What do you mean by replacement/substitution? The citation you gave concerns the applicability (in terms of plausibility and accuracy) of a particular model, although I think the spike vs. rate or temporal vs. rate dichotomy is overly simplistic (obviously, one can't model synchrony or the information relayed by correlations among spike trains in a single neuron model, or at least not well, but fairly simple neuronal network models can take such information processing properties into account). Also, by "Izhikevich model" do you mean the one proposed in his 2003 IEEE paper? Because the man has an entire monograph on the subject: Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting (Computational Neuroscience). He's not only proposed various models, but approaches to modeling in general (actually, if you haven't read it, that's a great book to read).

You might want to check out the attached link, which is given as the main reference in the "article" (poster presentation?) you link to.

http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1001056

thank you dear Andrew  for your answer

In this paper ("Spiking networks and their rate-based equivalents: does it make sense to use Siegert neurons?") , the authors provide a model for neuron that can be replaced by spiking models (i.e.: LIF model). The authors emphasis on the complexity of spiking models, and suggest a model with the main properties but less complex. My question is that if we use a simple model like izhikevich model  (http://www.izhikevich.org/publications/index.htm / http://www.izhikevich.org/publications/spikes.htm) , this equivalent is necessary   or not? and also if I use a unsupervised method (i.e. STDP) is that useful?

All neuronal models are spiking models. Neural spikes are action potentials. The link you provided is somewhat unusual in the way terms are used (though by no means unique). More importantly, the question of the "neural code" is fairly distinct from learning models (supervised or unsupervised) It concerns centrally rate vs. timing, and the reasons for preferring either one or some combination of the two related to empirical evidence, not the efficacy of (un)supervised algorithms.

Neuronal network models can be divided into yet another dichotomy apart form that suggested in your link: those that seek to replicate the actual neurophysiological processes of neuronal dynamics and those that seek to create superior computational intelligence models/paradigm, regardless of whether or not they are biologically plausible. As for Izhikevich, he hasn't produced a singular neuron or neuronal network but many of each and a framework for approaching any and all neuronal models.

thank you