Péter Biró

Feeding strategy and growth of cyprinids in the littoral zone of Lake Balaton

The growth, diet and feeding strategy of five phytophil or phytolithophil species of Cyprinidae from the littoral habitats of Lake Balaton were investigated by examining their scales and foregut contents. The relationships between the total anterior radii of scales and the standard lengths were represented best by a power function for white bream Blicca bjoerkna, and linear functions for common bream Abramis brama, roach Rutilus rutilus and wild goldfish Carassius auratus gibelio, respectively. The backcalculated mean lengths for the first age groups of common bream, white bream and roach did not differ statistically from those obtained by direct observation on 0 group fish in late November 1995. Compared to other waters, common bream grows slowly, wild goldfish and roach rapidly, while the growth rate of white bream can be considered of medium speed in Lake Balaton. Common bream showed a generalized feeding pattern, consuming mainly chironomid larvae, detritus and Corophium curvispinun. Roach showed a clear shift between specialization for Dreissena and algae. Despite the dense population of D. polymorpha in the lake, the significance of the herbivorous adaptation of roach has not yet been made clear. Wild goldfish consumed mainly detritus but, in the open water region, it shifted to zooplankton. White bream preyed chiefly on D. polymorpha, but showed a mixed feeding pattern and utilized most of the available food resources. Carp had the most specialized feeding strategy and preyed mainly on D. polymorpha. According to the discriminant analysis, the five cyprinids exhibited significant food resource partitioning.

The College Admissions problem with lower and common quotas

We study two generalised stable matching problems motivated by the current matching scheme used in the higher education sector in Hungary. The first problem is an extension of the College Admissions problem in which the colleges have lower quotas as well as the normal upper quotas. Here, we show that a stable matching may not exist and we prove that the problem of determining whether one does is NP-complete in general. The second problem is a different extension in which, as usual, individual colleges have upper quotas, but, in addition, certain bounded subsets of colleges have common quotas smaller than the sum of their individual quotas. Again, we show that a stable matching may not exist and the related decision problem is NP-complete. On the other hand, we prove that, when the bounded sets form a nested set system, a stable matching can be found by generalising, in non-trivial ways, both the applicant-oriented and college-oriented versions of the classical Gale-Shapley algorithm. Finally, we present an alternative view of this nested case using the concept of choice functions, and with the aid of a matroid model we establish some interesting structural results for this case.

“Almost stable” matchings in the roommates problem

An instance of the classical Stable Roommates problem (sr) need not admit a stable matching. This motivates the problem of finding a matching that is “as stable as possible”, i.e. admits the fewest number of blocking pairs. In this paper we prove that, given an sr instance with n agents, in which all preference lists are complete, the problem of finding a matching with the fewest number of blocking pairs is NP-hard and not approximable within

Popular matchings in the marriage and roommates problems

n^{\frac{1}{2}-\varepsilon}

MAXIMUM WEIGHT CYCLE PACKING IN DIRECTED GRAPHS, WITH APPLICATION TO KIDNEY EXCHANGE PROGRAMS

, for any e>0, unless P=NP. If the preference lists contain ties, we improve this result to n1−e. Also, we show that, given an integer K and an sr instance I in which all preference lists are complete, the problem of deciding whether I admits a matching with exactly K blocking pairs is NP-complete. By contrast, if K is constant, we give a polynomial-time algorithm that finds a matching with at most (or exactly) K blocking pairs, or reports that no such matching exists. Finally, we give upper and lower bounds for the minimum number of blocking pairs over all matchings in terms of some properties of a stable partition, given an sr instance I.

Quantifying temporal variability in the metacommunity structure of stream fishes: the influence of non-native species and environmental drivers

Popular matchings have recently been a subject of study in the context of the so-called House Allocation Problem, where the objective is to match applicants to houses over which the applicants have preferences. A matching M is called popular if there is no other matching M′ with the property that more applicants prefer their allocation in M′ to their allocation in M. In this paper we study popular matchings in the context of the Roommates Problem, including its special (bipartite) case, the Marriage Problem. We investigate the relationship between popularity and stability, and describe efficient algorithms to test a matching for popularity in these settings. We also show that, when ties are permitted in the preferences, it is NP-hard to determine whether a popular matching exists in both the Roommates and Marriage cases.

Spatial distribution and short-term changes of benthic macrofauna in Lake Balaton (Hungary)

Centralized matching programs have been established in several countries to organize kidney exchanges between incompatible patient-donor pairs. At the heart of these programs are algorithms to solve kidney exchange problems, which can be modelled as cycle packing problems in a directed graph, involving cycles of length 2, 3, or even longer. Usually, the goal is to maximize the number of transplants, but sometimes the total benefit is maximized by considering the differences between suitable kidneys. These problems correspond to computing cycle packings of maximum size or maximum weight in directed graphs. Here we prove the APX-completeness of the problem of finding a maximum size exchange involving only 2-cycles and 3-cycles. We also present an approximation algorithm and an exact algorithm for the problem of finding a maximum weight exchange involving cycles of bounded length. The exact algorithm has been used to provide optimal solutions to real kidney exchange problems arising from the National Matching Scheme for Paired Donation run by NHS Blood and Transplant, and we describe practical experience based on this collaboration.

Management of pond ecosystems and trophic webs

Most studies characterize metacommunities based on a single snapshot of the spatial structure, which may be inadequate for taxa with high migratory behavior (e.g., fish). Here, we applied elements of metacommunity structure to examine variations in the spatial distributions of stream fishes over time and to explore possible structuring mechanisms. Although the major environmental gradients influencing species distributions remained largely the same in time, the best-fit pattern of metacommunity structure varied according to sampling occasion and whether or not we included non-native species in the analyses. Quasi-Clementsian and Clementsian structures were the predominant best-fit structures, indicating the importance of species turnover among sites and the existence of more or less discrete community boundaries. The environmental gradient most correlated with metacommunity structure was defined by altitude, area of artificial ponds in the catchment, and dissolved oxygen content. Our results suggest that the best-fit metacommunity structure of the native species can change in time in this catchment due to seasonal changes in distribution patterns. However, the distribution of non-native species throughout the landscape homogenizes the temporal variability in metacommunity structure of native species. Further studies are necessary from other regions to examine best-fit metacommunity structures of stream fishes within relatively short environmental gradients.

Solutions for the stable roommates problem with payments.

Spatial and short-term changes in the composition and density of the macrobenthic fauna were studied in Lake Balaton, a large shallow lake in Central Europe (Hungary). Spatial differences were examined along five transects and short-term changes at two stations of different trophic state. The macrobenthos consisted almost exclusively of Tubificidae and Chironomidae of the species Chironomus gr. plumosus, Procladius choreus, Tanypus punctipennis, Microchironomus tener and Cladotanytarsus sp. The Oligochaeta biomass showed a significant short-term decrease from 1995 to 1998, and their average biomass proved to be 0.86 and 0.79 g WFW (wet formalin weight) m-2 in 1996 and 1997, respectively. Chironomidae showed significant spatial and short-term differences following variations in primary production. Higher primary production resulted in higher biomass (up to 153.4 g WFW m-2 and 9785 ind. m-2 in 1995) of Chironomus-Procladius community, while lower primary production resulted in a very low biomass and abundance of the predatory Procladius-Tanypus-Microchironomus community (average: 3.16 g WFW m-2 and 1311 ind. m-2 in 1997). As compared to other lakes of similar climatic conditions, the total production of oligohaetes and chironomids proved to be very low in 1996 and 1997 (49.2 and 54.1 KJ m-2 yr-1, respectively). The 90% of the average chironomid production of Lake Balaton in 1996 and 1997 belonged to Ch. gr. plumosus (5.63 and 5.13 g m-2 yr-1), P. choreus (4.3 and 3.47 g m-2 yr-1) and T. punctipennis (0.27 and 2.21 g m-2 yr-1).

Three-Sided Stable Matchings with Cyclic Preferences

Abstract The productivity of common carp (Cyprinus carpio L.) varies among continents according to current fish-pond management practices and variations in trophic conditions and/or fish-carrying capacity. “Biomanipulation” as a management tool for aquatic communities is aimed at exploiting “top-down forces” or the “trophic cascade” in order to influence the food-web and efficiency of energy transfer from primary producers to fish. The aim of food-web manipulation in fish-ponds has usually been in contrast to that in natural waters. This paper focusses on the basic ecosystem processes and provides an overview of the efficiency of energy transfer in various lakes, ponds and reservoirs which may be influenced by food-web manipulation using different approaches (fertilization, stocking, chemical treatment, supplementary feeding). Several sources of data have also been summarized illustrating the relationships between stocking rate and fish production in a variety of natural and artificial ecosystems.