Fungal entomopathogens: new insights on their ecology

TL;DR: The recently discovered roles played by many entomopathogenic fungi are reviewed and new research strategies focused on alternate uses for these fungi are proposed.

About: This article is published in Fungal Ecology.The article was published on 2009-11-01 and is currently open access. It has received 497 citations till now.

Summary

1 Introduction

• Traffic assignment models describe the way in which the transportation demands flow through a given network.
• ∗Partially supported by ECOS-Conicyt program under grant No. C00E05 †Université de Paris I. ‡Departamento de Ingenieŕıa Matemática and Centro de Modelamiento Matemático, Universidad de Chile.
• The latter was formulated in the high dimensional space of route flows and the method of successive averages was proposed as a practical numerical scheme.

2 Deterministic traffic equilibrium

• Let G = (N, A) be a directed graph representing a traffic network, and D ⊆ N a set of destinations.
• Given the demands gdi ≥ 0 from each node i = d to each destination d ∈ D, a traffic assignment model seeks to predict how these demands flow throughout the network.
• The authors loosely refer to w∗ as being “the” equilibrium flow.

2.1 Arc-flow formulation

• As the number of paths is usually very large, the formulation (PH) is computationally inefficient.
• Not all elements in V are of this form since the latter allows flow along cycles which may be forbidden in H.
• Any such decomposition gives an equilibrium and, conversely, every equilibrium is of this form.

2.2 Dual formulation

• The main point when computing a traffic equilibrium is then to find the optimal arc-flow vector w∗.
• For the sake of completeness the authors provide a short proof of the equivalence.
• The dual variables are the arc travel times ta for a ∈ A and the time-to-destination variables τdi for d ∈ D and i = d.
• The existence of optimal solutions for (D) follows by proceeding in the other direction: take (w∗, v) optimal for (PV ) and let ta and τdi be corresponding multipliers.

3 Markovian traffic equilibrium

• A critical assumption in the deterministic model is the fact that all users perceive the same costs cr. Now, the difficulty to discriminate paths with similar costs, as well as small variations in the perception of travel time among different users, suggest the necessity to relax this assumption.
• The latter may be dualized to obtain a primal characterization of MTE which is the analog of the primal characterization (PV ) for the deterministic equilibrium, namely Theorem 3.

4.1 Arc capacities and saturation

• So far, the volume-delay functions sa(·) were assumed to be defined over [0,∞).
• Since very often the arcs have a maximal saturation capacity, it is useful to extend the model by considering strictly increasing continuous functions sa : [0, w̄a) → [0,∞).

4.2 Mixed deterministic/stochastic assignment

• The functions ϕdi ∈ E in the stochastic model are used to describe the flow distribution rule (10), and may differ from node to node: at some nodes one could consider logit distribution, while other nodes may be governed by probit or other discrete choice models.
• On the other hand, the deterministic model assumes that the flow entering each node is distributed among optimal arcs, which may also be written in the form (10) by taking ϕdi (z d) = max{zda : a ∈ A+i } and replacing the gradient by the subdifferential.
• This further explains the analogy between the characterizations (D̄) and (S), and leads naturally to consider the possibility of a hybrid model where some nodes have a stochastic distribution rule while other nodes are deterministic.
• The analysis carries over to this more general setting with (S) characterizing the traffic equilibrium, though Φ(·) will no longer be smooth.

4.3 Simultaneous mode/route selection and elastic demands.

• Noting that the graph G = (N, A) need not be limited to a single mode, the previous framework turns out to be flexible enough to handle more complex decision processes such as the simultaneous choice of mode and route.
• To this end it suffices to apply the model over a multi-modal graph built by connecting every origin and destination to one or several corresponding nodes on the subgraphs representing the basic transportation modes (car, bus, metro, walk, etc.).
• At every origin node one may adopt a particular distribution rule based on a logit or probit model, while at other nodes (e.g. the metro sub-network) one may use a deterministic rule.
• A further extension concerns the modelling of elastic demands.
• The option of not making a trip for a given OD pair may be simulated as usual by adding a no-trip arc which connects directly the origin to the destination, with cost equal to the inverse of the demand function (see [8]).

5 Numerical experiments

• In this short section the authors describe some numerical tests for solving the minimization problem (S).
• A Matlab implementation of MSA with constant stepsize αk ≡ α was tested on the traffic network of Siouxfalls, a small network of 24 nodes and 76 arcs with travel times sa(wa) = t0a[1 + ba( wa ca )pa ].
• Figure 3 illustrates the performance of this variant.
• The advantage of Newton’s method over MSA is less clear for medium precision computation.

6 Convergence of MSA

• The authors conclude the paper by establishing a sufficient condition for the convergence of MSA.
• This result can be seen as a discrete analog of the convergence analysis for continuous Riemannian gradient flows presented in [3, Alvarez, Bolte and Brahic].

Frequently asked questions

Q1. What are the contributions in "Fungal entomopathogens: new insights on their ecology" ?

Even though these organisms have been studied for more than 100 years, their effective use in the field remains elusive. In this paper, the authors review the recently discovered roles played by many entomopathogenic fungi and propose new research strategies focused on alternate uses for these fungi. 

Q2. What are the future works in "Fungal entomopathogens: new insights on their ecology" ?

Future research on entomopathogenic fungi should focus on trying to understand the ecology of the fungi in a context that focuses on their roles as endophytes, plant disease antagonists, rhizosphere colonizers, and plant growth promoters. The authors believe that insights gained from these studies will result in the effective use of these promising organisms as an integral part of agricultural systems throughout the world. 

Q3. What could be used to determine whether cell-cell signaling occurs between plant and fungus?

In vitro gene expression technologies could also be used to determine whether cell-cell signaling occurs between plant and fungus. 

Q4. How can the authors study the gene expression profiles of plant pathogens in the absence of other variables?

Using model plant systems, profiles of global gene expression in response to endophytic or rhizosphere colonization can be examined in the absence of other variables. 

Q5. What is the role of fungi in the saprotrophic phase of insect?

Some species of hypocrealean entomopathogens produce secondary metabolites within their insect hosts that are postulated to help the fungus outcompete opportunists during the saprotrophic phase of insect utilization (Strasser et al. 2000). 

Q6. What is the role of sclerotia in rhizospherecompetence?

The ability of M. anisopliae to form sclerotia may be important for rhizospherecompetence following a pattern seen in phytopathogenic fungi. 

Q7. What is the key to a successful exploitation of entomopathogenic ?

Although the potential for biological control of plant pathogens has been clearlydemonstrated with certain entomopathogenic fungi, the key to successful exploitation of these organisms in agriculture is identifying and understanding the operative mechanismsof biocontrol activity. 

Q8. What is the evidence that entomopathogenic fungi interact with plant roots?

in the rhizosphere free carbon is abundant and there is evidence that entomopathogenic fungi interact with plant roots for growth or survival (St. Leger 2008). 

Q9. What is the role of semiochemicals in the resistance mechanism of plants?

The semiochemicals are a component of theinduced resistance mechanism of plants and act as specific cues for beneficial arthropods to detect the presence of hosts (Dicke & Bruin 2001). 

Q10. What is the definition of a true paradigm shift?

A true paradigm shift would be a change from a dependence on chemicals to a total system approach (see Lewis et al. 1997) or to ecological engineering (see Gurr et al. 2004a, b). 

Q11. What is the requirement for complete coverage of the foliar surface?

The numerous, discrete, infective propagules provided by spore forms satisfy the requirement for complete coverage of the foliar surface to ensure contact and infection of the insect host. 

Q12. What was the stimulus for the idea of using fungal insect pathogens to manage pest insects?

The stimulus for the idea of using fungal insect pathogens to manage pest insects came largely from the ensuing silkworm-disease studies, after finding that the fungus also infected other insects (Audoin 1837). 

Q13. What are the roles of fungal entomopathogens in nature?

Additional roles for entomopathogenic fungi in natureVarious unexpected roles have been reported for fungal entomopathogens,including their presence as fungal endophytes, plant disease antagonists, rhizosphere colonizers and plant growth promoting fungi. 

Q14. What are the abiotic factors that may be used to control entomopath?

Such abiotic factors may include minerals needed as cofactors for production of bioactive compounds involved in biological control mechanisms of entomopathogenic fungi. 

Q15. What could be done to improve the effectiveness of entomopathogenic fungi?

These areas could lead to (1) a better understanding of the disparate ecological niches occupied by entomopathogenic fungi; (2) improved deployment for better pest control; and (3) improved production and formulation to enhance their efficacy. 

Q16. What is the common method of control of insect pests in the phylloplane?

For control of insect pests in the phylloplane, suspensions of aerial conidiaincluding blastospores are applied in spray applications, e.g. M. anisopliae var. 

Q17. What are the challenges to biological control with living fungal agents?

Production strategies for fungal biocontrol agentsBoth the rhizosphere and the phylloplane present unique challenges to biologicalcontrol with living fungal agents.