Bayesian methods for comparing species physiological and ecological response curves

Many ecological questions require information on species' optimal conditions or critical limits along environmental gradients. These attributes can be compared to answer questions on niche partitioning, species coexistence and niche conservatism. However, these comparisons are unconvincing when existing methods do not quantify the uncertainty in the attributes or rely on assumptions about the shape of species' responses to the environmental gradient. The aim of this study was to develop a model to quantify the uncertainty in the attributes of species response curves and allow them to be tested for substantive differences without making assumptions about the shape of the responses. We developed a model that used Bayesian penalised splines to produce and compare response curves for any two given species. These splines allow the data to determine the shape of the response curves rather than making a priori assumptions. The models were implemented using the R2OpenBUGS package for R, which uses Markov Chain Monte Carlo simulation to repetitively fit alternative response curves to the data. As each iteration produces a different curve that varies in optima, niche breadth and limits, the model estimates the uncertainty in each of these attributes and the probability that the two curves are different. The models were tested using two datasets of mosses from Antarctica. Both datasets had a high degree of scatter, which is typical of ecological research. This noise resulted in considerable uncertainty in the optima and limits of species response curves, but substantive differences were found. Schistidium antarctici was found to inhabit wetter habitats than Ceratodon purpureus, and Polytrichastrum alpinum had a lower optimal temperature for photosynthesis than Chorisodontium aciphyllum under high light conditions. Our study highlights the importance of considering uncertainty in physiological optima and other attributes of species response curves. We found that apparent differences in optima of 7.5 °C were not necessarily substantive when dealing with noisy ecological data, and it is necessary to consider the uncertainty in attributes when comparing the curves for different species. The model introduced here could increase the robustness of research on niche partitioning, species coexistence and niche conservatism.     

Damage and ecological characteristics of termite Neotermes koshunensis on Taiwan cherry tree Cerasus campanulata in Okinawa Island

Termites are typical house pests that can also be harmful pests for living trees, although this topic has not received much attention. To clarify the damage to trees caused by dry-wood termites (Neotermes koshunensis), and the ecological characteristics of such damage, we conducted a study on Taiwan cherry trees (Cerasus campanulata) grown in parks, historical sites, and streets in the central-southern area of Okinawa Island, a subtropical region. Damage by N. koshunensis was confirmed in 21 of the 36 sites surveyed (58.3%) and in 76 of the 1076 trees surveyed (7.1%). However, damage by Formosan subterranean termites (Coptotermes formosanus), a house pest, was only observed at six sites (16.7%), and 10 trees (0.9%), indicating that most damage was caused by N. koshunensis. Furthermore, the probability of the presence of damaged trees close to other damaged trees was significantly higher than the probability of the presence of damaged trees close to undamaged trees, implying that destructive colonies spread from damaged trees to other trees nearby. Therefore, care for trees in the initial stages of termite invasion seems to be the best method for preventing the spread N. koshunensis damage to other trees in the same area. To our knowledge, this study is the first to report that dry-wood termite N. koshunensis are harmful pests for Taiwan cherry trees in Okinawa Island. Our results could be used to establish dry-wood termite countermeasures for garden tree species.     

Variable detectability in long-term population surveys of small mammals

Simple survey methods for small mammals, such as indices of trap captures per unit effort, are often the only practicable means of monitoring populations over the long term and at landscape scale and the only source of valuable historical data. They include two fundamental assumptions about the target populations (uniform distribution and equal detectability). Concern has often been expressed that, if these assumptions are violated, conventional density indices could give misleading results. Site occupancy analysis (SOA) can detect significantly uneven distribution of local populations (from variation in probability of occupancy) and reliability of indices of abundance (from variation in detectability) without requiring enumeration. We use this method to examine standardised capture records from long-term population surveys of non-commensal house mice (Mus musculus), ship rats (Rattus rattus), Norway rats (Rattus norvegicus) and stoats (Mustela erminea), sampled in four representative temperate forest habitats in New Zealand. Best fit models generated by SOA were consistent with (1) constant or random probability of occupancy for stoats and dynamic equilibrium probability of occupancy for most populations of mice and rats; (2) widespread site-specific variation in probability of detection, especially substantial in rats and correlated with habitat covariates; (3) direct correlations between detectability and density index in mice and rats sampled at 50 m intervals over 3 days, probably because the effects on the density index of variation in numbers available to be caught (population size) were much larger than the effects of changes in catchability (individual behaviour); (4) declines after 6 days in detectability of stoats and rats sampled at 3–400 m intervals over 10 days, attributed to a local trap-out effect. Longer-term variations in the density index were consistent with observed changes in reproductive parameters and age structure that are known to follow variations in real numbers. We conclude that violations of the assumptions of uniform distribution and equal detectability, while real, were not sufficient to prevent these data from providing information adequate for (1) short-term population assessments (2) long-term, low-level monitoring and (3) preliminary modelling.     

Missing and forbidden links in mutualistic networks

Ecological networks are complexes of interacting species, but not all potential links among species are realized. Unobserved links are either missing or forbidden. Missing links exist, but require more sampling or alternative ways of detection to be verified. Forbidden links remain unobservable, irrespective of sampling effort. They are caused by linkage constraints. We studied one Arctic pollination network and two Mediterranean seed-dispersal networks. In the first, for example, we recorded flower-visit links for one full season, arranged data in an interaction matrix and got a connectance C of 15 per cent. Interaction accumulation curves documented our sampling of interactions through observation of visits to be robust. Then, we included data on pollen from the body surface of flower visitors as an additional link ‘currency’. This resulted in 98 new links, missing from the visitation data. Thus, the combined visit–pollen matrix got an increased C of 20 per cent. For the three networks, C ranged from 20 to 52 per cent, and thus the percentage of unobserved links (100 − C) was 48 to 80 per cent; these were assumed forbidden because of linkage constraints and not missing because of under-sampling. Phenological uncoupling (i.e. non-overlapping phenophases between interacting mutualists) is one kind of constraint, and it explained 22 to 28 per cent of all possible, but unobserved links. Increasing phenophase overlap between species increased link probability, but extensive overlaps were required to achieve a high probability. Other kinds of constraint, such as size mismatch and accessibility limitations, are briefly addressed.     

Gulls and plovers: host vigilance,kleptoparasite success and a model of kleptoparasite detection

Much interest has focused on the conflict between feeding and vigilance. However, because predator attacks are rarely observed, the adaptive value of time spent vigilant (or non-vigilant through feeding) is difficult to ascertain. On the assumption that the tactics used by plovers (lapwings, Vanellus vanellus and golden plover, Pluvialis apricaria) to avoid attack by kleptoparasitic black-headed gulls (Larus ridibundus) and predators are similar, we develop a model predicting the probability of a gull being detected over any distance. The assumptions of the model are that (a) plovers are attacked whilst nonvigilant (crouching and handling prey) and (b) attacks lasting longer than the target plover's non-vigilant period will be detected. Over many distances there was a fairly close match between the observed and expected risk of the gull being detected. The match was better when the model assumed gulls waited 1 s prior to attacking plovers with large profitable worms. The risks of kleptoparasitism and predation are compared and the adaptive value of the close match between observed and expected curves is discussed.     

Differences between Wheat Genotypes in Specific Activity of Ribulose-1,5-bisphosphate Carboxylase and the Relationship to Photosynthesis

The in vitro ribulose-1,5-bisphosphate (RuBP) carboxylase activity per unit of leaf nitrogen was found to be 30% greater in Triticum aestivum than in T. monococcum. This was due to a higher specific activity of the enzyme from T. aestivum, as the amount of RuBP carboxylase protein per unit of total leaf nitrogen did not differ between the genotypes. The occurrence of higher specific activity of RuBP carboxylase is shown to correlate with possession of the large subunit derived from the B genome of wheat.

Despite the greater RuBP carboxylase activity per unit of leaf nitrogen in T. aestivum, the initial slopes of curves relating rate of CO₂ assimilation to intercellular p(CO₂) are similar in T. aestivum and T. monococcum for the same nitrogen content per unit leaf area. The similarity of the initial slopes is the result of a greater resistance to CO₂ transfer between the intercellular spaces and the site of carboxylation in T. aestivum than in T. monococcum.

     

The Use of DFP32 as a Red Cell Tag with and without Simultaneous Tagging with Chromium51 in Certain Animals in the Presence or Absence of Random Destruction

DFP³², used to label erythrocytes in vitro, combines with cell constituents in two stages, the first almost immediate and involving tributyrinase inactivation, the second slower (more than 40 minutes) involving cholinesterase inactivation. Raising the DFP concentration increases the amount irreversibly bound, but increases even more the immediate post-transfusion elution, and DFP is unsuited for investigating erythrocyte viability of stored samples. In vivo tagging by intramuscular injection is satisfactory and normal survival curves are linear since the sample tagged has normal age distribution of cells in absence of random destruction. Here DFP³² curves are easier to interpret than Cr⁵¹ curves. In sheep, chromium elution occurs at two different rates producing a rapid initial drop followed by a slower one of about 3 per cent daily. Random destruction alters cell age distribution. New equations are derived for cases in which this is constant both with and without chromium elution; they were applied satisfactorily to dog and sheep blood. Analysis of such curves is difficult; approximate values for random destruction rates can be obtained though not potential life spans. Chromium curves can be analyzed only with the help of DFP³² or similar curves, and yield little additional information. DFP³² and chromium can be used simultaneously to provide controls.     

Multiple comparisons in the randomization analysis of designed experiments with growth curve responses

A randomization approach to multiple comparisons is developed for comparing several growth curves in randomized experiments. The exact Type I probability error rate for these comparisons may be prespecified, and a Type I error probability for each component test can be evaluated. These procedures are free of many of the standard assumptions for analyzing growth curves and for making multiple comparisons. An application of the procedure gives all pairwise comparisons among the mean growth curves associated with four treatments in an animal experiment using a Youden square design, where growth curves are obtained on monitoring hormone levels over time.     

Overview of the spaceflight radiation environment and its impact on cell biology experiments

Variables studied in typical cellular radiation biology experiments are cell killing, mutagenesis, transformation to malignancy, heritable damage, and DNA damage and repair. Dose response curves for cells exposed to low-LET radiations and some high LET radiations are well known. The low-LET dose rate in low earth orbit is roughly 1.0 mSv/day, the heavy-ion (Z>2) flux is about 1.0 particle/cm2-s corresponding to about 0.3 mSv/day, and the integrated neutron flux is roughly 2 neutrons/cm2-s corresponding to 0.012 mGy/d or, assuming a QF of 10, 0.12 mSv/d. Published dose-response curves were used to estimate the probability that a mammalian cell will be affected by each of the above types of damage. As a general approximation the exposure of an experimental cell population to the space radiation environment for 100 days will result in the following probabilities of damage per cell: cell killing based on clonogenicity 0.02, mutagenesis per locus based on phenotype analysis 1 x 10(-6), point mutation induction 2 x 10(-8) per locus, malignant transformation in vitro based on colony morphology 1.2 x 10(-5), heritable damage based on colony size 0.02, and induced DNA double-strand breaks based on fragment analysis by electrophoresis 3.5/cell or 0.26/cell after repair. Most of these figures are accurate to within a factor of 2. Thus the spaceflight radiation environment has essentially undetectable impact on typical cell biology experiments unless experimental goals involve the precise measurement of one of the above end-points. Other in vitro end-points, such as tissue morphogenesis and cell differentiation, are expected to be similarly unaffected by the spaceflight radiation environment.     

Isolation and properties of an inhibitor of phospholipase A from Bothrops neuwiedii venom

An inhibitor of phoapholipase A has been isolated from Bothrops neuwiedii venom after gel filtrations through Sephadex G-50 (pH 4.5), Sephadex G-25 (pH 7.6), Sephadex G-15 (pH 4.0), and chromatography on SE-Sephadex C-25 (pH 4.2–4.5). When subjected to paper electrophoresis, the inhibitor migrates as a simple compound with isoelectric point near pH 6.8. Aminoacid composition, sensitivity toward proteases, and the absorption spectrum fit in well with a polypeptide structure lacking tyrosine and tryptophan. In the absence of EDTA, an inactive, anionic derivative appears in inhibitor preparations; the reaction can be reversed by 2-mercaptoethanol. Direct interaction of enzyme and inhibitor is proved by the inhibition of enzyme activity and the chromatography of enzyme-inhibitor mixtures. Titration of inhibitor with venom phospholipases A (isoenzymes P-1 and P-2) yields sigmoid-shaped concentration-inhibition curves, with P-1 far more sensitive than P-2. The enzyme-inhibitor interaction depends on pH since it is tight at pH 4.5 but does not occur at pH 7.5. Presence of thiol groups in inhibitor is consistent with (a) characteristic spectral changes after reaction of inhibitor with PMB ⁴ and NEM; (b) the inhibitor inhibition by PMB, NEM, iodoacetate, and Hg²⁺, and (c) the reversal of PMB inhibition with reduced glutathione. Since phospholipase A is insensitive towards Hg²⁺, addition of Hg²⁺ to enzyme-inhibitor mixtures (or crude venom samples) causes an apparent enzyme activation (deinhibition). When substrate (egg-yolk lipoprotein) is added to enzyme-inhibitor mixtures, the reaction kinetics show an initial “lag-period” which is proportional to the inhibitor concentration. The “lag-period” does not occur in the absence of inhibitor or in the presence of Hg²⁺, that inactivates the inhibitor.     

Further studies on the induction of mutation in Haemophilus influenzae by N-methyl-N′-nitro-N-nitrosoguanidine: Lack of an inducible error-free repair system and the effect of exposure medium

Haemophilis influenzae is shown to lack the inducible, error-free repair system for alkylation damage that others have found in Escherichia coli. Prior growth in a low concentration of N-methyl-N′-nitro-N-nitrosoguanidine had only an additive effect on a subsequent brief exposure to a high concentration. Furthermore, chloramphenicol did not significantly modify the mutagenic response. In both respects, H. influenzae differs from E. coli. Experiments carried out in preparation for these tests showed that exposure to N-methyl-N′-nitro-N-nitrosoguanidine in complex growth medium was more effective by about an order of magnitude than exposure in pH 6.0 tris-maelare buffer in inducing mutations, in killing the cells, and in causing strand breaks in the preexisting DNA and gaps in newly synthesized DNA. Thus the effect of the medium is on the amount of initial damage rather than on some special feature of the mutation process. Part but not all of the effect can be accounted for by the difference in pH of the 2 media. The nature of the mutagenic process is the same under the 2 exposure conditions; i.e., reparable pre-mutational damage is produced by the agent and subsequently converted to final mutation by replication. The dose—effect curves have a non-linear initial portion under both exposure conditions, and possible reasons for this non-linearity are discussed.     

The probability of obtaining complex kinetic curves for enzyme mechanisms with cubic terms in the pseudo-steady state rate equations

A number of details required for the classification of 3 : 3 double reciprocal plots are provided. It is shown that the ν(S) plot for a 3 : 3 function can have at most four inflexions and at most two inflexions adjacent to a turning point. Using this information, a classification of 3 : 3 ν(S) plots into ten main varieties with several subclasses is reported. The problem of defining the probability with which a given mechanism can give rise to specific curve shape features is considered. Applying this technique, the probability with which four simple enzyme mechanisms can give rise to 3 : 3 curve shapes is computed. It is shown that a 3 : 3 saturation function can have no turning points, at most two inflexions and at most one inflexion in double reciprocal space. The probability with which the available 3 : 3 shapes can arise is also computed. It is concluded that, with realistic values for rate constants, chemically reasonable enzyme mechanisms leading to rate equations of degree n : n can generate most of the kinetic profiles available to a rational function of degree n : n with positive coefficients. The probability of obtaining specific curve shapes is not so characteristic of the particular mechanism for 3:3 rate equations as it is for 2:2 rate equations. The probability of obtaining highly complex curves with several turning points or inflexions is rather lower for the enzyme mechanisms than with general 3 : 3 rational functions. There is a high probability that 3 : 3 mechanisms will generate kinetic curves that are geometrically similar to those possible for degree 2 : 2 but this is not so for binding isotherms. Hence differentiating 3 : 3 from 2 : 2 rate equations from experimental kinetic data is more likely to be successful by non-linear regression to the whole data set than by demonstrating a specific 3 : 3 feature. Binding curves, on the other hand, for three or more sites should give Scatchard plots with inflexions, features not possible with second degree equations which are conic sections in this space.     

Probability distributions of ancestries and genealogical distances on stochastically generated rooted binary trees

The stationary birth-only, or Yule-Furry, process for rooted binary trees has been analysed with a view to developing explicit expressions for two fundamental statistical distributions: the probability that a randomly selected leaf is preceded by N nodes, or “ancestors”, and the probability that two randomly selected leaves are separated by N nodes. For continuous-time Yule processes, the first of these distributions is presented in closed analytical form as a function of time, with time being measured with respect to the moment of “birth” of the common ancestor (which is essentially inaccessible to phylogenetic analysis), or with respect to the instant at which the first bifurcation occurred.The second distribution is shown to follow in an iterative manner from a hierarchy of second-order ordinary differential equations.For Yule trees of a given number n of tips, expressions have been derived for the mean and variance for each of these distributions as functions of n, as well as for the distributions themselves.In addition, it is shown how the methods developed to obtain these distributions can be employed to find, with minor effort, expressions for the expectation values of two statistics on Yule trees, the Sackin index (sum over all root-to-leaf distances), and the sum over all leaf-to-leaf distances.     

Analysis of mutant frequency curves and survival curves applied to the AL hybrid cell system

A model is presented for the statistical analysis of survival curves and mutant frequency curves for a hybrid cell system. The derivation of the model is given in the Appendix, and depends on simple assumptions about the distribution of insults, their repair, and the loss of a marker that is not rescued. A single formula (5) is found which relates a survival curve to the mutant frequency curve, i. e., the response curve for production of mutants per 10(5) survivors induced by a mutagen. The analysis is applied to loss of the a1 gene in AL-J1 hybrid cells submitted to Cesium gamma-rays. Previous experimental data using X-rays was reported by Waldren et al. (1986: Proc. Natl. Acad. Sci, USA 83, 4839.) Also, a derived formula (10), which predicts the probability that in a surviving cell a marker is lost and not rescued, will form the basis for testing the validity of the model in the future using new experimental data.     

Appendix: A model of plaque formation

Equations describing plaque formation in soft agar have been based on certain simplifying assumptions, for which data are presented. The derived equations permit one to calculate (i) average plaque size as a function of the initial density of indicator cells (D_o), (ii) the number of cells lysed per plaque as a function of D_o, and (iii) the cumulative number of cells lysed at various stages of plaque development. The calculated values agree well with those determined experimentally.     

Evaluation of feral pig removal in Hawaiian preserves

The Nature Conservancy of Hawaii (TNC) recently embarked on an ambitious ungulate control programme throughout their preserves on the islands of Maui and Molokai. The aim of the programme was local eradication of feral pigs (Sus scrofa) and they wanted some way of evaluating their progress. Catch-effort models have previously been applied to cumulative pig dispatches during an island eradication programme (Ramsey et al. 2009; Conservation Biology 23: 449-459). These models simultaneously estimate the parameters describing the initial population size and the probability of detecting an individual per unit of hunting effort, which can then be used to evaluate the likelihood of eradication. However these models rely on a number of assumptions including that the system is closed except for removals and that the relationship between hunting effort and the probability of detection is constant throughout the experiment. As the TNC control programme progressed it became clear the both these assumptions were violated and more pigs were often caught per unit of effort on the later compared with the earlier hunts. There was ongoing immigration into the preserves through breaks in the fence and via unfenced boundaries. Also, later hunts seemed to be more successful per unit of effort than earlier ones, presumably because hunters learnt the best way to cover the area and where the sites most likely to contain pigs were. We described how we incorporated this learning process into a catch-effort model using Bayesian updating in order to evaluate the efficacy of the control programme.     

Towards a quantitative definition of plant hormone sensitivity

Abstract A definition of plant hormone sensitivity is proposed which is based on the initial rates of responses at different hormone concentrations. By analogy with enzyme kinetics, it is concluded that simple concentration-response curves can be described by a function containing three ‘sensitivity parameters’. Objective methods for determining the values of these parameters and for comparing curves are described. These methods are used to describe the responses of Commelina communis L. stomata to abscisic acid. If certain assumptions are valid, the sensitivity parameters can be assigned physicochemical meanings. To validate the assumptions, certain experimental criteria must be fulfilled and these are discussed.     

The repair rate of radiation-induced DNA damage: a stochastic interpretation based on the gamma function

There is a large body of evidence that stress-induced DNA damage may be responsible for cell lethality, cancer proneness and/or immune reaction. However, statistical features of their repair rate remain poorly documented. In order to interpret the shape of the radiation-induced DNA damage repair curves with a minimum of biological assumptions, we introduced the concept of repair probability, specific to any individual radiation-induced DNA damage, whatever its biochemical type. We strengthened the apparent paradox that the repair rate of a population of DNA damage is time-dependent even if the repair rate of the individual DNA damage is constant. Hence, the existing models, based on a dual approach of the DNA repair may be insufficient for describing the DNA repair rate over a large range of repair times. Since the repair probability of DNA damage cannot be assessed individually, the measurement of the DNA repair rate is assumed to consist in determining the instantaneous mean of all repair probabilities. The relevance of this model was examined with different endpoints: cell species, genotypes, radiation type and chromatin condensation. The Euler's Gamma function was shown to provide the distribution the most consistent with such hypotheses. Furthermore, formulas, deduced from the Gamma distribution, were found to be compatible with our previous model, empirically defined but based on a variable repair half-time.     

On the estimation of species richness based on the accumulation of previously unrecorded species

Estimation of species richness of local communities has become an important topic in community ecology and monitoring. Investigators can seldom enumerate all the species present in the area of interest during sampling sessions. If the location of interest is sampled repeatedly within a short time period, the number of new species recorded is typically largest in the initial sample and decreases as sampling proceeds, but new species may be detected if sampling sessions are added. The question is how to estimate the total number of species. The data collected by sampling the area of interest repeatedly can be used to build species accumulation curves: the cumulative number of species recorded as a function of the number of sampling sessions (which we refer to as “species accumulation data”). A classic approach used to compute total species richness is to fit curves to the data on species accumulation with sampling effort. This approach does not rest on direct estimation of the probability of detecting species during sampling sessions and has no underlying basis regarding the sampling process that gave rise to the data. Here we recommend a probabilistic, nonparametric estimator for species richness for use with species accumulation data. We use estimators of population size that were developed for capture‐recapture data, but that can be used to estimate the size of species assemblages using species accumulation data. Models of detection probability account for the underlying sampling process. They permit variation in detection probability among species. We illustrate this approach using data from the North American Breeding Bird Survey (BBS). We describe other situations where species accumulation data are collected under different designs (e.g., over longer periods of time, or over spatial replicates) and that lend themselves to of use capture‐recapture models for estimating the size of the community of interest. We discuss the assumptions and interpretations corresponding to each situation.     

Effect of oxygen on freezing damage. 3. Modification by -mercaptoethylamine

The effect of β-mercaptoethylamine (MEA) on the oxygen-freezing-effect observed in E. coli strains was studied. In E. coli B_{s − 1}, a repair deficient strain, MEA reversed the increased radiation sensitivity characteristic of the oxygen-freezing-effect. MEA also affected the number and type of free radicals in frozen bacteria, including the generation of a typical “organosulfur” radical under certain conditions. MEA caused similar free radical effects in E. coli B/r which does not show an oxygen-freezing-effect. These results support the hypothesis that the oxygen-freezing effect is mediated by free radical reactions and that E. coli B/r can repair such damage. It is suggested that the enhancement of freezing damage by oxygen could play an important role in some types of cryotoxicity and that MEA or other free radical reactants would be effective cryoprotective agents under such circumstances.