Looking for a needle in a haystack: inference about individual fitness components in a heterogeneous population

Studies of wild vertebrates have provided evidence of substantial differences in lifetime reproduction among individuals and the sequences of life history ‘states’ during life (breeding, nonbreeding, etc.). Such differences may reflect ‘fixed’ differences in fitness components among individuals determined before, or at the onset of reproductive life. Many retrospective life history studies have translated this idea by assuming a ‘latent’ unobserved heterogeneity resulting in a fixed hierarchy among individuals in fitness components. Alternatively, fixed differences among individuals are not necessarily needed to account for observed levels of individual heterogeneity in life histories. Individuals with identical fitness traits may stochastically experience different outcomes for breeding and survival through life that lead to a diversity of ‘state’ sequences with some individuals living longer and being more productive than others, by chance alone. The question is whether individuals differ in their underlying fitness components in ways that cannot be explained by observable ‘states’ such as age, previous breeding success, etc. Here, we compare statistical models that represent these opposing hypotheses, and mixtures of them, using data from kittiwakes. We constructed models that accounted for observed covariates, individual random effects (unobserved heterogeneity), first‐order Markovian transitions between observed states, or combinations of these features. We show that individual sequences of states are better accounted for by models incorporating unobserved heterogeneity than by models including first‐order Markov processes alone, or a combination of both. If we had not considered individual heterogeneity, models including Markovian transitions would have been the best performing ones. We also show that inference about age‐related changes in fitness components is sensitive to incorporation of underlying individual heterogeneity in models. Our approach provides insight into the sources of individual heterogeneity in life histories, and can be applied to other data sets to examine the ubiquity of our results across the tree of life.     

The basic reproduction number for complex disease systems: defining R(0) for tick-borne infections

Characterizing the basic reproduction number, R(0), for many wildlife disease systems can seem a complex problem because several species are involved, because there are different epidemiological reactions to the infectious agent at different life-history stages, or because there are multiple transmission routes. Tick-borne diseases are an important example where all these complexities are brought together as a result of the peculiarities of the tick life cycle and the multiple transmission routes that occur. We show here that one can overcome these complexities by separating the host population into epidemiologically different types of individuals and constructing a matrix of reproduction numbers, the so-called next-generation matrix. Each matrix element is an expected number of infectious individuals of one type produced by a single infectious individual of a second type. The largest eigenvalue of the matrix characterizes the initial exponential growth or decline in numbers of infected individuals. Values below 1 therefore imply that the infection cannot establish. The biological interpretation closely matches that of R(0) for disease systems with only one type of individual and where infection is directly transmitted. The parameters defining each matrix element have a clear biological meaning. We illustrate the usefulness and power of the approach with a detailed examination of tick-borne diseases, and we use field and experimental data to parameterize the next-generation matrix for Lyme disease and tick-borne encephalitis. Sensitivity and elasticity analyses of the matrices, at the element and individual parameter levels, allow direct comparison of the two etiological agents. This provides further support that transmission between cofeeding ticks is critically important for the establishment of tick-borne encephalitis.     

Effects of early experience on the behaviour of yearling rhesus monkeys (Macaca mulatta) in the presence of a strange object: classification and correlation approaches

Special techniques are needed to help us understand the long-term effects of infants' experiences of their relationships with their mothers, especially when direct experimental control of the interaction between mother and young is impossible, or could distort their relationship. A classification approach is developed to show how outcomes in individuals can be predicted from their earlier experiences and characteristics. Four-week-old rhesus monkey infants' characteristic levels of enterprise persisted through their first year, but could be reduced in certain individuals who had been kept off their mothers by high rates of early maternal rejection. Correlational approaches are difficult to interpret when they fail to confirm simple effects of experience or of individual characteristics, because they are based on groups not individuals, and because certain individuals can affect the values of correlation coefficients in ways that cannot be specified without using a classification approach. The possible effects on correlation coefficients of inconsistent individuals, and of being unable to specify which infants respond in which ways to relevant variables were discussed.     

Latent multinomial models for extended batch-mark data

Batch marking is common and useful for many capture–recapture studies where individual marks cannot be applied due to various constraints such as timing, cost, or marking difficulty. When batch marks are used, observed data are not individual capture histories but a set of counts including the numbers of individuals first marked, marked individuals that are recaptured, and individuals captured but released without being marked (applicable to some studies) on each capture occasion. Fitting traditional capture–recapture models to such data requires one to identify all possible sets of capture–recapture histories that may lead to the observed data, which is computationally infeasible even for a small number of capture occasions. In this paper, we propose a latent multinomial model to deal with such data, where the observed vector of counts is a non-invertible linear transformation of a latent vector that follows a multinomial distribution depending on model parameters. The latent multinomial model can be fitted efficiently through a saddlepoint approximation based maximum likelihood approach. The model framework is very flexible and can be applied to data collected with different study designs. Simulation studies indicate that reliable estimation results are obtained for all parameters of the proposed model. We apply the model to analysis of golden mantella data collected using batch marks in Central Madagascar.     

Genotypes of Helicobacter pylori in Polish population

Here we have studied the genetic diversity of Helicobacter pylori strains recovered from 64 individual patients, 5 family members and 13 unsuccessfully treated patients. The recovered bacteria were finger-printed by the PCR-RFLP and RAPD methods and virulence associated loci (cagPAI, vacA) were PCR studied. Unique differentiation of every independently isolated strain from not-related persons was possible by RAPD technique. In PCR-RFLP technique several profile groups (7 and 15) for particular endonuclease tested were found. Eleven patients carried strains of the same gene profile (PCR-RFLP) and the same overall genotype (RAPD) before and after therapy. In the family studies, essentially the same strain was found in different relatives in three cases, and different strains were found in the other two cases. Island of cagPAI was present in 79% of all strains tested, half and one-fifth of all strains tested presented, s1am2 and s1m1 alleles of vacA gene, respectively. Independently from identity or diversity of pre- and post-treatment strains and strains recovered from the family members we have been observed identical cagPAI/vacA genotypes. These results suggest that H. pylori infections in Poland can be mixed, although just one strain may often predominate, and that inter-family transmission may be significant even in this high risk society. The genetic feature of virulence-associated loci are similar to those seen elsewhere in Europe, although strains that carry the cagPAI and the potentially more toxigenic alleles of the vacA gene are more common. RAPD technique is proven as most differentiating, however PCR-RFLP allows for easy recognition of mixed infection with two or more different strains. Molecular typing study in case of children therapy may allow reduce rate of relapses by reduction of possible transmission from family source.     

Estimating the number of genes in a polygenic system by genotype assay.

A new method, genotype assay, is described for estimating k the number of genes or more strictly the number of effective factors responsible for variation of a continuous kind. The central feature is the determination of the proportion of individuals in the Fn generation of a cross between two pure breeding lines that are heterozygous at, at least, one locus by an assay of their Fn+2 grand progeny families. The observed proportion is then equated to a theoretical expectation which is a function of the number of genes involved. Expectations generalised to cover any generation n for experimental designs in which every Fn individual is assayed by comparing two Fn+2 grand progeny families have been derived for two limiting cases; one in which all genotypic differences are expressed as phenotypic differences and the other where the expression is minimised by imposing the maximum and relational balancing out of the contributions of individual gene loci. Equating the observed proportion of heterozygotes to these expectations therefore, leads to an upper and a lower estimate of k corresponding with these two limiting conditions. The reliability and sensitivity of the estimates depends primarily on n the generation chosen for study, the number of individuals (m) assayed from that generation and the number of individuals (l) raised in each Fn+2 grand progeny family. The two variables m and l being the principal determinants of the variances of the family means set the lower limit to the size of the gene effects that can be detected. The method is illustrated by assays of the F3 and F5 generations of two crosses between conditioned lines of Nicotiana rustica for three characters. The estimates are, without exception, as great as or greater than those obtained by alternative procedures. They show large, consistent increases between the F3 and F5 that cannot be traced to greater sensitivity of the latter generation and hence are presumably genuine.     

Simultaneous estimation of mortality and dispersal rates of an artificially released population

Mark-recapture methods cannot estimate both mortality and dispersal rates of a wild population simultaneously. However, when an artificially cultured population is released into an area, the initial population size and the initial population distribution are usually known. If artificially cultured individuals are released with marks or distinguished from wild individuals or if no wild individual exists in the study area, we can estimate both the mortality and dispersal rates of the artificial population. The numbers of dispersed and dead individuals are estimated from the dispersal rate from the diffusion model and the total decreasing rate estimated from a mark-recapture data. We can estimate both the time-dependent and time-independent dispersal rates from the data. We choose the best fit model that has the smallest value of Akaike's Information Criteria. We also consider ‘concentric circles approximation” of spatial distribution, in which the cumulative and frequency distributions are analytically obtained.     

A competitive coexistence principle?

Competitive exclusion – n species cannot coexist on fewer than n limiting resources in a constant and isolated environment – has been a central ecological principle for the past century. Since empirical studies cannot universally demonstrate exclusion, this principle has mainly relied on mathematical proofs. Here we investigate the predictions of a new approach to derive functional responses in consumer/resource systems. Models usually describe the temporal dynamics of consumer/resource systems at a macroscopic level – i.e. at the population level. Each model may be pictured as one time-dependent macroscopic trajectory. Each macroscopic trajectory is, however, the product of many individual fates and from combinatorial considerations can be realized in many different ways at the microscopic – or individual – level. Recently it has been shown that, in systems with large enough numbers of consumer individuals and resource items, one macroscopic trajectory can be realized in many more ways than any other at the individual – or microscopic – level. Therefore, if the temporal dynamics of an ecosystem are assumed to be the outcome of only statistical mechanics – that is, chance – a single trajectory is near-certain and can be described by deterministic equations. We argue that these equations can serve as a null to model consumer-resource dynamics, and show that any number of species can coexist on a single resource in a constant, isolated environment. Competition may result in relative rarity, which may entail exclusion in finite samples of discrete individuals, but exclusion is not systematic. Beyond the coexistence/exclusion outcome, our model also predicts that the relative abundance of any two species depends simply on the ratio of their competitive abilities as computed from – and only from – their intrinsic kinetic and stoichiometric parameters.     

Analysing censored data in agricultural research: A review with examples and software tips

Metric data are usually assessed on a continuous scale with good precision, but sometimes agricultural researchers cannot obtain precise measurements of a variable. Values of such a variable cannot then be expressed as real numbers (e.g., 1.51 or 2.56), but often can be represented by intervals into which the values fall (e.g., from 1 to 2 or from 2 to 3). In this situation, statisticians talk about censoring and censored data, as opposed to missing data, where no information is available at all. Traditionally, in agriculture and biology, three methods have been used to analyse such data: (a) when intervals are narrow, some form of imputation (e.g., mid‐point imputation) is used to replace the interval and traditional methods for continuous data are employed (such as analyses of variance [ANOVA] and regression); (b) for time‐to‐event data, the cumulative proportions of individuals that experienced the event of interest are analysed, instead of the individual observed times‐to‐event; (c) when intervals are wide and many individuals are collected, non‐parametric methods of data analysis are favoured, where counts are considered instead of the individual observed value for each sample element. In this paper, we show that these methods may be suboptimal: The first one does not respect the process of data collection, the second leads to unreliable standard errors (SEs), while the third does not make full use of all the available information. As an alternative, methods of survival analysis for censored data can be useful, leading to reliable inferences and sound hypotheses testing. These methods are illustrated using three examples from plant and crop sciences.     

Optimum spacing of genetic markers for determining linkage between marker loci and quantitative trait loci

The cost of experiments aimed at determining linkage between marker loci and quantitative trait loci (QTL) was investigated as a function of marker spacing and number of individuals scored. It was found that for a variety of experimental designs, fairly wide marker spacings (ca. 50 cM) are optimum or close to optimum for initial studies of marker-QTL linkage, in the sense of minimizing overall cost of the experiment. Thus, even when large numbers of more or less evenly spaced markers are available, it will not always be cost effective to make full utilization of this capacity. This is particularly true when costs of rearing and trait evaluation per individual scored are low, as when marker data are obtained on individuals raised and evaluated for quantitative traits as part of existing programs. When costs of rearing and trait evaluation per individual scored are high, however, as in human family data collection carried out primarily for subsequent marker — QTL analyses, or when plants or animals are raised specifically for purposes of marker — QTL linkage experiments, optimum spacing may be rather narrow. It is noteworthy that when marginal costs of additional markers or individuals are constant, total resources allocated to a given experiment will determine total number of individuals sampled, but not the optimal marker spacing.     

Managing Disease Risks from Trade: Strategic Behavior with Many Choices and Price Effects

An individual’s infectious disease risks, and hence the individual’s incentives for risk mitigation, may be influenced by others’ risk management choices. If so, then there will be strategic interactions among individuals, whereby each makes his or her own risk management decisions based, at least in part, on the expected decisions of others. Prior work has shown that multiple equilibria could arise in this setting, with one equilibrium being a coordination failure in which individuals make too few investments in protection. However, these results are largely based on simplified models involving a single management choice and fixed prices that may influence risk management incentives. Relaxing these assumptions, we find strategic interactions influence, and are influenced by, choices involving multiple management options and market price effects. In particular, we find these features can reduce or eliminate concerns about multiple equilibria and coordination failure. This has important policy implications relative to simpler models.     

Maximizing gain per effort by using clonal replicates in genetic tests

Summary Models for predicting cummulative genetic gain from recurrent selection applicable to predominantly outcrossing plant species are derived to include the effect of observations on clonal replicates (ramets) in addition to observations on individuals and family means. Such models are discussed with special reference to forest trees. The consequence of redistributing effort from individuals to ramets is investigated for several conditions with a fixed number of families and fixed total test size. Factors that affect the distribution of variance among sources and factors that affect individual selection intensity are the primary determinants of the optimum distribution of effort. The optimum number of ramets ranged from 1 to 6 for the conditions tested and the efficiency of redistribution (ratio of gain for the optimum distribution to the gain for the single-ramet, or non-clonal case) ranged from 1.00 to 1.20. Using clonal replicates in genetic tests usually results in increased cummulative genetic gain relative to non-clonal tests, without an increase in test effort.     

Mixed-Effects Modelling of Scale Growth Profiles Predicts the Occurrence of Early and Late Fish Migrants

Fish growth is commonly used as a proxy for fitness but this is only valid if individual growth variation can be interpreted in relation to conspecifics'' performance. Unfortunately, assessing individual variation in growth rates is problematic under natural conditions because subjects typically need to be marked, repeated measurements of body size are difficult to obtain in the field, and recaptures may be limited to a few time events which will generally vary among individuals. The analysis of consecutive growth rings (circuli) found on scales and other hard structures offers an alternative to mark and recapture for examining individual growth variation in fish and other aquatic vertebrates where growth rings can be visualized, but accounting for autocorrelations and seasonal growth stanzas has proved challenging. Here we show how mixed-effects modelling of scale growth increments (inter-circuli spacing) can be used to reconstruct the growth trajectories of sea trout (Salmo trutta) and correctly classify 89% of individuals into early or late seaward migrants (smolts). Early migrants grew faster than late migrants during their first year of life in freshwater in two natural populations, suggesting that migration into the sea was triggered by ontogenetic (intrinsic) drivers, rather than by competition with conspecifics. Our study highlights the profound effects that early growth can have on age at migration of a paradigmatic fish migrant and illustrates how the analysis of inter-circuli spacing can be used to reconstruct the detailed growth of individuals when these cannot be marked or are only caught once.     

Social living mitigates the costs of a chronic illness in a cooperative carnivore

Infection risk is assumed to increase with social group size, and thus be a cost of group living. We assess infection risk and costs with respect to group size using data from an epidemic of sarcoptic mange (Sarcoptes scabiei) among grey wolves (Canis lupus). We demonstrate that group size does not predict infection risk and that individual costs of infection, in terms of reduced survival, can be entirely offset by having sufficient numbers of pack‐mates. Infected individuals experience increased mortality hazards with increasing proportions of infected pack‐mates, but healthy individuals remain unaffected. The social support of group hunting and territory defence are two possible mechanisms mediating infection costs. This is likely a common phenomenon among other social species and chronic infections, but difficult to detect in systems where infection status cannot be measured continuously over time.     

Evolution of cooperation: cooperation defeats defection in the cornfield model

"Cooperation" defines any behavior that enhances the fitness of a group (e.g. a community or species), but which, by its nature, can be exploited by selfish individuals, meaning, firstly, that selfish individuals derive an advantage from exploitation which is greater than the average advantage that accrues to unselfish individuals. Secondly, exploitation has no intrinsic fitness value except in the presence of the "cooperative behavior". The mathematics is described by the simple Prisoner's Dilemma Game (PDG). It has previously been shown that koinophilia (the avoidance of sexual mates displaying unusual or atypical phenotypic features, such as mutations) stabilizes any inherited strategy in the simple or iterated PDG, meaning that it cannot be displaced by rare forms of alternative behavior which arise through mutation or occasional migration. In the present model equal numbers of cooperators and defectors (in the simple PDG) were randomly spread in a two-dimensional "cornfield" with uniformly distributed resources. Every individual was koinophilic, and interacted (sexually and in the PDG tournaments) only with individuals from within its immediate neighborhood. This model therefore tested whether cooperation can outcompete defection or selfishness in a straight, initially equally matched, evolutionary battle. The results show that in the absence of koinophilia cooperation was rapidly driven to extinction. With koinophilia there was a very rapid loss of cooperators in the first few generations, but thereafter cooperation slowly spread, ultimately eliminating defection completely. This result was critically dependent on sampling effects of neighborhoods. Small samples (resulting from low population densities or small neighborhood sizes) increase the probability that a chance neighborhood comes to consist predominantly of cooperators. A sexual preference for the most common phenotype in the neighborhood then makes that phenotype more common still. Once this occurs cooperation's spread becomes almost inevitable.     

Close relatives in population samples: Evaluation of the consequences for genetic stock identification

Determining the origin of individuals in mixed population samples is key in many ecological, conservation and management contexts. Genetic data can be analyzed using genetic stock identification (GSI), where the origin of single individuals is determined using Individual Assignment (IA) and population proportions are estimated with Mixed Stock Analysis (MSA). In such analyses, allele frequencies in a reference baseline are required. Unknown individuals or mixture proportions are assigned to source populations based on the likelihood that their multilocus genotypes occur in a particular baseline sample. Representative sampling of populations included in a baseline is important when designing and performing GSI. Here, we investigate the effects of family sampling on GSI, using both simulated and empirical genotypes for Atlantic salmon (Salmo salar). We show that nonrepresentative sampling leading to inclusion of close relatives in a reference baseline may introduce bias in estimated proportions of contributing populations in a mixed sample, and increases the amount of incorrectly assigned individual fish. Simulated data further show that the induced bias increases with increasing family structure, but that it can be partly mitigated by increased baseline population sample sizes. Results from standard accuracy tests of GSI (using only a reference baseline and/or self‐assignment) gave a false and elevated indication of the baseline power and accuracy to identify stock proportions and individuals. These findings suggest that family structure in baseline population samples should be quantified and its consequences evaluated, before carrying out GSI.     

Individually Unique Body Color Patterns in Octopus (Wunderpus photogenicus) Allow for Photoidentification

Studies on the longevity and migration patterns of wild animals rely heavily on the ability to track individual adults. Non-extractive sampling methods are particularly important when monitoring animals that are commercially important to ecotourism, and/or are rare. The use of unique body patterns to recognize and track individual vertebrates is well-established, but not common in ecological studies of invertebrates. Here we provide a method for identifying individual Wunderpus photogenicus using unique body color patterns. This charismatic tropical octopus is commercially important to the underwater photography, dive tourism, and home aquarium trades, but is yet to be monitored in the wild. Among the adults examined closely, the configurations of fixed white markings on the dorsal mantle were found to be unique. In two animals kept in aquaria, these fixed markings were found not to change over time. We believe another individual was photographed twice in the wild, two months apart. When presented with multiple images of W. photogenicus, volunteer observers reliably matched photographs of the same individuals. Given the popularity of W. photogenicus among underwater photographers, and the ease with which volunteers can correctly identify individuals, photo-identification appears to be a practical means to monitor individuals in the wild.     

Using pooled data to estimate variance components and breeding values for traits affected by social interactions

Background

Through social interactions, individuals affect one another’s phenotype. In such cases, an individual’s phenotype is affected by the direct (genetic) effect of the individual itself and the indirect (genetic) effects of the group mates. Using data on individual phenotypes, direct and indirect genetic (co)variances can be estimated. Together, they compose the total genetic variance that determines a population’s potential to respond to selection. However, it can be difficult or expensive to obtain individual phenotypes. Phenotypes on traits such as egg production and feed intake are, therefore, often collected on group level. In this study, we investigated whether direct, indirect and total genetic variances, and breeding values can be estimated from pooled data (pooled by group). In addition, we determined the optimal group composition, i.e. the optimal number of families represented in a group to minimise the standard error of the estimates.

Methods

This study was performed in three steps. First, all research questions were answered by theoretical derivations. Second, a simulation study was conducted to investigate the estimation of variance components and optimal group composition. Third, individual and pooled survival records on 12 944 purebred laying hens were analysed to investigate the estimation of breeding values and response to selection.

Results

Through theoretical derivations and simulations, we showed that the total genetic variance can be estimated from pooled data, but the underlying direct and indirect genetic (co)variances cannot. Moreover, we showed that the most accurate estimates are obtained when group members belong to the same family. Additional theoretical derivations and data analyses on survival records showed that the total genetic variance and breeding values can be estimated from pooled data. Moreover, the correlation between the estimated total breeding values obtained from individual and pooled data was surprisingly close to one. This indicates that, for survival in purebred laying hens, loss in response to selection will be small when using pooled instead of individual data.

Conclusions

Using pooled data, the total genetic variance and breeding values can be estimated, but the underlying genetic components cannot. The most accurate estimates are obtained when group members belong to the same family.