and reduced temporal variability in the same demographic traits. These interspecific relationships show that the life-history characteristics of a species can predict basic features of interspecific variation in population dynamical characteristics of marine fish, which should have implications for the choice of harvest strategy to facilitate sustainable yields.     

Historical distribution and regional dynamics of two Brassica species

Plants often show a patchy distribution. This can be related to the discontinuous distribution of environmental variables that define suitable habitat. Metapopulation theory suggests that additional patchiness may be caused by the dynamics of local extinctions and recolonisations. However, the contribution of these two mechanisms to explaining the observed patterns, and thus the applicability of metapopulation theory to plants remains controversial partly because population turnover may occur at long time‐scales not usually covered by ecological studies. We analyzed the role of environmental variation and population turnover in determining the distribution of two Brassica species, an annual and a perennial, along 44 km of coastline in Dorset, UK. Mapped occurrence and abundance of both species in recent years was compared with distributions from a 70 yr‐old dataset and a survey of present‐day environmental parameters. Abiotic and vegetation parameters were correlated with the occurrence of both species in binary logistic regression models and explained spatial auto‐correlation in the Brassica distributions. These regression models suggest that neither species is occupying all potential habitat in the region studied. The relationship between historical and present distributions differed between the species. While an historical signal was very weak in the annual B. nigra, it had a large influence in predicting the present distribution of the perennial B. oleracea. This suggests local extinction and colonisation events for B. nigra over the 70 yr period, but not for B. oleracea which showed little evidence of population turnover. Our results demonstrate that the consideration of large time‐scales can reveal patterns of regional dynamics. We conclude that metapopulation dynamics might be possible for our annual but can be ruled out for our perennial study species over the past 70 yr. We argue that beyond this time‐scale possible metapopulation dynamics may be overridden by faster processes of environmental change.     

Modeling population dynamics of two cockroach species: effects of the circadian clock, interspecific competition and pest control

The German cockroach Blattella germanica is obviously one of the most spread household pests in the world, and is now virtually impossible to sustain outside human constructions. The double-striped cockroach B. bisignata, on the other hand, is limited to Southeast Asia and mostly living in the open space, yet is able to establish in cockroach-free households, too. In this article, we develop a stage-structured population model of these two species to explore (i) whether their circadian clocks impact their long-term population dynamics, (ii) which of these species is a superior competitor, and (iii) how stringent potential pest control strategies have to be to significantly impact established populations of the German cockroach. The results of the model are as follows. Firstly, phase shifts in the light-to-dark cycle did not affect cockroach population dynamics unless males and females were out of phase and their mate finding abilities rather limited. In addition, for the hypothesized circadian clock genotypes, the shorter is the inactivity period relative to the activity one or the less arrhythmic is the population, the more viable the population is and the quicker it grows to large numbers. Secondly, the German cockroach was the superior competitor: it was able to invade and drive out established populations of the double-striped cockroach and prevent any invasion of the latter. Finally, only a significant and simultaneous reduction in a number of most sensitive German cockroach parameters resulted in species extirpation. Only carefully designed and data-based models of German (and double-striped) cockroach population dynamics can be helpful in our quest to win the fight over this unwelcome but very sturdy species.