Estimation of a Nonlinear Density-Dependence Parameter for Wild Turkey

Abstract: Although previous research and theory has suggested that wild turkey (Meleagris gallopavo) populations may be subject to some form of density dependence, there has been no effort to estimate and incorporate a density-dependence parameter into wild turkey population models. To estimate a functional relationship for density dependence in wild turkey, we analyzed a set of harvest-index time series from 11 state wildlife agencies. We tested for lagged correlations between annual harvest indices using partial autocorrelation analysis. We assessed the ability of the density-dependent theta-Ricker model to explain harvest indices over time relative to exponential or random walk growth models. We tested the homogeneity of the density-dependence parameter estimates (θ) from 3 different harvest indices (spring harvest no. reported harvest/effort, survey harvest/effort) and calculated a weighted average based on each estimate's variance and its estimated covariance with the other indices. To estimate the potential bias in parameter estimates from measurement error, we conducted a simulation study using the theta-Ricker with known values and lognormally distributed measurement error. Partial autocorrelation function analysis indicated that harvest indices were significantly correlated only with their value at the previous time step. The theta-Ricker model performed better than the exponential growth or random walk models for all 3 indices. Simulation of known parameters and measurement error indicated a strong positive upward bias in the density-dependent parameter estimate, with increasing measurement error. The average density-dependence estimate, corrected for measurement error ranged 0.25 ≤ θC ≤ 0.49, depending on the amount of measurement error and assumed spring harvest rate. We infer that density dependence is nonlinear in wild turkey, where growth rates are maximized at 39-42% of carrying capacity. The annual yield produced by density-dependent population growth will tend to be less than that caused by extrinsic environmental factors. This study indicates that both density-dependent and density-independent processes are important to wild turkey population growth, and we make initial suggestions on incorporating both into harvest management strategies.     

A Multivariate Method for the Parameter Estimation in Biorhythms

A suitable multivariate method is described for the periodic observations of a group of individuals having comparable periods and amplitudes. Simultaneous confidence region can be obtained for the parameters of the group as a whole instead of an individual. The study of periodic behaviour of a group is more realistic than the study of the behaviour of an individual. An application of human leucocyte counts in microfilariasis (W. bancrofti) infection has been described.     

Novel Growth Regime of MDCK II Model Tissues on Soft Substrates

It is well established that MDCK II cells grow in circular colonies that densify until contact inhibition takes place. Here, we show that this behavior is only typical for colonies developing on hard substrates and report a new growth phase of MDCK II cells on soft gels. At the onset, the new phase is characterized by small, three-dimensional droplets of cells attached to the substrate. When the contact area between the agglomerate and the substrate becomes sufficiently large, a very dense monolayer nucleates in the center of the colony. This monolayer, surrounded by a belt of three-dimensionally packed cells, has a well-defined structure, independent of time and cluster size, as well as a density that is twice the steady-state density found on hard substrates. To release stress in such dense packing, extrusions of viable cells take place several days after seeding. The extruded cells create second-generation clusters, as evidenced by an archipelago of aggregates found in a vicinity of mother colonies, which points to a mechanically regulated migratory behavior.     

Novel Growth Regime of MDCK II Model Tissues on Soft Substrates

It is well established that MDCK II cells grow in circular colonies that densify until contact inhibition takes place. Here, we show that this behavior is only typical for colonies developing on hard substrates and report a new growth phase of MDCK II cells on soft gels. At the onset, the new phase is characterized by small, three-dimensional droplets of cells attached to the substrate. When the contact area between the agglomerate and the substrate becomes sufficiently large, a very dense monolayer nucleates in the center of the colony. This monolayer, surrounded by a belt of three-dimensionally packed cells, has a well-defined structure, independent of time and cluster size, as well as a density that is twice the steady-state density found on hard substrates. To release stress in such dense packing, extrusions of viable cells take place several days after seeding. The extruded cells create second-generation clusters, as evidenced by an archipelago of aggregates found in a vicinity of mother colonies, which points to a mechanically regulated migratory behavior.Studying the growth of cell colonies is an important step in the understanding of processes involving coordinated cell behavior such as tissue development, wound healing, and cancer progression. Apart from extremely challenging in vivo studies, artificial tissue models are proven to be very useful in determining the main physical factors that affect the cooperativity of cells, simply because the conditions of growth can be very well controlled. One of the most established cell types in this field of research is the Madin-Darby canine kidney epithelial cell (MDCK), originating from the kidney distal tube (1). A great advantage of this polarized epithelial cell line is that it retained the ability for contact inhibition (2), which makes it a perfect model system for studies of epithelial morphogenesis.Organization of MDCK cells in colonies have been studied in a number of circumstances. For example, it was shown that in three-dimensional soft Matrigel, MDCK cells form a spherical enclosure of a lumen that is enfolded by one layer of polarized cells with an apical membrane exposed to the lumen side (3). These structures can be altered by introducing the hepatocyte growth factor, which induces the formation of linear tubes (4). However, the best-studied regime of growth is performed on two-dimensional surfaces where MDCK II cells form sheets and exhibit contact inhibition. Consequently, the obtained monolayers are well characterized in context of development (5), mechanical properties (6), and obstructed cell migration (7–9).Surprisingly, in the context of mechanics, several studies of monolayer formation showed that different rigidities of polydimethylsiloxane gels (5) and polyacrylamide (PA) gels (9) do not influence the nature of monolayer formation nor the attainable steady-state density. This is supposedly due to long-range forces between cells transmitted by the underlying elastic substrate (9). These results were found to agree well with earlier works on bovine aortic endothelial cells (10) and vascular smooth muscle cells (11), both reporting a lack of sensitivity of monolayers to substrate elasticity. Yet, these results are in stark contrast with single-cell experiments (12–15) that show a clear response of cell morphology, focal adhesions, and cytoskeleton organization to substrate elasticity. Furthermore, sensitivity to the presence of growth factors that are dependent on the elasticity of the substrate in two (16) and three dimensions (4) makes this result even more astonishing. Therefore, we readdress the issue of sensitivity of tissues to the elasticity of the underlying substrate and show that sufficiently soft gels induce a clearly different tissue organization.We plated MDCK II cells on soft PA gels (Young’s modulus E = 0.6 ± 0.2 kPa), harder PA gels (E = 5, 11, 20, 34 kPa), and glass, all coated with Collagen-I. Gels were prepared following the procedure described in Rehfeldt et al. (17); rigidity and homogeneity of the gels was confirmed by bulk and microrheology (see the Supporting Material for comparison). Seeding of MDCK II cells involved a highly concentrated solution dropped in the middle of a hydrated gel or glass sample. For single-cell experiments, cells were dispersed over the entire dish. Samples were periodically fixed up to Day 12, stained for nuclei and actin, and imaged with an epifluorescence microscope. Details are described in the Supporting Material.On hard substrates and glass it was found previously that the area of small clusters expands exponentially until the movement of the edge cannot keep up with the proliferation in the bulk (5). Consequently, the bulk density increases toward the steady state, whereas the density of the edge remains low. At the same time, the colony size grows subexponentially (5). This is what we denote “the classical regime of growth”. Our experiments support these observations for substrates with E ≥ 5 kPa. Specifically, on glass, colonies start as small clusters of very low density of 700 ± 200 cells/mm² (Fig. 1, A and B), typically surrounded by a strong actin cable (Fig. 1, B and C). Interestingly, the spreading area of single cells (Fig. 1 A) on glass was found to be significantly larger, i.e., (2.0 ± 0.9) × 10⁻³ mm². After Day 4 (corresponding cluster area of 600 ± 100 mm²), the density in the center of the colony reached the steady state with 6,800 ± 500 cells/mm², whereas the mean density of the edge profile grew to 4,000 ± 500 cells/mm². This density was retained until Day 12 (cluster area 1800 ± 100 mm²), which is in agreement with previous work (9).Open in a separate windowFigure 1Early phase of cluster growth on hard substrates. (A) Well-spread single cells, and small clusters with a visible actin cable 6 h after seeding. (B) Within one day, clusters densify and merge, making small colonies. (C) Edge of clusters from panel B.In colonies grown on 0.6 kPa gels, however, we encounter a very different growth scenario. The average spreading area of single cells is (0.34 ± 0.3) × 10⁻³ mm², which is six times smaller than on glass substrates (Fig. 2 A). Clusters of only few cells show that cells have a preference for cell-cell contacts (a well-established flat contact zone can be seen at the cell-cell interface in Fig. 2 A) rather than for cell-substrate contacts (contact zone is diffusive and the shape of the cells appears curved). The same conclusion emerges from the fact that dropletlike agglomerates, resting on the substrate, form spontaneously (Fig. 2 A), and that attempts to seed one single cluster of 90,000 cells fail, resulting in a number of three-dimensional colonies (Fig. 2 A). When the contact area with the substrate exceeds 4.7 × 10⁻³ mm², a monolayer appears in the center of such colonies (Fig. 2 B). The colonies can merge, and if individual colonies are small, the collapse into a single domain is associated with the formation of transient irregular structures (Fig. 2 B). Ultimately, large elliptical colonies (average major/minor axis of e = 1.8 ± 0.6) with a smooth edge are formed (Fig. 2 C), unlike on hard substrates where circular clusters (e = 1.06 ± 0.06) with a ragged edge comprise the characteristic phenotype.Open in a separate windowFigure 2Early phase of cluster growth on soft substrates. (A) Twelve hours after seeding, single cells remain mostly round and small. They are found as individual, or within small, three-dimensional structures (top). The latter nucleate a monolayer in their center (bottom), if the contact area with the substrate exceeds ∼5 × 10⁻³ mm². (B) Irregularly-shaped clusters appear due to merging of smaller droplets. A stable monolayer surrounded by a three-dimensional belt of densely packed cells is clearly visible, even in larger structures. (C) All colonies are recorded on Day 4.Irrespective of cluster size, in the new regime of growth, the internal structure is built of two compartments (Fig. 2 B):

• 1.The first is the edge (0.019 ± 0.05-mm wide), a three-dimensional structure of densely packed cells. This belt is a signature of the new regime because on hard substrates the edge is strictly two-dimensional (Fig. 1 C).
• 2.The other is the centrally placed monolayer with a spatially constant density that is very weakly dependent on cluster size and age (Fig. 3). The mean monolayer density is 13,000 ± 2,000 cells/mm², which is an average over 130 clusters that are up to 12 days old and have a size in the range of 10⁻³ to 10 mm², each shown by a data point in Fig. 3. This density is twice the steady-state density of the bulk tissue in the classical regime of growth.Open in a separate windowFigure 3Monolayer densities in colonies grown on 0.6 kPa substrates, as a function of the cluster size and age. Each cluster is represented by a single data point signifying its mean monolayer density. (Black lines) Bulk and (red dashed lines) edge of steady-state densities from monolayers grown on glass substrates. Error bars are omitted for clarity, but are discussed in the Supporting Material.

Until Day 4, the monolayer is very homogeneous, showing a nearly hexagonal arrangement of cells. From Day 4, however, defects start to appear in the form of small holes (typical size of (0.3 ± 0.1) × 10⁻³ mm²). These could be attributed to the extrusions of viable cells, from either the belt or areas of increased local density in the monolayer (inset in Fig. 4). This suggests that extrusions serve to release stress built in the tissue, and, as a consequence, the overall density is decreased.Open in a separate windowFigure 4Cell nuclei within the mother colony and in the neighboring archipelago of second-generation clusters grown on 0.6 kPa gels at Day 12. (Inset; scale bar = 10 μm) Scar in the tissue, a result of a cell-extrusion event. (Main image; scale bar = 100 μm) From the image of cell nuclei (left), it is clear that there are no cells within the scar, whereas the image of actin (right) shows that the cytoplasm of the cells at the edge has closed the hole.Previous reports suggest that isolated MDCK cells undergo anoikis 8 h after losing contact with their neighbors (18). However, in this case, it appears that instead of dying, the extruded cells create new colonies, which can be seen as an archipelago surrounding the mother cluster (Fig. 4). The viability of off-cast cells is further evidenced by the appearance of single cells and second-generation colonies with sizes varying over five orders of magnitude, from Day 4 until the end of the experiment, Day 12. Importantly, no morphological differences were found in the first- and second-generation colonies.In conclusion, we show what we believe to be a novel phase of growth of MDCK model tissue on soft PA gels (E = 0.6 kPa) that, to our knowledge, despite previous similar efforts (9), has not been observed before. This finding is especially interesting in the context of elasticity of real kidneys, for which a Young’s modulus has been found to be between 0.05 and 5 kPa (19,20). This coincides with the elasticity of substrates studied herein, and opens the possibility that the newly found phase of growth has a particular biological relevance. Likewise, the ability to extrude viable cells may point to a new migratory pathway regulated mechanically by the stresses in the tissue, the implication of which we hope to investigate in the future.     

Experimental Parameter Estimation Method for Nonlinear Viscoelastic Composite Material Models: An Application on Arterial Tissue

This study is aimed at setting a method of experimental parameter estimation for large-deforming nonlinear viscoelastic continuous fibre-reinforced composite material model. Specifically, arterial tissue was investigated during experimental research and parameter estimation studies, due to medical, scientific and socio-economic importance of soft tissue research. Using analytical formulations for specimens under combined inflation/extension/torsion on thick-walled cylindrical tubes, in vitro experiments were carried out with fresh sheep arterial segments, and parameter estimation procedures were carried out on experimental data. Model restrictions were pointed out using outcomes from parameter estimation. Needs for further studies that can be developed are discussed.     

An Improved Parameter Estimation Method for Hodgkin-Huxley Models

We consider whole-cell voltage-clamp data of isolated currents characterized by the Hodgkin-Huxley paradigm. We examine the errors associated with the typical parameter estimation method for these data and show them to be unsatisfactorally large especially if the time constants of activation and inactivation are not sufficiently separated. The size of these errors is due to the fact that the steady-state and kinetic properties of the current are estimated disjointly. We present an improved parameter estimation method that utilizes all of the information in the voltage-clamp conductance data to estimate steady-state and kinetic properties simultaneously and illustrate its success compared to the standard method using simulated data and data from P. interruptus shal channels expressed in oocytes.     

A New Method Using Hexamethyldisilazane for Preparation of Soft Insect Tissues for Scanning Electron Microscopy

A new rapid procedure for preparing soft internal tissues from insects that allows air drying was found to compare favorably with tissues prepared by critical point drying. In the new procedure, tissues were fixed in 1% glutaraldehyde, dehydrated through a graded ethanol series, immersed in hexamethyldisilazane (HMDS) for 5 minutes, and air dried. Tissues prepared by both the HMDS treatment and by critical point drying were coated with gold for scanning electron microscopy. Tissues prepared by the HMDS treatment did not shrink or distort upon air drying and excellent surface detail was preserved. The HMDS treatment required about 5 minutes, whereas the critical point drying procedure required about 1.5 hours.     

A New Method for the Analysis of Soft Tissues with Data Acquired under Field Conditions

Analyzing soft-tissue structures is particularly challenging due to the lack of homologous landmarks that can be reliably identified across time and specimens. This is particularly true when data are to be collected under field conditions. Here, we present a method that combines photogrammetric techniques and geometric morphometrics methods (GMM) to quantify soft tissues for their subsequent volumetric analysis. We combine previously developed methods for landmark data acquisition and processing with a custom program for volumetric computations. Photogrammetric methods are a particularly powerful tool for field studies as they allow for image acquisition with minimal equipment requirements and for the acquisition of the spatial coordinates of points (anatomical landmarks or others) from these images. For our method, a limited number of homologous landmarks, i.e., points that can be found on any specimen independent of space and time, and further distinctive points, which may vary over time, space and subject, are identified on two-dimensional photographs and their three-dimensional coordinates estimated using photogrammetric methods. The three-dimensional configurations are oriented by the spatial principal components (PCs) of the homologous points. Crucially, this last step orients the configuration such that x and y-information (PC1 and PC2 coordinates) constitute an anatomically-defined plane with the z-values (PC3 coordinate) in the direction of interest for volume computation. The z-coordinates are then used to estimate the volume of the tissue. We validate our method using a physical, geometric model of known dimensions and physical (wax) models designed to approximate perineal swellings in female macaques. To demonstrate the usefulness and potential of our method, we use it to estimate the volumes of Barbary macaque sexual swellings recorded in the field with video images. By analyzing both the artificial data and real monkey swellings, we validate our method''s accuracy and illustrate its potential for application in important areas of biological research.     

A Simple Method of Transferring Tissues

It is a common practice among histologists while preparing tissues for sectioning to transfer the tissues from one reagent to another by means of small forceps or a spatula. This method can be used safely when the type of tissue being studied is of such a nature that it will not be injured by these operations. When, however, the tissue is fragile, extreme care must be exercised, if the above method is employed, to prevent damage. In a recent study of maturation and and fertilization of the hen's egg, difficulty was experienced due to breakage of blastodiscs while transferring them from one reagent to another. In order to reduce the chances of damage and to facilitate and simplify the operation of transferring these fragile tissues, the tissue carrier described in the following paragraph was designed.     

Novel Approach to Nonlinear PID Parameter Optimization Using Ant Colony Optimization Algorithm

This paper presents an application of an Ant Colony Optimization （ACO） algorithm to optimize the parameters in the design of a type of nonlinear PID controller. The ACO algorithm is a novel heuristic bionic algorithm, which is based on the behaviour of real ants in nature searching for food. In order to optimize the parameters of the nonlinear PID controller using ACO algorithm, an objective function based on position tracing error was constructed, and elitist strategy was adopted in the improved ACO algorithm. Detailed simulation steps are presented. This nonlinear PID controller using the ACO algorithm has high precision of control and quick response.     

A General Nonlinear Least Squares Data Reconciliation and Estimation Method for Material Flow Analysis

The extraction, transformation, use, and disposal of materials can be represented by directed, weighted networks, known in the material flow analysis (MFA) community as Sankey or flow diagrams. However, the construction of such networks is dependent on data that are often scarce, conflicting, or do not directly map onto a Sankey diagram. By formalizing the forms of data entry, a nonlinear constrained optimization program for data estimation and reconciliation can be formulated for reconciling data sets for MFA problems where data are scarce, in conflict, do not directly map onto a Sankey diagram, and are of variable quality. This method is demonstrated by reanalyzing an existing MFA of global steel flows, and the resulting analytical solution measurably improves upon their manual solution.     

Structure and Stress-Strain Relationship of Soft Tissues

The mechanical properties of a soft tissue are related to itsstructure. Weshall illustrate this by the properties of thearteries and the lung. Viscoelasticity, strain rate effects,pseudo-elasticity, and constitutive equations ar discussed.The mecahnical properties of an organ is, however, not onlybased onthe tissues of the organ, but also on its geometry andrelationship to the neighboring organs. A typical example isthe blood vessel. The capillary blood vessels of the mesenteryare "rigid"; those in the bat's wing are "distensible"; whereasthe capillaries of the lung are "sheet" like: rigid in one plane,and compliant in another. The stress-strain relationship ofthe systemic arteries is highly nonlinear, stiffening exponentiallywith increasing strains; yet that of the pulmonary arteriesin the lung is linear. The systemic veins are easily collapsible;yet the pulmonary veins in the lung are not: they remain patentwhen the blood pressure falls below the alveolargas pressure.The explanation of these differences lies in the varied interactionsbetween the blood vessels and the surrounding tissues in differentorgans. The implications of these differences on blood circulationare pointed out. Therole of ultrastructure is discussed.     

An S-System Parameter Estimation Method (SPEM) for biological networks

Advances in experimental biology, coupled with advances in computational power, bring new challenges to the interdisciplinary field of computational biology. One such broad challenge lies in the reverse engineering of gene networks, and goes from determining the structure of static networks, to reconstructing the dynamics of interactions from time series data. Here, we focus our attention on the latter area, and in particular, on parameterizing a dynamic network of oriented interactions between genes. By basing the parameterizing approach on a known power-law relationship model between connected genes (S-system), we are able to account for non-linearity in the network, without compromising the ability to analyze network characteristics. In this article, we introduce the S-System Parameter Estimation Method (SPEM). SPEM, a freely available R software package (http://www.picb.ac.cn/ClinicalGenomicNTW/temp3.html), takes gene expression data in time series and returns the network of interactions as a set of differential equations. The methods, which are presented and tested here, are shown to provide accurate results not only on synthetic data, but more importantly on real and therefore noisy by nature, biological data. In summary, SPEM shows high sensitivity and positive predicted values, as well as free availability and expansibility (because based on open source software). We expect these characteristics to make it a useful and broadly applicable software in the challenging reconstruction of dynamic gene networks.