A Cayley tree immune network model with antibody dynamics

A Cayley tree model of idiotypic networks that includes both B cell and antibody dynamics is formulated and analysed. As in models with B cells only, localized states exist in the network with limited numbers of activated clones surrounded by virgin or near-virgin clones. The existence and stability of these localized network states are explored as a function of model parameters. As in previous models that have included antibody, the stability of immune and tolerant localized states are shown to depend on the ratio of antibody to B cell lifetimes as well as the rate of antibody complex removal. As model parameters are varied, localized steady-states can break down via two routes: dynamically, into chaotic attractors, or structurally into percolation attractors. For a given set of parameters percolation and chaotic attractors can coexist with localized attractors, and thus there do not exist clear cut boundaries in parameter space that separate regions of localized attractors from regions of percolation and chaotic attractors. Stable limit cycles, which are frequent in the two-clone antibody B cell (AB) model, are only observed in highly connected networks. Also found in highly connected networks are localized chaotic attractors. As in experiments by Lundkvistet al. (1989.Proc. natn. Acad. Sci. U.S.A. 86, 5074–5078), injection ofAb ₁ antibodies into a system operating in the chaotic regime can cause a cessation of fluctuations ofAb ₁ andAb ₂ antibodies, a phenomenon already observed in the two-clone AB model. Interestingly, chaotic fluctuations continue at higher levels of the tree, a phenomenon observed by Lundkvistet al. but not accounted for previously.     

Low-dimensional chaotic attractors in the rat brain

The existence of chaotic attractors for discrete time series, derived from the occurrences of spikes during electrophysiological recordings, was investigated. The time series included between 800 and 5200 points per analyzed record. The spike trains were recorded in the substantia nigra pars reticulata (n=13) and in the auditory thalamus (n=14). The experiments were performed on anesthetized rats during spontaneous activity and during auditory stimulation. According to standard methods of dynamical systems theory, an embedding space was constructed using delay coordinates. The embedding and correlation dimensions were computed by means of the correlation integrals. For 7 of 27 samples, a deterministic structure with a low embedding dimension (ranging between 2 and 6) and a correlation dimension between 0.14 and 3.3 could be determined. Evidence was found that the sensory stimulation may affect the chaotic behavior. Single units recorded simultaneously from the same electrode tip may display different chaotic dynamics, even with a similar time-locked response to the stimulus onset.     

Climate response among growth increments of fish and trees

Significant correlations were found among the annual growth increments of stream fish, trees, and climate variables in the Ozark region of the United States. The variation in annual growth increments of rock bass (Ambloplites rupestris) from the Jacks Fork River was significantly correlated over 22 years with the ring width of four tree species: white oak (Quercus alba), post oak (Quercus stellata), shortleaf pine (Pinus echinata) and eastern red cedar (Juniperus virginiana). Rock bass growth and tree growth were both significantly correlated with July rainfall and stream discharge. Variations in annual growth of smallmouth bass (Micropterus dolomieu) from four streams were significantly correlated over 29 years (1939–1968) with mean May maximum air temperature but not with tree growth. The magnitude and significance of correlations among growth increments from fish and trees imply that conditions such as topography, stream gradient, organism age, and the distribution of a population relative to its geographic range can influence the climatic response of an organism. The timing and intensity of climatic variables may produce different responses among closely related species.     

Effect of landscape factors on fish distribution in arctic Alaskan lakes

1. The distribution of species is affected by many factors operating at a variety of temporal and spatial scales in a heterogeneous landscape. In lakes, fish communities are dynamic, influenced by landscape‐level factors that control colonisation and extinction. 2. We used classification and regression tree (CART) analyses to quantify the importance of landscape‐level factors in determining the distribution of fish species in 168 arctic Alaskan lakes. Factors including lake size, depth, outflow gradient, distance to other lakes, lake order, altitude, river drainage and age of glacial surface were analysed. These factors could affect either access of fish to a lake (colonisation variables), or their survival in a lake that already had been colonised (extinction variables). 3. The presence of a species was predicted accurately in 78.4% ± 10.5% (mean ± SD) of cases, and absence in 75.0% ± 6.1% of cases. The relative importance of extinction versus colonisation variables varied with species. Extinction variables were most important for lake trout (Salvelinus namaycush) and slimy sculpin (Cottus cognatus), a mixture of extinction and colonisation variables was important for arctic char (Salvelinus alpinus), and colonisation variables were most important for arctic grayling (Thymallus arcticus) and round whitefish (Prosopium cylindraceum). 4. Ecological differences among species account for much of the difference in relative importance of colonisation versus extinction variables. In addition, stream piracy events have occurred over geologic time scales, which have resulted in lakes that are currently inaccessible but support relict fish populations. 5. Climate warming, currently occurring in the arctic, is likely to alter further the stream network, which could have dramatic effects on fish distributions by affecting access to isolated lakes or isolating lakes that are currently accessible.     

The effect of seasonal harvesting on stage-structured population models

In most models of population dynamics, increases in population due to birth are assumed to be time-independent, but many species reproduce only during a single period of the year. We propose an exploited single-species model with stage structure for the dynamics in a fish population for which births occur in a single pulse once per time period. Since birth pulse populations are often characterized with a discrete time dynamical system determined by its Poincaré map, we explore the consequences of harvest timing to equilibrium population sizes under seasonal dependence and obtain threshold conditions for their stability, and show that the timing of harvesting has a strong impact on the persistence of the fish population, on the volume of mature fish stock and on the maximum annual-sustainable yield. Moreover, our results imply that the population can sustain much higher harvest rates if the mature fish is removed as early in the season (after the birth pulse) as possible. Further, the effects of harvesting effort and harvest timing on the dynamical complexity are also investigated. Bifurcation diagrams are constructed with the birth rate (or harvesting effort or harvest timing) as the bifurcation parameter, and these are observed to display rich structure, including chaotic bands with periodic windows, pitch-fork and tangent bifurcations, non-unique dynamics (meaning that several attractors coexist) and attractor crisis. This suggests that birth pulse, in effect, provides a natural period or cyclicity that makes the dynamical behavior more complex.This work is supported by National Natural Science Foundation of China (10171106)     

Evidence of alternate attractors from a whole-ecosystem regime shift experiment

Ecosystems sometimes shift between different states or dynamic regimes. Theory attributes these shifts to multiple ecosystem attractors. However, documenting multiple ecosystem attractors is difficult, particularly at spatial and temporal scales relevant to ecosystem management. We manipulated the fish community of a lake with the goal of causing trophic cascades and shifting the food web from a planktivore-dominated state to an alternate piscivore-dominated state. We evaluated evidence that the shifts in the fish community comprise alternate attractors using two complementary approaches. First, we calculated phase space trajectories to visualize the shift between attractors. Second, we computed generalized autoregressive conditional heteroskedasticity (GARCH) models and the Brock–Dechert–Scheinkman (BDS) test for linearity. The reconstructed phase space trajectories show the system departing a point attractor, entering a limit cycle, and then shifting to a new point attractor. The GARCH and BDS results indicate that linear explanations are not sufficient to explain the observed patterns. The results provide evidence for alternate attractors based on high-frequency time series of field measurements.     

Remote sensing tracks daily radial wood growth of evergreen needleleaf trees

Relationships between gross primary productivity (GPP) and the remotely sensed photochemical reflectance index (PRI) suggest that time series of foliar PRI may provide insight into climate change effects on carbon cycling. However, because a large fraction of carbon assimilated via GPP is quickly returned to the atmosphere via respiration, we ask a critical question—can PRI time series provide information about longer term gains in aboveground carbon stocks? Here we study the suitability of PRI time series to understand intra‐annual stem‐growth dynamics at one of the world's largest terrestrial carbon pools—the boreal forest. We hypothesized that PRI time series can be used to determine the onset (hypothesis 1) and cessation (hypothesis 2) of radial growth and enable tracking of intra‐annual tree growth dynamics (hypothesis 3). Tree‐level measurements were collected in 2018 and 2019 to link highly temporally resolved PRI observations unambiguously with information on daily radial tree growth collected via point dendrometers. We show that the seasonal onset of photosynthetic activity as determined by PRI time series was significantly earlier (p < .05) than the onset of radial tree growth determined from the point dendrometer time series which does not support our first hypothesis. In contrast, seasonal decline of photosynthetic activity and cessation of radial tree growth was not significantly different (p > .05) when derived from PRI and dendrometer time series, respectively, supporting our second hypothesis. Mixed‐effects modeling results supported our third hypothesis by showing that the PRI was a statistically significant (p < .0001) predictor of intra‐annual radial tree growth dynamics, and tracked these daily radial tree‐growth dynamics in remarkable detail with conditional and marginal coefficients of determination of 0.48 and 0.96 (for 2018) and 0.43 and 0.98 (for 2019), respectively. Our findings suggest that PRI could provide novel insights into nuances of carbon cycling dynamics by alleviating important uncertainties associated with intra‐annual vegetation response to climate change.     

Species-Specific Growth Responses to Climate Variations in Understory Trees of a Central African Rain Forest

Basic knowledge of the relationships between tree growth and environmental variables is crucial for understanding forest dynamics and predicting vegetation responses to climate variations. Trees growing in tropical areas with a clear seasonality in rainfall often form annual growth rings. In the understory, however, tree growth is supposed to be mainly affected by interference for access to light and other resources. In the semi-deciduous Mayombe forest of the Democratic Republic of Congo, the evergreen species Aidia ochroleuca, Corynanthe paniculata and Xylopia wilwerthii dominate the understory. We studied their wood to determine whether they form annual growth rings in response to changing climate conditions. Distinct growth rings were proved to be annual and triggered by a common external factor for the three species. Species-specific site chronologies were thus constructed from the cross-dated individual growth-ring series. Correlation analysis with climatic variables revealed that annual radial stem growth is positively related to precipitation during the rainy season but at different months. The growth was found to associate with precipitation during the early rainy season for Aidia but at the end of the rainy season for Corynanthe and Xylopia. Our results suggest that a dendrochronological approach allows the understanding of climate–growth relationships in tropical forests, not only for canopy trees but also for evergreen understory species and thus arguably for the whole tree community. Global climate change influences climatic seasonality in tropical forest areas, which is likely to result in differential responses across species with a possible effect on forest composition over time.     

Statistical properties of flip-flop processes associated to the chaotic behavior of systems with strange attractors

The chaotic behavior of systems with strange attractors can be discussed by examining the flip-flop process associated to the system dynamics. This was already shown by Lorenz (1963) in his first seminal paper. A somewhat surprising result was obtained by Aizawa (1982), who, studying the same Lorenz attractor at the parameter valuer=28, reached the conclusion that the associated flip-flop was a typical Markov process. Since the process is generated in a deterministic way, one may wonder if the Aizawa result is accidental, depending on the particular parameter value, or if a similar conclusion can be extended to other systems, with different attractors. Our conclusions are that the Aizawa result is mostly accidental, because for other parameter values and for other attractors there are sharp deviations from the Markovian process.     

Linking variability of tree water use and growth with species resilience to environmental changes

Tree growth is an indicator of tree vitality and its temporal variability is linked to species resilience to environmental changes. Second-order statistics that quantify the cross-scale temporal variability of ecophysiological time series (statistical memory) could provide novel insights into species resilience. Species with high statistical memory in their tree growth may be more affected by disturbances, resulting in lower overall resilience and higher vulnerability to environmental changes. Here, we assessed the statistical memory, as quantified with the decay in standard deviation with increasing time scale, in tree water use and growth of co-occurring European larch Larix decidua and Norway spruce Picea abies along an elevational gradient in the Swiss Alps using measurements of stem radius changes, sap flow and tree-ring widths. Local-scale interspecific differences between the two conifers were further explored at the European scale using data from the International Tree-Ring Data Bank. Across the analysed elevational gradient, tree water use showed steeper variability decay with increasing time scale than tree growth, with no significant interspecific differences, highlighting stronger statistical memory in tree growth processes. Moreover, Norway spruce displayed slower decay in growth variability with increasing time scale (higher statistical memory) than European larch; a pattern that was also consistent at the European scale. The higher statistical memory in tree growth of Norway spruce in comparison to European larch is indicative of lower resilience of the former in comparison to the latter, and could potentially explain the occurrence of European larch at higher elevations at the Alpine treeline. Single metrics of resilience cannot often summarize the multifaceted aspects of ecosystem functioning, thus, second-order statistics that quantify the strength of statistical memory in ecophysiological time series could complement existing resilience indicators, facilitating the assessment of how environmental changes impact forest growth trajectories and ecosystem services.     

The piscivore feeding guild of fishes in small freshwater ecosystems

Synopsis Analysis of the piscivore guild in fish species-rich lake and stream systems in eastern Ontario showed the co-occurrence of three types: (1) specialists that became piscivorous at the age of a few weeks (Esox, Micropterus); (2) ‘secondary’ piscivores that are fish-eaters only later in life (Perca, Ambloplites); and (3) species in which fish consumption is limited to taking some larvae (Lepomis macrochirus). In the first group the basic series of dietary shifts that characterize many long-lived fish (i.e. zooplankton followed by small invertebrates then large invertebrates and finally fish); is greatly accelerated. Prey size increases with growth. Overall prey selection was on the basis of body size and abundance. Most piscivores took a range of fish prey. There was little evidence of specialization at the species level. Esox and Micropterus spawn some weeks ahead of their major prey species. This is seen as adaptive. Their young harvest the larvae of the latter. The ensuing predator/prey association with growth is highly advantageous to the piscivore as prey of optimum body size are thus continually available.     

Evidence for climate‐driven synchrony of marine and terrestrial ecosystems in northwest Australia

The effects of climate change are difficult to predict for many marine species because little is known of their response to climate variations in the past. However, long‐term chronologies of growth, a variable that integrates multiple physical and biological factors, are now available for several marine taxa. These allow us to search for climate‐driven synchrony in growth across multiple taxa and ecosystems, identifying the key processes driving biological responses at very large spatial scales. We hypothesized that in northwest (NW) Australia, a region that is predicted to be strongly influenced by climate change, the El Niño Southern Oscillation (ENSO) phenomenon would be an important factor influencing the growth patterns of organisms in both marine and terrestrial environments. To test this idea, we analyzed existing growth chronologies of the marine fish Lutjanus argentimaculatus, the coral Porites spp. and the tree Callitris columellaris and developed a new chronology for another marine fish, Lethrinus nebulosus. Principal components analysis and linear model selection showed evidence of ENSO‐driven synchrony in growth among all four taxa at interannual time scales, the first such result for the Southern Hemisphere. Rainfall, sea surface temperatures, and sea surface salinities, which are linked to the ENSO system, influenced the annual growth of fishes, trees, and corals. All four taxa had negative relationships with the Niño‐4 index (a measure of ENSO status), with positive growth patterns occurring during strong La Niña years. This finding implies that future changes in the strength and frequency of ENSO events are likely to have major consequences for both marine and terrestrial taxa. Strong similarities in the growth patterns of fish and trees offer the possibility of using tree‐ring chronologies, which span longer time periods than those of fish, to aid understanding of both historical and future responses of fish populations to climate variation.     

Multiple attractors in stage-structured population models with birth pulses

In most models of population dynamics, increases in population due to birth are assumed to be time-independent, but many species reproduce only during a single period of the year. A single species stage-structured model with density-dependent maturation rate and birth pulse is formulated. Using the discrete dynamical system determined by its Poincaré map, we report a detailed study of the various dynamics, including (a) existence and stability of nonnegative equilibria, (b) nonunique dynamics, meaning that several attractors coexist, (c) basins of attraction (defined as the set of the initial conditions leading to a certain type of attractor), (d) supertransients, and (e) chaotic attractors. The occurrence of these complex dynamic behaviour is related to the fact that minor changes in parameter or initial values can strikingly change the dynamic behaviours of system. Further, it is shown that periodic birth pulse, in effect, provides a natural period or cyclicity that allows multiple oscillatory solutions in the continuous dynamical systems.     

The value of crossdating to retain high‐frequency variability,climate signals,and extreme events in environmental proxies

High‐resolution biogenic and geologic proxies in which one increment or layer is formed per year are crucial to describing natural ranges of environmental variability in Earth's physical and biological systems. However, dating controls are necessary to ensure temporal precision and accuracy; simple counts cannot ensure that all layers are placed correctly in time. Originally developed for tree‐ring data, crossdating is the only such procedure that ensures all increments have been assigned the correct calendar year of formation. Here, we use growth‐increment data from two tree species, two marine bivalve species, and a marine fish species to illustrate sensitivity of environmental signals to modest dating error rates. When falsely added or missed increments are induced at one and five percent rates, errors propagate back through time and eliminate high‐frequency variability, climate signals, and evidence of extreme events while incorrectly dating and distorting major disturbances or other low‐frequency processes. Our consecutive Monte Carlo experiments show that inaccuracies begin to accumulate in as little as two decades and can remove all but decadal‐scale processes after as little as two centuries. Real‐world scenarios may have even greater consequence in the absence of crossdating. Given this sensitivity to signal loss, the fundamental tenets of crossdating must be applied to fully resolve environmental signals, a point we underscore as the frontiers of growth‐increment analysis continue to expand into tropical, freshwater, and marine environments.     

Environmental drivers interactively affect individual tree growth across temperate European forests

Forecasting the growth of tree species to future environmental changes requires a better understanding of its determinants. Tree growth is known to respond to global‐change drivers such as climate change or atmospheric deposition, as well as to local land‐use drivers such as forest management. Yet, large geographical scale studies examining interactive growth responses to multiple global‐change drivers are relatively scarce and rarely consider management effects. Here, we assessed the interactive effects of three global‐change drivers (temperature, precipitation and nitrogen deposition) on individual tree growth of three study species (Quercus robur/petraea, Fagus sylvatica and Fraxinus excelsior). We sampled trees along spatial environmental gradients across Europe and accounted for the effects of management for Quercus. We collected increment cores from 267 trees distributed over 151 plots in 19 forest regions and characterized their neighbouring environment to take into account potentially confounding factors such as tree size, competition, soil conditions and elevation. We demonstrate that growth responds interactively to global‐change drivers, with species‐specific sensitivities to the combined factors. Simultaneously high levels of precipitation and deposition benefited Fraxinus, but negatively affected Quercus’ growth, highlighting species‐specific interactive tree growth responses to combined drivers. For Fagus, a stronger growth response to higher temperatures was found when precipitation was also higher, illustrating the potential negative effects of drought stress under warming for this species. Furthermore, we show that past forest management can modulate the effects of changing temperatures on Quercus’ growth; individuals in plots with a coppicing history showed stronger growth responses to higher temperatures. Overall, our findings highlight how tree growth can be interactively determined by global‐change drivers, and how these growth responses might be modulated by past forest management. By showing future growth changes for scenarios of environmental change, we stress the importance of considering multiple drivers, including past management and their interactions, when predicting tree growth.     

Omnivory by Planktivores Stabilizes Plankton Dynamics, but May Either Promote or Reduce Algal Biomass

Classical models of phytoplankton–zooplankton interaction show that with nutrient enrichment such systems may abruptly shift from limit cycles to stable phytoplankton domination due to zooplankton predation by planktivorous fish. Such models assume that planktivorous fish eat only zooplankton, but there are various species of filter-feeding fish that may also feed on phytoplankton. Here, we extend these classical models to systematically explore the effects of omnivory by planktivorous fish. Our analysis indicates that if fish forage on phytoplankton in addition to zooplankton, the alternative attractors predicted by the classical models disappear for all realistic parameter settings, even if omnivorous fish have a strong preference for zooplankton. Our model also shows that the level of fish biomass above which zooplankton collapse should be higher when fish are omnivorous than when fish are zooplanktivorous. We also used the model to explore the potential effects of the now increasingly common practice of stocking lakes with filter-feeding fish to control cyanobacteria. Because omnivorous filter-feeding fish forage on phytoplankton as well as on the main grazers of phytoplankton, the net effect of such fish on the phytoplankton biomass is not obvious. Our model suggests that there may be a unimodal relationship between the biomass of omnivorous filter-feeding fish and the biomass of phytoplankton. This implies that to manage for reductions in phytoplankton biomass, heavy stocking or strong reduction of such fish is best.     

Understanding behaviour to improve the welfare of an ornamental fish

Some common practices in aquaculture, ornamental trade and fish facilities may disturb the behavioural repertoire of fish and its natural adaptive value, reducing welfare and impairing fish production. Hence, it is necessary to understand fish behaviour, as well as the factors affecting it, to improve the quality of fish's life under artificial environment. Here, we reviewed the behaviour of the angelfish Pterophyllum scalare, an Amazonian cichlid used worldwide both as an ornamental fish and as a fish model in scientific research. We characterized social, reproductive and feeding behaviour, as well as the amazing cognitive ability of the angelfish. In addition, we reviewed the effects of environmental enrichment and suggested some important variables that need to be considered for rearing P. scalare. In this review, we show for the first time a synthesis on behaviour and a best practice overview to improve the welfare of angelfish as a target species. Nonetheless, most topics reviewed fit a broader set of fish species, particularly ornamental ones. This synthesis can therefore open a path for further behavioural research applied to the welfare of angelfish and bring insights to other fish species.     

东北地区两个主要树种地上生物量通用方程构建

目前,东北落叶松地上生物量方程主要采用分树种或把不同树种归为一体的方法,但是,既能反映落叶松生物量与自变量的平均关系,又能反映不同树种间生物量差异程度的通用性落叶松生物量方程迄今尚未构建。因此,以东北地区兴安落叶松和长白落叶松地上生物量数据为研究对象,构建一元(自变量为胸径)、二元(自变量为胸径和树高)和三元(自变量为胸径、树高和冠幅)的不同树种生物量通用方程。由于起源和地域的不同,生物量可能会存在一定程度差异,进而,在所构建的不同树种生物量通用方程的基础上,考虑起源和地域的差异,利用哑变量方法构建既能考虑不同树种又能考虑林分起源和不同地域的东北落叶松地上生物量通用方程,并利用加权最小二乘法剔除方程异方差。结果表明:通过哑变量方法构建不同树种生物量模型方法可行;不论是传统的生物量方程,还是只考虑树种或同时考虑树种、起源和地域的通用生物量方程,增加自变量能提高方程预测效果,即,三元生物量方程预测精度最高,二元生物量方程次之,一元生物量方程最低;当同时考虑树种、起源和地域时,方程预测精度最高,只考虑树种的生物量通用方程次之,传统生物量方程最低。因此,如果数据允许,建议构建考虑不同树种、起源和地域的三元生物量方程估计东北地区长白落叶松和兴安落叶松地上生物量。     

Diameter Growth of Juvenile Trees after Gap Formation in a Bolivian Rain Forest: Responses are Strongly Species‐specific and Size‐dependent

We evaluated growth responses to gap formation for juvenile individuals of three canopy rain forest species: Peltogyne cf. heterophylla, Clarisia racemosa and Cedrelinga catenaeformis. Gaps were formed during selective logging operations 7 yr before sampling in a Bolivian rain forest. We collected wood samples for tree‐ring analyses at different distances to the stump (<10, 10–40 and >40 m) and from trees with different diameters (5–30 cm diameter at breast height [dbh]). Tree‐rings width was measured in at least two radii and converted to average diameter growth. Changes in 7‐yr median diameter growth before and after selective logging were analyzed. Diameter growth rates significantly increased by 0.7–0.8 mm/yr after gap formation for P. heterophylla and C. catenaeformis, but not for C. racemosa. We applied a multiple regression analysis to explain variation in growth responses of P. heterophylla and C. catenaeformis by distance to logging gap and tree size. For P. heterophylla we found that growth increase occurring close to logging gaps was strongest for large juvenile trees (20–25 cm dbh) and almost absent in small juveniles. For C. catenaeformis, variation in growth responses was not related to tree size or distance to gaps. Our results show that growth responses to gap formation strongly differ across species and tree sizes. This finding calls for caution in the interpretation of growth releases in tree‐ring series, as gap formation does not necessarily invoke growth responses and if such growth responses occur, their strength is species‐ and size specific.