Towards a general theory of adaptive walks on rugged landscapes

Adaptive evolution, to a large extent, is a complex combinatorial optimization process. In this article we take beginning steps towards developing a general theory of adaptive "walks" via fitter variants in such optimization processes. We introduce the basic idea of a space of entities, each a 1-mutant neighbor of many other entities in the space, and the idea of a fitness ascribed to each entity. Adaptive walks proceed from an initial entity, via fitter neighbors, to locally or globally optimal entities that are fitter than their neighbors. We develop a general theory for the number of local optima, lengths of adaptive walks, and the number of alternative local optima accessible from any given initial entity, for the baseline case of an uncorrelated fitness landscape. Most fitness landscapes are correlated, however. Therefore we develop parts of a universal theory of adaptation on correlated landscapes by adaptive processes that have sufficient numbers of mutations per individual to "jump beyond" the correlation lengths in the underlying landscape. In addition, we explore the statistical character of adaptive walks in two independent complex combinatorial optimization problems, that of evolving a specific cell type in model genetic networks, and that of finding good solutions to the traveling salesman problem. Surprisingly, both show similar statistical features, encouraging the hope that a general theory for adaptive walks on correlated and uncorrelated landscapes can be found. In the final section we explore two limits to the efficacy of selection. The first is new, and surprising: for a wide class of systems, as the complexity of the entities under selection increases, the local optima that are attainable fall progressively closer to the mean properties of the underlying space of entities. This may imply that complex biological systems, such as genetic regulatory systems, are "close" to the mean properties of the ensemble of genomic regulatory systems explored by evolution. The second limit shows that with increasing complexity and a fixed mutation rate, selection often becomes unable to pull an adapting population to those local optima to which connected adaptive walks via fitter variants exist. These beginning steps in theory development are applied to maturation of the immune response, and to the problem of radiation and stasis. Despite the limitations of the adaptive landscape metaphor, we believe that further development along the lines begun here will prove useful.     

Random field models for fitness landscapes

 In many cases fitness landscapes are obtained as particular instances of random fields by randomly assigning a large number of parameters. Models of this type are often characterized reasonably well by their covariance matrices. We characterize isotropic random fields on finite graphs in terms of their Fourier series expansions and investigate the relation between the covariance matrix of the random field model and the correlation structure of the individual landscapes constructed from this random field. Correlation measures are a good characteristic of “rugged landscapes” models as they are closely related to quantities like the number of local optima or the length of adaptive walks. Our formalism suggests to approximate landscape with known autocorrelation function by a random field model that has the same correlation structure. Received: 10 November 1995 / Revised version: 19 February 1996     

Organic fields sustain weed metacommunity dynamics in farmland landscapes

Agro-ecosystems constitute essential habitat for many organisms. Agricultural intensification, however, has caused a strong decline of farmland biodiversity. Organic farming (OF) is often presented as a more biodiversity-friendly practice, but the generality of the beneficial effects of OF is debated as the effects appear often species- and context-dependent, and current research has highlighted the need to quantify the relative effects of local- and landscape-scale management on farmland biodiversity. Yet very few studies have investigated the landscape-level effects of OF; that is to say, how the biodiversity of a field is affected by the presence or density of organically farmed fields in the surrounding landscape. We addressed this issue using the metacommunity framework, with weed species richness in winter wheat within an intensively farmed landscape in France as model system. Controlling for the effects of local and landscape structure, we showed that OF leads to higher local weed diversity and that the presence of OF in the landscape is associated with higher local weed biodiversity also for conventionally farmed fields, and may reach a similar biodiversity level to organic fields in field margins. Based on these results, we derive indications for improving the sustainable management of farming systems.     

A convenient and robust method for construction of combinatorial and random mutant libraries

Here we describe a convenient and robust ligase-independent method for construction of combinatorial and random mutant libraries. The homologous genes flanked by plasmid-derived DNA sequences are fragmented, and the random fragments are reassembled in a self-priming polymerase reaction to obtain chimeric genes. The product is then mixed with linearized vector and two pairs of flanking primers, followed by assembly of the chimeric genes and linearized vector by PCR to introduce recombinant plasmids of a combinatorial library. Commonly, it is difficult to find proper restriction sites during the construction of recombinant plasmids after DNA shuffling with multiple homologous genes. However, this disadvantage can be overcome by using the ligase-independent method because the steps of DNA digestion and ligation can be avoided during library construction. Similarly, DNA sequences with random mutations introduced by error-prone PCR can be used to construct recombinant plasmids of a random mutant library with this method. Additionally, this method can meet the needs of large and comprehensive DNA library construction.     

Landscape-moderated biodiversity effects of agri-environmental management: a meta-analysis

Agri-environmental management (AEM) is heralded as being key to biodiversity conservation on farmland, yet results of these schemes have been mixed, making their general utility questionable. We test with meta-analysis whether the benefits of AEM for species richness and abundance of plants and animals are determined by the surrounding landscape context. Across all studies (109 observations for species richness and 114 observations for abundance), AEM significantly increased species richness and their abundance. More specifically, we test the hypothesis that AEM benefits species richness and abundance (i.e. increases the difference between fields with and without AEM) more in simple than in complex landscapes. In croplands, species richness but not abundance was significantly enhanced in simple but not in complex landscapes. In grasslands, AEM effectively enhanced species richness and abundance regardless of landscape context. Pollinators were significantly enhanced by AEM in simple but not in complex landscapes in both croplands and grasslands. Our results highlight that the one-size-fits-all approach of many agri-environmental programmes is not an efficient way of spending the limited funds available for biodiversity conservation on farmland. Therefore, we conclude that AEM should be adapted to landscape structure and the species groups at which they are targeted.     

Finding the Missing Link between Landscape Structure and Population Dynamics: A Spatially Explicit Perspective

We construct and explore a general modeling framework that allows for a systematic investigation of the impact of changes in landscape structure on population dynamics. The essential parts of the framework are a landscape generator with independent control over landscape composition and physiognomy, an individual-based spatially explicit population model that simulates population dynamics within heterogeneous landscapes, and scale-dependent landscape indices that depict the essential aspects of landscape that interact with dispersal and demographic processes. Landscape maps are represented by a grid of 50x50 cells and consist of good-quality, poor-quality, or uninhabitable matrix habitat cells. The population model was shaped in accordance to the biology of European brown bears (Ursus arctos), and demographic parameters were adjusted to yield a source-sink configuration. Results obtained with the spatially explicit model do not confirm results of earlier nonspatial source-sink models where addition of sink habitat resulted in a decrease of total population size because of dilution of high-quality habitat. Our landscape indices, which describe scale-dependent correlation between and within habitat types, were able to explain variations in variables of population dynamics (mean number of females with sink home ranges, mean number of females with source home ranges, and mean dispersal distance) caused by different landscape structure. When landscape structure changed, changes in these variables generally followed the corresponding change of an appropriate landscape index in a linear way. Our general approach incorporates source-sink dynamics as well as metapopulation dynamics, and the population model can easily be modified for other species groups.     

Enhancing spider families and spider webs in Indian rice fields for conservation biological control,considering local and landscape management

Spiders are omnipresent, occurring in almost all terrestrial habitats. They are generalist predators and important for conservation biocontrol in agricultural fields, helping to reduce pesticide applications. In this study, we examined how spider families and spider web types in rice fields are related to local and landscape management. Samples were taken in differently managed rice fields adjoining either homegarden polycultures or banana monocultures. Furthermore, landscape structure, prey abundance, herb richness and cover were taken into account. The results showed that prey availability explained most of the variation in spiders and their web’s abundance, indicating that spiders in the rice fields can potentially contribute to pest control. Adjacent habitat had no effect on the spider populations, but maintaining fallow fields in the surrounding landscape seems to be a useful measure to promote Erigoninae in rice fields. There was no evidence that local management practices such as fertiliser and pesticide use had an impact on spider families, which appeared to be due to the low level of these inputs. Spider web sampling can complement spider sampling as it detects spiders hidden at the base of the rice tillers, which are likely to be missed by sweep netting. Additionally, tetragnathid webs are easy to observe and thus can be used as an indication for farmers not to spray pesticides as spiders are potentially controlling the pest species. Interviews with farmers made clear that many farmers in the study area showed their interest in management methods that promote biological pest control.     

A Novel T-type Overhangs Improve the Enzyme-Free Cloning of PCR Products

PCR product cloning is the foundational technology for almost all fields in the life sciences. Numerous innovative methods have been designed during the past few decades. Enzyme-free cloning is the only one that avoids post-amplification enzymatic treatments, making the technique reliable and cost effective. However, the complementary staggered overhangs used in enzyme-free cloning tend to result in self-ligation of the vector under some circumstances. Here, we describe a “T-type” enzyme-free cloning method: instead of designing the complementary staggered overhangs used in conventional enzyme-free cloning, we create “T-type” overhangs that reduce the possibility of self-ligation and are more convenient for multi-vector cloning. In this study, we systematically optimize “T-type” enzyme-free cloning, compare its cloning background with that in conventional enzyme-free cloning, and demonstrate a promising application of this technique in multi-vector cloning. Our method simplifies post-amplification procedures and greatly reduces cost, offering a competitive option for PCR product cloning.     

The NK model of rugged fitness landscapes and its application to maturation of the immune response

Adaptive evolution is, to a large extent, a complex combinatorial optimization process. Such processes can be characterized as "uphill walks on rugged fitness landscapes". Concrete examples of fitness landscapes include the distribution of any specific functional property such as the capacity to catalyze a specific reaction, or bind a specific ligand, in "protein space". In particular, the property might be the affinity of all possible antibody molecules for a specific antigenic determinant. That affinity landscape presumably plays a critical role in maturation of the immune response. In this process, hypermutation and clonal selection act to select antibody V region mutant variants with successively higher affinity for the immunizing antigen. The actual statistical structure of affinity landscapes, although knowable, is currently unknown. Here, we analyze a class of mathematical models we call NK models. We show that these models capture significant features of the maturation of the immune response, which is currently thought to share features with general protein evolution. The NK models have the important property that, as the parameter K increases, the "ruggedness" of the NK landscape varies from a single peaked "Fujiyama" landscape to a multi-peaked "badlands" landscape. Walks to local optima on such landscapes become shorter as K increases. This fact allows us to choose a value of K that corresponds to the experimentally observed number of mutational "steps", 6-8, taken as an antibody sequence matures. If the mature antibody is taken to correspond to a local optimum in the model, tuning the model requires that K be about 40, implying that the functional contribution of each amino acid in the V region is affected by about 40 others. Given this value of K, the model then predicts several features of "antibody space" that are in qualitative agreement with experiment: (1) The fraction of fitter variants of an initial "roughed in" germ line antibody amplified by clonal selection is about 1-2%. (2) Mutations at some sites of the mature antibody hardly affect antibody function at all, but mutations at other sites dramatically decrease function. (3) The same "roughed in" antibody sequence can "walk" to many mature antibody sequences. (4) Many adaptive walks can end on the same local optimum. (5) Comparison of different mature sequences derived from the same initial V region shows evolutionary hot spots and parallel mutations. All these predictions are open to detailed testing by obtaining monoclonal antibodies early in the immune response and carrying out in vitro mutagenesis and adaptive hill climbing with respect to affinity for the immunizing antigen.     

More pests but less pesticide applications: Ambivalent effect of landscape complexity on conservation biological control

In agricultural landscapes, the amount and organization of crops and semi-natural habitats (SNH) have the potential to promote a bundle of ecosystem services due to their influence on ecological community at multiple spatio-temporal scales. SNH are relatively undisturbed and are often source of complementary resources and refuges, therefore supporting more diverse and abundant natural pest enemies. However, the nexus of SNH proportion and organization with pest suppression is not trivial. It is thus crucial to understand how the behavior of pest and natural enemy species, the underlying landscape structure, and their interaction, may influence conservation biological control (CBC). Here, we develop a generative stochastic landscape model to simulate realistic agricultural landscape compositions and configurations of fields and linear elements. Generated landscapes are used as spatial support over which we simulate a spatially explicit predator-prey dynamic model. We find that increased SNH presence boosts predator populations by sustaining high predator density that regulates and keeps pest density below the pesticide application threshold. However, predator presence over all the landscape helps to stabilize the pest population by keeping it under this threshold, which tends to increase pest density at the landscape scale. In addition, the joint effect of SNH presence and predator dispersal ability among hedge and field interface results in a stronger pest regulation, which also limits pest growth. Considering properties of both fields and linear elements, such as local structure and geometric features, provides deeper insights for pest regulation; for example, hedge presence at crop field boundaries clearly strengthens CBC. Our results highlight that the integration of species behaviors and traits with landscape structure at multiple scales is necessary to provide useful insights for CBC.     

Turn designation, sampling rate and the misidentification of power laws in movement path data using maximum likelihood estimates

Many authors have claimed to observe animal movement paths that appear to be Lévy walks, i.e. a random walk where the distribution of move lengths follows an inverse power law. A Lévy walk is known to be the optimal search strategy of a particular class of random walks in certain environments; hence, it is important to distinguish correctly between Lévy walks and other types of random walks in observed animal movement paths. Evidence of a power law distribution in the step length distribution of observed animal movement paths is often used to classify a particular movement path as a Lévy walk. However, there is some doubt about the accuracy of early studies that apparently found Lévy walk behaviour. A recently accepted method to determine whether a movement path truly exhibits Lévy walk behaviour is based on an analysis of move lengths with a maximum likelihood estimate using Akaike weights. Here, we show that simulated (non-Lévy) random walks representing different types of animal movement behaviour (a composite correlated random walk; pooled data from a set of random walks with different levels of correlation and three-dimensional correlated random walks projected into one dimension) can all show apparent power law behaviour typical of Lévy walks when using the maximum likelihood estimation method. The probability of the movement path being identified as having a power law step distribution is related to both the sampling rate used by the observer and the way that ‘turns’ or ‘reorientations’ in the movement path are designated. However, identification is also dependent on the nature and properties of the simulated path, and there is currently no standard method of observation and analysis that is robust for all cases. Our results indicate that even apparently robust maximum likelihood methods can lead to a mismatch between pattern and process, as paths arising from non-Lévy walks exhibit Lévy-like patterns.     

Role of Fourier transform infrared spectroscopy in the rehearsal phase of combinatorial chemistry: a thin-layer chromatography equivalent for on-support monitoring of solid-phase organic synthesis

The adaptation of diverse organic reactions to solid supports requires significant reaction optimization efforts. A convenient on-support analytical method functionally similar to TLC in solution chemistry is very advantageous. As a TLC-equivalent method, the single bead FTIR is a simple, sensitive, fast, and convenient analytical method to monitor SPOS without stopping the reaction or cleaving the product. As with TLC, single bead FTIR provides a wide range of information such as qualitative assessment, quantitative determination, and reaction kinetics. Studies with the single bead FTIR have not only provided a tool for daily monitoring of the solid-phase reactions, but a way to understand the properties of polymer-bound substrate and the nature of polymer-supported organic reactions. It has assisted in the selection of a wide range of reaction conditions rapidly for SPOS in the rehearsal phase of combinatorial chemistry. Due to its convenience and efficiency, FTIR internal reflection spectroscopy has evolved as a useful analytical methodology for monitoring of combinatorial chemistry reactions directly on polymer surface.     

Bistability, bifurcations, and Waddington's epigenetic landscape

Waddington's epigenetic landscape is probably the most famous and most powerful metaphor in developmental biology. Cells, represented by balls, roll downhill through a landscape of bifurcating valleys. Each new valley represents a possible cell fate and the ridges between the valleys maintain the cell fate once it has been chosen. Here I examine models of two important developmental processes - cell-fate induction and lateral inhibition - and ask whether the landscapes for these models at least qualitatively resemble Waddington's picture. For cell-fate induction, the answer is no. The commitment of a cell to a new fate corresponds to the disappearance of a valley from the landscape, not the splitting of one valley into two, and it occurs through a type of bifurcation - a saddle-node bifurcation - that possesses an intrinsic irreversibility that is missing from Waddington's picture. Lateral inhibition, a symmetrical cell-cell competition process, corresponds better to Waddington's picture, with one valley reversibly splitting into two through a pitchfork bifurcation. I propose an alternative epigenetic landscape that has numerous valleys and ridges right from the start, with the process of cell-fate commitment corresponding to the irreversible disappearance of some of these valleys and ridges, via cell-fate induction, complemented by the creation of new valleys and ridges through processes like cell-cell competition.     

Representing genetic variation as continuous surfaces: an approach for identifying spatial dependency in landscape genetic studies

Landscape genetics, an emerging field integrating landscape ecology and population genetics, has great potential to influence our understanding of habitat connectivity and distribution of organisms. Whereas typical population genetics studies summarize gene flow as pairwise measures between sampling localities, landscape characteristics that influence population genetic connectivity are often continuously distributed in space. Thus, there are currently gaps in both the ability to analyze genotypic data in a continuous spatial context and our knowledge of expected of landscape genetic structure under varying conditions. We present a framework for generating continuous “genetic surfaces”, evaluate their statistical properties, and quantify statistical behavior of landscape genetic structure in a simple landscape. We simulated microsatellite genotypes under varying parameters (time since vicariance, migration, effective population size) and used ancestry (q) values from STRUCTURE to interpolate a genetic surface. Using a spatially adjusted Pearson's correlation coefficient to test the significance of landscape variable(s) on genetic structure we were able to detect landscape genetic structure on a contemporary time scale (≥5 generations post vicariance, migration probability ≤0.10) even when population differentiation was minimal (F_ST≥0.00015). We show that genetic variation can be significantly correlated with geographic distance even when genetic structure is due to landscape variable(s), demonstrating the importance of testing landscape influence on genetic structure. Finally, we apply genetic surfacing to analyze an empirical dataset of black bears from northern Idaho USA. We find black bear genetic variation is a function of distance (autocorrelation) and habitat patch (spatial dependency), consistent with previous results indicating genetic variation was influenced by landscape by resistance. These results suggest genetic surfaces can be used to test competing hypotheses of the influence of landscape characteristics on genetic structure without delineation of categorical groups.     

Properties of selected mutations and genotypic landscapes under Fisher's geometric model

The fitness landscape—the mapping between genotypes and fitness—determines properties of the process of adaptation. Several small genotypic fitness landscapes have recently been built by selecting a handful of beneficial mutations and measuring fitness of all combinations of these mutations. Here, we generate several testable predictions for the properties of these small genotypic landscapes under Fisher's geometric model of adaptation. When the ancestral strain is far from the fitness optimum, we analytically compute the fitness effect of selected mutations and their epistatic interactions. Epistasis may be negative or positive on average depending on the distance of the ancestral genotype to the optimum and whether mutations were independently selected, or coselected in an adaptive walk. Simulations show that genotypic landscapes built from Fisher's model are very close to an additive landscape when the ancestral strain is far from the optimum. However, when it is close to the optimum, a large diversity of landscape with substantial roughness and sign epistasis emerged. Strikingly, small genotypic landscapes built from several replicate adaptive walks on the same underlying landscape were highly variable, suggesting that several realizations of small genotypic landscapes are needed to gain information about the underlying architecture of the fitness landscape.     

Towards a resource‐based habitat approach for spatial modelling of vector‐borne disease risks

Given the veterinary and public health impact of vector‐borne diseases, there is a clear need to assess the suitability of landscapes for the emergence and spread of these diseases. Current approaches for predicting disease risks neglect key features of the landscape as components of the functional habitat of vectors or hosts, and hence of the pathogen. Empirical–statistical methods do not explicitly incorporate biological mechanisms, whereas current mechanistic models are rarely spatially explicit; both methods ignore the way animals use the landscape (i.e. movement ecology). We argue that applying a functional concept for habitat, i.e. the resource‐based habitat concept (RBHC), can solve these issues. The RBHC offers a framework to identify systematically the different ecological resources that are necessary for the completion of the transmission cycle and to relate these resources to (combinations of) landscape features and other environmental factors. The potential of the RBHC as a framework for identifying suitable habitats for vector‐borne pathogens is explored and illustrated with the case of bluetongue virus, a midge‐transmitted virus affecting ruminants. The concept facilitates the study of functional habitats of the interacting species (vectors as well as hosts) and provides new insight into spatial and temporal variation in transmission opportunities and exposure that ultimately determine disease risks. It may help to identify knowledge gaps and control options arising from changes in the spatial configuration of key resources across the landscape. The RBHC framework may act as a bridge between existing mechanistic and statistical modelling approaches.     

多功能景观研究进展

多功能景观是当前景观生态学研究的热点问题之一,已成为景观生态学新的研究方向,但其概念、研究方法等诸多内容仍缺少系统地研究和介绍。多功能景观研究通过优化景观结构来增强景观的多功能性,是实现区域景观可持续发展的重要手段。探讨了多功能景观的概念,提出了当前国内外多功能景观的主要研究方向和研究方法。今后应进一步开展有关多功能景观的实践研究,继续完善其评价方法,并建立景观功能及其服务的监测机制。以期为将来开展景观规划与景观管理研究提供科学依据。     

The effect of landscape structure on dispersal distances of the Eurasian red squirrel

Landscape structure can affect dispersal and gene flow in a species. In urban areas, buildings, roads, and small habitat patches make the landscape highly fragmented and can inhibit movement and affect dispersal behavior. Similarly, in rural forested areas, large open areas, such as fields, may act as barriers to movement. We studied how landscape structure affects natal dispersal distances of Eurasian red squirrels (Sciurus vulgaris) in an urban area and a rural area in Finland, by monitoring juvenile red squirrels with radio telemetry. We observed extremely long dispersal distances—up to 16 km—in the rural study area, but shorter distances—on average only half a kilometer—in the urban study area. The landscape structure affected the eventual dispersal paths; in the rural landscape, dispersers favored spruce dominated areas and avoided fields along their dispersal route, although they occasionally even crossed wide fields. In the urban landscape, squirrels preferred areas with deciduous or coniferous trees. The movement steps made by dispersers were longer in the more hostile landscape compared to forested areas. Despite these effects on movement path, the landscape structure only had a minor effect on straight line dispersal distances moved from the natal nest. In other words, individuals moved longer distances and were likely to circumvent barriers in their path, but this did not affect how far they settled from their natal home. This result indicates that, although landscape structure has obvious effects on movement, it still may have only a small effect on other aspects of the population, for example, gene flow.     

Understanding Patchy Landscape Dynamics: Towards a Landscape Language

Patchy landscapes driven by human decisions and/or natural forces are still a challenge to be understood and modelled. No attempt has been made up to now to describe them by a coherent framework and to formalize landscape changing rules. Overcoming this lacuna was our first objective here, and this was largely based on the notion of Rewriting Systems, also called Formal Grammars. We used complicated scenarios of agricultural dynamics to model landscapes and to write their corresponding driving rule equations. Our second objective was to illustrate the relevance of this landscape language concept for landscape modelling through various grassland managements, with the final aim to assess their respective impacts on biological conservation. For this purpose, we made the assumptions that a higher grassland appearance frequency and higher land cover connectivity are favourable to species conservation. Ecological results revealed that dairy and beef livestock production systems are more favourable to wild species than is hog farming, although in different ways. Methodological results allowed us to efficiently model and formalize these landscape dynamics. This study demonstrates the applicability of the Rewriting System framework to the modelling of agricultural landscapes and, hopefully, to other patchy landscapes. The newly defined grammar is able to explain changes that are neither necessarily local nor Markovian, and opens a way to analytical modelling of landscape dynamics.