The influence of trade-off shape on evolutionary behaviour in classical ecological scenarios

Trade-off shapes are crucial to evolutionary outcomes. However, due to different ecological feedbacks their implications may depend not only on the trade-off being considered but also the ecological scenario. Here, we apply a novel geometric technique, trade-off and invasion plots (TIPs), to examine in detail how the shape of trade-off relationships affect evolutionary outcomes under a range of classic ecological scenarios including Lotka-Volterra type and host-parasite interactions. We choose models of increasing complexity in order to gain an insight into the features of ecological systems that determine the evolutionary outcomes. In particular we focus on when evolutionary attractors, repellors and branching points occur and how this depends on whether the costs are accelerating (benefits become ‘increasingly’ costly), decelerating (benefits become ‘decreasingly’ costly) or constant. In all cases strongly accelerating costs lead to attractors while strongly decelerating ones lead to repellors, but with weaker relationships, this no longer holds. For some systems weakly accelerating costs may lead to repellors and decelerating costs may lead to attractors. In many scenarios it is weakly decelerating costs that lead to branching points, but weakly accelerating and linear costs may also lead to disruptive selection in particular ecological scenarios. Using our models we suggest a classification of ecological interactions, based on three distinct criteria, that can produce one of four fundamental TIPs which allow for different evolutionary behaviour. This provides a baseline theory which may inform the prediction of evolutionary outcomes in similar yet unexplored ecological scenarios. In addition we discuss the implications of our results to a number of specific life-history trade-offs in the classic ecological scenarios represented by our models.     

Conditions for the initial increase of new alleles with frequency dependent selection

The paper presents the derivation of conditions for the initial increase of a new allele in a fairly general model of a one locus genetic system. Incorporated within the model are frequency dependent selection coefficients which allow the study of viability differences, fertility differences, segregation distortion and certain forms of non-random mating. Since in many models it is necessary to go beyond linear terms, quadratic, cubic and quartic terms are also derived explicitly and details given of their extension to higher degrees.     

Interspecific competition affects growth and herbivore damage of Brassica napus in the field

Resource competition can influence plant fitness either directly, or indirectly by influencing the amount of herbivore damage received by plants in the field. We previously found that competition could constrain the constitutive and woundinduced expression of defensive trypsin inhibitors in pot-grown Brassica napus seedlings in the greenhouse, suggesting that the ability of a plant to chemically defend itself could be constrained by competition in the field. Guided by these results, we investigated whether competition would affect growth and the presence of herbivores and herbivore damage on B. napus plants in the field. We established sixteen 1 m 2 plots in the field in a 7 x7 mgrid. Nine two-week-old B. napus seedlings were transplanted from the greenhouse into each 1 m 2 plot. Half of the plots were kept weed-free and half were left to develop interspecific weed competi-tors.After six weeks, three randomly chosen plants in each plot were measured for height, number of leaves, leaf area removed by herbivores, and the presence of aphids, leaf miners, and eggs of ladybird beetles. Consistent with the induction of the shade-avoidance response, plants in plots with weed competitors were significantly taller and had half as many leaves as plants in weed-free plots. Competing plants also had 60% more leaf arearemoved by herbivores, an 80% higher proportion of leaves with aphids, and an equal proportion of leaves with leaf miners. In this study, weed competition had dramatic effects on growth, leaf area removal by herbivores, and the presence of aphids on B. napus plants in the field. Together with our demonstration that competition can constrain the expression of trypsin inhibitor activity, these results suggest that resource competition may limit theability of a plant to defend itself from natural enemies, leading to greater herbivory. In turn, increased herbivory on competing plants could exacerbate the direct effects of competition on plant fitness.     

Strategy selection under predation; evolutionary analysis of the emergence of cohesive aggregations

Why do animals form groups? This question has formed the basis of numerous scientific studies over the last hundred years and still remains a controversial topic. Predation is one of the foremost candidates, yet the precise mechanism remains quantitatively elusive. Here I investigate in silico the effect of ongoing predation on groups of heterogeneous individuals behaving according to a well-documented individual based model. I examine the resultant evolutionary trajectories and describe the final selected states and their stability with reference to a qualitatively modified version of adaptive dynamics. The speed of individuals is found to dominate the selection of the final state over other parameters in the model. The relative stability of the groups and their internal configurations are discussed with reference to novel structural correlation functions that are defined and introduced. The results reveal the importance of tightly bound toroidal group structures as an intermediate state prior to the emergence of slow compact groups. The study also indicates the need to more accurately model the speed distributions in real aggregations.     

Consequences of asymmetric competition between resident and invasive defoliators: A novel empirically based modelling approach

Invasive species can have profound effects on a resident community via indirect interactions among community members. While long periodic cycles in population dynamics can make the experimental observation of the indirect effects difficult, modelling the possible effects on an evolutionary time scale may provide the much needed information on the potential threats of the invasive species on the ecosystem. Using empirical data from a recent invasion in northernmost Fennoscandia, we applied adaptive dynamics theory and modelled the long term consequences of the invasion by the winter moth into the resident community. Specifically, we investigated the outcome of the observed short-term asymmetric preferences of generalist predators and specialist parasitoids on the long term population dynamics of the invasive winter moth and resident autumnal moth sharing these natural enemies. Our results indicate that coexistence after the invasion is possible. However, the outcome of the indirect interaction on the population dynamics of the moth species was variable and the dynamics might not be persistent on an evolutionary time scale. In addition, the indirect interactions between the two moth species via shared natural enemies were able to cause asynchrony in the population cycles corresponding to field observations from previous sympatric outbreak areas. Therefore, the invasion may cause drastic changes in the resident community, for example by prolonging outbreak periods of birch-feeding moths, increasing the average population densities of the moths or, alternatively, leading to extinction of the resident moth species or to equilibrium densities of the two, formerly cyclic, herbivores.     

Conditional dispersal under kin competition: extension of the Hamilton-May model to brood size-dependent dispersal

I consider a site-based model with contest competition among siblings, and assume that dispersal is conditional on the number of offspring in the natal site. Evolutionarily stable populations contain threshold dispersal strategies, which retain a certain number of offspring in the natal site and disperse the rest (if the actual number of offspring is less than the threshold, then all offspring are retained). Due to the discrete nature of the strategy set (the threshold must be integer), the ESS may not be unique or may not exist. In the latter case, two neighboring threshold strategies coexist in the evolutionarily stable population. Dispersal first decreases and then increases as a function of dispersal mortality, such that all but one offspring should be dispersed both when dispersal mortality is very small or very high. Population-level dispersal fractions are often similar to the unconditional ESS, but differ strongly when fecundity is small and dispersal mortality is high.     

Resident-invader dynamics and the coexistence of similar strategies

We study the resident-invader dynamics for a given class of models of unstructured populations of finite-dimensional strategies. We prove various results on the existence and uniqueness of -limit sets in the interior of the resident-invader population state space, and we classify the generically possible types of dynamics in terms of the invasion conditions when the resident and invader strategies are similar to one another.This work was supported by the Academy of Finland     

The form of host density-dependence and the likelihood of host-pathogen cycles in forest-insect systems

Forest-insect systems frequently show cyclic dynamics which has been of considerable interest to both experimental and theoretical ecologists. One important issue has been the manner in which density-dependence acting on the host population through resource competition influences the likelihood of population cycles. Existing models make contradictory predictions. Here, we explore two models that allow different forms of density-dependence to be examined. We find that host density-dependence can influence the persistence of the host-pathogen interaction, the likelihood of population cycles and the stability of the host-pathogen interaction. In particular, over-compensatory density-dependence is likely to lead to host-pathogen cycles while under-compensatory density-dependence can promote stability. We discuss these differences with reference to the different forms of intraspecific competition and recent developments in insect population ecology.     

Habitat-specific estimates of competition in stream salmonids: A field test of the isodar model of habitat selection

Summary The population densities of sympatric Atlantic salmon,Salmo salar and brook charr,Salvelinus fontinalis, were measured in riffle and pool stream habitats to test whether non-linear isodars, a multispecific model of habitat selection based on ideal distribution assumptions, could (1) predict the distribution of densities between habitats and (2) reproduce the processes postulated to underlie spatial segregation and species interactions in previous laboratory and field studies. The model provided a good fit to observed density patterns and indicated that habitat suitability declined non-linearly with increased heterospecific competitor densities. Competitive effects in riffles appeared to be due to exploitative resource use, with salmon always emerging as the superior competitor. No evidence was found for interference competition in riffles. In contrast, interspecific competition in pools seemed to occur through exploitation and interference. The specific identity of the superior competitor in pools depended on the density of both species; pools provided the charr with refuge from competition with the salmon, presumably through the adoption by the charr of density-dependent behaviours, such as schooling and group foraging, that mitigated the negative impact of the salmon. Charr were displaced from the riffles toward the pools as the total salmon density increased. The isodar analysis, based on limited density data, successfully reproduced the processes suggested to underlie spatial segregation in previous field and laboratory studies and provided new insights into how changes in competitor densities modify habitat suitability in this system.     

Towards a theory of the evolution of butterfly colour patterns under directional and disruptive selection

Two general models for the transspecific evolution of butterfly colour patterns are advanced: directional selection acting equally on both sexes, and disruptive selection involving periods of polymorphism. To consider possible outcomes of me latter process, a morphism notation based on an integrated classification for polymorphism and sexual dimorphism is developed. This notation is used to examine the properties of all morphism transformations possible from the minimal expressions of the nine morphism categories, as reached through defined minimum step changes. The significance of such pathway models is analysed in terms of general properties of butterfly polymorphism. The potential use of pathway models in evolutionary studies is briefly discussed, mainly with respect to phylogenetics, and ideas on the evolution of genetic dominance.     

The strength of competition among individual trees and the biomass-density trajectories of the cohort

We simulated the self-thinning of Rhizophora mangle mangrove forests with the spatially explicit simulation model KiWi. This model is an application of the field-of-neighbourhood (FON) approach, which describes an individual tree by a competition function defined on the zone of influence (ZOI) around the stem. The FON causes growth depression of the trees involved. Sustained growth depression results in tree death. We propose a subdivision of the biomass density trajectories (bdt), obtained during the thinning process, into four segments related to characteristic shapes of the stem diameter distribution of the cohort. A positive skewness of the stem diameter distribution, indicating that the majority of the individuals are small and hindered in growth, is necessary for the occurrence of a linear segment within the bdt, the so-called 'self-thinning line'. This segment is the third bdt segment according to our classification. It is reached when the positive skewness of the stem diameter distribution is maximal and ends when the skewness reaches its second zero transition. The thinning line is therefore linked to the homogenisation process, which forces the symmetry of the stem distribution. We show that the ongoing search for a universal slope for the linear segment of the biomass-density trajectory (bdt) cannot succeed, since it is species-specific and may also be site-dependent. The slope increases with increasing competition strength of the individuals. Nevertheless, the lower limit of the slope is pre-defined by geometrical constraints and modified by the actual strength of the neighbourhood competition. Although the simulations were all carried out with growth parameters of the mangrove species Rhizophora mangle, our results should be qualitatively valid and form a plausible theoretical framework to account for different biomass-density trajectories.     

The importance of carrying capacity,fertility, and viability for the competitive ability of populations

Summary A simple mathematical model is analyzed which describes the behaviour of a population under the influence of viability and fertility as well as carrying capacity and competition by another species. One locus with two alleles determining viability, fertility, and carrying capacity is considered. Throughout the analysis absolute rather than relative numbers are used. The following results have been obtained: 1. The species producing more zygotes wins the competition. 2. Absolute numbers must be used for viability and fertility in theoretical considerations, because the outcome of competition may be changed by using different absolute numbers of the same relation. 3. Differences in viability are amplified by limiting the number of individuals. 4. Differences in every parameter can be compensated by any other parameter.     

The foraging behavior of granivorous rodents and short-term apparent competition among seeds

The foraging behavior of a predator species is thought to bethe cause of short-term apparent competition among those preyspecies that share the predator. Short-term apparent competitionis the negative indirect effect that one prey species has onanother prey species via its effects on predator foraging behavior.In theory, the density-dependent foraging behavior of granivorousrodents and their preference for certain seeds are capable ofinducing short-term apparent competition among seed species.In this study, I examined the foraging behavior of two heteromyidrodent species (family Heteromyidae), Merriam's kangaroo rats(Dipodomys merriami) and little pocket mice (Perognathus longimembris).In one experiment I tested the preferences of both rodent speciesfor the seeds of eight plant species. Both rodent species exhibiteddistinct but variable preferences for some seeds and avoidanceof others. However, the differences in preference appearedto have only an occasional effect on the strength of the short-termapparent competition detected in a field experiment. In anotherexperiment, I found that captive individuals of both rodentspecies had approximately equal foraging effort (i.e., timespent foraging) in patches that contained a highly preferredseed type (Oryzopsis hymenoides) regardless of seed densityand the presence of a less preferred seed type (Astragalus cicer)in the patches. The rodents also harvested a large proportionof O. hymenoides seeds regardless of initial seed density;this precluded a negative indirect effect of A. cicer on O.hymenoides. But there was a negative indirect effect of O.hymenoides on A. cicer caused by rodents having a lower foragingeffort in patches that only contained A. cicer seeds than inpatches that contained A. cicer and O. hymenoides seeds. Theindirect interaction between O. hymenoides and A. cicer thusrepresented a case of short-term apparent competition thatwas non-reciprocal. Most importantly, it was caused by theforaging behavior of the rodents.     

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     

Physical constrints on the evolution of ctenophore size and shape

Summary Cilia bundled into combs or ctenes are an evolutionary innovation that allow comb jellies (animals in the phylum Ctenophora) to swim faster and grow to sizes at least two orders of magnitude larger than animals that propel themselves by beating single cilia. Ctenophore size, shape and swimming behaviors, however, may be constrained by the mechanisms that coordinate comb plate oscillations.Oscillations of comb plates onPleurobrachia bachei (a cydippid comb jelly), are coupled by fluid interactions between combs. Ctenes beat metachronously (in sequence) and the flows generated byP. bachei are retarded by the amount of time it takes a wave to pass down a group of ctenes. Our model predicts thatP. bachei size is constrained by the maximum thrust that can be produced by ctenes that beat in sequence and our flow visualization studies suggest that swimming via metachronous comb oscillations may constrainP. bachei to spherical shapes.In contrast, comb plate oscillations onMnemiopsis leidyi, a lobate comb jelly, are neurally coordinated and groups of ctenes beat in synchrony. As a result, fluid flows generated byM. leidyi are not retarded by the passage of metachronal waves down each comb row.M. leidyi reach sizes 15 times larger, but swim relatively slower (body lengths per second) thanP. bachei.We propose that propulsion via metachronous or synchronous comb plate oscillations has played an important role in the evolution of ctenophore shape and size and may have divided comb jellies into two evolutionary lineages.     

Optimal foraging and community structure: The allometry of herbivore food selection and competition

I address the selection of plants with different characteristics by herbivores of different body sizes by incorporating allometric relationships for herbivore foraging into optimal foraging models developed for herbivores. Herbivores may use two criteria in maximizing their nutritional intake when confronted with a range of food resources: a minimum digestibility and a minimum cropping rate. Minimum digestibility should depend on plant chemical characteristics and minimum cropping rate should depend on the density of plant items and their size (mass). If herbivores do select for these plant characteristics, then herbivores of different body sizes should select different ranges of these characteristics due to allometric relationships in digestive physiology, cropping ability and nutritional demands. This selectivity follows a regular pattern such that a herbivore of each body size can exclusively utilize some plants, while it must share other plants with herbivores of other body sizes. I empirically test this hypothesis of herbivore diet selectivity and the pattern of resource use that it produces in the field and experimentally. The findings have important implications for competition among herbivores and their population and community ecology. Furthermore, the results may have general applicability to other types of foragers, with general implications for how biodiversity is influenced.     

The adaptive dynamics of the evolution of host resistance to indirectly transmitted microparasites

We use adaptive dynamics and pairwise invadability plots to examine the evolutionary dynamics of host resistance to microparasitic infection transmitted indirectly via free stages. We investigate trade-offs between pathogen transmission rate and intrinsic growth rate. Adaptive dynamics distinguishes various evolutionary outcomes associated with repellors, attractors or branching points. We find criteria corresponding to these and demonstrate that a major factor deciding the evolutionary outcome is whether trade-offs are acceleratingly or deceleratingly costly. We compare and contrast two models and show how the differences between them lead to different evolutionary outcomes.